text: 6 [7] J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, [30] G. Balasubramanian, P. Neumann, D. Twitchen, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, and C. Monroe, Nature 551, 601 (2017). J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. [8] H. Bernien, S. Schwartz, A. Keesling, H. Levine, Hemmer, F. Jelezko, and J. Wrachtrup, Nature Ma- A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. En- terials (2009). dres, M. Greiner, et al., Nature 551, 579 (2017). [31] C. S. Shin, C. E. Avalos, M. C. Butler, H.-J. Wang, [9] A. M. Childs, Quantum Info. Comput. 5, 456 S. J. Seltzer, R.-B. Liu, A. Pines, and V. S. Bajaj, (2005). Phys. Rev. B 88, 161412 (2013). [10] A. Broadbent, J. Fitzsimons, and E. Kasheﬁ, in [32] Z.-H. Wang and S. Takahashi, Phys. Rev. B 87, Proceedings of the 50th Annual IEEE Symposium on 115122 (2013). Foundations of Computer (IEEE Computer society, [33] L. T. Hall, J. H. Cole, and L. C. L. Hollenberg, 2009) pp. 517–527. Phys. Rev. B 90, 075201 (2014). [11] V. Dunjko, E. Kasheﬁ, and A. Leverrier, Phys. Rev. [34] H. M. Pastawski, P. R. Levstein, and G. Usaj, Phys. Lett. 108, 200502 (2012). Rev. Lett. 75, 4310 (1995). [12] T. Morimae and K. Fujii, Nature Communications [35] D. G. Cory, M. D. Price, and T. F. Havel, Physica 3, 1036 (2012). D: Nonlinear Phenomena 120, 82 (1998), proceed- [13] V. Dunjko, J. F. Fitzsimons, C. Portmann, and ings of the Fourth Workshop on Physics and Con- R. Renner, “Composable security of delegated quan- sumption. tum computation,” in Advances in Cryptology – [36] R. Laﬂamme, E. Knill, D. G. Cory, E. M. Fortu- ASIACRYPT 2014: 20th International Conference nato, T. Havel, C. Miquel, R. Martinez, C. Ne- on the Theory and Application of Cryptology and grevergne, G. Ortiz, M. A. Pravia, Y. Sharf, Information Security, Kaoshiung, Taiwan, R.O.C., S. Sinha, R. Somma, and L. Viola, Los Alamos December 7-11, 2014, Proceedings, Part II, edited Science , 226 (2002), quant-ph/0207172. by P. Sarkar and T. Iwata (Springer Berlin Heidel- [37] D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, berg, Berlin, Heidelberg, 2014) pp. 406–425. 207901 (2004). [14] T. Morimae, V. Dunjko, and E. Kasheﬁ, Quantum [38] B. P. Lanyon, C. Hempel, D. Nigg, M. Mu¨ller, Information and Computation 15, 0200 (2015). R. Gerritsma, F. Z¨ahringer, P. Schindler, J. T. Bar- [15] D. Aharonov, M. Ben-Or, and E. Eban, in Inno- reiro, M. Rambach, G. Kirchmair, M. Hennrich, vations in Computer Science - ICS 2010 (Tsinghua P. Zoller, R. Blatt, and C. F. Roos, Science 334, University, 2010) pp. 453–469. 57 (2011). [16] D. Aharonov, M. Ben-Or, E. Eban, and U. Ma- [39] I. Arrazola, J. S. Pedernales, L. Lamata, and hadev, (2017), arXiv:1704.04487. E. Solano, Scientiﬁc Reports 6, 30534 (2016), ar- [17] J. F. Fitzsimons and E. Kasheﬁ, Phys. Rev. A 96, ticle. 012303 (2017). [40] A. Bermudez, L. Tagliacozzo, G. Sierra, and [18] A. Gheorghiu, T. Kapourniotis, and E. Kasheﬁ, P. Richerme, Phys. Rev. B 95, 024431 (2017). (2017), arXiv:1709.06984. [41] J. Cho, D. G. Angelakis, and S. Bose, Phys. Rev. [19] M. Gaudin, J. Phys. France 37, 1087 (1976). A 78, 062338 (2008). [20] J. M. Taylor, A. Imamoglu, and M. D. Lukin, Phys. [42] U. L. Heras, A. Mezzacapo, L. Lamata, S. Filipp, Rev. Lett. 91, 246802 (2003). A. Wallraﬀ, and E. Solano, Phys. Rev. Lett. 112, [21] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, 200501 (2014). and V. Z. Enolskii, Journal of Physics A: Mathemat- [43] Y. Salath´e, M. Mondal, M. Oppliger, J. Hein- ical and General 38, 7831 (2005). soo, P. Kurpiers, A. Potoˇcnik, A. Mezzacapo, [22] I. A. Merkulov, A. L. Efros, and M. Rosen, Phys. U. Las Heras, L. Lamata, E. Solano, S. Filipp, and Rev. B 65, 205309 (2002). A. Wallraﬀ, Phys. Rev. X 5, 021027 (2015). [23] A. V. Khaetskii, D. Loss, and L. Glazman, Phys. [44] L. Lamata, Scientiﬁc Reports 7, 43768 (2017), arti- Rev. Lett. 88, 186802 (2002). cle. [24] R. de Sousa and S. Das Sarma, Phys. Rev. B 68, [45] W. Yao, R.-B. Liu, and L. J. Sham, Phys. Rev. B 115322 (2003). 74, 195301 (2006). [25] J. Schliemann, A. Khaetskii, and D. Loss, Journal [46] R.-B. Liu, W. Yao, and L. J. Sham, New J. Phys. of Physics: Condensed Matter 15, R1809 (2003). 9, 226 (2007). [26] S. I. Erlingsson and Y. V. Nazarov, Phys. Rev. B [47] S. Bravyi, D. P. DiVincenzo, and D. Loss, Annals 70, 205327 (2004). of Physics 326, 2793 (2011). [27] E. A. Chekhovich, M. N. Makhonin, A. I. Tar- [48] J. Kempe, A. Kitaev, and O. Regev, SIAM Journal takovskii, A. Yacoby, H. Bluhm, K. C. Nowack, and on Computing 35, 1070 (2006). L. M. K. Vandersypen, Nature Materials 12, 494 [49] S. P. Jordan and E. Farhi, Phys. Rev. A 77, 062329 (2013), review Article. (2008). [28] J. Wrachtrup and F. Jelezko, Journal of Physics: [50] C. H. Bennett and G. Brassard, in Proceedings of Condensed Matter 18, S807 (2006). IEEE International Conference on Computers, Sys- [29] L. Childress, M. V. Gurudev Dutt, J. M. Taylor, tems and Signal Processing (1984) pp. 175–179. A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hem- [51] A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. mer, and M. D. Lukin, Science 314, 281 (2006). DiVincenzo, D. Loss, M. Sherwin, and A. Small,

label: reference

text: J.

text: Zhang,

text: G.

text: Pagano,

text: P.

text: W.

text: Hess,

text: A.

text: Kyprianidis,

text: G.

text: Balasubramanian,

text: P.

text: Neumann,

text: D.

text: Twitchen,

text: P.

text: Becker,

text: H.

text: Kaplan,

text: A.

text: V.

text: Gorshkov,

text: Z.-X.

text: Gong,

text: M.

text: Markham,

text: R.

text: Kolesov,

text: N.

text: Mizuochi,

text: J.

text: Isoya,

text: and

text: C.

text: Monroe,

text: Nature

text: J.

text: Achard,

text: J.

text: Beck,

text: J.

text: Tissler,

text: V.

text: Jacques,

text: P.

text: R.

text: H.

text: Bernien,

text: S.

text: Schwartz,

text: A.

text: Keesling,

text: H.

text: Levine,

text: Hemmer,

text: F.

text: Jelezko,

text: and

text: J.

text: Wrachtrup,

text: Nature

text: Ma-

text: A.

text: Omran,

text: H.

text: Pichler,

text: S.

text: Choi,

text: A.

text: S.

text: Zibrov,

text: M.

text: En-

text: terials

text: dres,

text: M.

text: Greiner,

text: et

text: al.,

text: Nature

text: C.

text: S.

text: Shin,

text: C.

text: E.

text: Avalos,

text: M.

text: C.

text: Butler,

text: H.-J.

text: Wang,

text: A.

text: M.

text: Childs,

text: Quantum

text: Info.

text: Comput.

text: S.

text: J.

text: Seltzer,

text: R.-B.

text: Liu,

text: A.

text: Pines,

text: and

text: V.

text: S.

text: Bajaj,

text: Phys.

text: Rev.

text: B

text: A.

text: Broadbent,

text: J.

text: Fitzsimons,

text: and

text: E.

text: Kasheﬁ,

text: in

text: Z.-H.

text: Wang

text: and

text: S.

text: Takahashi,

text: Phys.

text: Rev.

text: B

text: Proceedings

text: of

text: the

text: Annual

text: IEEE

text: Symposium

text: on

text: Foundations

text: of

text: Computer

text: (IEEE

text: Computer

text: society,

text: L.

text: T.

text: Hall,

text: J.

text: H.

text: Cole,

text: and

text: L.

text: C.

text: L.

text: Hollenberg,

text: pp.

text: Phys.

text: Rev.

text: B

text: V.

text: Dunjko,

text: E.

text: Kasheﬁ,

text: and

text: A.

text: Leverrier,

text: Phys.

text: Rev.

text: H.

text: M.

text: Pastawski,

text: P.

text: R.

text: Levstein,

text: and

text: G.

text: Usaj,

text: Phys.

text: Lett.

text: Rev.

text: Lett.

text: T.

text: Morimae

text: and

text: K.

text: Fujii,

text: Nature

text: Communications

text: D.

text: G.

text: Cory,

text: M.

text: D.

text: Price,

text: and

text: T.

text: F.

text: Havel,

text: Physica

text: D:

text: Nonlinear

text: Phenomena

text: proceed-

text: V.

text: Dunjko,

text: J.

text: F.

text: Fitzsimons,

text: C.

text: Portmann,

text: and

text: ings

text: of

text: the

text: Fourth

text: Workshop

text: on

text: Physics

text: and

text: Con-

text: R.

text: Renner,

text: “Composable

text: security

text: of

text: delegated

text: quan-

text: sumption.

text: tum

text: computation,”

text: in

text: Advances

text: in

text: Cryptology

text: R.

text: Laﬂamme,

text: E.

text: Knill,

text: D.

text: G.

text: Cory,

text: E.

text: M.

text: Fortu-

text: ASIACRYPT

text: International

text: Conference

text: nato,

text: T.

text: Havel,

text: C.

text: Miquel,

text: R.

text: Martinez,

text: C.

text: Ne-

text: on

text: the

text: Theory

text: and

text: Application

text: of

text: Cryptology

text: and

text: grevergne,

text: G.

text: Ortiz,

text: M.

text: A.

text: Pravia,

text: Y.

text: Sharf,

text: Information

text: Security,

text: Kaoshiung,

text: Taiwan,

text: R.O.C.,

text: S.

text: Sinha,

text: R.

text: Somma,

text: and

text: L.

text: Viola,

text: Los

text: Alamos

text: December

text: Proceedings,

text: Part

text: II,

text: edited

text: Science

text: by

text: P.

text: Sarkar

text: and

text: T.

text: Iwata

text: (Springer

text: Berlin

text: Heidel-

text: D.

text: Porras

text: and

text: J.

text: I.

text: Cirac,

text: Phys.

text: Rev.

text: Lett.

text: berg,

text: Berlin,

text: Heidelberg,

text: pp.

text: T.

text: Morimae,

text: V.

text: Dunjko,

text: and

text: E.

text: Kasheﬁ,

text: Quantum

text: B.

text: P.

text: Lanyon,

text: C.

text: Hempel,

text: D.

text: Nigg,

text: M.

text: Mu¨ller,

text: Information

text: and

text: Computation

text: R.

text: Gerritsma,

text: F.

text: Z¨ahringer,

text: P.

text: Schindler,

text: J.

text: T.

text: Bar-

text: D.

text: Aharonov,

text: M.

text: Ben-Or,

text: and

text: E.

text: Eban,

text: in

text: Inno-

text: reiro,

text: M.

text: Rambach,

text: G.

text: Kirchmair,

text: M.

text: Hennrich,

text: vations

text: in

text: Computer

text: Science

text: ICS

text: (Tsinghua

text: P.

text: Zoller,

text: R.

text: Blatt,

text: and

text: C.

text: F.

text: Roos,

text: Science

text: University,

text: pp.

text: D.

text: Aharonov,

text: M.

text: Ben-Or,

text: E.

text: Eban,

text: and

text: U.

text: Ma-

text: I.

text: Arrazola,

text: J.

text: S.

text: Pedernales,

text: L.

text: Lamata,

text: and

text: hadev,

text: E.

text: Solano,

text: Scientiﬁc

text: Reports

text: ar-

text: J.

text: F.

text: Fitzsimons

text: and

text: E.

text: Kasheﬁ,

text: Phys.

text: Rev.

text: A

text: ticle.

text: A.

text: Bermudez,

text: L.

text: Tagliacozzo,

text: G.

text: Sierra,

text: and

text: A.

text: Gheorghiu,

text: T.

text: Kapourniotis,

text: and

text: E.

text: Kasheﬁ,

text: P.

text: Richerme,

text: Phys.

text: Rev.

text: B

text: J.

text: Cho,

text: D.

text: G.

text: Angelakis,

text: and

text: S.

text: Bose,

text: Phys.

text: Rev.

text: M.

text: Gaudin,

text: J.

text: Phys.

text: France

text: A

text: J.

text: M.

text: Taylor,

text: A.

text: Imamoglu,

text: and

text: M.

text: D.

text: Lukin,

text: Phys.

text: U.

text: L.

text: Heras,

text: A.

text: Mezzacapo,

text: L.

text: Lamata,

text: S.

text: Filipp,

text: Rev.

text: Lett.

text: A.

text: Wallraﬀ,

text: and

text: E.

text: Solano,

text: Phys.

text: Rev.

text: Lett.

text: E.

text: A.

text: Yuzbashyan,

text: B.

text: L.

text: Altshuler,

text: V.

text: B.

text: Kuznetsov,

text: and

text: V.

text: Z.

text: Enolskii,

text: Journal

text: of

text: Physics

text: A:

text: Mathemat-

text: Y.

text: Salath´e,

text: M.

text: Mondal,

text: M.

text: Oppliger,

text: J.

text: Hein-

text: ical

text: and

text: General

text: soo,

text: P.

text: Kurpiers,

text: A.

text: Potoˇcnik,

text: A.

text: Mezzacapo,

text: I.

text: A.

text: Merkulov,

text: A.

text: L.

text: Efros,

text: and

text: M.

text: Rosen,

text: Phys.

text: U.

text: Las

text: Heras,

text: L.

text: Lamata,

text: E.

text: Solano,

text: S.

text: Filipp,

text: and

text: Rev.

text: B

text: A.

text: Wallraﬀ,

text: Phys.

text: Rev.

text: X

text: A.

text: V.

text: Khaetskii,

text: D.

text: Loss,

text: and

text: L.

text: Glazman,

text: Phys.

text: L.

text: Lamata,

text: Scientiﬁc

text: Reports

text: arti-

text: Rev.

text: Lett.

text: cle.

text: R.

text: de

text: Sousa

text: and

text: S.

text: Das

text: Sarma,

text: Phys.

text: Rev.

text: B

text: W.

text: Yao,

text: R.-B.

text: Liu,

text: and

text: L.

text: J.

text: Sham,

text: Phys.

text: Rev.

text: B

text: J.

text: Schliemann,

text: A.

text: Khaetskii,

text: and

text: D.

text: Loss,

text: Journal

text: R.-B.

text: Liu,

text: W.

text: Yao,

text: and

text: L.

text: J.

text: Sham,

text: New

text: J.

text: Phys.

text: of

text: Physics:

text: Condensed

text: Matter

text: S.

text: I.

text: Erlingsson

text: and

text: Y.

text: V.

text: Nazarov,

text: Phys.

text: Rev.

text: B

text: S.

text: Bravyi,

text: D.

text: P.

text: DiVincenzo,

text: and

text: D.

text: Loss,

text: Annals

text: of

text: Physics

text: E.

text: A.

text: Chekhovich,

text: M.

text: N.

text: Makhonin,

text: A.

text: I.

text: Tar-

text: J.

text: Kempe,

text: A.

text: Kitaev,

text: and

text: O.

text: Regev,

text: SIAM

text: Journal

text: takovskii,

text: A.

text: Yacoby,

text: H.

text: Bluhm,

text: K.

text: C.

text: Nowack,

text: and

text: on

text: Computing

text: L.

text: M.

text: K.

text: Vandersypen,

text: Nature

text: Materials

text: S.

text: P.

text: Jordan

text: and

text: E.

text: Farhi,

text: Phys.

text: Rev.

text: A

text: review

text: Article.

text: J.

text: Wrachtrup

text: and

text: F.

text: Jelezko,

text: Journal

text: of

text: Physics:

text: C.

text: H.

text: Bennett

text: and

text: G.

text: Brassard,

text: in

text: Proceedings

text: of

text: Condensed

text: Matter

text: IEEE

text: International

text: Conference

text: on

text: Computers,

text: Sys-

text: L.

text: Childress,

text: M.

text: V.

text: Gurudev

text: Dutt,

text: J.

text: M.

text: Taylor,

text: tems

text: and

text: Signal

text: Processing

text: pp.

text: A.

text: S.

text: Zibrov,

text: F.

text: Jelezko,

text: J.

text: Wrachtrup,

text: P.

text: R.

text: Hem-

text: A.

text: Imamoglu,

text: D.

text: D.

text: Awschalom,

text: G.

text: Burkard,

text: D.

text: P.

text: mer,

text: and

text: M.

text: D.

text: Lukin,

text: Science

text: DiVincenzo,

text: D.

text: Loss,

text: M.

text: Sherwin,

text: and

text: A.

text: Small,


text: Comorbid CAD and Ventricular Hypertrophy Compromise The Perfusion of Myocardial Tissue at Subcritical Stenosis of Epicardial Coronaries slam bbas E A Kobri El Kobba Medical Complex, Cairo, Egypt Abstract BACKGROUND: Most studies of CAD revascularization have been based on and reported according to angiographic criteria which don’t consider the relation between the resulting effective ﬂow distal to the stenosis and the demand of a hypertrophied myocardial tissue. MODEL: Mathematical model of the myocardial perfusion in comorbid CAD and ventricular hypertrophy using Poiseuille’s law. The analysis yields that the curve, which represents the relation between the perfusion and the severity of CAD depending on angiographic and/or angiophysiologic criteria, is shifted to the right by the effect of myocardial tissue hypertrophy. The right shift of said curve, which is directly proportional to the degree of ventricular hypertrophy, indicates that the perfusion of the corresponding myocardial tissue is compromised at angiographically and/or angiophysiologically subsigniﬁcant stenosis of the supplying epicardial vessel. RESULTS: Patients with comorbid CAD and left ventricular hypertrophy are more sensitive to CAD-related hemodynamic changes. They are more prone to develop ischemic complications, than their peers with isolated CAD regarding the same degree of coronary stenosis. CONCLUSION: Patients with comorbid CAD and ventricular hypertrophy suffer from myocardial hypoperfusion at angiographically and/or angiophysiologically subcritical epicardial stenosis. Accordingly; the comorbidity of both diseases should be considered upon designing of the treatment regime. ackground B vasodilatation, irritate the nerve endings leading to anginal pain [5]. Combined coronary artery disease and ventricular hypertrophy are not uncommon; The treatment strategy for treating CAD they both share hypertension, which affects aims to improve survival and/or relieve ∼ 26% of the world population [1], as a risk symptoms [6] including dyspnea and stable factor. Accumulation of atheromatous plaques angina pectoris. Said strategy usually involves under tunica intima of the epicardial arteries anti-anginal medications and/or PCI, or CABG restricts the blood ﬂow to the supplied cardiac in case of complex CAD and/or left main tissue. Chronic high-grade narrowing of the involvement, for achieving those aims. Trials coronary arteries induces subendocardial show that revascularization by PCI or CABG is ischemia during the escalation of the my- more effective than a strategy of medical ther- ocardial oxygen demand throughout exercise apy alone, in relieving symptoms like angina or stress [2]. The strained myocytes release and dyspnea. Besides; it improves the quality mediators like adenosine and bradykinin [3][4] of life by reducing the use of anti-angina drugs which in addition to stimulating coronary and increasing exercise capacity [7][8][9][10]. 1

text: Comorbid

label: title

font: KZAANI+URWPalladioL-Bold

text: CAD

text: and

text: Ventricular

text: Hypertrophy

text: Compromise

text: The

text: Perfusion

text: of

text: Myocardial

text: Tissue

text: at

text: Subcritical

text: Stenosis

text: of

text: Epicardial

text: Coronaries

text: slam

label: author

font: UPIECY+TeXPalladioL-SC

text: bbas

text: E

font: GUZCLO+URWPalladioL-Roma

text: A

text: Kobri

label: paragraph

text: El

text: Kobba

text: Medical

text: Complex,

text: Cairo,

text: Egypt

text: Abstract

text: BACKGROUND:

label: abstract

text: Most

text: studies

text: of

text: CAD

text: revascularization

text: have

text: been

text: based

text: on

text: and

text: reported

text: according

text: to

text: angiographic

text: criteria

text: which

text: don’t

text: consider

text: the

text: relation

text: between

text: the

text: resulting

text: effective

text: ﬂow

text: distal

text: to

text: the

text: stenosis

text: and

text: the

text: demand

text: of

text: a

text: hypertrophied

text: myocardial

text: tissue.

text: MODEL:

text: Mathematical

text: model

text: of

text: the

text: myocardial

text: perfusion

text: in

text: comorbid

text: CAD

text: and

text: ventricular

text: hypertrophy

text: using

text: Poiseuille’s

text: law.

text: The

text: analysis

text: yields

text: that

text: the

text: curve,

text: which

text: represents

text: the

text: relation

text: between

text: the

text: perfusion

text: and

text: the

text: severity

text: of

text: CAD

text: depending

text: on

text: angiographic

text: and/or

text: angiophysiologic

text: criteria,

text: is

text: shifted

text: to

text: the

text: right

text: by

text: the

text: effect

text: of

text: myocardial

text: tissue

text: hypertrophy.

text: The

text: right

text: shift

text: of

text: said

text: curve,

text: which

text: is

text: directly

text: proportional

text: to

text: the

text: degree

text: of

text: ventricular

text: hypertrophy,

text: indicates

text: that

text: the

text: perfusion

text: of

text: the

text: corresponding

text: myocardial

text: tissue

text: is

text: compromised

text: at

text: angiographically

text: and/or

text: angiophysiologically

text: subsigniﬁcant

text: stenosis

text: of

text: the

text: supplying

text: epicardial

text: vessel.

text: RESULTS:

text: Patients

text: with

text: comorbid

text: CAD

text: and

text: left

text: ventricular

text: hypertrophy

text: are

text: more

text: sensitive

text: to

text: CAD-related

text: hemodynamic

text: changes.

text: They

text: are

text: more

text: prone

text: to

text: develop

text: ischemic

text: complications,

text: than

text: their

text: peers

text: with

text: isolated

text: CAD

text: regarding

text: the

text: same

text: degree

text: of

text: coronary

text: stenosis.

text: CONCLUSION:

text: Patients

text: with

text: comorbid

text: CAD

text: and

text: ventricular

text: hypertrophy

text: suffer

text: from

text: myocardial

text: hypoperfusion

text: at

text: angiographically

text: and/or

text: angiophysiologically

text: subcritical

text: epicardial

text: stenosis.

text: Accordingly;

text: the

text: comorbidity

text: of

text: both

text: diseases

text: should

text: be

text: considered

text: upon

text: designing

text: of

text: the

text: treatment

text: regime.

text: ackground

text: B

text: vasodilatation,

text: irritate

text: the

text: nerve

text: endings

text: leading

text: to

text: anginal

text: pain

text: Combined

text: coronary

text: artery

text: disease

text: and

text: ventricular

text: hypertrophy

text: are

text: not

text: uncommon;

text: The

text: treatment

text: strategy

text: for

text: treating

text: CAD

text: they

text: both

text: share

text: hypertension,

text: which

text: affects

text: aims

text: to

text: improve

text: survival

text: and/or

text: relieve

text: of

text: the

text: world

text: population

text: as

text: a

text: risk

text: symptoms

text: including

text: dyspnea

text: and

text: stable

text: factor.

text: Accumulation

text: of

text: atheromatous

text: plaques

text: angina

text: pectoris.

text: Said

text: strategy

text: usually

text: involves

text: under

text: tunica

text: intima

text: of

text: the

text: epicardial

text: arteries

text: anti-anginal

text: medications

text: and/or

text: PCI,

text: or

text: CABG

text: restricts

text: the

text: blood

text: ﬂow

text: to

text: the

text: supplied

text: cardiac

text: in

text: case

text: of

text: complex

text: CAD

text: and/or

text: left

text: main

text: tissue.

text: Chronic

text: high-grade

text: narrowing

text: of

text: the

text: involvement,

text: for

text: achieving

text: those

text: aims.

text: Trials

text: coronary

text: arteries

text: induces

text: subendocardial

text: show

text: that

text: revascularization

text: by

text: PCI

text: or

text: CABG

text: is

text: ischemia

text: during

text: the

text: escalation

text: of

text: the

text: my-

text: more

text: effective

text: than

text: a

text: strategy

text: of

text: medical

text: ther-

text: ocardial

text: oxygen

text: demand

text: throughout

text: exercise

text: apy

text: alone,

text: in

text: relieving

text: symptoms

text: like

text: angina

text: or

text: stress

text: The

text: strained

text: myocytes

text: release

text: and

text: dyspnea.

text: Besides;

text: it

text: improves

text: the

text: quality

text: mediators

text: like

text: adenosine

text: and

text: bradykinin

text: of

text: life

text: by

text: reducing

text: the

text: use

text: of

text: anti-angina

text: drugs

text: which

text: in

text: addition

text: to

text: stimulating

text: coronary

text: and

text: increasing

text: exercise

text: capacity


text: Journal of the American College of Cardiology, [34] Robert J Tomanek and Eduard I Dedkov. 49(21):2105–2111, 2007. Angiogenesis and arteriogenesis in car- diac hypertrophy. Modern concepts in an- [27] Nico HJ Pijls, William F Fearon, Pim AL giogenesis, pages 253–280, 2007. Tonino, Uwe Siebert, Fumiaki Ikeno, Bern- hard Bornschein, Marcel van’t Veer, Volker [35] Dirk J Duncker and Robert J Bache. Regu- Klauss, Ganesh Manoharan, Thomas En- lation of coronary blood ﬂow during exer- gstrøm, et al. Fractional ﬂow reserve cise. Physiological reviews, 88(3):1009–1086, versus angiography for guiding percuta- 2008. neous coronary intervention in patients [36] M HAROLD Laughlin. Effects of exercise with multivessel coronary artery disease: training on coronary transport capacity. 2-year follow-up of the fame (fractional Journal of Applied Physiology, 58(2):468–476, ﬂow reserve versus angiography for mul- 1985. tivessel evaluation) study. Journal of the American College of Cardiology, 56(3):177– [37] M Harold Laughlin. Physical activity in 184, 2010. prevention and treatment of coronary dis- ease: the battle line is in exercise vascular [28] Beverly H Lorell and Blase A Carabello. cell biology. Medicine & Science in Sports & Left ventricular hypertrophy. Circulation, Exercise, 36(3):352–362, 2004. 102(4):470–479, 2000. [38] Charles B Treasure, J Larry Klein, [29] Stephen Gunther and William Grossman. Joseph A Vita, Steven V Manoukian, Determinants of ventricular function in George H Renwick, Andrew P Selwyn, pressure-overload hypertrophy in man. Peter Ganz, and R Wayne Alexander. Circulation, 59(4):679–688, 1979. Hypertension and left ventricular hy- pertrophy are associated with impaired [30] Peter H Sugden. Signaling in myocar- endothelium-mediated relaxation in hu- dial hypertrophy. Circulation Research, man coronary resistance vessels. Circula- 84(6):633–646, 1999. tion, 87(1):86–93, 1993. [31] TK Borg and ML Burgess. Holding it all [39] August D Pichard, Richard Gorlin, Harry together: organization and function (s) of Smith, John Ambrose, and Jose Meller. the extracellular matrix in the heart. Heart Coronary ﬂow studies in patients with Failure, 8:230–230, 1992. left ventricular hypertrophy of the hyper- tensive type: evidence for an impaired [32] Dhandapani Kuppuswamy, Charlene coronary vascular reserve. The American Kerr, Takahiro Narishige, Vijayku- journal of cardiology, 47(3):547–554, 1981. mar S Kasi, Donald R Menick, and [40] Grant W Reed, Jeffrey E Rossi, and George Cooper. Association of tyrosine- Christopher P Cannon. Acute myocardial phosphorylated c-src with the cytoskele- infarction. The Lancet, 389(10065):197–210, ton of hypertrophying myocardium. 2017. Journal of Biological Chemistry, 272(7):4500– 4508, 1997. [41] Peter Libby. Mechanisms of acute coro- nary syndromes and their implications for [33] Louis Terracio, Kristofer Rubin, Donald therapy. New England Journal of Medicine, Gullberg, ED Balog, Wayne Carver, Ron 368(21):2004–2013, 2013. Jyring, and Thomas K Borg. Expression of collagen binding integrins during cardiac [42] Pedro R Moreno. Vulnerable plaque: deﬁ- development and hypertrophy. Circulation nition, diagnosis, and treatment. Cardiol- research, 68(3):734–744, 1991. ogy clinics, 28(1):1–30, 2010. 9

text: Journal

font: UCMHRR+URWPalladioL-Ital

text: of

text: the

text: American

text: College

text: of

text: Cardiology,

text: Robert

text: J

text: Tomanek

text: and

text: Eduard

text: I

text: Dedkov.

text: Angiogenesis

text: and

text: arteriogenesis

text: in

text: car-

text: diac

text: hypertrophy.

text: Modern

text: concepts

text: in

text: an-

text: Nico

text: HJ

text: Pijls,

text: William

text: F

text: Fearon,

text: Pim

text: AL

text: giogenesis,

text: pages

text: Tonino,

text: Uwe

text: Siebert,

text: Fumiaki

text: Ikeno,

text: Bern-

text: hard

text: Bornschein,

text: Marcel

text: van’t

text: Veer,

text: Volker

text: Dirk

text: J

text: Duncker

text: and

text: Robert

text: J

text: Bache.

text: Regu-

text: Klauss,

text: Ganesh

text: Manoharan,

text: Thomas

text: En-

text: lation

text: of

text: coronary

text: blood

text: ﬂow

text: during

text: exer-

text: gstrøm,

text: et

text: al.

text: Fractional

text: ﬂow

text: reserve

text: cise.

text: Physiological

text: reviews,

text: versus

text: angiography

text: for

text: guiding

text: percuta-

text: neous

text: coronary

text: intervention

text: in

text: patients

text: M

text: HAROLD

text: Laughlin.

text: Effects

text: of

text: exercise

text: with

text: multivessel

text: coronary

text: artery

text: disease:

text: training

text: on

text: coronary

text: transport

text: capacity.

text: follow-up

text: of

text: the

text: fame

text: (fractional

text: Journal

text: of

text: Applied

text: Physiology,

text: ﬂow

text: reserve

text: versus

text: angiography

text: for

text: mul-

text: tivessel

text: evaluation)

text: study.

text: Journal

text: of

text: the

text: American

text: College

text: of

text: Cardiology,

text: M

text: Harold

text: Laughlin.

text: Physical

text: activity

text: in

text: prevention

text: and

text: treatment

text: of

text: coronary

text: dis-

text: ease:

text: the

text: battle

text: line

text: is

text: in

text: exercise

text: vascular

text: Beverly

text: H

text: Lorell

text: and

text: Blase

text: A

text: Carabello.

text: cell

text: biology.

text: Medicine

text: Science

text: in

text: Sports

text: Left

text: ventricular

text: hypertrophy.

text: Circulation,

text: Exercise,

text: Charles

text: B

text: Treasure,

text: J

text: Larry

text: Klein,

text: Stephen

text: Gunther

text: and

text: William

text: Grossman.

text: Joseph

text: A

text: Vita,

text: Steven

text: V

text: Manoukian,

text: Determinants

text: of

text: ventricular

text: function

text: in

text: George

text: H

text: Renwick,

text: Andrew

text: P

text: Selwyn,

text: pressure-overload

text: hypertrophy

text: in

text: man.

text: Peter

text: Ganz,

text: and

text: R

text: Wayne

text: Alexander.

text: Circulation,

text: Hypertension

text: and

text: left

text: ventricular

text: hy-

text: pertrophy

text: are

text: associated

text: with

text: impaired

text: Peter

text: H

text: Sugden.

text: Signaling

text: in

text: myocar-

text: endothelium-mediated

text: relaxation

text: in

text: hu-

text: dial

text: hypertrophy.

text: Circulation

text: Research,

text: man

text: coronary

text: resistance

text: vessels.

text: Circula-

text: tion,

text: TK

text: Borg

text: and

text: ML

text: Burgess.

text: Holding

text: it

text: all

text: August

text: D

text: Pichard,

text: Richard

text: Gorlin,

text: Harry

text: together:

text: organization

text: and

text: function

text: (s)

text: of

text: Smith,

text: John

text: Ambrose,

text: and

text: Jose

text: Meller.

text: the

text: extracellular

text: matrix

text: in

text: the

text: heart.

text: Heart

text: Coronary

text: ﬂow

text: studies

text: in

text: patients

text: with

text: Failure,

text: left

text: ventricular

text: hypertrophy

text: of

text: the

text: hyper-

text: tensive

text: type:

text: evidence

text: for

text: an

text: impaired

text: Dhandapani

text: Kuppuswamy,

text: Charlene

text: coronary

text: vascular

text: reserve.

text: The

text: American

text: Kerr,

text: Takahiro

text: Narishige,

text: Vijayku-

text: journal

text: of

text: cardiology,

text: mar

text: S

text: Kasi,

text: Donald

text: R

text: Menick,

text: and

text: Grant

text: W

text: Reed,

text: Jeffrey

text: E

text: Rossi,

text: and

text: George

text: Cooper.

text: Association

text: of

text: tyrosine-

text: Christopher

text: P

text: Cannon.

text: Acute

text: myocardial

text: phosphorylated

text: c-src

text: with

text: the

text: cytoskele-

text: infarction.

text: The

text: Lancet,

text: ton

text: of

text: hypertrophying

text: myocardium.

text: Journal

text: of

text: Biological

text: Chemistry,

text: Peter

text: Libby.

text: Mechanisms

text: of

text: acute

text: coro-

text: nary

text: syndromes

text: and

text: their

text: implications

text: for

text: Louis

text: Terracio,

text: Kristofer

text: Rubin,

text: Donald

text: therapy.

text: New

text: England

text: Journal

text: of

text: Medicine,

text: Gullberg,

text: ED

text: Balog,

text: Wayne

text: Carver,

text: Ron

text: Jyring,

text: and

text: Thomas

text: K

text: Borg.

text: Expression

text: of

text: collagen

text: binding

text: integrins

text: during

text: cardiac

text: Pedro

text: R

text: Moreno.

text: Vulnerable

text: plaque:

text: deﬁ-

text: development

text: and

text: hypertrophy.

text: Circulation

text: nition,

text: diagnosis,

text: and

text: treatment.

text: Cardiol-

text: research,

text: ogy

text: clinics,


text: (a) (b) (c) Fig. 2. Finding independent components by whitening (b) followed by a rotation (c). The whitened features have the same variance and therefore, an appropriate rotation can ﬁnd the original independent components. in which k is the iteration index and \mu is the learning rate. Algorithm 1 EASI with Modiﬁed Update Rule The learning rate does not necessarily need to change across Input: iterations, i.e. \muk = \mu. \bfx: input features The goal of EASI is to ﬁnd a separation matrix that provides Output: an estimate of independent components without having any B: separation matrix prior information about independent components, \bfs, or the \bfy: input features in the lower-dimensional space mixing matrix, A. This can be written as 1: repeat 2: Update \bfy according to Eq. 4 \bfy \times = B \times \bfx \times (4) 3: Apply cubic nonlinearity to \bfy n 1 n m m 1 - - 4: Calculate \bfy \bfy T I + \bfg(\bfy )\bfy T \bfy \bfg(\bfy )T k k k k k k 5: Update relative gradient where \bfy is a column vector of estimates of independent 6: Update separation matrix according to Eq. 6 components and B is the separation matrix. 7: until convergence The separation matrix can be found by applying the whiten- ing matrix followed by a rotation, i.e. Although the hardware implementation of EASI algorithm B \times = U \times W \times n m n n n m that is presented in [11] increases the clock frequency by an where U is an orthogonal matrix. An adaptive updating order of magnitude compared to its prior work, the design algorithm that keeps U an orthogonal matrix can be found suffers from poor scalability. Figure 3 depicts different stages by of hardware implementation of EASI algorithm based on [11]. The algorithm consists of ﬁve high-level stages where each U = U - \mu [\bfg(\bfy )\bfy T - \bfy \bfg(\bfy )T ]U (5) stage is responsible for one of the steps explained in Algo- k+1 k k k k k k k rithm 1. By calculating the number of adders and multipliers required for implementing each stage, one can observe that where \bfg(.) is a nonlinear function that introduces HOS into the hardware complexity of both adder and multiplier units is \scrO the problem. (mn2). This is obviously not a scalable algorithm and its A global adaptive updating algorithm for the separation hardware implementation will occupy the resources available matrix can be found by B = U W and plugging on an FPGA very quickly. k+1 k+1 k+1 in W and U from Eq. 3 and Eq. 5, respectively. By IV. PROPOSED SOLUTION k+1 k+1 neglecting the \mu2 term, the adaptive updating algorithm for B By looking at Eq. 6 carefully, we observe that the \bfy \bfy T -I can be written as k k term is in fact responsible for dealing with second-order - statistics while the \bfg(\bfy )\bfy T \bfy \bfg(\bfy )T term deals with k k k k - - - higher-order statistics. Adding this to what was explained B = B \mu [\bfy \bfy T I + \bfg(\bfy )\bfy T \bfy \bfg(\bfy )T ]B k+1 k k k k k k k k k in Fig. 2 and the fact that random projection is a suitable (6) algorithm for dealing with second-order statistics, we propose the following solution for implementing the EASI algorithm Eq. 6 is known as the EASI algorithm for independent more efﬁciently. Initially, input features are fed to a random component analysis. projection module that preserves the second-order distance E. Scalability Problem among these features, but reduces the dimensionality to an ##LTFigure## ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: (a)

text: (b)

text: (c)

text: Fig.

text: Finding

label: caption

text: independent

text: components

text: by

text: whitening

text: (b)

text: followed

text: by

text: a

text: rotation

text: (c).

text: The

text: whitened

text: features

text: have

text: the

text: same

text: variance

text: and

text: therefore,

text: an

text: appropriate

text: rotation

text: can

text: ﬁnd

text: the

text: original

text: independent

text: components.

text: in

text: which

text: k

text: is

text: the

text: iteration

text: index

text: and

text: \mu

text: is

text: the

text: learning

text: rate.

text: Algorithm

text: EASI

text: with

text: Modiﬁed

text: Update

text: Rule

text: The

text: learning

text: rate

text: does

text: not

text: necessarily

text: need

text: to

text: change

text: across

text: Input:

text: iterations,

text: i.e.

text: \muk

text: \mu.

text: \bfx:

text: input

text: features

text: The

text: goal

text: of

text: EASI

text: is

text: to

text: ﬁnd

text: a

text: separation

text: matrix

text: that

text: provides

text: Output:

text: an

text: estimate

text: of

text: independent

text: components

text: without

text: having

text: any

text: B:

text: separation

text: matrix

text: prior

text: information

text: about

text: independent

text: components,

text: \bfs,

text: or

text: the

text: \bfy:

text: input

text: features

text: in

text: the

text: lower-dimensional

text: space

text: mixing

text: matrix,

text: A.

text: This

text: can

text: be

text: written

text: as

text: repeat

text: Update

text: \bfy

text: according

text: to

text: Eq.

text: \bfy

text: \times

text: B

text: \times

text: \bfx

text: \times

text: Apply

text: cubic

text: nonlinearity

text: to

text: \bfy

text: n

text: n

text: m

text: m

text: Calculate

text: \bfy

text: \bfy

text: T

text: I

text: \bfg(\bfy

text: )\bfy

text: T

text: \bfy

text: \bfg(\bfy

text: )T

text: k

text: k

text: k

text: k

text: k

text: k

text: Update

text: relative

text: gradient

text: where

text: \bfy

text: is

text: a

text: column

text: vector

text: of

text: estimates

text: of

text: independent

text: Update

text: separation

text: matrix

text: according

text: to

text: Eq.

text: components

text: and

text: B

text: is

text: the

text: separation

text: matrix.

text: until

text: convergence

text: The

text: separation

text: matrix

text: can

text: be

text: found

text: by

text: applying

text: the

text: whiten-

text: ing

text: matrix

text: followed

text: by

text: a

text: rotation,

text: i.e.

text: Although

text: the

text: hardware

text: implementation

text: of

text: EASI

text: algorithm

text: B

text: \times

text: U

text: \times

text: W

text: \times

text: n

text: m

text: n

text: n

text: n

text: m

text: that

text: is

text: presented

text: in

text: increases

text: the

text: clock

text: frequency

text: by

text: an

text: where

text: U

text: is

text: an

text: orthogonal

text: matrix.

text: An

text: adaptive

text: updating

text: order

text: of

text: magnitude

text: compared

text: to

text: its

text: prior

text: work,

text: the

text: design

text: algorithm

text: that

text: keeps

text: U

text: an

text: orthogonal

text: matrix

text: can

text: be

text: found

text: suffers

text: from

text: poor

text: scalability.

text: Figure

text: depicts

text: different

text: stages

text: by

text: of

text: hardware

text: implementation

text: of

text: EASI

text: algorithm

text: based

text: on

text: The

text: algorithm

text: consists

text: of

text: ﬁve

text: high-level

text: stages

text: where

text: each

text: U

text: U

text: \mu

text: [\bfg(\bfy

text: )\bfy

text: T

text: \bfy

text: \bfg(\bfy

text: )T

text: ]U

text: stage

text: is

text: responsible

text: for

text: one

text: of

text: the

text: steps

text: explained

text: in

text: Algo-

text: k

text: k

text: k

text: k

text: k

text: k

text: k

text: rithm

text: By

text: calculating

text: the

text: number

text: of

text: adders

text: and

text: multipliers

text: required

text: for

text: implementing

text: each

text: stage,

text: one

text: can

text: observe

text: that

text: where

text: \bfg(.)

text: is

text: a

text: nonlinear

text: function

text: that

text: introduces

text: HOS

text: into

text: the

text: hardware

text: complexity

text: of

text: both

text: adder

text: and

text: multiplier

text: units

text: is

text: \scrO

text: the

text: problem.

text: This

text: is

text: obviously

text: not

text: a

text: scalable

text: algorithm

text: and

text: its

text: A

text: global

text: adaptive

text: updating

text: algorithm

text: for

text: the

text: separation

text: hardware

text: implementation

text: will

text: occupy

text: the

text: resources

text: available

text: matrix

text: can

text: be

text: found

text: by

text: B

text: U

text: W

text: and

text: plugging

text: on

text: an

text: FPGA

text: very

text: quickly.

text: in

text: W

text: and

text: U

text: from

text: Eq.

text: and

text: Eq.

text: respectively.

text: By

text: IV.

text: PROPOSED

text: SOLUTION

text: neglecting

text: the

text: term,

text: the

text: adaptive

text: updating

text: algorithm

text: for

text: B

text: By

text: looking

text: at

text: Eq.

text: carefully,

text: we

text: observe

text: that

text: the

text: \bfy

text: \bfy

text: T

text: -I

text: can

text: be

text: written

text: as

text: k

text: k

text: term

text: is

text: in

text: fact

text: responsible

text: for

text: dealing

text: with

text: second-order

text: statistics

text: while

text: the

text: \bfg(\bfy

text: )\bfy

text: T

text: \bfy

text: \bfg(\bfy

text: )T

text: term

text: deals

text: with

text: k

text: k

text: k

text: k

text: higher-order

text: statistics.

text: Adding

text: this

text: to

text: what

text: was

text: explained

text: B

text: B

text: \mu

text: [\bfy

text: \bfy

text: T

text: I

text: \bfg(\bfy

text: )\bfy

text: T

text: \bfy

text: \bfg(\bfy

text: )T

text: ]B

text: k

text: k

text: k

text: k

text: k

text: k

text: k

text: k

text: k

text: in

text: Fig.

text: and

text: the

text: fact

text: that

text: random

text: projection

text: is

text: a

text: suitable

text: algorithm

text: for

text: dealing

text: with

text: second-order

text: statistics,

text: we

text: propose

text: the

text: following

text: solution

text: for

text: implementing

text: the

text: EASI

text: algorithm

text: Eq.

text: is

text: known

text: as

text: the

text: EASI

text: algorithm

text: for

text: independent

text: more

text: efﬁciently.

text: Initially,

text: input

text: features

text: are

text: fed

text: to

text: a

text: random

text: component

text: analysis.

text: projection

text: module

text: that

text: preserves

text: the

text: second-order

text: distance

text: E.

text: Scalability

text: Problem

text: among

text: these

text: features,

text: but

text: reduces

text: the

text: dimensionality

text: to

text: an

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: v =8 1 Driver 1 B,0 B,1 B,2 5 z 1 v =6, v =5, v =4 2 3 4 Driver 2 A,0 A,1 A,2 z2 5 Figure 4: The economy in Example 3, with two locations A, B, two time periods and four riders. drivers 1 and 2 who was supposed to pick up rider 8 with value 90 is actually able to pick up rider 6, who has a higher value. Moreover, driver 3 is now able to pick up rider 5, however, she wouldn’t (cid:3) be dispatched to do so. One may think of a naive ﬁx, simply repeating the computation of the plan of a static CE mechanism at all times. The following example shows that the mechanism that computes a driver pessimal plan at all times fails to be incentive compatible. L { } Example 3. Consider the economy as shown in Figure 4, where there are two locations = A, B with distances δ(A, A) = δ(A, B) = δ(B, A) = δ(B, B) = 1. In the driver-pessimal plan computed at time 0, the anonymous trip prices are p = p = 5. Assume that both drivers 1 and 2 B,B,1 A,A,1 follow the plan at time 0, and reach (B, 1) and (A, 1) respectively. If the mechanism re-computes the plan at time 1, the new driver-pessimal plan would set a new price of 0 for the trip (B, B, 1)— the updated lowest market-clearing price for the trip. Therefore, if driver 1 follows the mechanism at all times, her total payment would actually be 0. Now consider the scenario where driver 2 follows the mechanism at time 0, but driver 1 deviates and relocates to A, so that both drivers are at location A at time 1. At time 1, when the mechanism recomputes the driver-pessimal plan, both drivers would take the trip (A, A, 1) and pick up riders 2 and 3 respectively. The updated (cid:3) driver-pessimal price for the trip (A, A, 1) would be 4, and this is a useful deviation for driver 1. Similarly, we show that the mechanism that repeatedly recomputes a driver-optimal plan is not envy-free, and can have incentive issues. See Example ?? in Appendix ??. In order to achieve incentive alignment and robustness to deviations, the STP mechanism allows re-planning after drivers’ deviations— and must now be able to address any new strategic considerations that can occur as a result of drivers being able to trigger re-planning through deviations. 4 The Spatial-Temporal Pricing Mechanism In this section, we introduce the Spatio-Temporal Pricing (STP) mechanism, which computes a driver-pessimal CE plan at the beginning of the planning horizon, and updates the plan using the same planning rule upon any deviation from the original plan. This leads to our main result: the STP mechanism is subgame-perfect incentive compatible, and is welfare-optimal, individually rational, budget balanced, and envy-free from any history onward. The STP mechanism also maintains our desire to avoid the use of time-extended contracts. 4.1 A Dynamic Mechanism We ﬁrst formally deﬁne a dynamic mechanism, that can use the history of actions to update the plan forward from the current state. Let s = (s , s , . . . , s ) denote the state of the ridesharing platform at time t, where s t ∈ D 1,t 2,t m,t i,t for each i describes the state of driver i. If driver i has entered the platform and is available 15 ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: v

text: Driver

text: z

text: v

text: v

text: v

text: Driver

text: Figure

text: The

text: economy

text: in

text: Example

text: with

text: two

text: locations

text: A,

text: B,

text: two

text: time

text: periods

text: and

text: four

text: riders.

text: drivers

text: and

text: who

text: was

text: supposed

text: to

text: pick

text: up

text: rider

text: with

text: value

text: is

text: actually

text: able

text: to

text: pick

text: up

text: rider

text: who

text: has

text: a

text: higher

text: value.

text: Moreover,

text: driver

text: is

text: now

text: able

text: to

text: pick

text: up

text: rider

text: however,

text: she

text: wouldn’t

text: be

text: dispatched

text: to

text: do

text: so.

text: One

text: may

text: think

text: of

text: a

text: naive

text: ﬁx,

text: simply

text: repeating

text: the

text: computation

text: of

text: the

text: plan

text: of

text: a

text: static

text: CE

text: mechanism

text: at

text: all

text: times.

text: The

text: following

text: example

text: shows

text: that

text: the

text: mechanism

text: that

text: computes

text: a

text: driver

text: pessimal

text: plan

text: at

text: all

text: times

text: fails

text: to

text: be

text: incentive

text: compatible.

text: L

text: Example

text: Consider

text: the

text: economy

text: as

text: shown

text: in

text: Figure

text: where

text: there

text: are

text: two

text: locations

text: A,

text: B

text: with

text: distances

text: δ(A,

text: A)

text: δ(A,

text: B)

text: δ(B,

text: A)

text: δ(B,

text: B)

text: In

text: the

text: driver-pessimal

text: plan

text: computed

text: at

text: time

text: the

text: anonymous

text: trip

text: prices

text: are

text: p

text: p

text: Assume

text: that

text: both

text: drivers

text: and

text: follow

text: the

text: plan

text: at

text: time

text: and

text: reach

text: (B,

text: and

text: (A,

text: respectively.

text: If

text: the

text: mechanism

text: re-computes

text: the

text: plan

text: at

text: time

text: the

text: new

text: driver-pessimal

text: plan

text: would

text: set

text: a

text: new

text: price

text: of

text: for

text: the

text: trip

text: (B,

text: B,

text: the

text: updated

text: lowest

text: market-clearing

text: price

text: for

text: the

text: trip.

text: Therefore,

text: if

text: driver

text: follows

text: the

text: mechanism

text: at

text: all

text: times,

text: her

text: total

text: payment

text: would

text: actually

text: be

text: Now

text: consider

text: the

text: scenario

text: where

text: driver

text: follows

text: the

text: mechanism

text: at

text: time

text: but

text: driver

text: deviates

text: and

text: relocates

text: to

text: A,

text: so

text: that

text: both

text: drivers

text: are

text: at

text: location

text: A

text: at

text: time

text: At

text: time

text: when

text: the

text: mechanism

text: recomputes

text: the

text: driver-pessimal

text: plan,

text: both

text: drivers

text: would

text: take

text: the

text: trip

text: (A,

text: A,

text: and

text: pick

text: up

text: riders

text: and

text: respectively.

text: The

text: updated

text: driver-pessimal

text: price

text: for

text: the

text: trip

text: (A,

text: A,

text: would

text: be

text: and

text: this

text: is

text: a

text: useful

text: deviation

text: for

text: driver

text: Similarly,

text: we

text: show

text: that

text: the

text: mechanism

text: that

text: repeatedly

text: recomputes

text: a

text: driver-optimal

text: plan

text: is

text: not

text: envy-free,

text: and

text: can

text: have

text: incentive

text: issues.

text: See

text: Example

text: in

text: Appendix

text: In

text: order

text: to

text: achieve

text: incentive

text: alignment

text: and

text: robustness

text: to

text: deviations,

text: the

text: STP

text: mechanism

text: allows

text: re-planning

text: after

text: drivers’

text: deviations—

text: and

text: must

text: now

text: be

text: able

text: to

text: address

text: any

text: new

text: strategic

text: considerations

text: that

text: can

text: occur

text: as

text: a

text: result

text: of

text: drivers

text: being

text: able

text: to

text: trigger

text: re-planning

text: through

text: deviations.

text: The

text: Spatial-Temporal

text: Pricing

text: Mechanism

text: In

text: this

text: section,

text: we

text: introduce

text: the

text: Spatio-Temporal

text: Pricing

text: (STP)

text: mechanism,

text: which

text: computes

text: a

text: driver-pessimal

text: CE

text: plan

text: at

text: the

text: beginning

text: of

text: the

text: planning

text: horizon,

text: and

text: updates

text: the

text: plan

text: using

text: the

text: same

text: planning

text: rule

text: upon

text: any

text: deviation

text: from

text: the

text: original

text: plan.

text: This

text: leads

text: to

text: our

text: main

text: result:

text: the

text: STP

text: mechanism

text: is

text: subgame-perfect

text: incentive

text: compatible,

text: and

text: is

text: welfare-optimal,

text: individually

text: rational,

text: budget

text: balanced,

text: and

text: envy-free

text: from

text: any

text: history

text: onward.

text: The

text: STP

text: mechanism

text: also

text: maintains

text: our

text: desire

text: to

text: avoid

text: the

text: use

text: of

text: time-extended

text: contracts.

text: A

text: Dynamic

text: Mechanism

text: We

text: ﬁrst

text: formally

text: deﬁne

text: a

text: dynamic

text: mechanism,

text: that

text: can

text: use

text: the

text: history

text: of

text: actions

text: to

text: update

text: the

text: plan

text: forward

text: from

text: the

text: current

text: state.

text: Let

text: s

text: (s

text: s

text: s

text: denote

text: the

text: state

text: of

text: the

text: ridesharing

text: platform

text: at

text: time

text: t,

text: where

text: s

text: t

text: D

text: m,t

text: i,t

text: for

text: each

text: i

text: describes

text: the

text: state

text: of

text: driver

text: i.

text: If

text: driver

text: i

text: has

text: entered

text: the

text: platform

text: and

text: is

text: available

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: For an available driver in location a who is not dispatched, the set of available actions in period t is A { | ∈ L ≤ } (h ) = (a, b, t) b s.t. t + δ(a, b) T . (26) i,t t An en route driver must continue the trip, and we have A { ∗ } (h ) = α (h ) . (27) i,t t i,t t (cid:80) After observing the action proﬁle α at time t, the mechanism pays each dispatched driver ∗ { ∗ } t ∗ { } πˆ (α , h ) = π (h )1 α = α and charges qˆ (α ) = q (h ) ∈D 1 α = (o , d , t, j) from i,t i,t t i,t t i,t i,t j t j t i t i,t j j each rider that requests a ride at time t. A mechanism is feasible if (i) it is possible for each available driver to take the dispatched trip, ∀ ∀ ∀ ∈ D(cid:80) ∈ L ∗ ∈ { | ∈ L ≤ } ∪ i.e. t, h , i , if s = (a, t) for some a , α (h ) (a, b, t) b , t + δ(a, b) T { t | ∈tR i,t } i,t t ∀ ∀ (o , d , τ , j) j , τ = t, o = a , and (ii) no rider is picked-up more than once, i.e. t, h , ∀ ∈j Rj j j { ∗ j } ≤ t j s.t. τ = t, ∈D 1 α (h ) = (o , d , τ , j) 1. From Deﬁnition 5, there is no payment j i t i,t t j j j ∗ to or from an en route or undispatched driver, a dispatched driver i who deviated from α (h ) at i,t t time t, or riders who are not picked up. H Let be the set of all possible histories up to time t. A strategy σ of driver i deﬁnes for all ∈t − ∈ H ∈ Ai times t [T 1] and all histories h , the action α = σ (h ) (h ). For a mechanism t t ∗ i,t i t i,t t that always dispatches all available drivers, let σ denote the straightforward strategy of always i following the mechanism’s dispatches. Let σ = (σ , . . . , σ ) be the strategy proﬁle, with σ− = (σ , . . . , σ − , σ , . . . , σ ). The 1 m i 1 i 1 i+1 m strategy proﬁle σ, together with the initial state s , and the rules of a mechanism, determines all 0 | | | actions and payments of all drivers through the entire planning horizon. Let σ , σ and σ− (cid:80) i ht ht i ht denote the strategy proﬁle from time t onward given history h for driver i, all drivers, and all t drivers but i, respectively. ∈ D − For each driver i , let πˆ (σ) = T 1 πˆ (σ (h ), h ) denote the total actual payments made i t=0 i,t i t t to driver i, where drivers follow σ and the history h is induced by the initial state and strategy ∈ { } t σ. For the riders, let xˆ (σ) 0, 1 be the indicator that rider j is picked-up at strategy proﬁle σ. ∗ j Let qˆ (σ) = xˆ (σ)q (h ) be the payment made by rider j at time τ . j j j τj j Fixing driver and rider types, a ridesharing mechanism induces an extensive form game. At ∈ A each time point t, each driver decides on an action α = σ (h ) (h ) to take based on strategy i,t i t i,t t σ and the history h , and receives payment πˆ (α , h ). The total payment πˆ (σ) to each driver is i t i,t i,t t i determined by the rules of the mechanism. We deﬁne the following properties. Deﬁnition 6 (Budget Balance). A ridesharing mechanism is budget balanced if for any set of riders and drivers, and any strategy proﬁle σ(cid:88)taken by th(cid:88)e drivers, we have ≥ qˆ (σ) πˆ (σ). (28) j i ∈R ∈D j i 17

text: For

text: an

text: available

text: driver

text: in

text: location

text: a

text: who

text: is

text: not

text: dispatched,

text: the

text: set

text: of

text: available

text: actions

text: in

text: period

text: t

text: is

text: A

label: equation

text: L

text: (h

text: (a,

text: b,

text: t)

text: b

text: s.t.

text: t

text: δ(a,

text: b)

text: T

text: i,t

text: t

text: An

text: en

text: route

text: driver

text: must

text: continue

text: the

text: trip,

text: and

text: we

text: have

text: A

text: (h

text: α

text: (h

text: i,t

text: t

text: i,t

text: t

text: After

text: observing

text: the

text: action

text: proﬁle

text: α

text: at

text: time

text: t,

text: the

text: mechanism

text: pays

text: each

text: dispatched

text: driver

text: t

text: πˆ

text: (α

text: h

text: π

text: (h

text: α

text: α

text: and

text: charges

text: qˆ

text: (α

text: q

text: (h

text: ∈D

text: α

text: (o

text: d

text: t,

text: j)

text: from

text: i,t

text: i,t

text: t

text: i,t

text: t

text: i,t

text: i,t

text: j

text: t

text: j

text: t

text: i

text: t

text: i,t

text: j

text: j

text: each

text: rider

text: that

text: requests

text: a

text: ride

text: at

text: time

text: t.

text: A

text: mechanism

text: is

text: feasible

text: if

text: (i)

text: it

text: is

text: possible

text: for

text: each

text: available

text: driver

text: to

text: take

text: the

text: dispatched

text: trip,

text: L

text: L

text: i.e.

text: t,

text: h

text: i

text: if

text: s

text: (a,

text: t)

text: for

text: some

text: a

text: α

text: (h

text: (a,

text: b,

text: t)

text: b

text: t

text: δ(a,

text: b)

text: T

text: t

text: ∈tR

text: i,t

text: i,t

text: t

text: (o

text: d

text: τ

text: j)

text: j

text: τ

text: t,

text: o

text: a

text: and

text: (ii)

text: no

text: rider

text: is

text: picked-up

text: more

text: than

text: once,

text: i.e.

text: t,

text: h

text: ∈j

text: Rj

text: j

text: j

text: j

text: t

text: j

text: s.t.

text: τ

text: t,

text: ∈D

text: α

text: (h

text: (o

text: d

text: τ

text: j)

text: From

text: Deﬁnition

text: there

text: is

text: no

text: payment

text: j

text: i

text: t

text: i,t

text: t

text: j

text: j

text: j

text: to

text: or

text: from

text: an

text: en

text: route

text: or

text: undispatched

text: driver,

text: a

text: dispatched

text: driver

text: i

text: who

text: deviated

text: from

text: α

text: (h

text: at

text: i,t

text: t

text: time

text: t,

text: or

text: riders

text: who

text: are

text: not

text: picked

text: up.

text: H

text: Let

text: be

text: the

text: set

text: of

text: all

text: possible

text: histories

text: up

text: to

text: time

text: t.

text: A

text: strategy

text: σ

text: of

text: driver

text: i

text: deﬁnes

text: for

text: all

text: ∈t

text: H

text: Ai

text: times

text: t

text: [T

text: and

text: all

text: histories

text: h

text: the

text: action

text: α

text: σ

text: (h

text: (h

text: For

text: a

text: mechanism

text: t

text: t

text: i,t

text: i

text: t

text: i,t

text: t

text: that

text: always

text: dispatches

text: all

text: available

text: drivers,

text: let

text: σ

text: denote

text: the

text: straightforward

text: strategy

text: of

text: always

text: i

text: following

text: the

text: mechanism’s

text: dispatches.

text: Let

text: σ

text: (σ

text: σ

text: be

text: the

text: strategy

text: proﬁle,

text: with

text: σ−

text: (σ

text: σ

text: σ

text: σ

text: The

text: m

text: i

text: i

text: m

text: strategy

text: proﬁle

text: σ,

text: together

text: with

text: the

text: initial

text: state

text: s

text: and

text: the

text: rules

text: of

text: a

text: mechanism,

text: determines

text: all

text: actions

text: and

text: payments

text: of

text: all

text: drivers

text: through

text: the

text: entire

text: planning

text: horizon.

text: Let

text: σ

text: σ

text: and

text: σ−

text: i

text: ht

text: ht

text: i

text: ht

text: denote

text: the

text: strategy

text: proﬁle

text: from

text: time

text: t

text: onward

text: given

text: history

text: h

text: for

text: driver

text: i,

text: all

text: drivers,

text: and

text: all

text: t

text: drivers

text: but

text: i,

text: respectively.

text: D

text: For

text: each

text: driver

text: i

text: let

text: πˆ

text: (σ)

text: T

text: πˆ

text: (σ

text: (h

text: h

text: denote

text: the

text: total

text: actual

text: payments

text: made

text: i

text: i,t

text: i

text: t

text: t

text: to

text: driver

text: i,

text: where

text: drivers

text: follow

text: σ

text: and

text: the

text: history

text: h

text: is

text: induced

text: by

text: the

text: initial

text: state

text: and

text: strategy

text: t

text: σ.

text: For

text: the

text: riders,

text: let

text: xˆ

text: (σ)

text: be

text: the

text: indicator

text: that

text: rider

text: j

text: is

text: picked-up

text: at

text: strategy

text: proﬁle

text: σ.

text: j

text: Let

text: qˆ

text: (σ)

text: xˆ

text: (σ)q

text: (h

text: be

text: the

text: payment

text: made

text: by

text: rider

text: j

text: at

text: time

text: τ

text: j

text: j

text: j

text: τj

text: j

text: Fixing

text: driver

text: and

text: rider

text: types,

text: a

text: ridesharing

text: mechanism

text: induces

text: an

text: extensive

text: form

text: game.

text: At

text: A

text: each

text: time

text: point

text: t,

text: each

text: driver

text: decides

text: on

text: an

text: action

text: α

text: σ

text: (h

text: (h

text: to

text: take

text: based

text: on

text: strategy

text: i,t

text: i

text: t

text: i,t

text: t

text: σ

text: and

text: the

text: history

text: h

text: and

text: receives

text: payment

text: πˆ

text: (α

text: h

text: The

text: total

text: payment

text: πˆ

text: (σ)

text: to

text: each

text: driver

text: is

text: i

text: t

text: i,t

text: i,t

text: t

text: i

text: determined

text: by

text: the

text: rules

text: of

text: the

text: mechanism.

text: We

text: deﬁne

text: the

text: following

text: properties.

text: Deﬁnition

text: (Budget

text: Balance).

text: A

text: ridesharing

text: mechanism

text: is

text: budget

text: balanced

text: if

text: for

text: any

text: set

text: of

text: riders

text: and

text: drivers,

text: and

text: any

text: strategy

text: proﬁle

text: by

text: drivers,

text: we

text: have

text: qˆ

text: (σ)

text: πˆ

text: (σ).

text: j

text: i

text: ∈R

text: ∈D

text: j

text: i


text: the planning horizon and have no intrinsic preference for driving in one location over another or ending the planning period in a particular location. We do allow drivers to ﬁrst become available to dispatch from diverse locations, and in a staggered way, with diﬀerent drivers coming online at diﬀerent times. We model a rider’s value as her willingness-to-pay over-and-above a base payment that is set by the platform to cover driver costs. In this way, the prices that are computed through the STP mechanism correspond to the “surge” price, over-and-above the base payment for a trip. We prove the existence of anonymous, origin-destination, competitive equilibrium (CE) prices. By adopting origin-destination prices, the unit price of a trip can depend on market conditions at both the origin and destination.13 The STP mechanism employs driver-pessimal CE prices, computing a driver-pessimal CE plan at the beginning of the planning horizon and after driver deviations. This induces an extensive-form game among the drivers, where the total payoﬀ to each driver is determined by the mechanism’s dispatch and payment rules. The use of driver pessimal CE prices is an essential part of achieving smooth prices, and the proof of incentive alignment also makes use of the M(cid:92) concavity of min-cost ﬂow objectives [?]. The same connection to min-cost ﬂow leads to an eﬃcient algorithm to compute an optimal dispatching and prices, and operationalize the STP mechanism. The rest of the paper is organized as follows. After a brief discussion on related works in Section , we formally introduce the model in Section , and illustrate through an example that a myopic pricing mechanism, which naively clears the market for each location without considering future demand and supply, fails to be welfare-optimal or incentive aligned. In Section , we formulate the optimal planning problem and establish integrality properties of a linear-programming relaxation (Lemma 1). We show that a plan with anonymous trip prices is welfare-optimal if and only if it forms a competitive equilibrium (CE) (Lemma 2), and that optimal CE plans exist and are eﬃcient to compute. We also prove that drivers’ total payments among all CE plans form a lattice (Lemma 3). A class of static CE mechanisms are discussed, that incentivize drivers to always follow the mechanism’s dispatches (Theorem 1) but fail to be welfare-optimal or envy-free after driver deviations. We prove our main result in Section , that the STP mechanism is subgame-perfect incen- tive compatible, and is also individually rational, budget balanced, envy-free, and welfare optimal from any history onward (Theorem 2). We also prove an impossibility result, that no dominant- strategy mechanism has the same economic properties (Theorem 3). An empirical analysis con- ducted through simulation (Section ) suggests that the STP mechanism can achieve signiﬁcantly higher social welfare than a myopic pricing mechanism, and highlights the failure of incentive align- ment due to non-smooth prices in myopic mechanisms. We consider three stylized scenarios: the end of a sports event, the morning rush hour, and trips to and from the airport with imbalanced ﬂows. In all three scenarios, the STP mechanism achieves substantially higher social welfare as well as time-eﬃciency for drivers. We conclude in Section ?? with discussions on the eﬀect of re- laxing the model assumptions and directions of future work. Additional examples, omitted proofs, simulation results and relations to the literature are provided in the Appendix. 1.2 Related Work Banerjee et al. [?] adopt a queuing-theoretic approach in analyzing the eﬀect of dynamic pricing 13The idea that the unit price for a trip might depend on the destination is already familiar in taxi sys- tems, with trips to the suburbs billed with a surcharge to reﬂect that drivers will need to return to the city without a fare. Origin-destination pricing also seems practical. Indeed, ridesharing platforms are moving in this direction, and this is facilitated by the movement to quoting a total payment for a trip rather than an origin-based surge multiplier. https://newsroom.uber.com/upfront-fares-no-math-and-no-surprises/ https://blog.lyft.com/posts/now-live-see-your-ride-total https://www.bloomberg.com/news/articles/ 2017-05-19/uber-s-future-may-rely-on-predicting-how-much-you-re-willing-to-pay 4 ##LTLine##

text: the

text: planning

text: horizon

text: and

text: have

text: no

text: intrinsic

text: preference

text: for

text: driving

text: in

text: one

text: location

text: over

text: another

text: or

text: ending

text: the

text: planning

text: period

text: in

text: a

text: particular

text: location.

text: We

text: do

text: allow

text: drivers

text: to

text: ﬁrst

text: become

text: available

text: to

text: dispatch

text: from

text: diverse

text: locations,

text: and

text: in

text: a

text: staggered

text: way,

text: with

text: diﬀerent

text: drivers

text: coming

text: online

text: at

text: diﬀerent

text: times.

text: We

text: model

text: a

text: rider’s

text: value

text: as

text: her

text: willingness-to-pay

text: over-and-above

text: a

text: base

text: payment

text: that

text: is

text: set

text: by

text: the

text: platform

text: to

text: cover

text: driver

text: costs.

text: In

text: this

text: way,

text: the

text: prices

text: that

text: are

text: computed

text: through

text: the

text: STP

text: mechanism

text: correspond

text: to

text: the

text: “surge”

text: price,

text: over-and-above

text: the

text: base

text: payment

text: for

text: a

text: trip.

text: We

text: prove

text: the

text: existence

text: of

text: anonymous,

text: origin-destination,

text: competitive

text: equilibrium

text: (CE)

text: prices.

text: By

text: adopting

text: origin-destination

text: prices,

text: the

text: unit

text: price

text: of

text: a

text: trip

text: can

text: depend

text: on

text: market

text: conditions

text: at

text: both

text: the

text: origin

text: and

text: The

text: STP

text: mechanism

text: employs

text: driver-pessimal

text: CE

text: prices,

text: computing

text: a

text: driver-pessimal

text: CE

text: plan

text: at

text: the

text: beginning

text: of

text: the

text: planning

text: horizon

text: and

text: after

text: driver

text: deviations.

text: This

text: induces

text: an

text: extensive-form

text: game

text: among

text: the

text: drivers,

text: where

text: the

text: total

text: payoﬀ

text: to

text: each

text: driver

text: is

text: determined

text: by

text: the

text: mechanism’s

text: dispatch

text: and

text: payment

text: rules.

text: The

text: use

text: of

text: driver

text: pessimal

text: CE

text: prices

text: is

text: an

text: essential

text: part

text: of

text: achieving

text: smooth

text: prices,

text: and

text: the

text: proof

text: of

text: incentive

text: alignment

text: also

text: makes

text: use

text: of

text: the

text: concavity

text: of

text: min-cost

text: ﬂow

text: objectives

text: The

text: same

text: connection

text: to

text: min-cost

text: ﬂow

text: leads

text: to

text: an

text: eﬃcient

text: algorithm

text: to

text: compute

text: an

text: optimal

text: dispatching

text: and

text: prices,

text: and

text: operationalize

text: the

text: STP

text: mechanism.

text: The

text: rest

text: of

text: the

text: paper

text: is

text: organized

text: as

text: follows.

text: After

text: a

text: brief

text: discussion

text: on

text: related

text: works

text: in

text: Section

text: we

text: formally

text: introduce

text: the

text: model

text: in

text: Section

text: and

text: illustrate

text: through

text: an

text: example

text: that

text: a

text: myopic

text: pricing

text: mechanism,

text: which

text: naively

text: clears

text: the

text: market

text: for

text: each

text: location

text: without

text: considering

text: future

text: demand

text: and

text: supply,

text: fails

text: to

text: be

text: welfare-optimal

text: or

text: incentive

text: aligned.

text: In

text: Section

text: we

text: formulate

text: the

text: optimal

text: planning

text: problem

text: and

text: establish

text: integrality

text: properties

text: of

text: a

text: linear-programming

text: relaxation

text: (Lemma

text: We

text: show

text: that

text: a

text: plan

text: with

text: anonymous

text: trip

text: prices

text: is

text: welfare-optimal

text: if

text: and

text: only

text: if

text: it

text: forms

text: a

text: competitive

text: equilibrium

text: (CE)

text: (Lemma

text: and

text: that

text: optimal

text: CE

text: plans

text: exist

text: and

text: are

text: eﬃcient

text: to

text: compute.

text: We

text: also

text: prove

text: that

text: drivers’

text: total

text: payments

text: among

text: all

text: CE

text: plans

text: form

text: a

text: lattice

text: (Lemma

text: A

text: class

text: of

text: static

text: CE

text: mechanisms

text: are

text: discussed,

text: that

text: incentivize

text: drivers

text: to

text: always

text: follow

text: the

text: mechanism’s

text: dispatches

text: (Theorem

text: but

text: fail

text: to

text: be

text: welfare-optimal

text: or

text: envy-free

text: after

text: driver

text: deviations.

text: We

text: prove

text: our

text: main

text: result

text: in

text: Section

text: that

text: the

text: STP

text: mechanism

text: is

text: subgame-perfect

text: incen-

text: tive

text: compatible,

text: and

text: is

text: also

text: individually

text: rational,

text: budget

text: balanced,

text: envy-free,

text: and

text: welfare

text: optimal

text: from

text: any

text: history

text: onward

text: (Theorem

text: We

text: also

text: prove

text: an

text: impossibility

text: result,

text: that

text: no

text: dominant-

text: strategy

text: mechanism

text: has

text: the

text: same

text: economic

text: properties

text: (Theorem

text: An

text: empirical

text: analysis

text: con-

text: ducted

text: through

text: simulation

text: (Section

text: suggests

text: that

text: the

text: STP

text: mechanism

text: can

text: achieve

text: signiﬁcantly

text: higher

text: social

text: welfare

text: than

text: a

text: myopic

text: pricing

text: mechanism,

text: and

text: highlights

text: the

text: failure

text: of

text: incentive

text: align-

text: ment

text: due

text: to

text: non-smooth

text: prices

text: in

text: myopic

text: mechanisms.

text: We

text: consider

text: three

text: stylized

text: scenarios:

text: the

text: end

text: of

text: a

text: sports

text: event,

text: the

text: morning

text: rush

text: hour,

text: and

text: trips

text: to

text: and

text: from

text: the

text: airport

text: with

text: imbalanced

text: ﬂows.

text: In

text: all

text: three

text: scenarios,

text: the

text: STP

text: mechanism

text: achieves

text: substantially

text: higher

text: social

text: welfare

text: as

text: well

text: as

text: time-eﬃciency

text: for

text: drivers.

text: We

text: conclude

text: in

text: Section

text: with

text: discussions

text: on

text: the

text: eﬀect

text: of

text: re-

text: laxing

text: the

text: model

text: assumptions

text: and

text: directions

text: of

text: future

text: work.

text: Additional

text: examples,

text: omitted

text: proofs,

text: simulation

text: results

text: and

text: relations

text: to

text: the

text: literature

text: are

text: provided

text: in

text: the

text: Appendix.

text: Related

text: Work

text: Banerjee

text: et

text: al.

text: adopt

text: a

text: queuing-theoretic

text: approach

text: in

text: analyzing

text: the

text: eﬀect

text: of

text: dynamic

text: pricing

text: idea

text: that

text: the

text: unit

text: price

text: for

text: a

text: trip

text: might

text: depend

text: on

text: the

text: destination

text: is

text: already

text: familiar

text: in

text: taxi

text: sys-

text: tems,

text: with

text: trips

text: to

text: the

text: suburbs

text: billed

text: with

text: a

text: surcharge

text: to

text: reﬂect

text: that

text: drivers

text: will

text: need

text: to

text: return

text: to

text: the

text: city

text: without

text: a

text: fare.

text: Origin-destination

text: pricing

text: also

text: seems

text: practical.

text: Indeed,

text: ridesharing

text: platforms

text: are

text: moving

text: in

text: this

text: direction,

text: and

text: this

text: is

text: facilitated

text: by

text: the

text: movement

text: to

text: quoting

text: a

text: total

text: payment

text: for

text: a

text: trip

text: rather

text: than

text: an

text: origin-based

text: surge

text: multiplier.

text: ##LTLine##


text: would be p = 8, and p + p = 8, therefore p = 5, p = 3 and p = 2 and A,B,0 A,A,0 A,A,1 A,A,0 A,A,1 A,A,0 p = 6 would both support the driver-pessimal CE outcome. A,A,1 Lattice Structure: We can check that the lowest price for the trips (A, A, 0) and (A, A, 1) under all CE outcomes would be 2 and 3 respectively. However, setting p = 2 and p = 3 wouldn’t ≥ A,A,0 A,A,1 form a CE, since rider 3 is willing to pay 8 thus p 8. This implies that trip prices under all A,B,0 CE outcomes do not form a lattice. As a consequence, riders’ utilities under all CE outcomes do not form a lattice either. Rider-side VCG Prices: Moreover, we can check that p = 2 is what rider 1 should be charged A,A,0 under the VCG payment rule: if rider 1 isn’t present, rider 3 gets picked up thus the total welfare for the rest of the economy increases from v = 6 to v = 8. Similarly, rider 2’s VCG payment 2 3 would be p = 3. This shows that the VCG payment on the rider side may not support a A,A,1 welfare-optimal CE outcome. Rider-side IC: This example also implies that the STP mechanism is not incentive compatible on the rider’s side. Under any driver-pessimal outcome, we know that one of the riders 1 and 2 would be charged a payment that is higher than their VCG price. A simple analysis would show that if the rider who is charged higher than the VCG price reports the VCG price as her value, then her payment under the STP mechanism would be exactly her VCG price. This is a useful deviation. More generally, this also shows that no welfare-optimal CE outcome would be incentive compatible ≥ (cid:3) on the rider’s side, since p + p 8 under any CE outcome. A,A,0 A,A,1 It is not a coincidence that the lowest possible prices for each rider under all CE outcomes is equal to their rider-side VCG prices. The following theorem shows that the minimum CE prices and the rider-side VCG prices always coincide. Theorem 4 (Minimum CE = Rider-Side VCG). For a rider that is picked up in any welfare- optimal dispatching, her rider-side VCG price is equal to the minimum price for her trip among all CE outcomes. ∈ R Proof. For simplicity of notation, assume that driver j requests the trip (a, b, t), has value v , j and is picked up under some welfare-optimal dispatching. We need to show that, (i) the price p under any CE outcome is at least the rider-side VCG payment for rider j, and a,b,t (ii) there exists an CE outcome where rider j’s trip price is at most her rider-side VCG payment. Combining (i) and (ii), we know that the rider-side VCG payment has to be the lowest CE price for the trip among all CE outcomes. D R D R Let W˜ ( , ) be the optimal welfare achieved by the set of drivers and the set of riders , i.e. D ∪ { } R the optimal objective of (6). Moreover, we denote W˜ ( (a, b, t) , ) as the optimal objective of (6) if the trip capacity constraint (7) for this speciﬁc trip is relaxed by 1, i.e. there is an additional driver that is only able to complete an (a, b, t) trip. D R D ∪ { } R Similarly, denote W ( , ) as the optimal objective of (11) and W ( (a, b, t) , ) as the optimal objective of (11) with an extra (a, b, t) trip capacity. From the integrality of the LP D R D R D ∪ (11) under (S1) and (S2), we know that W˜ ( , ) = W ( , ), however, we only know W˜ ( { } R ≤ D ∪{ } R (a, b, t) , ) W ( (a, b, t) , ) since with the additional (a, b, t) trip it is not obvious whether the LP relaxation is still integral. Part (i): To prove (i), ﬁrst observe that with the same argument on subgradients as in the proof of Lemma 3, we show that the price p under any CE outcome is lower bounded by the welfare a,b,t 33

text: would

text: be

text: p

text: and

text: p

text: p

text: therefore

text: p

text: p

text: and

text: p

text: and

text: p

text: would

text: both

text: support

text: the

text: driver-pessimal

text: CE

text: outcome.

text: Lattice

text: Structure:

text: We

text: can

text: check

text: that

text: the

text: lowest

text: price

text: for

text: the

text: trips

text: (A,

text: A,

text: and

text: (A,

text: A,

text: under

text: all

text: CE

text: outcomes

text: would

text: be

text: and

text: respectively.

text: However,

text: setting

text: p

text: and

text: p

text: wouldn’t

text: form

text: a

text: CE,

text: since

text: rider

text: is

text: willing

text: to

text: pay

text: thus

text: p

text: This

text: implies

text: that

text: trip

text: prices

text: under

text: all

text: CE

text: outcomes

text: do

text: not

text: form

text: a

text: lattice.

text: As

text: a

text: consequence,

text: riders’

text: utilities

text: under

text: all

text: CE

text: outcomes

text: do

text: not

text: form

text: a

text: lattice

text: either.

text: Rider-side

text: VCG

text: Prices:

text: Moreover,

text: we

text: can

text: check

text: that

text: p

text: is

text: what

text: rider

text: should

text: be

text: charged

text: under

text: the

text: VCG

text: payment

text: rule:

text: if

text: rider

text: isn’t

text: present,

text: rider

text: gets

text: picked

text: up

text: thus

text: the

text: total

text: welfare

text: for

text: the

text: rest

text: of

text: the

text: economy

text: increases

text: from

text: v

text: to

text: v

text: Similarly,

text: rider

text: VCG

text: payment

text: would

text: be

text: p

text: This

text: shows

text: that

text: the

text: VCG

text: payment

text: on

text: the

text: rider

text: side

text: may

text: not

text: support

text: a

text: welfare-optimal

text: CE

text: outcome.

text: Rider-side

text: IC:

text: This

text: example

text: also

text: implies

text: that

text: the

text: STP

text: mechanism

text: is

text: not

text: incentive

text: compatible

text: on

text: the

text: rider’s

text: side.

text: Under

text: any

text: driver-pessimal

text: outcome,

text: we

text: know

text: that

text: one

text: of

text: the

text: riders

text: and

text: would

text: be

text: charged

text: a

text: payment

text: that

text: is

text: higher

text: than

text: their

text: VCG

text: price.

text: A

text: simple

text: analysis

text: would

text: show

text: that

text: if

text: the

text: rider

text: who

text: is

text: charged

text: higher

text: than

text: the

text: VCG

text: price

text: reports

text: the

text: VCG

text: price

text: as

text: her

text: value,

text: then

text: her

text: payment

text: under

text: the

text: STP

text: mechanism

text: would

text: be

text: exactly

text: her

text: VCG

text: price.

text: This

text: is

text: a

text: useful

text: deviation.

text: More

text: generally,

text: this

text: also

text: shows

text: that

text: no

text: welfare-optimal

text: CE

text: outcome

text: would

text: be

text: incentive

text: compatible

text: on

text: the

text: rider’s

text: side,

text: since

text: p

text: p

text: under

text: any

text: CE

text: outcome.

text: It

text: is

text: not

text: a

text: coincidence

text: that

text: the

text: lowest

text: possible

text: prices

text: for

text: each

text: rider

text: under

text: all

text: CE

text: outcomes

text: is

text: equal

text: to

text: their

text: rider-side

text: VCG

text: prices.

text: The

text: following

text: theorem

text: shows

text: that

text: the

text: minimum

text: CE

text: prices

text: and

text: the

text: rider-side

text: VCG

text: prices

text: always

text: coincide.

text: Theorem

text: (Minimum

text: CE

text: Rider-Side

text: VCG).

text: For

text: a

text: rider

text: that

text: is

text: picked

text: up

text: in

text: any

text: welfare-

text: optimal

text: dispatching,

text: her

text: rider-side

text: VCG

text: price

text: is

text: equal

text: to

text: the

text: minimum

text: price

text: for

text: her

text: trip

text: among

text: all

text: CE

text: outcomes.

text: R

text: Proof.

text: For

text: simplicity

text: of

text: notation,

text: assume

text: that

text: driver

text: j

text: requests

text: the

text: trip

text: (a,

text: b,

text: t),

text: has

text: value

text: v

text: j

text: and

text: is

text: picked

text: up

text: under

text: some

text: welfare-optimal

text: dispatching.

text: We

text: need

text: to

text: show

text: that,

text: (i)

text: the

text: price

text: p

text: under

text: any

text: CE

text: outcome

text: is

text: at

text: least

text: the

text: rider-side

text: VCG

text: payment

text: for

text: rider

text: j,

text: and

text: a,b,t

text: (ii)

text: there

text: exists

text: an

text: CE

text: outcome

text: where

text: rider

text: j’s

text: trip

text: price

text: is

text: at

text: most

text: her

text: rider-side

text: VCG

text: payment.

text: Combining

text: (i)

text: and

text: (ii),

text: we

text: know

text: that

text: the

text: rider-side

text: VCG

text: payment

text: has

text: to

text: be

text: the

text: lowest

text: CE

text: price

text: for

text: the

text: trip

text: among

text: all

text: CE

text: outcomes.

text: D

text: R

text: D

text: R

text: Let

text: W˜

text: be

text: the

text: optimal

text: welfare

text: achieved

text: by

text: the

text: set

text: of

text: drivers

text: and

text: the

text: set

text: of

text: riders

text: i.e.

text: D

text: R

text: the

text: optimal

text: objective

text: of

text: Moreover,

text: we

text: denote

text: W˜

text: (a,

text: b,

text: t)

text: as

text: the

text: optimal

text: objective

text: of

text: if

text: the

text: trip

text: capacity

text: constraint

text: for

text: this

text: speciﬁc

text: trip

text: is

text: relaxed

text: by

text: i.e.

text: there

text: is

text: an

text: additional

text: driver

text: that

text: is

text: only

text: able

text: to

text: complete

text: an

text: (a,

text: b,

text: t)

text: trip.

text: D

text: R

text: D

text: R

text: Similarly,

text: denote

text: W

text: as

text: the

text: optimal

text: objective

text: of

text: and

text: W

text: (a,

text: b,

text: t)

text: as

text: the

text: optimal

text: objective

text: of

text: with

text: an

text: extra

text: (a,

text: b,

text: t)

text: trip

text: capacity.

text: From

text: the

text: integrality

text: of

text: the

text: LP

text: D

text: R

text: D

text: R

text: D

text: under

text: and

text: we

text: know

text: that

text: W˜

text: W

text: however,

text: we

text: only

text: know

text: W˜

text: R

text: D

text: R

text: (a,

text: b,

text: t)

text: W

text: (a,

text: b,

text: t)

text: since

text: with

text: the

text: additional

text: (a,

text: b,

text: t)

text: trip

text: it

text: is

text: not

text: obvious

text: whether

text: the

text: LP

text: relaxation

text: is

text: still

text: integral.

text: Part

text: (i):

text: To

text: prove

text: (i),

text: ﬁrst

text: observe

text: that

text: with

text: the

text: same

text: argument

text: on

text: subgradients

text: as

text: in

text: the

text: proof

text: of

text: Lemma

text: we

text: show

text: that

text: the

text: price

text: p

text: under

text: any

text: CE

text: outcome

text: is

text: lower

text: bounded

text: by

text: the

text: welfare

text: a,b,t


text: computes a driver-optimal CE outcome at all times, regardless of whether deviation happened. Under the CE outcome computed at time 0 as in Figure ??, both riders 1 and 2 are picked up, and the prices for the trips are both p = p = 1. B,B,2 A,A,2 Assume that both drivers 1 and 2 follow the mechanism until time 2, the new driver-optimal outcome computed at time 2 would be as illustrated in Figure ??, where the price for the trip (B, B, 2) becomes 10, the highest market-clearing price at this state. This shows that the “time 0” plan of the mechanism, i.e. the actual outcome where all drivers follow the mechanism’s dispatch at all times, is not envy-free for drivers, since the total payment to driver 1 is 10, higher than that of driver 2. Now consider the scenario where driver 2 stayed in location B at time 0 instead of following the dispatch and relocate to location A. Under the optimal CE outcome from time 1 onward as illus- trated in Figure ??, the two drivers take the paths ((B, B, 1), (B, B, 2)) and ((B, A, 1), (A, A, 2)) respectively, and pick up the two drivers. The IC property of the mechanism now depends on how to break ties among driver-optimal CE plans, but as long as the mechanism dispatches driver 2 to take the path ((B, B, 1), (B, B, 2)) with non-zero probability (which would be the case if ties are broken uniformly at random), this would be a useful deviation for driver 2. Once driver 2 followed the plan and reach (B, 2) and driver 1 arrived at (A, 2), the newly updated price for the (cid:3) trip (B, B, 2) would again become 10. C Proofs We provide in this section proofs that were omitted from the body of the paper. C.1 Minimum Cost Flow The technical results in this paper made extensive use of the reduction of an optimal dispatch- ing problem for ridesharing to a minimum cost ﬂow (MCF) problem, where drivers ﬂow through a network, with nodes corresponding to (location, time) pairs, and the edge costs equal to the negations (additive inverse) of rider values. See [?] for an introduction to MCF. We brieﬂy present notations and the formulation of the MCF problems in this section. N E N E E → Z∪{−∞} Let G = ( , ) be a directed graph with a node set and an edge set . Let c : E → Z∪{ ∞} E → R be the lower capacity function, c¯ : + be the upper capacity function, and let γ : ∈ E ∈ N − ∈ N be the cost function. For each edge e , denote ∂+e as the initial (tail) node of e and ∂ e − as the terminal (head) node of e. That is, ∂+e = n and ∂ e = n for the edge e = (n , n ). E → R 1 ≤ 2 ≤ 1 ∈2 E A feasible ﬂow f is a function f : such that c(e) f(e) c¯(e) for each e . Its N → R (cid:88) (cid:88) boundary ∂f : is deﬁned as { | ∈ E } − { | ∈ E − } ∂f(n) = f(e) e , ∂+e = n f(e) e , ∂ e = n . Intuitively, a node n for which ∂f(n) > 0 is a source of the ﬂow, and a node n is a sink if ∂f(n) < 0. R|N| Let ξ be a vector in , the m(cid:40)inimum cost(cid:12)for any ﬂow with boundary co(cid:41)ndition ξ is: (cid:88) (cid:12) (cid:12) (cid:12) (cid:12) ω(ξ) = inf γ(e)f(e) f : feasible ﬂow with ∂f = ξ . (35) f ∈E e ⇒ Optimal Dispatching MCF Given an instance of the optimal dispatching problem with L R D planning horizon T , locations , distances δ, riders and drivers , we construct a corresponding 38 ##LTLine## ##LTLine##

text: computes

text: a

text: driver-optimal

text: CE

text: outcome

text: at

text: all

text: times,

text: regardless

text: of

text: whether

text: deviation

text: happened.

text: Under

text: the

text: CE

text: outcome

text: computed

text: at

text: time

text: as

text: in

text: Figure

text: both

text: riders

text: and

text: are

text: picked

text: up,

text: and

text: the

text: prices

text: for

text: the

text: trips

text: are

text: both

text: p

text: p

text: Assume

text: that

text: both

text: drivers

text: and

text: follow

text: the

text: mechanism

text: until

text: time

text: the

text: new

text: driver-optimal

text: outcome

text: computed

text: at

text: time

text: would

text: be

text: as

text: illustrated

text: in

text: Figure

text: where

text: the

text: price

text: for

text: the

text: trip

text: (B,

text: B,

text: becomes

text: the

text: highest

text: market-clearing

text: price

text: at

text: this

text: state.

text: This

text: shows

text: that

text: the

text: “time

text: 0”

text: plan

text: of

text: the

text: mechanism,

text: i.e.

text: the

text: actual

text: outcome

text: where

text: all

text: drivers

text: follow

text: the

text: mechanism’s

text: dispatch

text: at

text: all

text: times,

text: is

text: not

text: envy-free

text: for

text: drivers,

text: since

text: the

text: total

text: payment

text: to

text: driver

text: is

text: higher

text: than

text: that

text: of

text: driver

text: Now

text: consider

text: the

text: scenario

text: where

text: driver

text: stayed

text: in

text: location

text: B

text: at

text: time

text: instead

text: of

text: following

text: the

text: dispatch

text: and

text: relocate

text: to

text: location

text: A.

text: Under

text: the

text: optimal

text: CE

text: outcome

text: from

text: time

text: onward

text: as

text: illus-

text: trated

text: in

text: Figure

text: the

text: two

text: drivers

text: take

text: the

text: paths

text: ((B,

text: B,

text: (B,

text: B,

text: and

text: ((B,

text: A,

text: (A,

text: A,

text: respectively,

text: and

text: pick

text: up

text: the

text: two

text: drivers.

text: The

text: IC

text: property

text: of

text: the

text: mechanism

text: now

text: depends

text: on

text: how

text: to

text: break

text: ties

text: among

text: driver-optimal

text: CE

text: plans,

text: but

text: as

text: long

text: as

text: the

text: mechanism

text: dispatches

text: driver

text: to

text: take

text: the

text: path

text: ((B,

text: B,

text: (B,

text: B,

text: with

text: non-zero

text: probability

text: (which

text: would

text: be

text: the

text: case

text: if

text: ties

text: are

text: broken

text: uniformly

text: at

text: random),

text: this

text: would

text: be

text: a

text: useful

text: deviation

text: for

text: driver

text: Once

text: driver

text: followed

text: the

text: plan

text: and

text: reach

text: (B,

text: and

text: driver

text: arrived

text: at

text: (A,

text: the

text: newly

text: updated

text: price

text: for

text: the

text: trip

text: (B,

text: B,

text: would

text: again

text: become

text: C

text: Proofs

text: We

text: provide

text: in

text: this

text: section

text: proofs

text: that

text: were

text: omitted

text: from

text: the

text: body

text: of

text: the

text: paper.

text: Minimum

text: Cost

text: Flow

text: The

text: technical

text: results

text: in

text: this

text: paper

text: made

text: extensive

text: use

text: of

text: the

text: reduction

text: of

text: an

text: optimal

text: dispatch-

text: ing

text: problem

text: for

text: ridesharing

text: to

text: a

text: minimum

text: cost

text: ﬂow

text: (MCF)

text: problem,

text: where

text: drivers

text: ﬂow

text: through

text: a

text: network,

text: with

text: nodes

text: corresponding

text: to

text: (location,

text: time)

text: pairs,

text: and

text: the

text: edge

text: costs

text: equal

text: to

text: the

text: negations

text: (additive

text: inverse)

text: of

text: rider

text: values.

text: See

text: for

text: an

text: introduction

text: to

text: MCF.

text: We

text: brieﬂy

text: present

text: notations

text: and

text: the

text: formulation

text: of

text: the

text: MCF

text: problems

text: in

text: this

text: section.

text: N

text: E

text: N

text: E

text: E

text: Z∪{−∞}

text: Let

text: G

text: be

text: a

text: directed

text: graph

text: with

text: a

text: node

text: set

text: and

text: an

text: edge

text: set

text: Let

text: c

text: E

text: Z∪{

text: E

text: R

text: be

text: the

text: lower

text: capacity

text: function,

text: c¯

text: be

text: the

text: upper

text: capacity

text: function,

text: and

text: let

text: γ

text: E

text: N

text: N

text: be

text: the

text: cost

text: function.

text: For

text: each

text: edge

text: e

text: denote

text: ∂+e

text: as

text: the

text: initial

text: (tail)

text: node

text: of

text: e

text: and

text: e

text: as

text: the

text: terminal

text: (head)

text: node

text: of

text: e.

text: That

text: is,

text: ∂+e

text: n

text: and

text: e

text: n

text: for

text: the

text: edge

text: e

text: (n

text: n

text: E

text: R

text: ∈2

text: E

text: A

text: feasible

text: ﬂow

text: f

text: is

text: a

text: function

text: f

text: such

text: that

text: c(e)

text: f(e)

text: c¯(e)

text: for

text: each

text: e

text: Its

text: N

text: R

text: boundary

text: ∂f

text: is

text: deﬁned

text: as

text: E

text: E

text: ∂f(n)

text: f(e)

text: e

text: ∂+e

text: n

text: f(e)

text: e

text: e

text: n

text: Intuitively,

text: a

text: node

text: n

text: for

text: which

text: ∂f(n)

text: is

text: a

text: source

text: of

text: the

text: ﬂow,

text: and

text: a

text: node

text: n

text: is

text: a

text: sink

text: if

text: ∂f(n)

text: R|N|

text: Let

text: ξ

text: be

text: a

text: vector

text: in

text: the

text: any

text: ﬂow

text: with

text: boundary

text: ξ

text: is:

text: ω(ξ)

text: inf

text: γ(e)f(e)

text: f

text: feasible

text: ﬂow

text: with

text: ∂f

text: ξ

text: f

text: ∈E

text: e

text: Optimal

text: Dispatching

text: MCF

text: Given

text: an

text: instance

text: of

text: the

text: optimal

text: dispatching

text: problem

text: with

text: L

text: R

text: D

text: planning

text: horizon

text: T

text: locations

text: distances

text: δ,

text: riders

text: and

text: drivers

text: we

text: construct

text: a

text: corresponding

text: ##LTLine##

text: ##LTLine##