Orbifold cup products and ring structures on Hochschild cohomologies

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an $S^1$-equivariant version of the Chen--Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology

Cumulative Prospect Theory Based Dynamic Pricing for Shared Mobility on Demand Services

Cumulative Prospect Theory (CPT) is a modeling tool widely used in behavioral economics and cognitive psychology that captures subjective decision making of individuals under risk or uncertainty. In this paper, we propose a dynamic pricing strategy for Shared Mobility on Demand Services (SMoDSs) using a passenger behavioral model based on CPT. This dynamic pricing strategy together with dynamic routing via a constrained optimization algorithm that we have developed earlier, provide a complete solution customized for SMoDS of multi-passenger transportation. The basic principles of CPT and the derivation of the passenger behavioral model in the SMoDS context are described in detail. The implications of CPT on dynamic pricing of the SMoDS are delineated using computational experiments involving passenger preferences. These implications include interpretation of the classic fourfold pattern of risk attitudes, strong risk aversion over mixed prospects, and behavioral preferences of self reference. Overall, it is argued that the use of the CPT framework corresponds to a crucial building block in designing socio-technical systems by allowing quantification of subjective decision making under risk or uncertainty that is perceived to be otherwise qualitative.Comment: 17 pages, 6 figures, and has been accepted for publication at the 58th Annual Conference on Decision and Control, 201

Study of the Brazil and Falkland currents using their images of Nimbus 5 and oceanographic data in 1972 - 1973

The Western Edge of the Sub-tropical Convergence of the South-western Atlantic Ocean, called the Front, which is a thermal discontinuity between the Brazil and Falkland Currents, was studied utilizing the Temperature Humidity Infrared Radiometer (THIR) of Nimbus V in the 10.5 to 12.5 micrometers channel and historical oceanographic data. Some important results obtained are: the oceanographic Front could be detected from Nimbus THIR data; oceanographic charts showed that the transition zone where the Brazil and the Falkland Currents meet was the Front detected from satellite data; ocean current speeds calculated with THIR data were of the same order of magnitude as those calculated oceanographically; fisheries statistics for Pargo Roseo showed that the maximum catches were in September of 1973, in the period when the Front was observed most distinctly and clearly. The results showed the great potentiality of satellite data to study surface thermal structures, surface currents and oceanic fisheries

Fast-Light in a Photorefractive Crystal for Gravitational Wave Detection

We demonstrate superluminal light propagation using two frequency multiplexed pump beams to produce a gain doublet in a photorefractive crystal of Ce:BaTiO3. The two gain lines are obtained by two-wave mixing between a probe field and two individual pump fields. The angular frequencies of the pumps are symmetrically tuned from the frequency of the probe. The frequency difference between the pumps corresponds to the separation of the two gain lines; as it increases, the crystal gradually converts from normal dispersion without detuning to an anomalously dispersive medium. The time advance is measured as 0.28 sec for a pulse propagating through a medium with a 2Hz gain separation, compared to the same pulse propagating through empty space. We also demonstrate directly anomalous dispersion profile using a modfied experimental configuration. Finally, we discuss how anomalous dispersion produced this way in a faster photorefractive crystal (such as SPS: Sn2P2S6) could be employed to enhance the sensitivity-bandwidth product of a LIGO type gravitational wave detector augmented by a White Light Cavity.Comment: 14 pages, 5 figure

Kan replacement of simplicial manifolds

We establish a functor $Kan$ from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.Comment: 19 pages, 11 figures, Lemma 2.2 improved, Prop.-Def. 2.3 modified. to appear in Letters in Mathematical Physic

Muon Pair Production by Electron-Photon Scatterings

The cross section for muon pair productions by electrons scattering over photons, $\sigma_{MPP}$, is calculated analytically in the leading order. It is pointed out that for the center-of-mass energy range, $s \geq 5 m^{2}_{\mu}$, the cross section for $\sigma_{MPP}$ is less than $1 \mu$b. The differential energy spectrum for either of the resulting muons is given for the purpose of high-energy neutrino astronomy. An implication of our result for a recent suggestion concerning the high-energy cosmic neutrino generation through this muon pair is discussed.Comment: a comment added, to appear in Phys. Rev. D, Rapid Communicatio

Towards Dynamic Pricing for Shared Mobility on Demand using Markov Decision Processes and Dynamic Programming

In a Shared Mobility on Demand Service (SMoDS), dynamic pricing plays an important role in the form of an incentive for the decision of the empowered passenger on the ride offer. Strategies for determining the dynamic tariff should be suitably designed so that the incurred demand and supply are balanced and therefore economic efficiency is achieved. In this manuscript, we formulate a discrete time Markov Decision Process (MDP) to determine the probability desired by the SMoDS platform corresponding to the acceptance rate of each empowered passenger at each state of the system. We use Estimated Waiting Time (EWT) as the metric for the balance between demand and supply, with the goal that EWT be regulated around a target value. We then develop a Dynamic Programming (DP) algorithm to derive the optimal policy of the MDP that regulates EWT around the target value. Computational experiments are conducted that demonstrate the regulation of EWT is effective, through various scenarios. The overall demonstration is carried out offline. The MDP formulation together with the DP algorithm can be utilized to an online determination of the dynamic tariff by integrating with our earlier works on Cumulative Prospect Theory based passenger behavioral modeling and the AltMin dynamic routing algorithm, and form the subject of future works.Comment: 17 pages, 6 figures, and has been accepted for publication at the 23rd IEEE International Conference on Intelligent Transportation Systems, 202