Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. To model such scenarios, we supplement the classical Fisher model of a market by introducing {\em transaction costs}. For every buyer $i$ and every good $j$, there is a transaction cost of \cij; if the price of good $j$ is $p_j$, then the cost to the buyer $i$ {\em per unit} of $j$ is p_j + \cij. This allows the same good to be sold at different (effective) prices to different buyers. We provide a combinatorial algorithm that computes $\epsilon$-approximate equilibrium prices and allocations in $O\left(\frac{1}{\epsilon}(n+\log{m})mn\log(B/\epsilon)\right)$ operations - where $m$ is the number goods, $n$ is the number of buyers and $B$ is the sum of the budgets of all the buyers

Probing the indefinite CP nature of the Higgs Boson through decay distributions in the process e+e−→ttˉΦe^+e^-\to t\bar{t}\Phi

The recently discovered scalar resonance at the LHC is now almost confirmed to be a Higgs Boson, whose CP properties are yet to be established. At the ILC with and without polarized beams, it may be possible to probe these properties at high precision. In this work, we study the possibility of probing departures from the pure CP-even case, by using the decay distributions in the process $e^+ e^- \to t \bar{t} \Phi$, with $\Phi$ mainly decaying into a $b\bar b$ pair. We have compared the case of a minimal extension of the SM case (Model I) with an additional pseudoscalar degree of freedom, with a more realistic case namely the CP-violating Two-Higgs Doublet Model (Model II) that permits a more general description of the couplings. We have considered the ILC with $\sqrt{s}=800$\,GeV and integrated luminosity of $300\, {\rm fb}^{-1}$. Our main findings are that even in the case of small departures from the CP-even case, the decay distributions are sensitive to the presence of a CP-odd component in Model II, while it is difficult to probe these departures in Model I unless the pseudoscalar component is very large. Noting that the proposed degrees of beam polarization increases the statistics, the process demonstrates the effective role of beam polarization in studies beyond the Standard Model. Further, our study shows that an indefinite CP Higgs would be a sensitive laboratory to physics beyond the SM.Comment: 14 pages using revtex, 10 figures, corresponds to version accepted for publication in Phys. Rev. D.; compared to v1, discussion extended, figure added, table added, section reorganize

Weakly supervised 3D Reconstruction with Adversarial Constraint

Supervised 3D reconstruction has witnessed a significant progress through the use of deep neural networks. However, this increase in performance requires large scale annotations of 2D/3D data. In this paper, we explore inexpensive 2D supervision as an alternative for expensive 3D CAD annotation. Specifically, we use foreground masks as weak supervision through a raytrace pooling layer that enables perspective projection and backpropagation. Additionally, since the 3D reconstruction from masks is an ill posed problem, we propose to constrain the 3D reconstruction to the manifold of unlabeled realistic 3D shapes that match mask observations. We demonstrate that learning a log-barrier solution to this constrained optimization problem resembles the GAN objective, enabling the use of existing tools for training GANs. We evaluate and analyze the manifold constrained reconstruction on various datasets for single and multi-view reconstruction of both synthetic and real images

Where we stand on structure dependence of ISGMR in the Zr-Mo region: Implications on K_\infty

Isoscalar giant resonances, being the archetypal forms of collective nuclear behavior, have been studied extensively for decades with the goal of constraining bulk nuclear properties of the equation of state, as well as for modeling dynamical behaviors within stellar environments. An important such mode is the isoscalar electric giant monopole resonance (ISGMR) that can be understood as a radially symmetric density vibration within the saturated nuclear volume. The field has a few key open questions, which have been proposed and remain unresolved. One of the more provocative questions is the extra high-energy strength in the $A\approx 90$ region, which manifested in large percentages of the $E0$ sum rule in $^{92}$Zr and $^{92}$Mo above the main ISGMR peak. The purpose of this article is to introduce these questions within the context of experimental investigations into the phenomena in the zirconium and molybdenum isotopic chains, and to address, via a discussion of previously published and preliminary results, the implications of recent experimental efforts on extraction of the nuclear incompressibility from this data.Comment: 9 pages, 7 figures, invited to be submitted to a special issue of EPJA honoring Prof. P. F. Bortigno

Isolating CP-violating \gamma ZZ coupling in e+e- \to \gamma Z with transverse beam polarizations

We revisit the process $e^+e^- \to \gamma Z$ at the ILC with transverse beam polarization in the presence of anomalous CP-violating $\gamma Z Z$ coupling $\lambda_1$ and $\gamma \gamma Z$ coupling $\lambda_2$. We point out that if the final-state spins are resolved, then it becomes possible to fingerprint the anomalous coupling {\rm Re}$\lambda_1$.90% confidence level limit on {\rm Re}$\lambda_1$ achievable at ILC with center-of-mass energy of 500 GeV or 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of $10^{-2}$ when the helicity of $Z$ is used and $10^{-3}$ when the helicity of $\gamma$ is used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. The benefits of such polarization programmes at the ILC are compared and contrasted for the process at hand. We also discuss possible methods by which one can isolate events with a definite helicity for one of the final-state particles.Comment: 13 pages, 9 figures, using RevTex; v2 is a significantly revised version of v1, and corresponds to the version that has been published in Physical Review