Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing "photon" of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.Comment: 16 pages, 7 figures, published versio

Combining Spot and Futures Markets: A Hybrid Market Approach to Dynamic Spectrum Access

Dynamic spectrum access is a new paradigm of secondary spectrum utilization and sharing. It allows unlicensed secondary users (SUs) to exploit opportunistically the under-utilized licensed spectrum. Market mechanism is a widely-used promising means to regulate the consuming behaviours of users and, hence, achieves the efficient allocation and consumption of limited resources. In this paper, we propose and study a hybrid secondary spectrum market consisting of both the futures market and the spot market, in which SUs (buyers) purchase under-utilized licensed spectrum from a spectrum regulator, either through predefined contracts via the futures market, or through spot transactions via the spot market. We focus on the optimal spectrum allocation among SUs in an exogenous hybrid market that maximizes the secondary spectrum utilization efficiency. The problem is challenging due to the stochasticity and asymmetry of network information. To solve this problem, we first derive an off-line optimal allocation policy that maximizes the ex-ante expected spectrum utilization efficiency based on the stochastic distribution of network information. We then propose an on-line VickreyCClarkeCGroves (VCG) auction that determines the real-time allocation and pricing of every spectrum based on the realized network information and the pre-derived off-line policy. We further show that with the spatial frequency reuse, the proposed VCG auction is NP-hard; hence, it is not suitable for on-line implementation, especially in a large-scale market. To this end, we propose a heuristics approach based on an on-line VCG-like mechanism with polynomial-time complexity, and further characterize the corresponding performance loss bound analytically. We finally provide extensive numerical results to evaluate the performance of the proposed solutions.Comment: This manuscript is the complete technical report for the journal version published in INFORMS Operations Researc

Mask-ShadowGAN: Learning to Remove Shadows from Unpaired Data

This paper presents a new method for shadow removal using unpaired data, enabling us to avoid tedious annotations and obtain more diverse training samples. However, directly employing adversarial learning and cycle-consistency constraints is insufficient to learn the underlying relationship between the shadow and shadow-free domains, since the mapping between shadow and shadow-free images is not simply one-to-one. To address the problem, we formulate Mask-ShadowGAN, a new deep framework that automatically learns to produce a shadow mask from the input shadow image and then takes the mask to guide the shadow generation via re-formulated cycle-consistency constraints. Particularly, the framework simultaneously learns to produce shadow masks and learns to remove shadows, to maximize the overall performance. Also, we prepared an unpaired dataset for shadow removal and demonstrated the effectiveness of Mask-ShadowGAN on various experiments, even it was trained on unpaired data.Comment: Accepted to ICCV 201

A Beam Tracing with Precise Antialiasing for Polyhedral Scenes

International audienceRay tracing is one of the most important rendering techniques used in computer graphics. A fundamental problem of classical ray tracers is the well-known aliasing. With small objects, or small shadows, aliasing becomes a crucial problem to solve. Beam tracers can be considered as an extension of classical ray tracers. They replace the concept of infinitesimal ray by that of beam but they are generally more complex than ray tracers. The new method presented in this paper is a high quality beam tracer that provides a robust and general antialiasing for polyhedral scenes. Compared to similar beam tracers, this method has some major advantages: - complex and expensive computations of conventional beam-object intersection are entirely avoided, so an extension to some non polyhedral scenes such as CSG ones is possible; - usual approximations or complex approaches for refraction computations are avoided. Moreover, this method is entirely compatible with the usual improvements of classical ray tracing (spatial subdivisions or hierarchical bounding volumes)

The Markov chain tree theorem and the state reduction algorithm in commutative semirings

We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm which computes the Markov chain tree vector of a stochastic matrix.Comment: 13 page

Shadow Rendering through Translucent Materials

Tato práce se zabývá výpočtem stínů skrze průsvitné materiály pomocí metody zvané Barevné stochastické stínové mapy a její praktickou implementací v knihovnách OpenGL. Na začátku této práce je představena metoda Stínových map. V další části jsou zkráceně popsány vybrané způsoby řešení zobrazování průhledných objektů ve scéně. Následuje detailnější vysvětlení metody Barevných stochastických stínových map. V poslední části je popsána implementace demonstrační aplikace v jazyce C++, zhodnocení dosažených výsledků a návrh možností pokračování projektu.This paper describes the calculation of shadows through translucent materials using a method called Colored Stochastic Shadow Maps and its practical implementation in OpenGL libraries. At the beginning of this work a Shadow mapping method is introduced. The next section shortly describes selected ways of dealing with rendering of transparent objects in the scene. This is followed by detailed explanation of the method Colored Stochastic Shadow Maps. The last section describes the implementation of demonstration application in C++ language, evalution of the results and proposal of options to continue the project.