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Marginal values of a stochastic game
No full textZero-sum stochastic games are parameterized by payoffs, transitions, and possibly a discount rate. In this article, we study how the main solution concepts, the discounted and undiscounted values, vary when these parameters are perturbed. We focus on the marginal values, introduced by Mills in 1956 in the context of matrix games—that is, the directional derivatives of the value along any fixed perturbation. We provide a formula for the marginal values of a discounted stochastic game. Further, under mild assumptions on the perturbation, we provide a formula for their limit as the discount rate vanishes and for the marginal values of an undiscounted stochastic game. We also show, via an example, that the two latter differ in general
Distinct stabilization of the human T cell leukemia virus type 1 immature Gag lattice
No full textHuman T cell leukemia virus type 1 (HTLV-1) immature particles differ in morphology from other retroviruses, suggesting a distinct way of assembly. Here we report the results of cryo-electron tomography studies of HTLV-1 virus-like particles assembled in vitro, as well as derived from cells. This work shows that HTLV-1 uses a distinct mechanism of Gag–Gag interactions to form the immature viral lattice. Analysis of high-resolution structural information from immature capsid (CA) tubular arrays reveals that the primary stabilizing component in HTLV-1 is the N-terminal domain of CA. Mutagenesis analysis supports this observation. This distinguishes HTLV-1 from other retroviruses, in which the stabilization is provided primarily by the C-terminal domain of CA. These results provide structural details of the quaternary arrangement of Gag for an immature deltaretrovirus and this helps explain why HTLV-1 particles are morphologically distinct
Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse
No full textThe Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely, integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of almost every ellipse that preserves integrability near the boundary, is itself an ellipse. We apply this result to study local spectral uniqueness of ellipses using the connection between the wave trace of the Laplacian and the dynamics near the boundary and establish local uniqueness for almost all of them
Average and expected distortion of Voronoi paths and scapes
No full textThe approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about 4/Pi. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes
LNCS
No full textI give a personal account about the wave of new research activities that rose in the 1990s on the specification, verification, and control of real-time systems
Climbing up a random subgraph of the hypercube
No full textLet Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is an increasing path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is obtained by switching some zero coordinate in vi to a one coordinate in vi+1.
Form a random subgraph Qdp by retaining each edge in E(Qd) independently with probability p. We show that there is a phase transition with respect to the length of a longest increasing path around p=ed. Let α be a constant and let p=αd. When αe, whp there is a path of length d−2 in Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the all-zero and all-one vertices percolate or not
Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study
No full textWe compute the rotational anisotropy of the free energy of −RuCl3 in an external magnetic field. This quantity, known as the magnetotropic susceptibility, , relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of −RuCl3 and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to 30K—an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic spin susceptibility in this model of −RuCl3 displays scaling behavior =(/) at high temperatures. Once the uniform susceptibility departs from the Curie law (i.e., at the energy scale of the exchange interactions), it appears to transition to an emergent scalinglike behavior, characterized by a different function at lower temperatures, stemming from the locality of torque fluctuations. We observe a remarkable numerical match between experiment and simulations and we also find qualitative agreement with the pure Kitaev model. In comparison, for the XXZ Heisenberg Hamiltonian, the scaling =(/) breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law and never reemerges at low temperatures
TMLR
No full textScore-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time T1 by adding noise to the data, (ii) estimate its score function, and (iii) use such estimate to run a reverse process. As the reverse process is initialized with the stationary distribution of the forward one, the existing analysis paradigm requires T1→∞. This is however problematic: from a theoretical viewpoint, for a given precision of the score approximation, the convergence guarantee fails as T1 diverges; from a practical viewpoint, a large T1 increases computational costs and leads to error propagation. This paper addresses the issue by considering a version of the popular predictor-corrector scheme: after running the forward process, we first estimate the final distribution via an inexact Langevin dynamics and then revert the process. Our key technical contribution is to provide convergence guarantees which require to run the forward process only for a fixed finite time T1. Our bounds exhibit a mild logarithmic dependence on the input dimension and the subgaussian norm of the target distribution, have minimal assumptions on the data, and require only to control the L2 loss on the score approximation, which is the quantity minimized in practice
Fabricable 3D wire art
No full textThis paper presents a computational method for automatically creating fabricable 3D wire sculptures from various input modalities, including 3D models, images, and even text. There are several challenges to wire art creation. For example, artists must express the desired visual as a sparse wire representation. It is also difficult to manually bend wires in the air without guidance to fabricate the designed 3D curves. Our workflow solves these challenges by using two core techniques. First, we present an algorithm that automatically generates a fabricable 3D curve representation of the target based on a loss function that measures the semantic distance between the rendered curve and the target. The loss function can be defined using different pre-trained vision-language neural networks to generate wire art from different input types. The loss function is then optimized using differentiable rendering specifically targeting 3D parametric curves. Our method can incorporate various fabrication constraints on the wire as additional regularization terms in the optimization process. Second, we present an algorithm to generate a 3D printable jig structure that can be used to fabricate the generated wire path. The major challenge in the jig generation stems from the design of an intersection-free surface mesh for 3D printing, which we address with our inflation algorithm. The experimental results indicate that our method can handle a wider range of input types and can produce physically fabricable wire shapes compared to previous wire generation methods. Various wire arts have been fabricated using our 3D-printed jig to demonstrate its effectiveness in 3D wire bending
Simple and tight complexity lower bounds for solving Rabin games
No full textWe give a simple proof that assuming the Exponential Time Hypothesis (ETH), determining the winner of a Rabin game cannot be done in time 2o(k log k) · nO(1), where k is the number of pairs of vertex subsets involved in the winning condition and n is the vertex count of the game graph. While this result follows from the lower bounds provided by Calude et al [SIAM J. Comp. 2022], our reduction is considerably simpler and arguably provides more insight into the complexity of the problem. In fact, the analogous lower bounds discussed by Calude et al, for solving Muller games and multidimensional parity games, follow as simple corollaries of our approach. Our reduction also highlights the usefulness of a certain pivot problem — Permutation SAT — which may be of independent interest