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The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that…
Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectrums of these…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not…
In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove…
We develop a classical well-posedness and regularity theory on a finite connected weighted graph for an extended mean field game system, its associated master equation, and a Hamilton-Jacobi- Bellman equation on the probability simplex, all…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
Imitation learning is a data-driven approach to learning policies from expert behavior, but it is prone to unreliable outcomes in out-of-sample (OOS) regions. While previous research relying on stable dynamical systems guarantees…
In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
Non-local games are a powerful tool to distinguish between correlations possible in classical and quantum worlds. Kalai et al. (STOC'23) proposed a compiler that converts multipartite non-local games into interactive protocols with a single…
In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…
We derive exact formulas for bipartite von Neumann entanglement entropy after partial projective local measurement in $1+1$ dimensional conformal field theories with periodic and open boundary conditions. After defining the set up we will…
In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras. In particular, we start with families of…
The problem of two companies of agents with one-step memory playing game is investigated in the context of the Iterated Prisoner's Dilemma under the partial imitation rule, where a player can imitate only those moves that he has observed in…
We present an efficient reduction that converts any machine learning algorithm into an interactive protocol, enabling collaboration with another party (e.g., a human) to achieve consensus on predictions and improve accuracy. This approach…
This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
A natural generalization of Krein's theorem to a pair of commuting tuples $\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in…