A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry

We consider a non-relativistic limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a covariant ‘membrane Newton-Cartan’ (MNC) geometry. The local tangent space is split into three ‘longitudinal’ and eight ‘transverse’ directions, related only by Galilean rather than Lorentzian symmetries. This generalises the ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The finite action then gives a set of equations that is invariant under longitudinal and transverse rotations, Galilean boosts and local dilatations. We supplement these equations with an extra Poisson equation, coming from the subleading action. Reduction along a longitudinal direction gives the known SNC theory with the addition of RR gauge fields, while reducing along a transverse direction yields a new non-relativistic theory associated to D2 branes. We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

Numerical Solution of Asymmetric Auctions

We propose the backward indifference derivation (BID) algorithm, a new method to numerically approximate the pure strategy Nash equilibrium (PSNE) bidding functions in asymmetric first-price auctions. The BID algorithm constructs a sequence of finite-action PSNE that converges to the continuum-action PSNE by finding where bidders are indifferent between actions. Consequently, our approach differs from prevailing numerical methods that consider a system of poorly behaved differential equations. After proving convergence (conditional on knowing the maximum bid), we evaluate the numerical performance of the BID algorithm on four examples, two of which have not been previously addressed.

Instanton worldlines in five-dimensional Ω-deformed gauge theory

We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an SU(1, 3) conformal symmetry. These actions have a Lagrange multiplier which imposes a novel Ω-deformed anti-self-dual gauge field constraint. Using a generalised ’t Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.

Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels

We study subgame $$\phi $$ ϕ -maxmin strategies in two-player zero-sum stochastic games with a countable state space, finite action spaces, and a bounded and universally measurable payoff function. Here, $$\phi $$ ϕ denotes the tolerance function that assigns a nonnegative tolerated error level to every subgame. Subgame $$\phi $$ ϕ -maxmin strategies are strategies of the maximizing player that guarantee the lower value in every subgame within the subgame-dependent tolerance level as given by $$\phi $$ ϕ . First, we provide necessary and sufficient conditions for a strategy to be a subgame $$\phi $$ ϕ -maxmin strategy. As a special case, we obtain a characterization for subgame maxmin strategies, i.e., strategies that exactly guarantee the lower value at every subgame. Secondly, we present sufficient conditions for the existence of a subgame $$\phi $$ ϕ -maxmin strategy. Finally, we show the possibly surprising result that each game admits a strictly positive tolerance function $$\phi ^*$$ ϕ ∗ with the following property: if a player has a subgame $$\phi ^*$$ ϕ ∗ -maxmin strategy, then he has a subgame maxmin strategy too. As a consequence, the existence of a subgame $$\phi $$ ϕ -maxmin strategy for every positive tolerance function $$\phi $$ ϕ is equivalent to the existence of a subgame maxmin strategy.

Moduli spaces of Calabi-Yau d-folds as gravitational-chiral instantons

Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension d ≤ 4 is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations of motion of gravity with matter). More precisely, the moduli geometry of Calabi-Yau d-folds (d ≤ 4) describes instantons of (E)AdS Einstein gravity coupled to a standard chiral model.From the point of view of the low-energy physics of string/M-theory compactified on the Calabi-Yau X, the various fields propagating on its moduli space are the couplings appearing in the effective Lagrangian "Image missing".

Online Learning over a Finite Action Set with Limited Switching

This paper studies the value of switching actions in the Prediction From Experts problem (PFE) and Adversarial Multiarmed Bandits problem (MAB). First, we revisit the well-studied and practically motivated setting of PFE with switching costs. Many algorithms achieve the minimax optimal order for both regret and switches in expectation; however, high probability guarantees are an open problem. We present the first algorithms that achieve this optimal order for both quantities with high probability. This also implies the first high probability guarantees for several other problems, and, in particular, is efficiently adaptable to online combinatorial optimization with limited switching. Next, to investigate the value of switching actions more granularly, we introduce the switching budget setting, which limits algorithms to a fixed number of (costless) switches. Using this result and several reductions, we unify previous work and completely characterize the complexity of this switching budget setting up to small polylogarithmic factors: for both PFE and MAB, for all switching budgets, and for both expectation and high probability guarantees. Interestingly, as the switching budget decreases, the minimax regret rate admits a phase transition for PFE but not for MAB. These results recover and generalize the known minimax rates for the (arbitrary) switching cost setting.

Convergence, continuity, recurrence and Turing completeness in dynamic epistemic logic1

The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the Stone topology, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behaviour of said maps. Among the recurrence results, we show maps induced by finite action models may have uncountably many recurrent points, even when initiated on a finite input model. Several recurrence results draws on the class of action models being Turing complete, for which the paper provides proof in the postcondition-free case. As upper bounds, it is shown that either 1 atom, 3 agents and preconditions of modal depth 18 or 1 atom, 7 agents and preconditions of modal depth 3 suffice for Turing completeness.

Nearly Optimal Regret for Stochastic Linear Bandits with Heavy-Tailed Payoffs

In this paper, we study the problem of stochastic linear bandits with finite action sets. Most of existing work assume the payoffs are bounded or sub-Gaussian, which may be violated in some scenarios such as financial markets. To settle this issue, we analyze the linear bandits with heavy-tailed payoffs, where the payoffs admit finite 1+epsilon moments for some epsilon in (0,1]. Through median of means and dynamic truncation, we propose two novel algorithms which enjoy a sublinear regret bound of widetilde{O}(d^(1/2)T^(1/(1+epsilon))), where d is the dimension of contextual information and T is the time horizon. Meanwhile, we provide an Omega(d^(epsilon/(1+epsilon))T^(1/(1+epsilon))) lower bound, which implies our upper bound matches the lower bound up to polylogarithmic factors in the order of d and T when epsilon=1. Finally, we conduct numerical experiments to demonstrate the effectiveness of our algorithms and the empirical results strongly support our theoretical guarantees.