Related papers: Duality, thermodynamics, and the linear programmin…
In these lectures I shall explain how a new-found nonabelian duality can be used to solve some outstanding questions in particle physics. The first lecture introduces the concept of electromagnetic duality and goes on to present its…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of --…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from…
This paper is about output-feedback control problems for general linear systems in the presence of given state-, control-, disturbance-, and measurement error constraints. Because the traditional separation theorem in stochastic control is…
Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes…
Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization,…
We revisit the problem of maximizing expected logarithmic utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the seminal paper of Davis and Norman [Math. Operation…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713], stochastic…
Understanding the thermodynamics of the duplication process is a fundamental step towards a comprehensive physical theory of biological systems. However, the immense complexity of real cells obscures the fundamental tensions between energy…
Integrated global food system analysis is hampered by the fragmentation of data among food types, processes, and scales. Studies also often neglect the connection to human metabolism -- the ultimate driver of food demand. Here we use a…
The paper present one of attempts to apply the thermodynamics laws to economics. Introducing common thermodynamic parameters and considering world economics as a one macrosystem, authors demonstrate the possible consequences of entropy…
We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…