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The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
Unit commitment (UC) is a fundamental problem in the day-ahead electricity market, and it is critical to solve UC problems efficiently. Mathematical optimization techniques like dynamic programming, Lagrangian relaxation, and mixed-integer…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
We formulate the swarming optimization problem as a weakly coupled, dissipative dynamical system governed by a controlled energy dissipation rate and initial velocities that adhere to the nonequilibrium Onsager principle. In this framework,…
We present a new optimization-based method for aggregating preferences in settings where each voter expresses preferences over pairs of alternatives. Our approach to identifying a consensus partial order is motivated by the observation that…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
We have obtained an electromagnetic PIC (EM-PIC) algorithm based on time-space-extended particle in cell model. In this model particles are shaped objects extended over time and space around Lagrangian markers. Sources carried by these…
We present a variational free-energy formulation for distributionally robust decision-making with ambiguity in the generative model. The formulation, related to a broad range of learning and control frameworks, yields a minimax optimal…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
Agreement is a foundational problem in distributed computing that have been studied extensively for over four decades. Recently, Meir, Mirault, Peleg and Robinson introduced the notion of \emph{Energy Efficient Agreement}, where the goal is…
Computational complexity is a particularly important objective. The idea of Landauer principle was extended through mapping three classic problems (sorting,ordered searching and max of N unordered numbers) into Maxwell demon thought…