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Consider a population of heterogenous agents whose choice behaviors are partially \textit{comparable} according to a given \textit{primitive ordering}.The set of choice functions admissible in the population specifies a \textit{choice…
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…
The trace approximation problem for Toeplitz matrices and its applications to stationary processes dates back to the classic book by Grenander and Szeg\"o, "Toeplitz forms and their applications". It has then been extensively studied in the…
A long-standing hypothesis in neuroscience is that the central nervous system accomplishes complex motor behaviors through the combination of a small number of motor primitives. Many studies in the last couples of decades have identified…
Data science requires time-consuming iterative manual activities. In particular, activities such as data selection, preprocessing, transformation, and mining, highly depend on iterative trial-and-error processes that could be sped-up…
With the development of pre-trained language models, the dense retrieval models have become promising alternatives to the traditional retrieval models that rely on exact match and sparse bag-of-words representations. Different from most…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
We discuss a fast approximate solution to the associated classical -- classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynomials are solutions to a fourth-order quadratic eigenvalue…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g.…
The objective of this work is to augment the basic abilities of a robot by learning to use new sensorimotor primitives to enable the solution of complex long-horizon problems. Solving long-horizon problems in complex domains requires…
We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, including complexity, regularity, and algorithms. Specifically, we…
Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
The rise of foundation models has shifted focus from resource-intensive fine-tuning to prompt engineering, a paradigm that steers model behavior through input design rather than weight updates. While manual prompt engineering faces…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
Some top-down problem specifications, if executed directly, may compute sub-problems repeatedly. Instead, we may want a bottom-up algorithm that stores solutions of sub-problems in a table to be reused. It can be tricky, however, to figure…
A general and basic model of primordial evolution--a soup of reacting finitary and discrete processes--is employed to identify and analyze fundamental mechanisms that generate and maintain complex structures in prebiotic systems. The…