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We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…

Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…

An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…

Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…

The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…

In this paper, we are concern with the multiplicity of solutions for a p-Laplacian problem. A weaker super-quadratic assumptions is required on the nonlinearity. Under the weaker condition we give a new proof for the infinite solutions…

This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…

This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…

We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…

Trustworthiness in artificial intelligence depends not only on what a model decides, but also on how it handles and explains cases in which a reliable decision cannot be made. In critical domains such as healthcare and finance, a reject…

The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…

What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…

The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what…

Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs…

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…

New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…

This paper presents a theory of non-linear integer/real arithmetic and algorithms for reasoning about this theory. The theory can be conceived as an extension of linear integer/real arithmetic with a weakly-axiomatized multiplication…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

What is the value of input information in solving linear programming? The celebrated ellipsoid algorithm tells us that the full information of input constraints is not necessary; the algorithm works as long as there exists an oracle that,…