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Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization…
A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic…
Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…
We propose a framework to study models of computation of indeterministic data, represented by abstract "distributions". In these distributions, probabilities are replaced by "amplitudes" drawn from a fixed semi-ring $S$, of which the…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
When solving time-dependent partial differential equations(PDEs), traditional physics-informed neural networks (PINNs) have inherent limitations: due to the lack of temporal causality, the network is forced to learn the later-time control…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
In this paper we introduce the DMR -- a prototype-based method and network architecture for deep learning which is using a decision tree (DT)-based inference and synthetic data to balance the classes. It builds upon the recently introduced…
Integer linear programs $\min\{c^T x : A x = b, x \in \mathbb{Z}^n_{\ge 0}\}$, where $A \in \mathbb{Z}^{m \times n}$, $b \in \mathbb{Z}^m$, and $c \in \mathbb{Z}^n$, can be solved in pseudopolynomial time for any fixed number of constraints…
Declarative spatial reasoning denotes the ability to (declaratively) specify and solve real-world problems related to geometric and qualitative spatial representation and reasoning within standard knowledge representation and reasoning (KR)…
In recent years, to sustain the resource-intensive computational needs for training deep neural networks (DNNs), it is widely accepted that exploiting the parallelism in large-scale computing clusters is critical for the efficient…
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
We design a deterministic subexponential time algorithm that takes as input a multivariate polynomial $f$ computed by a constant-depth circuit over rational numbers, and outputs a list $L$ of circuits (of unbounded depth and possibly with…
Transient stability simulation of a large-scale and interconnected electric power system involves solving a large set of differential algebraic equations (DAEs) at every simulation time-step. With the ever-growing size and complexity of…
We revisit the Subset Sum problem over the finite cyclic group $\mathbb{Z}_m$ for some given integer $m$. A series of recent works has provided near-optimal algorithms for this problem under the Strong Exponential Time Hypothesis. Koiliaris…
Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an $n\times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1,\ldots,v_n$, one by one. After seeing each vector $v_i$, we…
By assuming some widely-believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d\geq2$ squares subjected to given congruence conditions is NP-complete. On the other hand, we develop…
We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the…