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The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory…
In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming…
The implementation of reliable and efficient geometric algorithms is a challenging task. The reason is the following conflict: On the one hand, computing with rounded arithmetic may question the reliability of programs while, on the other…
A new method is proposed in this paper to learn overcomplete dictionary from training data samples. Differing from the current methods that enforce similar sparsity constraint on each of the input samples, the proposed method attempts to…
Consistency regularization has prevailed in semi-supervised semantic segmentation and achieved promising performance. However, existing methods typically concentrate on enhancing the Image-augmentation based Prediction consistency and…
Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…
Generation expansion planning (GEP) is a prominent example of capacity expansion problems in operations research. Being generally NP-hard, GEP optimization models can become intractable when nonconvex dynamics, time-coupling constraints,…
In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences of period $pq$ is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, we derive…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
In this paper, we propose a novel variable selection approach in the framework of high-dimensional linear models where the columns of the design matrix are highly correlated. It consists in rewriting the initial high-dimensional linear…
A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…
Ritt-Wu's algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for…
Genetic Algorithms (GAs) are known for their efficiency in solving combinatorial optimization problems, thanks to their ability to explore diverse solution spaces, handle various representations, exploit parallelism, preserve good…
In this paper we introduce a General Dynamic String-Averaging (GDSA) iterative scheme and investigate its convergence properties in the inconsistent case, that is, when the input operators don't have a common fixed point. The Dynamic…
Constraint Acquisition (CA) systems can be used to assist in the modeling of constraint satisfaction problems. In (inter)active CA, the system is given a set of candidate constraints and posts queries to the user with the goal of finding…
Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an…
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity}, per information bit, of encoding and decoding. It also…
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and…
We consider the problem of length generalization in sequence prediction. We define a new metric of performance in this setting -- the Asymmetric-Regret -- which measures regret against a benchmark predictor with longer context length than…
Pre-trained sequence-to-sequence (seq-to-seq) models have significantly improved the accuracy of several language generation tasks, including abstractive summarization. Although the fluency of abstractive summarization has been greatly…