Related papers: On Recurrence Relations of Multi-dimensional Seque…
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…
We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop…
We consider the problem of learning a linear subspace from data corrupted by outliers. Classical approaches are typically designed for the case in which the subspace dimension is small relative to the ambient dimension. Our approach works…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
It is well known that recurrent sandpile configurations can be characterized as the optimal solution of certain optimization problems. In this article, we present two new integer linear programming models, one that computes recurrent…
Key to multitask learning is exploiting relationships between different tasks to improve prediction performance. If the relations are linear, regularization approaches can be used successfully. However, in practice assuming the tasks to be…
Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data, and presents such information as functions of input data sizes. Most of the analysis tools for logic…
Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…
Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of two-agent problems can be formulated as bilinear programs. We present a successive approximation algorithm that…
In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS)…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
A common form of MapReduce application involves discovering relationships between certain pairs of inputs. Similarity joins serve as a good example of this type of problem, which we call a "some-pairs" problem. In the framework of Afrati et…
We present the Mathematica package DREAM for arbitrarily high precision computation of multiloop integrals within the DRA (Dimensional Recurrence & Analyticity) method as solutions of dimensional recurrence relations. Starting from these…
Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of…
In this paper we show how to recover a spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result we obtain…
Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding…
A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…