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In pure exploration problems, a statistician sequentially collects information to answer a question about some stochastic and unknown environment. The probability of returning a wrong answer should not exceed a maximum risk parameter…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the asymptotics of multivariate rational generating functions…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
Path planning of Robot is one of the challenging fields in the area of Robotics research. In this paper, we proposed a novel algorithm to find path between starting and ending position for an intelligent system. An intelligent system is…
In this paper, we propose the first optimum process scheduling algorithm for an increasingly prevalent type of heterogeneous multicore (HEMC) system that combines high-performance big cores and energy-efficient small cores with the same…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
We propose a real-time decision framework for multimodal freight dispatch through a system of hierarchical hubs, using a probabilistic model for transit times. Instead of assigning a fixed time to each transit, we advocate using historical…
The eccentric pie chart, a generalization of the traditional pie chart is introduced. An arbitrary point is fixed within the circle and rays are drawn from it. A sector is bounded by a pair of neighboring rays and the arc between them, The…
We study the problem of computing the isolated regular solutions of a system \((f_1,\ldots,f_n)\) of \(n\) polynomial equations in \(n\) variables \((X_1, \dots, X_n)\) over a field of characteristic zero \(k\). We focus on systems with a…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
This paper proposes a new numerical optimization algorithm inspired by the strawberry plant for solving complicated engineering problems. Plants like strawberry develop both runners and roots for propagation and search for water resources…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…