相关论文: Computation of Atomic Fibers of Z-Linear Maps

The use of tapered optical fibers, i.e., optical nanofibers, for spectroscopy and the detection of small numbers of particles, such as neutral atoms or molecules, has been gaining ground in recent years. In this review, we briefly introduce…

The nature of atomic vapors, their natural alignment with interatomic transitions, and their ease of use make them highly suited for spectrally narrow-banded optical filters. Atomic filters come in two flavors: a filter based on the…

Given topological spaces X and Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y . We consider a computational version, where X, Y are given as finite simplicial complexes, and the…

Atomic norm minimization (ANM) is a key approach for line spectral estimation (LSE). Most related algorithms formulate ANM as a semidefinite programming (SDP), which incurs high computational cost. In this letter, we revisit the ANM problem…

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…

The main goal of the paper is to introduce methods which compute B\'ezier curves faster than Casteljau's method does. These methods are based on the spectral factorization of a $n\times n$ Bernstein matrix, $B^e_n(s)= P_nG_n(s)P_n^{-1}$,…

We derive a path counting formula for two-dimensional lattice path model on a plane with filter restrictions. A filter is a line that restricts the path passing it to one of possible directions. Moreover, each path that touches this line is…

We introduce and explore an approach for constructing force fields for small molecules, which combines intuitive low body order empirical force field terms with the concepts of data driven statistical fits of recent machine learned…

Photonic systems offer a promising platform for interconnecting quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic…

In this note, we discuss planar lattices generated by their atoms. We prove that if $L$ is a planar lattice generated by $n$ atoms, then both the left and the right boundaries of $L$ have at most $n+1$ elements. On the other hand, $L$ can…

The parametric lattice-point counting problem is as follows: Given an integer matrix $A \in Z^{m \times n}$, compute an explicit formula parameterized by $b \in R^m$ that determines the number of integer points in the polyhedron $\{x \in…

Packet reordering is an important property of network traffic that should be captured by analytical models of the Transmission Control Protocol (TCP). We study a combinatorial problem motivated by RESTORED, a TCP modeling methodology that…

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…

Let X be an algebraic curve over Q and t a non-constant Q-rational function on X such that Q(t) is a proper subfield of Q(X). For every integer n pick a point P_n on X such that t(P_n)=n. We conjecture that, for large N, among the number…

The Quantum Fisher Information Matrix (QFIM) is a fundamental quantity in various subfields of quantum physics. It plays a crucial role in the study of parameterized quantum states, as it quantifies their sensitivity to variations in its…

The use of machine learning is becoming increasingly common in computational materials science. To build effective models of the chemistry of materials, useful machine-based representations of atoms and their compounds are required. We…

Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…

We consider an inverse problem for a finite graph $(X,E)$ where we are given a subset of vertices $B\subset X$ and the distances $d_{(X,E)}(b_1,b_2)$ of all vertices $b_1,b_2\in B$. The distance of points $x_1,x_2\in X$ is defined as the…

An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…

Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account…