相关论文: Computation of Atomic Fibers of Z-Linear Maps
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
Consider a semi-algebraic set A in R^d constructed from the sets which are determined by inequalities p_i(x)>0, p_i(x)\ge 0, or p_i(x)=0 for a given list of polynomials p_1,...,p_m. We prove several statements that fit into the following…
Wiring diagrams are given for a quantum algorithm processor in CMOS to compute, in parallel, all divisors of an n-bit integer. Lines required in a wiring diagram are proportional to n. Execution time is proportional to the square of n.
This manuscript presents a general recursive formula to estimate the size of fibers associated with algebraic maps from graphs to summary statistics of importance for social network analysis, such as number of edges (graph density), degree…
We give a definition of an integer-valued function $\sum_i \alpha_i x ^*_i$ derived from arrow diagrams for the ambient isotopy classes of oriented spherical curves. Then, we introduce certain elements of the free $\mathbb{Z}$-module…
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth atoms trapped in an…
We provide a numerical method to calculate comprehensively the microwave and the laser spectra of ultracold bosonic atoms in optical lattices at finite temperatures. Our formulation is built up with the sum rules, up to the second order,…
In Chapter 4 of [25] Triebel proved two theorems concerning pointwise multipliers and diffeomorphisms in function spaces of Besov and Triebel-Lizorkin type. In each case he presented two approaches, one via atoms and one via local means.…
We propose a way of characterizing the algorithms computing a Walsh-Hadamard transform that consist of a sequence of arrays of butterflies ($I_{2^{n-1}}\otimes \text{DFT}_2$) interleaved by linear permutations. Linear permutations are those…
We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix $A\in \mathbb{R}^{m\times n}$, the kernel problem requires a positive vector in the kernel of $A$, and the image problem requires a…
Results from the calculation of the basic characteristics of the photonic crystal fiber with two rings of holes are presented by the approach which takes into account the exact distribution of the refractive index over the cross section of…
We present programmable two-dimensional arrays of microscopic atomic ensembles consisting of more than 400 sites with nearly uniform filling and small atom number fluctuations. Our approach involves direct projection of light patterns from…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We investigate the possibility that linear arrays of atoms can guide matter waves, much as fiber optics guide light. We model the atomic line as a quasi-1D array of s wave point scatterers embedded in 2D. Our theoretical study reveals how…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…