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

We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…

With its three independent parameters, the $ABCD$ matrix serves as the beam transfer matrix in optics. If it is transformed to an equi-diagonal form, the matrix has only two independent parameters determined by optical devices. It is shown…

We train a model atom to recognize hand-written digits between 0 and 9, employing intense light--matter interaction as a computational resource. For training, individual images of hand-written digits in the range 0-9 are converted into…

Several different approximations and techniques have been developed for the calculation of atomic structure, ionization, and excitation of atoms and ions. These techniques have been used to compute large amounts of spectroscopic data of…

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide…

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…

This work demonstrates that, for a simple case of 10 randomly positioned atoms, a neural network can be trained to infer atomic coordinates from Patterson maps. The network was trained entirely on synthetic data. For the training set, the…

Let $Q_n = \{0, 1\}^n$ be a hypercube graph. The initial segment $I_k \subseteq Q_n$ is the subset consisting of the first $k$ vertices of $Q_n$ in the binary order. A pair of integers $(a, b) \in \mathbb{Z}_{>0}^2$ is said to be fit if,…

Despite being the main tool to visualize molecules at the atomic scale, AFM with CO-functionalized metal tips is unable to chemically identify the observed molecules. Here we present a strategy to address this challenging task using deep…

In this paper we consider polynomial representability of functions defined over $Z_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to…

We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of…

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive…

We show that programmable photonic circuit architectures composed of alternating mixing layers and active layers offer a high degree of flexibility. This alternating configuration enables the systematic tailoring of both the network's depth…

We introduce an accurate, self-contained and automatic atom based numerical algorithm to characterize grain distributions in two dimensional Phase Field Crystal simulations. Four input parameters must be set by the user and their effect is…

The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be…

We introduce the notion of set-wise injective maps and provide results about fiber embeddings. Our results improve some previous results in this area.

A set of rules is defined to systematically number the groups and the atoms of organic molecules and, particularly, of polypeptides in a modular manner. Supported by this numeration, a set of internal coordinates is defined. These…

Optics and photonics has recently captured interest as a platform to accelerate linear matrix processing, that has been deemed as a bottleneck in traditional digital electronic architectures. In this paper, we propose an all-photonic…

The cyclic polytope $C(n,d)$ is the convex hull of any $n$ points on the moment curve ${(t,t^2,...,t^d):t \in \reals}$ in $\reals^d$. For $d' >d$, we consider the fiber polytope (in the sense of Billera and Sturmfels) associated to the…

An $F$-algebra $A$ with unit $1$ is said to be a locally matrix algebra if an arbitrary finite collection of elements $a_1,$ $\ldots,$ $a_s $ from $ A$ lies in a subalgebra $B$ with $1$ of the algebra $A$, that is isomorphic to a matrix…