Related papers: A New Angle on L2 Regularization
We reexamine the relativistic 2+1 dimensional Lee model in light-front coordinates on flat space and on a space-time with a spatial section given by a compact manifold in the usual canonical formalism. The simpler 2+1 dimension is chosen…
Top sensitivity Ring Laser Gyroscopes based on a simple mechanical scheme, so called heterolithic, have shown to operate on a continuous basis; since the mirror positions are not fixed, unwanted signals can occur, and data selection is…
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…
We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N$_2$, CO$_2$, and O$_2$ molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization…
Let $K$ be a convex body in an affine chart of the $n$ dimensional real Projective space $\mathbb{RP}^n$, $n \geq 3$, let $H$ be a hyperplane which is not a support hyperplane of $K$ and let $p_1,p_2 \in \mathbb{RP}^n \setminus H$ be two…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
Probabilistic cross-identification has been successfully applied to a number of problems in astronomy from matching simple point sources to associating stars with unknown proper motions and even radio observations with realistic morphology.…
We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…
Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…
The origin of complex structures, randomness, and irreversibility are analyzed in the scale free SL(2,R) analysis, which is an extension of the ordinary analysis based on the recently uncovered scale free $C^{2^n-1}$ solutions to linear…
In the present paper we examine the relationship between several type $A$ cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes cluster algebras from surfaces, and encode several existing…
The phase of spins in the quasi-two-dimensional (Q2D) XY model has emerged as a topic of significant interest across multiple physics subfields. Here, we propose a short-range (SR) Q2D XY model defined on a plane perpendicularly intersected…
We have analyzed in detail the angular polarization properties in the center of mass reference frame of Landau's two-photon spherical states in momentum space. The angular distributions for fixed values of $J$ and $M$ do not depend on the…
We study the version of the C-Planarity problem in which edges connecting the same pair of clusters must be grouped into pipes, which generalizes the Strip Planarity problem. We give algorithms to decide several families of instances for…
Recent advances in contrastive learning have enlightened diverse applications across various semi-supervised fields. Jointly training supervised learning and unsupervised learning with a shared feature encoder becomes a common scheme.…
We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.
Separable Hamiltonian systems either in sphero-conical coordinates on a $S^2$ sphere or in elliptic coordinates on a ${\mathbb R}^2$ plane are described in an unified way. A back and forth route connecting these Liouville Type I separable…
Let $L$ be a distributive lattice and $R(L)$ the associated Hibi ring. We compute $\reg R(L)$ when $L$ is a planar lattice and give a lower bound for $\reg R(L)$ when $L$ is non-planar, in terms of the combinatorial data of $L.$ As a…
Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing.…
We construct a class of supersymmetric boundary interactions in N=2 field theories on the half-space, which depend on parameters that are not at all renormalized or not renormalized in perturbation theory beyond one-loop. This can be used…