Related papers: Master Teapots and Entropy Algorithms for the Mand…
Non-orientable manifolds, such as the M\"obius strip and the Klein bottle, defy conventional geometric intuition through their twisted boundary conditions. As a result, topological defects on non-orientable manifolds give rise to novel…
In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this…
Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained domains for heat…
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…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic function-germs on a germ of a complex analytic space to…
This note is a shortened version of my dissertation thesis, defended at Stony Brook University in December 2004. It illustrates how dynamic complexity of a system evolves under deformations. The objects I considered are quartic polynomial…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
A clear understanding of topology of higher-dimensional objects is important in many branches of both pure and applied mathematics. In this survey we attempt to present some results of higher-dimensional topology in a way which makes clear…
Classical knot theory deals with {\em diagrams} and {\em invariants}. By means of horizontal {\em trisecants}, we construct a new theory of classical braids with invariants valued in {\em pictures}. These pictures are closely related to…
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of…
We extend two results from the theory of geodesic flows to the magnetic setting on manifolds of arbitrary dimension. First, we investigate the magnetic ray transform and establish a tensor tomography result. Second, we define and analyze…
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the…
Physical quantities obtained from the microcanonical entropy surfaces of classical spin systems show typical features of phase transitions already in finite systems. It is demonstrated that the singular behaviour of the microcanonically…
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For…
Using Matrix theory, we propose a technique on how to compute the entangle- ment entropy between a supergravity probe and modes on a spherical membrane. We demonstrate that a membrane stretched between the probe and the sphere entangles…
The quantum $5$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on…
We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all $2^N$ bipartitions of an $N$-party pure quantum system by means of a (generalized) adjacency…
Little is known about the global structure of the basins of attraction of Newton's method in two or more complex variables. We make the first steps by focusing on the specific Newton mapping to solve for the common roots of $P(x,y) =…