Related papers: Parametric Resurgences of the Second Painlev\'e Eq…
Second order recurrence relations of real numbers arise form various applications in discrete time dynamical systems as well as in the context on Markov chains. Solutions to the recurrence relations are fully defined by the first two…
This article studies a confluence of a pair of regular singular points to an irregular one in a generic family of time-dependent Hamiltonian systems in dimension 2. This is a general setting for the understanding of the degeneration of the…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
There are at present two known string theories in $(2,2)$ dimensions. One of them is the well known $N=2$ string, and the other one is a more recently constructed $N=1$ spacetime supersymmetric string. They are both based on certain…
We study a three-dimensional gauge theory obtained from the dimensional reduction of a D4-brane worldvolume theory in the background of space-time moduli. An SL(3) symmetry in this theory, which acts on fields as well as coupling constants,…
This paper investigates the double descent phenomenon in two-layer neural networks, focusing on the role of L1 regularization and representation dimensions. It explores an alternative double descent phenomenon, named sparse double descent.…
The generalized Hastings-McLeod solutions to the inhomogeneous Painlev\'{e}-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths,…
We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using…
We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. In the sequel to Ammari, Waters, Zhang (2015), we use pseudodifferential methods for the problem of…
We use exponential asymptotic analysis to identify the relevance of Stokes' phenomenon to integrability in discrete systems. We study Stokes' phenomenon in two discrete problems with the same (leading-order) continuous limit, a…
Two-dimensional quadratic algebras are generalizations of Lie algebras that include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical…
In these lecture proceedings, we describe some of the fundamental mathematical concepts that underlie supersymmetric string theory and field theory, and their role in describing and testing dualities. In particular, we provide a pedagogical…
We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on periodic lattice systems…
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
In these lecture notes for the Les Houches School on Quantum Geometry I give an introductory overview of non-perturbative aspects of topological string theory. After a short summary of the perturbative aspects, I first consider the…
We identify new, rather serious, physical and axiomatic inconsistencies of the current formulation of string theories due to the lack of invariant units necessary for measurements, lack of preservation in time of Hermiticity-observability,…
The observation of light super-partners from a supersymmetric extension to the Standard Model is an intensely sought-after experimental outcome, providing an explanation for the stabilization of the electroweak scale and indicating the…
Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral…
We show that there is a full correspondence between the parameters space of the degenerate biconfluent Heun connection (BHC) and that of Painlev\'{e} IV that admits special solutions. The BHC degenerates when either the Stokes' data for the…