We examine population structures for their ability to maintain diversity in neutral evolution. We use the general framework of evolutionary graph theory and consider birth-death (bd) and death-birth (db) updating. The population is of size $N$. Initi...
Expressions for scaling limits of random walks, such as those obtained in several areas of the Probability theory literature, are of great significance in characterizing long term, stationary behavior of random processes. Presumably, in the limit of...
We present the alternative topological twisting of N=4 Yang-Mills, in which the path integral is dominated not by instantons, but by flat connections of the COMPLEXIFIED gauge group. The theory is nontrivial on compact orientable four-manifolds wit...
We give a formula for the Carathéodory distance on the Neil parabola, the variety ${z^2=w^3}$ restricted to the bidisk; thus making it the first variety with a singularity to have its Carathéodory distance explicitly computed. In addition, we relat...
Versions of well known function theoretic operator theory results of Szego and Widom are established for the Neil algebra. The Neil algebra is the subalgebra of the algebra of bounded analytic functions on the unit disc consisting of those functions...
In spite of remarkable recent advances, quantum computers still lack useful applications. A promising direction for such utility is offered by the simulation of the dynamics of many-body quantum systems, which cannot be efficiently computed classical...
In this monograph, we lay some foundations of a theory of infinite dimensional Euclidean lattices - and more generally, of infinite dimensional Hermitian vector bundles over some "arithmetic curve" ${\rm Spec}\,\mathcal{O}_K$ attached to the ring of...
We study the local group velocity defined as the weak value of the velocity operator in the (1+1) dimensional Klein-Gordon as well as Dirac theory. It was shown by Berry [ J. Phys. A 45, 185308 (2012)] that when the pre- and post-selected states for...
Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon pla...
We propose an indirect inference strategy for estimating heterogeneous-agent business cycle models with micro data. At its heart is a first-order vector autoregression that is grounded in linear filtering theory as the cross-section grows large. The...
As part of stratification of Cohen-Macaulay rings, we introduce and develop the theory of Goto rings, generalizing the notion of almost Gorenstein rings originally defined by V. Barucci and R. Fröberg in 1997. What has dominated the series of resear...
The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fröberg for one-dimensional Noetherian local rings which are analytically unramified has been generalized by S. Goto, N. Matsuoka and T. T. Phuong to one-dimensional Cohen-Ma...
Splitting operation in Matroid Theory does not preserve graphicness, connectedness, cographicness, etc. Also, the splitting of binary gammoid does not necessarily be binary gammoid after splitting. We have characterized a class of graphic matroids th...
Gravitational wave signals from compact astrophysical sources such as those observed by LIGO and Virgo require a high-accuracy, theory-based waveform model for the analysis of the recorded signal. Current inspiral-merger-ringdown models are calibrate...
Within the Closed Time Path Formalism of Thermal Field Theory we calculate the hard photon emission rate as well as the collisional energy-loss rate for a quark-gluon plasma away from chemical equilibrium. Mass singularities are shown to be dynamic...
We consider Dynamical Supersymmetry Breaking (DSB) in models with classical flat directions. We analyze a number of examples, and develop a systematic approach to determine if classical flat directions are stabilized in the full quantum theory, or...
The current status of effective field theory (EFT) descriptions of nucleon-nucleon (NN) interactions is briefly reviewed, and a new formulation of EFT which treats pion interactions perturbatively is presented. This approach differs from the Kaplan...
We study classical continuous automorphisms of the torus (cat maps) from the viewpoint of the Koopman theory. We find analytical formulae for Koopman modes defined coherently on the whole of the torus, and their decompositions associated with the par...
We study the theory of convergence for CAT$(0)$-lattices (that is groups $Γ$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing phenomena, expla...
This paper addresses the problem of controlling the temporal dynamics of complex nonlinear network-coupled dynamical systems, specifically in terms of neurodynamics. Based on the Lyapunov direct method, we derive a control strategy with theoretical g...