Related papers: The Connected Isentropes Conjecture in a Space of …
On subsets E of the Mandelbrot set M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding…
We study polynomials that are orthogonal with respect to a varying quartic weight \exp(-N(x^2/2+tx^4/4)) for t<0, where the orthogonality takes place on certain contours in the complex plane. Inspired by developments in 2D quantum gravity,…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
We prove the existence of families of distinct isotopy classes of physical unknots through the key concept of parametrised thickness. These unknots have prescribed length, tube thickness, a uniform bound on curvature, and cannot be…
In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional systems, are suitable for detecting jump discontinuities along circles on the sphere. More precisely, such edges…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
We study the group of self-equivalences of a partially postcritically finite branched cover and answer a question of Adam Epstein about contractibility of certain deformation spaces of rational maps.
We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using…
Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…
This paper investigates quasi-homogeneous integrable systems by analyzing their Laurent series solutions near movable singularities, motivated by patterns observed in Kovalevskaya exponents of four-dimensional Painlev\'e-type equations. We…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…
Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through…
In connection with the Entropy Conjecture it is known that the topological entropy of a continuous graph map is bounded from below by the spectral radius of the induced map on the first homology group. We show that in the case of a…
We derive a sufficient condition for topological horseshoe and uniform hyperbolicity of a 4-dimensional symplectic map, which is introduced by coupling the two 2-dimensional H\'enon maps via linear terms. The coupled H\'enon map thus…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
We prove the sets of polynomials on configuration spaces are cores of Dirichlet forms describing interacting Brownian motion in infinite dimensions. Typical examples of these stochastic dynamics are Dyson's Brownian motion and Airy…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
The self-assembly of hard polyhedral particles confined to a flat interface is studied using Monte Carlo simulations. The particles are pinned to the interface by restricting their movement in the direction perpendicular to it while…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…