Related papers: On hereditary models of polymers
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
An integrable system is often formulated as a flat connection, satisfying a Lax equation. It is given in terms of compatible systems having a common solution called the ``wave function" $\Psi$ living in a Lie group $G$, which satisfies some…
We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials.…
Prediction of material property is a key problem because of its significance to material design and screening. We present a brand-new and general machine learning method for material property prediction. As a representative example, polymer…
A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix…
The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We study the typical properties of polynomial Support Vector Machines within a Statistical Mechanics approach that allows us to analyze the effect of different normalizations of the features. If the normalization is adecuately chosen, there…
The question of complete integrability of evolution equations associated to $n\times n$ first order isospectral operators is investigated using the inverse scattering method. It is shown that for $n>2$, e.g. for the three-wave interaction,…
We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and…
A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale…
Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented…
We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain information about the matrix orthogonal polynomials and functions of second kind associated with a weight matrix. We deduce properties for the…