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From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental…
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum…
Aspects of the QCD parton densities are briefly reviewed, drawing some parallels to the density matrix formulation of quantum mechanics, exemplified by Wigner functions. We elaborate on the solution of their evolution equations using…
QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution,…
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…
Let $\{X_i\}_{i=-\infty}^{\infty}$ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_i,...,X_{i+\ell-1}),i\geq 1$, are overlapping blocks of length $\ell$…
Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
We present a general method for the solution of the renormalization group equations for the non-forward parton distributions on the two-loop level in the flavour singlet channel based on an orthogonal polynomial reconstruction. Using this…
This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev…
Perturbation series in QCD are generally asymptotic and suffer from so-called infrared renormalon ambiguities. In the context of the standard operator product expansion in MS-bar these ambiguities are compensated by matrix elements of…
Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang…
Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general…