Related papers: Renormalon chains contributions to the non-singlet…
We propose to modify the saturation model of Golec-Biernat and Wusthoff by including DGLAP evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large Q^2 region. The successful…
The supergravity solutions to various $p$-branes are presented and typically it breaks one quarter of supersymmetry except for the D1 brane case, where it breaks one half of supersymmetry and are manifestly non-relativistic in nature. The…
We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally…
Using the dynamic renormalization group (DRG) technique, we analyze general nonlinearities in a conservative nonlinear growth equation with non-conserved gaussian white noise. We show that they fall in two classes only: the…
In the literature, motivated by the observed peculiar neutrino mixing pattern and a preliminary experimental hint for maximal Dirac CP phase (i.e., $\delta \sim 3\pi/2$), a lot of flavor and CP symmetries have been proposed to help us…
By the method of coupling and Girsanov transformation, Harnack inequalities [F.-Y. Wang, 1997] and strong Feller property are proved for the transition semigroup associated with the multivalued stochastic evolution equation on a Gelfand…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
We show that it is possible to improve the infrared aspects of the standard treatment of the DGLAP evolution theory to take into account a large class of higher order corrections that significantly improve the precision of the theory for…
In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [arXiv:0807.1594], of the radial and chordal variant of the Loewner differential equation, which is of…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
I review the recent progress on the perturbative QCD approach to exclusive $B$ meson decays, discussing the comparison of collinear and $k_T$ factorizations, the CP asymmetry in the $B^0\to\pi^+\pi^-$ decay, penguin enhancement, the…
This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification,…
We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space…
In these lectures we give a concise introduction to the ideas of renormalon calculus in QED and QCD. We focus in particular on the example of the Adler D function of vacuum polarization, and on relations between perturbative renormalon…
A characterisation of the quantum stochastic bounded generators of irreversible quantum state evolutions is given. This suggests the general form of quantum stochastic evolution equation with respect to the Poisson (jumps), Wiener…
The effects of the first nonlinear corrections to the DGLAP evolution equations are studied by using the recent HERA data for the structure function $F_2(x,Q^2)$ of the free proton and the parton distributions from CTEQ5L and CTEQ6L as a…
As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain non-linear Poisson brackets which are ``cocycle perturbations'' of the linear Poisson bracket. We show that these special Poisson…
We discuss the generalization of the leading-twist light-cone distribution amplitude for light mesons including QED effects. This generalization was introduced to describe virtual collinear photon exchanges above the strong-interaction…
In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…
In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. The proposed PDE has the form of continuity equation that arises in various research areas, e.g. fluid dynamics and…