Seyed Majid Saberi Fathi

Quantum-mechanical decay laws in the neutral kaons

The Hamiltonian Friedrichs model [1] describing the evolution of a two-level system coupled to a continuum is used in order to modelize the decay of the kaon states K1, K2. Using different cut-off functions of the continuous degrees of freedom, we show that this model leads to a CP violation that qualitatively fits with experimental data improving previous numerical estimates. We also discuss the relation of our model to other models of open systems.

Geometrical comparison of two protein structures using Wigner-D functions.

In this article, we develop a quantitative comparison method for two arbitrary protein structures. This method uses a root‐mean‐square deviation characterization and employs a series expansion of the proteins shape function in terms of the Wigner‐D functions to define a new criterion, which is called a “similarity value.” We further demonstrate that the expansion coefficients for the shape function obtained with the help of the Wigner‐D functions correspond to structure factors. Our method addresses the common problem of comparing two proteins with different numbers of atoms. We illustrate it with a worked example. Proteins 2014; 82:2756–2769.

A simple method for finding a protein’s ligand-binding pockets

BackgroundThis paper provides a simple and rapid method for a protein-clustering strategy. The basic idea implemented here is to use computational geometry methods to predict and characterize ligand-binding pockets of a given protein structure. In addition to geometrical characteristics of the protein structure, we consider some simple biochemical properties that help recognize the best candidates for pockets in a protein’s active site.ResultsOur results are shown to produce good agreement with known empirical results.ConclusionsThe method presented in this paper is a low-cost rapid computational method that could be used to classify proteins and other biomolecules, and furthermore could be useful in reducing the cost and time of drug discovery.

Wave-function model for the CP violation in mesons

In this paper, we propose a simple quantum model of the kaons decay providing an estimate of the CP symmetry violation parameter. We use the two-level Friedrichs Hamiltonian model to obtain a good quantitative agreement with the experimental estimate of the violation parameter for neutral kaons. A temporal wave-function approach, based on an analogy with spatial wave-functions, plays a crucial role in our model.

A quaternionic approach to x-ray transform inversion in \sbb{R}^3

A new derivation of the inverse of the x-ray transform is presented based on quaternion analysis. As pointed out by practitioners, a direct inversion formula offers more efficient reconstruction algorithms than tomographic inversion. It is shown that the new inverse formula is equivalent to the existing one. The advantage of this approach is that it paves the way for a potential inversion of the x-ray transform with a non-uniform attenuation map in three dimensions, which models single photon emission imaging in nuclear medicine.

Inversion formula for the non-uniformly attenuated x-ray transform for emission imaging in \mathbb {R}^{3} using quaternionic analysis

In this paper, we present a new derivation of the inverse of the non-uniformly attenuated x-ray transform in three dimensions, based on quaternion analysis. An explicit formula is obtained using a set of three-dimensional x-ray projection data. The result without attenuation is recovered as a special case.

The \mathbb {R}^{3} exponential x-ray transform inversion in quaternion analysis

In this paper, we present a new derivation of the inverse of the exponential x-ray transform in the three dimensions, based on quaternion analysis. An explicit formula is obtained using a set of three-dimensional x-ray projection data. The result without attenuation is recovered as a special case.

A new definition and properties of the similarity value between two protein structures

Knowledge regarding the 3D structure of a protein provides useful information about the protein’s functional properties. Particularly, structural similarity between proteins can be used as a good predictor of functional similarity. One method that uses the 3D geometrical structure of proteins in order to compare them is the similarity value (SV). In this paper, we introduce a new definition of the SV measure for comparing two proteins. To this end, we consider the mass of the protein’s atoms and concentrate on the number of protein’s atoms to be compared. This defines a new measure, called the weighted similarity value (WSV), adding physical properties to geometrical properties. We also show that our results are in good agreement with the results obtained by TM-SCORE and DALILITE. WSV can be of use in protein classification and in drug discovery.

Using Spectral Representation to Classify Proteins’ Conformational States

Numerous proteins are molecular targets for drug action and hence are important in drug discovery. Structure-based computational drug discovery relies on detailed information regarding protein conformations for subsequent drug screening in silico. There are two key issues in analyzing protein conformations in virtual screening. The first considers the protein’s conformational change in response to physical and chemical conditions. The second is the protein’s atomic resolution reconstruction from X-ray crystallography or nuclear magnetic resonance (NMR) data. In this latter problem, information is needed regarding the sample’s position relative to the source of X-rays. Here, we introduce a new measure for classifying protein conformational states using spectral representation and Wigner’s D-functions. Predictions based on the new measure are in good agreement with conformational states of proteins. These results could also be applied to improve conformational alignment of the snapshots given by protein crystallography.

Entropy and Transport in Billiards

Recent progress of the theory of dynamical systems and billiards sheds new light on the nonequilibrium statistical mechanics. Mixing, weak mixing and continuous spectrum are associated to relaxation to equilibrium via entropy increase. The properties of the relaxation time are reflected in the transport properties, which could be anomalous both in Sinai’ billiard with infinite horizon and in the barrier billiard. Numerical simulations are presented to corroborate these properties.