A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

Concurrent multiresponse non-linear screening: Robust profiling of webpage performance

Profiling engineered data with robust mining methods continues attracting attention in knowledge engineering systems. The purpose of this article is to propose a simple technique that deals with non-linear multi-factorial multi-characteristic screening suitable for knowledge discovery studies. The method is designed to proactively seek and quantify significant information content in engineered mini-datasets. This is achieved by deploying replicated fractional-factorial sampling schemes. Compiled multi-response data are converted to a single master-response effectuated by a series of distribution-free transformations and multi-compressed data fusions. The resulting amalgamated master response is deciphered by non-linear multi-factorial stealth stochastics intended for saturated schemes. The stealth properties of our method target processing datasets which might be overwhelmed by a lack of knowledge about the nature of reference distributions at play. Stealth features are triggered to overcome restrictions regarding the data normality conformance, the effect sparsity assumption and the inherent collapse of the ‘unexplainable error’ connotation in saturated arrays. The technique is showcased by profiling four ordinary controlling factors that influence webpage content performance by collecting data from a commercial browser monitoring service on a large scale web host. The examined effects are: (1) the number of Cascading Style Sheets files, (2) the number of JavaScript files, (3) the number of Image files, and (4) the Domain Name System Aliasing. The webpage performance level was screened against three popular characteristics: (1) the time to first visual, (2) the total loading time, and (3) the customer satisfaction. Our robust multi-response data mining technique is elucidated for a ten-replicate run study dictated by an L₉(3⁴) orthogonal array scheme where any uncontrolled noise embedded contribution has not been necessarily excluded.     

Computational Design of Novel Allosteric Inhibitors for Plasmodium falciparum DegP

The serine protease, DegP exhibits proteolytic and chaperone activities, essential for cellular protein quality control and normal cell development in eukaryotes. The P. falciparum DegP is essential for the parasite survival and required to combat the oscillating thermal stress conditions during the infection, protein quality checks and protein homeostasis in the extra-cytoplasmic compartments, thereby establishing it as a potential target for drug development against malaria. Previous studies have shown that diisopropyl fluorophosphate (DFP) and the peptide SPMFKGV inhibit E. coli DegP protease activity. To identify novel potential inhibitors specific to PfDegP allosteric and the catalytic binding sites, we performed a high throughput in silico screening using Malaria Box, Pathogen Box, Maybridge library, ChEMBL library and the library of FDA approved compounds. The screening helped identify five best binders that showed high affinity to PfDegP allosteric (T0873, T2823, T2801, {"type":"entrez-protein","attrs":{"text":"RJC02337","term_id":"1480409465","term_text":"RJC02337"}}RJC02337, CD00811) and the catalytic binding site (T0078L, T1524, T2328, BTB11534 and 552691). Further, molecular dynamics simulation analysis revealed {"type":"entrez-protein","attrs":{"text":"RJC02337","term_id":"1480409465","term_text":"RJC02337"}}RJC02337, BTB11534 as the best hits forming a stable complex. WaterMap and electrostatic complementarity were used to evaluate the novel bio-isosteric chemotypes of {"type":"entrez-protein","attrs":{"text":"RJC02337","term_id":"1480409465","term_text":"RJC02337"}}RJC02337, that led to the identification of 231 chemotypes that exhibited better binding affinity. Further analysis of the top 5 chemotypes, based on better binding affinity, revealed that the addition of electron donors like nitrogen and sulphur to the side chains of butanoate group are more favoured than the backbone of butanoate group. In a nutshell, the present study helps identify novel, potent and Plasmodium specific inhibitors, using high throughput in silico screening and bio-isosteric replacement, which may be experimentally validated.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

An Integrated Two Phases Approach to Zn2+ Ions Electroreduction on Hg

The following two numerical models have been applied to zinc cations electroreduction in 1 M NaClO₄ water solution: a classical EE model describing the concentration of involved species in solution (semi infinitive diffusion region), an extended EE model describing both: the concentration of involved species in solution and the concentration of metallic zinc inside mercury drop (in limited area of diffusion). In the latter model the inner part of mercury drop and surrounding solution were treated as dynamic interrelated system. Both models were applied to experimental cyclic voltammetric CV data in 1 M NaClO₄, the results compared and discussed. The concentration profiles of all species including metallic zinc inside mercury drop were performed. The presented integrated model is essential for theoretical and analytical aspects of the electrochemistry of mercury soluble metal cations and amalgams.     

A rational approximation and its applications to nonlinear partial differential equations on the whole line

An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach.     

GaN氢化物气相外延生长系统的设计与制作

根据GaN氢化物气相外延生长(HVPE)的原理,设计制作了双温区卧式HVPE系统．根据实际生长中出现的问题和CaN样品的测试情况,对系统进行了逐步的调试和改进．     

Challenging Students to View the Concept of Area in Triangles in a Broad Context: Exploiting the Features of Cabri-II

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12–15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). Cabri-Geometry (software), Université de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct: (a) pairs of equivalent triangles “in as many ways as possible” and to study their area and their perimeter using any of the tools provided and (b) “any possible sequence of modifications of an original triangle into other equivalent ones”. As regards the concept of area and in contrast to a paper and pencil environment, Cabri provided students with different and potential opportunities in terms of: (a) means of construction, (b) control, (c) variety of representations and (d) linking representations, by exploiting its capability for continuous modifications. By exploiting these opportunities in the context of the given open tasks, students were helped by the tools provided to develop a broader view of the concept of area than the typical view they would construct in a typical paper and pencil environment.