The Laplace transform of the derivative of a function with finite jumps

Laplace transform of derivative of function with finite jump

Transfer matrix approach to layered systems with axial symmetry

The stress and displacement distribution in a layered medium is found by means of transfer matrices. The surface loading exhibits axial symmetry, and each layer is of infinite extent in the horizontal direction, of constant depth, and is considered to be linearly elastic, homogeneous, and isotropic. The method developed has the built-in advantage of enforcing interface continuity conditions automatically. Its application to layered composites shows the flexibility with which it predicts the local as well as the global response of the medium

The Use of Experimental Structures to Model Protein Dynamics

The number of solved protein structures submitted in the Protein Data Bank (PDB) has increased dramatically in recent years. For some specific proteins, this number is very high—for example, there are over 550 solved structures for HIV-1 protease, one protein that is essential for the life cycle of human immunodeficiency virus (HIV) which causes acquired immunodeficiency syndrome (AIDS) in humans. The large number of structures for the same protein and its variants include a sample of different conformational states of the protein. A rich set of structures solved experimentally for the same protein has information buried within the dataset that can explain the functional dynamics and structural mechanism of the protein. To extract the dynamics information and functional mechanism from the experimental structures, this chapter focuses on two methods—Principal Component Analysis (PCA) and Elastic Network Models (ENM). PCA is a widely used statistical dimensionality reduction technique to classify and visualize high-dimensional data. On the other hand, ENMs are well-established simple biophysical method for modeling the functionally important global motions of proteins. This chapter covers the basics of these two. Moreover, an improved ENM version that utilizes the variations found within a given set of structures for a protein is described. As a practical example, we have extracted the functional dynamics and mechanism of HIV-1 protease dimeric structure by using a set of 329 PDB structures of this protein. We have described, step by step, how to select a set of protein structures, how to extract the needed information from the PDB files for PCA, how to extract the dynamics information using PCA, how to calculate ENM modes, how to measure the congruency between the dynamics computed from the principal components (PCs) and the ENM modes, and how to compute entropies using the PCs. We provide the computer programs or references to software tools to accomplish each step and show how to use these programs and tools. We also include computer programs to generate movies based on PCs and ENM modes and describe how to visualize them

Long-range correlation and multifractality in Bach's Inventions pitches

We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view we find same second moment exponents (after double profiling) in ranges (1.7-1.8) in his works. Comparing MF-DFA results of original series to those for shuffled and surrogate series we can distinguish multifractality due to long-range correlations and a broad probability density function. Finally we determine the scaling exponents and singularity spectrum. We conclude fat tail has more effect in its multifractality nature than long-range correlations.Comment: 18 page, 6 figures, to appear in JSTA

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term

Out-of-core solution of eigenproblems for macromolecular simulations

We consider the solution of large-scale eigenvalue problems that appear in the motion simulation of complex macromolecules on desktop platforms. To tackle the dimension of the matrices that are involved in these problems, we formulate out-of-core (OOC) variants of the two selected eigensolvers, that basically decouple the performance of the solver from the storage capacity. Furthermore, we contend with the high computational complexity of the solvers by off-loading the arithmetically-intensive parts of the algorithms to a hardware graphics accelerator

Transgenic expression of the dicotyledonous pattern recognition receptor EFR in rice leads to ligand-dependent activation of defense responses

Plant plasma membrane localized pattern recognition receptors (PRRs) detect extracellular pathogen-associated molecules. PRRs such as Arabidopsis EFR and rice XA21 are taxonomically restricted and are absent from most plant genomes. Here we show that rice plants expressing EFR or the chimeric receptor EFR::XA21, containing the EFR ectodomain and the XA21 intracellular domain, sense both Escherichia coli- and Xanthomonas oryzae pv. oryzae (Xoo)-derived elf18 peptides at sub-nanomolar concentrations. Treatment of EFR and EFR::XA21 rice leaf tissue with elf18 leads to MAP kinase activation, reactive oxygen production and defense gene expression. Although expression of EFR does not lead to robust enhanced resistance to fully virulent Xoo isolates, it does lead to quantitatively enhanced resistance to weakly virulent Xoo isolates. EFR interacts with OsSERK2 and the XA21 binding protein 24 (XB24), two key components of the rice XA21-mediated immune response. Rice-EFR plants silenced for OsSERK2, or overexpressing rice XB24 are compromised in elf18-induced reactive oxygen production and defense gene expression indicating that these proteins are also important for EFR-mediated signaling in transgenic rice. Taken together, our results demonstrate the potential feasibility of enhancing disease resistance in rice and possibly other monocotyledonous crop species by expression of dicotyledonous PRRs. Our results also suggest that Arabidopsis EFR utilizes at least a subset of the known endogenous rice XA21 signaling components

Nonlinearity of Mechanochemical Motions in Motor Proteins

The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors - myosin V and kinesin KIF1A - and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode, nor a superposition of such modes yield an approximation of strongly nonlinear dynamics.Comment: 10 pages, 6 figure

Toward a theory‐based specification of non‐pharmacological treatments in aging and dementia: Focused reviews and methodological recommendations

Introduction: Non‐pharmacological treatments (NPTs) have the potential to improve meaningful outcomes for older people at risk of, or living with dementia, but research often lacks methodological rigor and continues to produce mixed results. Methods: In the current position paper, experts in NPT research have specified treatment targets, aims, and ingredients using an umbrella framework, the Rehabilitation Treatment Specification System. Results: Experts provided a snapshot and an authoritative summary of the evidence for different NPTs based on the best synthesis efforts, identified main gaps in knowledge and relevant barriers, and provided directions for future research. Experts in trial methodology provide best practice principles and recommendations for those working in this area, underscoring the importance of prespecified protocols. Discussion: We conclude that the evidence strongly supports various NPTs in relation to their primary targets, and discuss opportunities and challenges associated with a unifying theoretical framework to guide future efforts in this area