Random Walk Analysis Research Articles

Random Walk Analysis of the Effect of Mechanical Degradation on All-Solid-State Battery Power

Mechanical and electrochemical phenomena are coupled in defining the battery reliability, particularly for solid-state batteries. Micro-cracks act as barriers to Li-ion diffusion in the electrolyte, increasing the average electrode’s tortuosity. In our previous work, we showed that solid electrolytes are likely to suffer from mechanical degradation if their fracture energy is lower than 4 J m− 2 [G. Bucci, T. Swamy, Y.-M. Chiang, and W. C. Carter, J. Mater. Chem. A (2017)]. Here we study the effect of electrolyte micro-cracking on the effective conductivity of composite electrodes. Via random analyzes, we predict the average diffusivity of lithium in a solid-state electrode to decrease linearly with the extension of mechanical degradation. Furthermore, the statistical distribution of first passage times indicates that the microstructure becomes more and more heterogeneous as damage progresses. In addition to power and capacity loss, a non-uniform increase of the electrode tortuosity can lead to heterogeneous lithiation and further stress localization. The understanding of these phenomena at the mesoscale is essential to the implementation of safe high-energy solid-state batteries.

Scaling analysis of random walks with persistence lengths: Application to self-avoiding walks.

We develop an approach for performing scaling analysis of N-step random walks (RWs). The mean square end-to-end distance, 〈R[over ⃗]_{N}^{2}〉, is written in terms of inner persistence lengths (IPLs), which we define by the ensemble averages of dot products between the walker's position and displacement vectors, at the jth step. For RW models statistically invariant under orthogonal transformations, we analytically introduce a relation between 〈R[over ⃗]_{N}^{2}〉 and the persistence length, λ_{N}, which is defined as the mean end-to-end vector projection in the first step direction. For self-avoiding walks (SAWs) on 2D and 3D lattices we introduce a series expansion for λ_{N}, and by Monte Carlo simulations we find that λ_{∞} is equal to a constant; the scaling corrections for λ_{N} can be second- and higher-order corrections to scaling for 〈R[over ⃗]_{N}^{2}〉. Building SAWs with typically 100 steps, we estimate the exponents ν_{0} and Δ_{1} from the IPL behavior as function of j. The obtained results are in excellent agreement with those in the literature. This shows that only an ensemble of paths with the same length is sufficient for determining the scaling behavior of 〈R[over ⃗]_{N}^{2}〉, being that the whole information needed is contained in the inner part of the paths.

From the Namib around the world: biogeography of the Inuleae–Plucheinae (Asteraceae)

AbstractAimWe investigated the historical biogeography of the Inuleae–Plucheinae (Asteraceae), a group of arid‐adapted plants with partly unresolved generic circumscriptions, in order to understand its origin and spatiotemporal evolutionary history in relation to the Cenozoic climate shifts.LocationGlobal, with highest species diversity in the Southern Hemisphere.MethodsThe spatiotemporal biogeography of the Plucheinae was estimated by both a discrete method using a set of general distribution areas, and a relaxed random walk based on extant species distributions. The topology was time calibrated using a combination of secondary node ages and secondary derived rates for included loci.ResultsOur results indicate the median age of the Plucheinae to be approximately 15.4 Ma. The biogeographical analyses infer an ancestral origin in southern Africa, with the relaxed random walk analysis narrowing the uncertainty down to an area reaching from coastal Namibia to the western Kalahari. Africa was colonized in a (south)western–(north)eastern direction following the spread of arid habitats. Ancestral representatives of the Plucheinae colonized South America on at least three separate occasions (13.0–4.0, 4.3–3.1 and 4.1–3.7 Ma), with one subsequent spread to North America. Australia was colonized three times between 3.6 and 0.4 Ma. Madagascar and the Mascarenes were colonized at least seven times.Main conclusionsThe origin of the Plucheinae is estimated to the Namib region, with early speciations and radiations concurring with the timing of aridification of southern Africa, following the increase in strength of the Antarctic Circumpolar Current and subsequent formation of the Benguela Upwelling at c. 11.8 Ma. The current biogeographical distribution of the Plucheinae is best explained by several Neogene long‐distance dispersal events from tropical Africa.

Random walk analysis for reflection and transmission of turbid media

AbstractThe reflection and transmission of light from a turbid slab is determined by considering a photon random walk within the medium. The reflection and transmission is obtained using the Beer‐Lambert law on each path through the slab. Path length probability densities are derived, then all paths are summed weighted by their probabilities. The results are simple expressions for the reflection and the transmission in terms of the physical properties of the medium. © 2016 Wiley Periodicals, Inc. Col Res Appl, 41, 580–584, 2016

Taking Control: Stealth Assessment of Deterministic Behaviors Within a Game-Based System

Game-based environments frequently afford students the opportunity to exert agency over their learning paths by making various choices within the environment. The combination of log data from these systems and dynamic methodologies may serve as a stealth means to assess how students behave (i.e., deterministic or random) within these learning environments. The current work captures variations in students’ behavior patterns by employing two dynamic analyses to classify students’ sequences of choices within an adaptive learning environment. Random Walk analyses and Hurst exponents were used to classify students’ interaction patterns as random or deterministic. Forty high school students interacted with the game-based system, iSTART-ME, for 11-sessions (pretest, 8 training sessions, posttest, and a delayed retention test). Analyses revealed that students who interacted in a more deterministic manner also generated higher quality self-explanations during training sessions. The results point toward the potential for dynamic analyses such as random walk analyses and Hurst exponents to provide stealth assessments of students’ learning behaviors while engaged within a game-based environment.

High-efficiency imaging through scattering media in noisy environments via sparse image reconstruction

High-efficiency imaging through highly scattering media is urgently desired for various applications. Imaging speed and imaging quality, which determine the imaging efficiency, are two inevitable indices for any optical imaging area. Based on random walk analysis in statistical optics, the elements in a transmission matrix (TM) actually obey Gaussian distribution. Instead of dealing with large amounts of data contained in TM and speckle pattern, imaging can be achieved with only a small number of the data via sparse representation. We make a detailed mathematical analysis of the elements-distribution of the TM of a scattering imaging system and study the imaging method of sparse image reconstruction (SIR). More specifically, we focus on analyzing the optimum sampling rates for the imaging of different structures of targets, which significantly influences both imaging speed and imaging quality. Results show that the optimum sampling rate exists in any noise-level environment if a target can be sparsely represented, and by searching for the optimum sampling rate, it can effectively balance the imaging quality and the imaging speed, which can maximize the imaging efficiency. This work is helpful for practical applications of imaging through highly scattering media with the SIR method.

Next-generation diagnostics and disease-gene discovery with the Exomiser.

Exomiser is an application that prioritizes genes and variants in next-generation sequencing (NGS) projects for novel disease-gene discovery or differential diagnostics of Mendelian disease. Exomiser comprises a suite of algorithms for prioritizing exome sequences using random-walk analysis of protein interaction networks, clinical relevance and cross-species phenotype comparisons, as well as a wide range of other computational filters for variant frequency, predicted pathogenicity and pedigree analysis. In this protocol, we provide a detailed explanation of how to install Exomiser and use it to prioritize exome sequences in a number of scenarios. Exomiser requires ∼3 GB of RAM and roughly 15-90 s of computing time on a standard desktop computer to analyze a variant call format (VCF) file. Exomiser is freely available for academic use from http://www.sanger.ac.uk/science/tools/exomiser.

Persistence and dispersal in a Southern Hemisphere glaciated landscape: the phylogeography of the spotted snow skink (Niveoscincus ocellatus) in Tasmania.

BackgroundThe aim of this research was to identify the effects of Pleistocene climate change on the distribution of fauna in Tasmania, and contrast this with biotic responses in other temperate regions in the Northern and Southern Hemisphere that experienced glacial activity during this epoch. This was achieved by examining the phylogeographic patterns in a widely distributed Tasmanian endemic reptile, Niveoscincus ocellatus. 204 individuals from 29 populations across the distributional range of N. ocellatus were surveyed for variation at two mitochondrial genes (ND2, ND4), and two nuclear genes (β-globin, RPS8). Phylogenetic relationships were reconstructed using a range of methods (maximum parsimony, Bayesian inference and haplotype networks), and the demographic histories of populations were assessed (AMOVA, Tajima’s D, Fu’s Fs, mismatch distributions, extended Bayesian skyline plots, and relaxed random walk analyses).ResultsThere was a high degree of mitochondrial haplotype diversity (96 unique haplotypes) and phylogeographic structure, where spatially distinct groups were associated with Tasmania’s Northeast and a large area covering Southeast and Central Tasmania. Phylogeographic structure was also present within each major group, but the degree varied regionally, being highest in the Northeast. Only the Southeastern group had a signature of demographic expansion, occurring during the Pleistocene but post-dating the Last Glacial Maximum. In contrast, nuclear DNA had low levels of variation and a lack of phylogeographic structure, and further loci should be surveyed to corroborate the mitochondrial inferences.ConclusionsThe phylogeographic patterns of N. ocellatus indicate Pleistocene range and demographic expansion in N. ocellatus, particularly in the Southeast and Central areas of Tasmania. Expansion in Central and Southeastern areas appears to have been more recent in both demographic and spatial contexts, than in Northeast Tasmania, which is consistent with inferences for other taxa of greater stability and persistence in Northeast Tasmania during the Last Glacial Maximum. These phylogeographic patterns indicate contrasting demographic histories of populations in close proximity to areas directly affected by glaciers in the Southern Hemisphere during the LGM.Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-015-0397-y) contains supplementary material, which is available to authorized users.

Superstatistical analysis and modelling of heterogeneous random walks.

Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

Nonlinear analysis of random walks: a tool to analyze nucleic acid sequences

We have performed a comparison of computer-generated random sequences with tRNAs nucleotide sequences present in Bacteria represented as random walks. Nucleotide sequence data of tRNA genes were obtained from the Institute for Genomic Research (TIGR) and the GeneBank library. Random sequence data (white noise) were obtained from the algorithm by Press and Teukolsky. Random walks of nucleotide sequences were obtained by letting the orbit walk a unit step in one of four directions (down, left, right, and up), depending upon the next base (A,C,G, and T) in the sequence, and the distances from the origin calculated. The Visual Basic routines here applied to perform the analysis are presented. Relative Lempel-Ziv complexity. Entropy (sum of the positive Lyapunov indexes) and Hurst indexes of nucleotide sequences and of computer-generated random data were evaluated over the distances of their random walk. Our data show that the values of nonlinear parameters obtained from the bacteria are lower than the values of randomly generated sequences (p<0.01, p<0.05, p<0.01), meaning that the tRNA sequence is more ordered than a pure destructured random data and it owns a “memory”. The observed deviation from pure randomness should be arisen from some constraints like the secondary structure of this biologic macromolecule and/or from the peculiar origin of this macromolecule by repeated subunits. These data indicate that evolution earlier chose nonrandom “alphabets”: order together randomness were present at the dawn of life. Our method, here presented and described, provides an efficient tool to assess the amount of order/disorder in the primary structure of nucleic acid sequences.

Second Order Approximation for the Distribution of the Maximum of a Random Walk with Negative Drift and Infinite Variance

Let $\xi,\xi_1,\xi_2,\ldots$ be independent identically distributed random variables, and set $a:=-{\bf E}\,\xi> 0$, $S_n:=\sum_{j=1}^n\xi_j$, $S_0=0$, $S:=\sup_{n\ge 0}S_n$, $F_+(t):={\bf P}(\xi\ge t)$, $F_-(t):={\bf P}(\xi\le-t)$, $F_+^I(t)=\int_t^\infty F_+(u)\,du$. It is well known (see, e.g., [N. Veraverbeke, Stoch. Process. Appl., 5 (1977), pp. 27--37], [A. A. Borovkov, Probability Theory, Springer, New York, 2013]) that if the function $F^I_+(t)$ is subexponential, then ${\bf P}(S\ge x)\sim{F_+^I(x)}/{a}$ as $x\to\infty$. Under the condition that ${\bf E}\,\xi^2<\infty$ and the function $F_+(x)$ is either regularly varying at infinity or semiexponential, the next term of the asymptotic expansion for ${\bf P}(S\ge x)$ as $x\to\infty$ (which is of the order of $F_+(x)$) was found in [A. A. Borovkov, Sib. Math. J., 43 (2002), pp. 995--1022] (see also [A. A. Borovkov and K. A. Borovkov, Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions, Cambridge University Press, Cambridge, UK, 2008]). I...

Spectral Graph Theory via Higher Order Eigenvalues and Applications to the Analysis of Random Walks

A basic goal in the field of spectral theory is to relate eigenvalues of matrices associated to a graph, namely the adjacency matrix, the Laplacian matrix or the random walk matrix, to the combinatorial properties of that graph. Classical results in this area mostly study the properties of first, second or the last eigenvalues of these matrices [2, 3, 4, 21]. In the last several years many of these results are extended and the bounds are improved using higher order eigenvalues. In this short monologue we overview several of these recent advances, and we describe one of the fundamental tools employed in these results, namely, the spectral embedding of graphs.

Does agency matter?: Exploring the impact of controlled behaviors within a game-based environment

When students exhibit control and employ a strategic plan of action over a situation they are said to be demonstrating agency (Bandura, 2001). The current work is comprised of two studies designed to investigate how agency manifests within students' choice patterns and ultimately influences self-explanation quality within the game-based system iSTART-2. In Study 1, 75 college students interacted freely within iSTART-2 for 2 h. Random walk and Entropy analyses were used to quantify the amount of control demonstrated in students' choice patterns, as well as to determine the relation between variations in these patterns and self-explanation performance within iSTART-2. Overall, students who demonstrated more controlled choice patterns generated higher quality self-explanations compared to students who exhibited more disordered choice patterns. This link between performance and controlled choice patterns is hypothesized to be driven, in part, by students' experiences of agency. That is, engaging in controlled patterns should be advantageous only when doing so is a result of students' strategic planning. In Study 2, this hypothesis was tested by assigning 70 students to a choice pattern (i.e., controlled or disordered) that had been yoked to students from Study 1, thus removing students' ability to exert agency over the iSTART-2 system. Results revealed no differences in self-explanation quality between the groups assigned to controlled and disordered choice patterns. Collectively, findings from these studies support the notion that success within game-based systems is related to students' ability to exert agency over their learning paths.

Spectral Properties of Non-Unitary Band Matrices

We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure results about the location and nature of the spectrum of such non-normal operators as a function of their parameters. We relate these results to the analysis of certain random quantum walks, the dynamics of which can be studied by means of iterates of such random non-unitary contraction operators.

Abstract 4176: Identifying analytes associated with poor prognosis in CRC

Abstract Cancer patients with undetectable micrometastases at the time of diagnosis are in danger of subsequent metastatic growth that worsens their outcome. Therefore, identification of these patients with latent metastases could reduce morbidity and mortality by helping physicians to choose whether to treat with an adjuvant therapy. In colorectal carcinoma (CRC), 20-30% of stage II patients will have a recurrence at a distant site after removal of the primary tumor. In order for cancer cells to metastasize, they must switch to an “invasive phenotype”. To identify molecular changes in cancer that drive invasion, our laboratory previously built a molecular network model of invasive subcellular structures termed invadopodia. Centrality and random walk analyses identified candidate signaling hubs that may control invadopodia formation or activity. To identify which of these hubs control invasion in specific cancers, we are mining reverse phase protein array (RPPA) data from publicly available human tumor datasets. In this study, we focused on analysis of RPPA data from TCGA in CRC patients, segregated by poor prognosis and good prognosis. We tested three different definitions of poor prognosis: recurrence, survival, and TNM status at diagnosis. We found several promising analytes that were significantly associated with each poor prognosis definition, and recurrence provided the best separation of good vs. poor prognosis. Interestingly, many of the analytes significantly associated with survival are involved in apoptosis. Additionally, we refined the analysis by using a subset of patients (stage I-II), which resulted in even better separation of good vs. poor prognosis. We identified several analytes that are already significantly associated with the invadopodia network (src kinase and PI 3-kinase). We also identified some potential new invadopodia regulators, such as Cox2. This method has potential both to improve CRC survival by identifying patients that need adjuvant therapy as well as identify novel drivers of invadopodia. Citation Format: Christi Lynn French, Alissa Weaver. Identifying analytes associated with poor prognosis in CRC. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 4176. doi:10.1158/1538-7445.AM2014-4176

Non-anomalous diffusion is not always Gaussian

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: i) the high-order moments, $\langle [x(t)]^q \rangle$ for $q>2$ and the probability density of the process exhibit multiscaling; ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; iii) positive order moments satisfying standard scaling do not imply an exact scaling property of the probability density.

First-principles derivation of reactive transport modeling parameters for particle tracking and PDE approaches

Both Eulerian and Lagrangian reactive transport simulations in natural media require selection of a parameter that controls the “promiscuity” of the reacting particles. In Eulerian models, measurement of this parameter may be difficult because its value will generally differ between natural (diffusion-limited) systems and batch experiments, even though both are modeled by reaction terms of the same form. And in Lagrangian models, there previously has been no a priori way to compute this parameter. In both cases, then, selection is typically done by calibration, or ad hoc. This paper addresses the parameter selection problem for Fickian transport by deriving, from first principles and D (the diffusion constant) the reaction-rate-controlling parameters for particle tracking (PT) codes and for the diffusion–reaction equation (DRE). Using continuous time random walk analysis, exact reaction probabilities are derived for pairs of potentially reactive particles based on D and their probability of reaction provided that they collocate. Simultaneously, a second PT scheme directly employing collocation probabilities is derived. One-to-one correspondence between each of D, the reaction radius specified for a PT scheme, and the DRE decay constant are then developed. These results serve to ground reactive transport simulations in their underlying thermodynamics, and are confirmed by simulations.

Modularity revisited: A novel dynamics-based concept for decomposing complex networks

Finding modules (or clusters) in large, complex networks is a challenging task, in particular if one is not interested in a full decomposition of the whole network into modules. We consider modular networks that also contain nodes that do not belong to one of modules but to several or to none at all. A new method for analyzing such networks is presented. It is based on spectral analysis of random walks on modular networks. In contrast to other spectral clustering approaches, we use different transition rules of the random walk. This leads to much more prominent gaps in the spectrum of the adapted random walk and allows for easy identification of the network's modular structure, and also identifying the nodes belonging to these modules. We also give a characterization of that set of nodes that do not belong to any module, which we call transition region. Finally, by analyzing the transition region, we describe an algorithm that identifies so called hub-nodes inside the transition region that are important connections between modules or between a module and the rest of the network. The resulting algorithms scale linearly with network size (if the network connectivity is sparse) and thus can also be applied to very large networks.

Protein Network for Associating Genes with Dementia

Association between causal genes and their genetic diseases is an important problem concerning human health. Linkage analysis is such a method that can identify which unknown disease genes are located in chromosomal region out of hundreds of candidate genes according to their functions, interactions, and pathways which is good identification of genes associated with general/hereditary disorders. Here, we used method for prioritization of candidate genes of Dementia by the use of a global network distance measure, Random Walk Analysis, which detects neurological disorder been associated with distribution of sub-network among the genes.

Not looking where you are leaping: a novel method of oriented travel in the caterpillar Calindoea trifascialis (Moore) (Lepidoptera: Thyrididae)

The prepupation caterpillar of the Southeast Asian moth Calindoea trifascialis constructs a leaf shelter that jumps across the ground using a jumping method novel among the insects. We found that movement path direction was correlated to the direction opposite to the most intense light. Correlated random walk (CRW) analyses found net squared displacements higher than predicted by a CRW, and fractal dimension analysis indicated straighter paths at large spatial scales. Rearing experiments showed high mortality from predation on the ground, but higher mortality resulted from sun exposure. We interpret jumping path orientation as an efficient search strategy to find shade in a variable landscape, given limited perception, in the presence of overheating and desiccation risks.