Singular Distribution Research Articles

Resilience-based infrastructure planning and asset management: Study of dual and singular water distribution infrastructure performance using a simulation approach

Dual water distribution systems have been proposed as a technological infrastructure solution to enhance the sustainability and resilience of urban water systems by improving performance and decreasing energy consumption. The dual system separately distributes non-potable water for outdoor demand and potable water for indoor demand. The objective of this study was to evaluate the long-term performance of dual water distribution systems versus singular systems under various scenarios of renewal strategies and demand fluctuations. To this end, a dynamic (time-dependent) simulation model was developed to capture long-term dynamics of water distribution infrastructure systems using empirical relationships. The model integrates utility agency’s renewal decision-making processes with the physical infrastructure degradation to simulate the long-term transformation of the pipeline network. Various system performance measures, including breakage, leakage, energy loss, level of service, and life-cycle costs, were simulated over a 50-year horizon. The simulation model was implemented using data from the City of Fort Collins, CO, and used to examine the long-term performance of the dual and singular water distribution systems. The analysis results enabled: (i) understanding the long-term transformation of water distribution systems; (ii) comparing different performance measures of dual and singular systems; and (iii) exploring the sensitivity of both systems to demand fluctuations.

Flexible belt hanging on two pulleys: Contact problem at non-material kinematic description

We propose a non-material finite element scheme for modelling large deformations of a closed flexible rod supported by two rigid pulleys in the field of gravity. The mixed Eulerian–Lagrangian kinematic description of circumferential and transverse displacements is beneficial for simulations of moving belt drives. The necessary C1 inter-element continuity in a compound coordinate system with Cartesian and polar domains requires a nonlinear finite element approximation. The theoretically predicted singular reaction force distribution prevents us from using the technique of Lagrange multipliers for normal contact. A novel semi-analytical solution of the static problem based on the integration of the equations of the nonlinear theory of rods in the free spans as well as in the segments of contact with pulleys is presented for the sake of validation. We demonstrate the mutual convergence of simulation results for a benchmark problem and additionally justify them by comparison against conventional Lagrangian finite element solutions.

Exchange bias and two steps magnetization reversal in porous Co/CoO layer

In this paper Co/CoO thick layers (hundreds of nanometers) of different porosity and oxidation degree were prepared in a magnetron sputtering deposition process by tailoring the DC sputtering power, as well as the process gas and target composition. The control of the synthesis parameters allowed the nanostructuration of the films with a singular distribution of closed pores and a controlled amount of CoO. We observed an exchange bias field of 2.8 KOe for porous Co/CoO composites, similar to Co/CoO bilayers but for coatings thicker than 300 nm. Besides, it was observed that the coating presents bistable magnetic features when cooled under zero field conditions as a result of the unusual exchange coupling.

Singular vector distribution of sample covariance matrices

AbstractWe consider a class of sample covariance matrices of the formQ=TXX*T*, whereX= (xij) is anM×Nrectangular matrix consisting of independent and identically distributed entries, andTis a deterministic matrix such thatT*Tis diagonal. Assuming thatMis comparable toN, we prove that the distribution of the components of the right singular vectors close to the edge singular values agrees with that of Gaussian ensembles provided the first two moments ofxijcoincide with the Gaussian random variables. For the right singular vectors associated with the bulk singular values, the same conclusion holds if the first four moments ofxijmatch those of the Gaussian random variables. Similar results hold for the left singular vectors if we further assume thatTis diagonal.

Eigenstate Thermalization, Random Matrix Theory, and Behemoths.

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones of contemporary quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this Letter. We report on the construction of highly nonlocal operators, behemoths, that are building blocks for various kinds of local and nonlocal operators. The behemoths have a singular distribution and width w∼D^{-1} (D being the Hilbert space dimension). From there, one may construct local operators with the ordinary Gaussian distribution and w∼D^{-1/2} in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with w∼D^{-δ}, 0<δ<1/2. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of nonintegrable many-body systems.

Two consistent estimators for the skew Brownian motion

The skew Brownian motion (SBm) is of primary importance in modeling diffusion in media with interfaces which arise in many domains ranging from population ecology to geophysics and finance. We show that the maximum likelihood procedure estimates consistently the parameter of an SBm observed at discrete times. The difficulties arise because the observed process is only null recurrent and has a singular distribution with respect to the one of the Brownian motion. Finally, using the idea of the expectation–maximization algorithm, we show that the maximum likelihood estimator can be naturally interpreted as the expected total number of positive excursions divided by the expected number of excursions given the observations. The theoretical results are illustrated by numerical simulations.

Fault Tolerant Control for Nonlinear Singular Stochastic Distribution Systems Based on Fuzzy Modeling

When the desired output probability density function (PDF) is unknown, the active fault-tolerant control (FTC) method for the non-Gaussian nonlinear singular stochastic distribution control (SDC) system is investigated in this paper. Algebraic constraints and the nonlinearity in singular systems make the design of fault diagnosis and fault-tolerant control more complex. Different from traditional static modeling methods, the linear fuzzy logic system is served for approximating the output PDF. Takagi-Sugeno (T-S) fuzzy model is used to describe the nonlinear system. Subsequently, a fuzzy descriptor fault diagnosis (FD) observer is used to provide the unknown fault information for the fault-tolerant controller design. Combining minimum entropy control and fault compensation algorithm, the minimum Shannon entropy fault tolerant control strategy is developed to compensate the performance losses caused by the fault. At last, simulation results are applied to demonstrate the effectiveness of the proposed algorithms.

Limiting spectral distributions of sums of products of non-Hermitian random matrices

For fixed l≥0 and m≥1, let Xn0, Xn1,..., Xnl be independent random n × n matrices with independent entries, let Fn0 := Xn0, Xn1-1,..., Xnl-1, and let Fn1,..., Fnm be independent random matrices of the same form as Fn0 . We show that as n → ∞, the matrices Fn0 and m−l+1/2Fn1 +...+ Fnm have the same limiting eigenvalue distribution. To obtain our results, we apply the general framework recently introduced in Götze, Kösters, and Tikhomirov 2015 to sums of products of independent random matrices and their inverses.We establish the universality of the limiting singular value and eigenvalue distributions, and we provide a closer description of the limiting distributions in terms of free probability theory.

On the limiting distribution of sample central moments

We investigate the limiting behavior of sample central moments, examining the special cases where the limiting (as the sample size tends to infinity) distribution is degenerate. Parent (non-degenerate) distributions with this property are called singular, and we show in this article that the singular distributions contain at most three supporting points. Moreover, using the delta-method, we show that the (second-order) limiting distribution of sample central moments from a singular distribution is either a multiple, or a difference of two multiples of independent Chi-square random variables with one degree of freedom. Finally, we present a new characterization of normality through the asymptotic independence of the sample mean and all sample central moments.

Experimental study of pore size distribution effect on phase transitions of hydrocarbons in nanoporous media

The phase behavior of a fluid in a nanoporous system is altered from that in the bulk due to confinement effects. There have been many experimental studies on this important effect, yet the vast majority are limited to porous media with a narrow or singular pore size distribution. However, natural porous media exhibit a broad pore size distribution. For example, in shale rocks the pore size ranges from several nanometers to hundreds of nanometers. It is not clear if a broad pore size distribution has a significant effect on the phase transition of nanoconfined fluids, and, if effects are present, how and why the phase behavior is altered. The effects of a distributed pore size on the bubble point of confined fluids as measured by differential scanning calorimetry (DSC) are not known. Here, we present an experimental study on the effect of pore size distribution on the liquid-vapor phase transition of n-hexane, n-octane and n-decane confined in nonporous media. We report a method to discretize the pore size distribution of natural shale rocks so that it can be mimicked using mixtures of synthetic nanoporous media. Using DSC, we show that the presence of a broad pore size distribution significantly alters the vapor-liquid phase transition of confined hydrocarbons. In fully saturated (i.e. filled) nanoporous media, the largest pore size dictates the onset of liquid-vapor phase transition (.i.e. bubblepoint). However, when the porous media is partially saturated, smaller pore sizes influence the bubblepoint. These findings suggest that there is a dependency of the confined fluid phase behavior on the fluid saturation in nanoporous media with a broad pore size distribution, which contributes to a broader understanding of phase transitions in natural porous media.

Anderson localization for radial tree graphs with random branching numbers

We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose entries are non-degenerate, independent, identically distributed random variables with singular distributions.

Generalized Flow-Box property for singular foliations

We introduce a notion of generalized Flow-Box property valid for general singular distributions and sub-varieties (based on a dynamical interpretation). Just as in the usual Flow-Box Theorem, we characterize geometrical and algebraic conditions of (quasi) transversality in order for an analytic sub-variety X (not necessarily regular) to be a section of a line foliation. We also discuss the case of more general foliations. This study is originally motivated by a question of Jean-Francois Mattei (Invent Math 103(2):297–325, 1991, Theorem 3.2.1) about the existence of local slices for a (non-compact) Lie group action.

Freedom in the wilderness: A study of a Darknet space

Mass media and journalistic accounts of Darknets have focused disproportionately on their criminogenic aspects. Moreover, research has focused mainly on the Darknet technology Tor. We wish to expand scholars’ knowledge of Darknets by exploring a different Darknet technology, Freenet. Using a combination of content analysis and grounded theory, this research asked three progressively complex questions. First, we asked: What are the types of content and the distribution of content on Freenet? Our findings show that Freenet fosters a singular distribution of content, with a high ratio of blogs (or flogs), child pornography, empty links, and Web 1.0 websites that archive information. We assumed that this content is not discrete points of data but instead produce sociologically interesting phenomena. Therefore, we ask: What are the content patterns on Freenet? Four patterns were identified. Freenet is (1) an archive of deviant data resistant to censorship, (2) a space dominated by content associated with masculinity, (3) a nonmarket space where commercial exchange is nonexistent, and (4) an empty space with many requests not returning information, and many flogs abandoned. We asked a third question: How does the analysis of Freenet inform current understandings of hacker culture? Freenet, we suggest, can be understood as a type of digital ‘wilderness’. It is a singular Darknet space, supporting a distinct set of hacker practices.

Random Cluster Number Feature and Cluster Characteristics of Indoor Measurement at 28 GHz

In this letter, we analyze cluster characteristics and millimeter wave channel characteristics based on an indoor channel measurement campaign at 28 GHz. The spatial properties of clusters are analyzed, and we investigate the intra-cluster angular spreads and the number of clusters. Also, we introduce the random cluster number (RCN) feature to the primary module of the International Mobile Telecommunications (IMT)-2020 channel model. The RCN is based on a Poisson distribution to simulate the evolution of clusters above 6 GHz to get distributions closer to real channel conditions. Examples of the singular value distributions with and without the RCN feature are given. From the comparisons, we can see the benefits of using the RCN feature in simulations with the IMT-2020 model.

Minimum rational entropy fault tolerant control for non-Gaussian singular stochastic distribution control systems using T-S fuzzy modelling

ABSTRACTIn this paper, a new fault diagnosis (FD) and fault tolerant control (FTC) algorithm for a non-Gaussian nonlinear singular stochastic distribution control (SDC) system is studied. The rational square-root fuzzy logic model is used to approximate the output probability density function of non-Gaussian processes and a Takagi-Sugeno (T-S) fuzzy model is employed to transform the non-Gaussian nonlinear SDC system into a fuzzy SDC system. An adaptive fuzzy fault diagnosis observer is constructed to achieve reconstruction of system state and fault. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the rational entropy subjected to mean constraint. Minimum rational entropy fault tolerant control is introduced to make the output of the past-fault SDC system still have the minimum uncertainty. Simulation results are provided to demonstrate the validity of the FD and minimum rational entropy FTC algorithm.

An Analytical Approach to the Determination of Optimal Perturbations in the Eady Model

Abstract Within the framework of the baroclinic instability Eady model, an analytical approach to the determination of optimal perturbations with a maximum of the energy growth rate or the ratio of the final and initial energies is considered. This approach is based on the energy balance equation and explicit expressions for the energy functionals resulting from the perturbation representation by means of the superposition of the edge Rossby waves (ERWs). The corresponding expressions are functions of the parameters of the initial perturbation, and the determination of optimal parameters reduces to the study of these functions on an extremum. For perturbations with zero potential vorticity (PV), the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and the phase shift between these distributions serve as parameters. Analytical formulas are obtained for the optimal phase shift and the maximum of the energy ratio, which determine their dependence on the wavenumber and optimization time. It is also shown that the optimal perturbations always have equal boundary amplitudes. The parameters of the optimal perturbations are compared with the parameters of the growing normal modes. It is established that there exists only one exponentially growing normal mode, which is the optimal perturbation. Along with the instability, the ERWs can be excited by their interaction with the initial vortex perturbations (PV ≠ 0). The optimal regime of ERWs excitation by the initial singular distribution of PV is investigated.

Boundary effect on crack kinking in a magnetoelectroelastic strip with a central crack

In this study, the boundary effect on crack kinking in a magnetoelectroelastic strip with a central crack vertical to the boundary under in-plane loadings has been investigated. By using integral transform techniques the mixed boundary value problem of the crack is reduced to the solution of dual integral equations, which can be further reduced to solving Fredholm integral equations of the second kind. Analytical solutions can be obtained when the width of the magnetoelectroelastic strip are of infinite size. The asymptotic fields around crack-tips have been obtained for the electrically and magnetically impermeable and permeable cracks, respectively. Crack kinking phenomenon is investigated by applying the criterion of maximum hoop stress intensity factor. Numerical results show that the material properties, the geometry of the cracked strip and the electric–magnetic-mechanical loading significantly affect the singular field distributions around the crack. Crack kinking is found for the permeable crack case while no kinking for the impermeable crack.

Spin Subdiffusion in the Disordered Hubbard Chain

We derive and study an effective spin model that explains the anomalous spin dynamics in the one-dimensional Hubbard model with strong potential disorder. Assuming that charges are localized, we show that spins are delocalized and their subdiffusive transport originates from a singular random distribution of spin exchange interactions. The exponent relevant for the subdiffusion is determined by the Anderson localization length and the density of the electrons. Although the analytical derivations are valid for low particle density, numerical results for the full model reveal a qualitative agreement up to half filling.

On the formal specification of sum-zero constrained intrinsic conditional autoregressive models

We propose a formal specification for sum-zero constrained intrinsic conditional autoregressive (ICAR) models. Our specification first projects a vector of proper conditional autoregressive spatial random effects onto a subspace where the projected vector is constrained to sum to zero, and after that takes the limit when the proper conditional autoregressive model approaches the ICAR model. As a result, we show that the sum-zero constrained ICAR model has a singular Gaussian distribution with zero mean vector and a unique covariance matrix. Previously, sum-zero constraints have typically been imposed on the vector of spatial random effects in ICAR models within a Markov chain Monte Carlo (MCMC) algorithm in what is known as centering-on-the-fly. This mathematically informal way to impose the sum-zero constraint obscures the actual joint density of the spatial random effects. By contrast, the present work elucidates a unique distribution for ICAR random effects. The explicit expressions for the resulting unique covariance matrix and density function are useful for the development of Bayesian methodology in spatial statistics which will be useful to practitioners. We illustrate the practical relevance of our results by using Bayesian model selection to jointly assess both spatial dependence and fixed effects.

GRAPHICAL MODELS FOR ZERO-INFLATED SINGLE CELL GENE EXPRESSION.

Bulk gene expression experiments relied on aggregations of thousands of cells to measure the average expression in an organism. Advances in microfluidic and droplet sequencing now permit expression profiling in single cells. This study of cell-to-cell variation reveals that individual cells lack detectable expression of transcripts that appear abundant on a population level, giving rise to zero-inflated expression patterns. To infer gene co-regulatory networks from such data, we propose a multivariate Hurdle model. It is comprised of a mixture of singular Gaussian distributions. We employ neighborhood selection with the pseudo-likelihood and a group lasso penalty to select and fit undirected graphical models that capture conditional independences between genes. The proposed method is more sensitive than existing approaches in simulations, even under departures from our Hurdle model. The method is applied to data for T follicular helper cells, and a high-dimensional profile of mouse dendritic cells. It infers network structure not revealed by other methods; or in bulk data sets. An R implementation is available at https://github.com/amcdavid/HurdleNormal.