Power-law Properties Research Articles

Power-law properties of nocturnal arrhythmia avalanches: A novel marker for incident cardiovascular events

BackgroundBursting nonsustained cardiac arrhythmia events are a common observation during sleep. ObjectivesThe purpose of this study was to investigate the hypothesis that nocturnal arrhythmia episode durations could follow a power law, whose exponent could predict long-term clinical outcomes. MethodsWe defined “nocturnal arrhythmia avalanche” (NAA) as any instance of a drop in electrocardiographic (ECG) template-matched R-R intervals ≥30% of R-R baseline, followed by a return to 90% of baseline. We studied NAA in ECG recordings obtained from the Sleep Heart Health Study (SHHS), Osteoporotic Fractures in Men Study (MrOS) Study, and Multi-Ethnic Study of Atherosclerosis (MESA). The association of nocturnal arrhythmia durations with a power-law distribution was evaluated and the association of derived power-law exponents (α) with major adverse cardiovascular (CV) events and mortality assessed with multivariable Cox regression. ResultsA total of 9176 participants were studied. NAA episodes distribution was consistent with power-law vs comparator distributions in all datasets studied (positive log likelihood ratio of power-law vs exponential in MESA: 83%; SHHS: 69%; MrOS: 81%; power-law vs log-normal in MESA: 95%; SHHS: 35%; MrOS: 64%). The NAA power-law exponent (α) showed a significant association of with adverse CV outcomes (association with CV mortality: SHHS hazard ratio 1.39 [1.07–1.79], P = .012; MrOS hazard ratio 1.42 [1.02–1.94], P = .039; association with CV events: MESA HR 3.46 [1.46–8.21], P = .005) in multivariable Cox regression, after adjusting for conventional CV risk factors and nocturnal ectopic rate. ConclusionThe NAA power-law exponent is a reproducible, predictive marker for incident CV events and mortality.

The Effect of Hyperelasticity and Nonlinearity on the Dynamic Behaviors of Hyperelastic Functionally Graded Beams on Nonlinear Elastic Foundation

Hyperelastic functionally graded materials have a wide range of application prospects in soft robotics and biomedical fields. This paper investigates the nonlinear free and forced vibrations of a hyperelastic functionally graded beam (HFGB) based on higher-order shear deformation beam theory. The geometrical nonlinearity is considered by using the von-Kármán’s nonlinear theory. The three-material-parameter free energy function named as Ishihara model is employed to characterize the hyperelastic material. The power-law gradient form along the thickness direction is adopted. The HFGB is resting on the elastic foundation. The Winkler, Pasternak and nonlinear stiffness coefficients are considered. The time-harmonic external force is applied to the HFGB. The nonlinear governing equations for the vibration of the HFGB are derived by using Hamilton’s principle, and are subsequently transformed into ordinary differential equations via Galerkin’s method. The nonlinear free vibration and primary resonance of the HFGB are investigated analytically by employing the extended Hamiltonian method and multiple scales method, respectively. The results indicate that the power-law index, slenderness ratio, material properties, and elastic foundation parameters have significant influences on the nonlinear frequency of free vibration as well as the frequency–response and force–response curves of forced vibration. The phase plane method is employed to analyze the system’s stability states under various excitation amplitudes. The relative error between the results of the current computational model and the published literature is less than 0.1 percent.

Machine Learning-Based Kernel Selector for SpMV Optimization in Graph Analysis

Sparse Matrix and Vector multiplication (SpMV) is one of the core algorithms in various large-scale scientific computing and real-world applications. With the rapid development of AI and big data, the input vector in SpMV becomes sparse in many application fields. Especially in some graph analysis calculations, the sparsity of the input vector will change with the running of the program, and the non-zero element distribution of the adjacency matrix of some graph data has the power law property, leading to serious load imbalance, which requires additional optimization means. Therefore, the optimal SpMV kernel may be different, and a single SpMV kernel can no longer meet the acceleration requirements. In this paper, we propose a decision tree-based adaptive SpMV framework, named DTSpMV, that can automatically select appropriate SpMV kernels according to different input data in iterations of graph computation. Based on the analysis of computing patterns, bit-array compression algorithms, and serial and parallel algorithms, we encapsulate nine SpMV kernels within the framework. We explore machine learning-based kernel selectors in terms of both accuracy and runtime overhead. Experimental results on NVIDIA Tesla T4 GPU show that our adaptive framework achieves the arithmetic average performance improvement of \(152\% \) compared to the SpMV kernel in cuSPARSE.

Segmental estimation and testing method for power-law distributions and some extensions

For discrete segmental power-law distributions, the probability ratio ft/ft+1 is a linear function of the exponent parameter. Based on this property, the estimation of the exponent parameter and a goodness-of-fit testing method are provided. The proposed testing method is parameter-independent and the testing statistic is proved to asymptotically follow a chi-square distribution. In the region where power-law properties exist, the testing method and the estimation method can be applied by segments, so they can also be used to determine interval endpoints. These methods can also be extended to other discrete distributions such as Yule distribution, Poisson distribution, Geometry distribution and so on. Some simulation results of synthetic truncated power-law distributions provide support for the effectiveness of the proposed methods. To demonstrate the applicability of the method, two empirical examples, word frequencies of the novel Moby Dick and US casuality numbers in the American Indian War, are analyzed.

Microrheological comparison of melanoma cells by atomic force microscopy

Melanoma is one of the most severe cancers due to its great potential to form metastasis. Recent studies showed the importance of mechanical property assessment in metastasis formation which depends on the cytoskeleton dynamics and cell migration. Although cells are considered purely elastic, they are viscoelastic entities. Microrheology atomic force microscopy (AFM) enables the assessment of elasticity and viscous properties, which are relevant to cell behavior regulation. The current work compares the mechanical properties of human neonatal primary melanocytes (HNPMs) with two melanoma cell lines (WM793B and 1205LU cells), using microrheology AFM. Immunocytochemistry of F-actin filaments and phosphorylated focal adhesion kinase (p-FAK) and cell migration assays were performed to understand the differences found in microrheology AFM regarding the tumor cell lines tested. AFM revealed that HNPMs and tumor cell lines had distinct mechanical properties. HNPMs were softer, less viscous, presenting a higher power-law than melanoma cells. Immunostaining showed that metastatic 1205LU cells expressed more p-FAK than WM793B cells. Melanoma cell migration assays showed that WM73B did not close the gap, in contrast to 1205LU cells, which closed the gap at the end of 23 h. These data seem to corroborate the high migratory behavior of 1205LU cells. Microrheology AFM applied to HNPMs and melanoma cells allowed the quantification of elasticity, viscous properties, glassy phase, and power-law properties, which have an impact in cell migration and metastasis formation. AFM study is important since it can be used as a biomarker of the different stages of the disease in melanoma.

Prandtl System of Equations with Self-Induced Pressure for the Case of Non-Newtonian Fluid: Dynamics of Boundary Layer Separation

The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties along a semi-infinite plate with a small localized irregularity on the surface is considered for large Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is constructed. The numerical simulation of the flow in the region near the surface was performed for different fluid indices. The results of investigations of the flow properties depending on the fluid index are presented. Namely, the boundary layer separation is investigated for different fluid indices, and the dynamics of vortex formation in this region is shown.

Testing the power-law hypothesis of the interconflict interval

War is an extreme form of collective human behaviour characterized by coordinated violence. We show that this nature of war is substantiated in the temporal patterns of conflict occurrence that obey power law. The focal metric is the interconflict interval (ICI), the interval between the end of a conflict in a dyad (i.e. a pair of states) and the start of the subsequent conflict in the same dyad. Using elaborate statistical tests, we confirmed that ICI samples compiled from the history of interstate conflicts from 1816 to 2014 followed a power-law distribution. We then demonstrate that the power-law properties of ICIs can be explained by a hypothetical model assuming an information-theoretic formulation of the Clausewitz thesis on war: the use of force is a means of interstate communication. Our findings help us to understand the nature of wars between regular states, the significance of which has increased since the Russian invasion of Ukraine in 2022.

Scale-dependent power law properties in hashtag usage time series of Weibo

We analyze the time series of hashtag numbers of social media data. We observe that the usage distribution of hashtags is characterized by a fat-tailed distribution with a size-dependent power law exponent and we find that there is a clear dependency between the growth rate distributions of hashtags and size of hashtags usage. We propose a generalized random multiplicative process model with a theory that explains the size dependency of the fat-tailed distribution. Numerical simulations show that our model reproduces these size-dependent properties nicely. We expect that our model is useful for understanding the mechanism of fat-tailed distributions in various fields of science and technology.

On sparsity, power-law, and clustering properties of graphex processes - ADDENDUM

On sparsity, power-law, and clustering properties of graphex processes - ADDENDUM

On sparsity, power-law, and clustering properties of graphex processes

AbstractThis paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse, almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that, under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for subgraph counts and for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph.

Rigorous plane-stress solution and buckling analysis of rectangular functionally graded plates subjected to non-uniform edge loads

In this article, analytical solutions for the buckling analysis of simply supported rectangular functionally graded (FG) plates subjected to various forms of non-uniform in-plane loads are presented. Both perfect and porous FG plates with power-law material property variation are considered. The analytical solution is obtained by adopting a two-step approach: First, a rigorous plane-stress solution is developed based on the superposition of Airy’s stress functions, and later, these stress solutions are used in the buckling load computation of the FG plate based on Galerkin’s technique. One key aspect of the proposed solution is that it can consider different non-uniform waveforms of the in-plane loads at two opposite sides of the plate. Results show that the nature of the edge load has a profound effect on the stress solution of the FG plates. Several tables and graphs are presented to obtain a qualitative and quantitative understanding of the buckling behavior of FG plates influenced by various plate design parameters which include plate aspect ratios, power-law exponent, and porosity index. Comparative studies are also presented to highlight some erroneous results published in the open literature. It can be emphasized that the analytical results reported here can be used as a reference to judge the accuracy of other numerical solutions such as the finite element method.

A DICHOTOMY OF STRONG OPEN SET CONDITION OF SELF-CONFORMAL SETS

Let [Formula: see text] be a [Formula: see text] self-conformal set. It is well known that [Formula: see text] satisfies the strong open set condition provided it satisfies the open set condition. A point [Formula: see text] is called a trivial point of [Formula: see text] if [Formula: see text] is a connected component of [Formula: see text]. Let [Formula: see text] be a strong open set for [Formula: see text]. In this paper, we show that whether [Formula: see text] contains a trivial point of [Formula: see text] determines several metrical and topological properties of [Formula: see text], including the maximal power law property and the dimension drop of the connected part of [Formula: see text].

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

The Analysis of the Power Law Feature in Complex Networks.

Consensus about the universality of the power law feature in complex networks is experiencing widespread challenges. In this paper, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that are more common than BA networks in the real world, and then we calculate their degree distributions; the results show that the tails of their degree distributions exhibit a distinct power law feature. Second, we suggest that in the real world two important factors-network size and node disappearance probability-will affect the analysis of power law characteristics in observation networks. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behavior of the degree distribution within its effective intervals.

Accurate solution for free vibration behaviour of stepped FGM plates implementing the dynamic stiffness method

In this article, free vibration response of stepped functionally graded material (FGM) plate is studied through the implementation of dynamic stiffness method (DSM). The material model of the plate is assumed to have the power-law (P-FGM) property variation through the thickness. The kinematic variables within the Kirchhoff’s plate theory are defined by considering the concept of the physical neutral surface to avoid the bending-stretching coupling of the P-FGM plate. The governing equation of motion pertaining to a single plate element are obtained through the application of Hamilton’s principle. Levy type (closed form) solution to this equation of motion is sought to formulate the DS matrix through the implementation of displacement and force edge conditions at the two opposite ends of the plate. The dynamic stiffness (DS) matrix is first formulated for a single FGM plate element and later these DS matrices are suitably assembled to obtain the global DS matrix of the stepped FGM plate. The assembled global DS matrix is finally solved using the Wittrick-William’s algorithm to compute the accurate natural frequencies of the stepped FGM plates. Through different comparisons, it has been demonstrated that the frequency results obtained from the DSM are very accurate for the stepped P-FGM plates. New set of results are also presented by varying different geometrical and material parameter of the stepped plate. The results reported from this parametric study will be beneficial in the design phase of various stepped P-FGM plates.

SOME CHAOTIC MATHEMATICAL MODELS WITH STOCHASTIC RESETTING

A system of three nonlinear equations that depict chaotic behavior was considered in this work. We looked at four cases: one with a power-law property; one with a fading memory effect; one with a transition from stretched exponential to power-law; and one with a stochastic component. We have presented a detailed analysis of stability and we have suggested a number similar to the reproductive number in the case of epidemiology. At this stage, we did not provide a physical meaning for such a number. However, such a number may be useful. A numerical scheme based on the Lagrange polynomial interpolation was used to solve the respective models numerically. Numerical simulations were performed for different values of fractional orders and densities of randomness and piecewise ideas.

Free vibration analysis of uniform thickness and stepped P-FGM plates: A FSDT-based dynamic stiffness approach

In this article, the dynamic stiffness method (DSM) is implemented to analyze the out-of-plane free vibration behavior of uniform thickness and stepped functionally graded plates with power-law material property variation (P-FGM) along the thickness direction. The P-FGM plate is discretized suitably in a number of segments, and for each segment the dynamic stiffness (DS) matrix is formulated. The displacement field is defined with respect to the physical neutral surface of the plate based on the first-order shear deformation theory (FSDT). Assuming Levy-type plate boundary conditions, the governing differential equations are solved exactly to obtain the DS matrix pertaining to a plate segment. Finally, the eigenvalues and eigenvectors of the assembled global DS matrix are computed using the Wittrick–Williams algorithm to obtain the natural frequencies and mode shapes of various P-FGM plate configurations. It is shown that the frequency results obtained using DSM are very accurate as the method utilizes the exact solution of the governing differential equations. It is emphasized that FSDT-based frequency results for stepped P-FGM plates are reported, for the first time, in this article, and these results can be used as benchmark solutions for comparison purposes.

A Structure-Aware Storage Optimization for Out-of-Core Concurrent Graph Processing

With the huge demand for graph analytics in many real-world applications, massive iterative graph processing jobs are concurrently performed on the same graphs and suffer from significant high data access cost. To lower the data access cost toward high performance, several out-of-core concurrent graph processing solutions are recently designed to handle concurrent jobs by enabling these jobs to share the accesses of the same graph data. However, the set of active vertices in each partition are usually different for various concurrent jobs and also evolve with time, where some high-degree ones (or called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hub-vertices</i> ) of these active vertices require more iterations to converge due to the power-law property of real-world graphs. In consequence, existing solutions still suffer from much unnecessary I/O traffic, because they have to entirely load each partition into the memory for concurrent jobs even if most vertices in this partition are inactive and may be shared by a few jobs. In this paper, we propose an efficient structure-aware storage system, called GraphSO, for higher throughput of the execution of concurrent graph processing jobs. It can be integrated into existing out-of-core graph processing systems to promote the execution efficiency of concurrent jobs with lower I/O overhead. The key design of GraphSO is a fine-grained storage management scheme. Specifically, it logically divides the partitions of existing graph processing systems into a series of small same-sized chunks. At runtime, these small chunks with active vertices are judiciously loaded by GraphSO to construct new logical partitions (i.e., each logical partition is a subset of active chunks) for existing graph processing systems to handle, where the most-frequently-used chunks are preferentially loaded to construct the logical partitions and the other ones are delayed to wait to be required by more jobs. In this way, it can effectively spare the cost of loading the graph data associated with the inactive vertices with low repartitioning overhead and can also enable the loaded graph data to be fully shared by concurrent jobs. Moreover, GraphSO also designs a buffering strategy to efficiently cache the most-frequently-used chunks in the main memory to further minimize the I/O traffic by avoiding repeated load of them. Experimental results show that GraphSO improves the throughput of GridGraph, GraphChi, X-Stream, DynamicShards, LUMOS, Graphene, and Wonderland by 1.4-3.5 times, 2.1-4.3 times, 1.9-4.1 times, 1.9-2.9 times, 1.5-3.1 times, 1.3-1.5 times, and 1.3-2.7 times after integrating with them, respectively.

Relations between topological and metrical properties of self-affine Sierpiński sponges

We investigate two Lipschitz invariants of metric spaces defined by δ-connected components, called the maximal power law property and the perfectly disconnectedness. The first property has been studied in literature for some self-similar sets and Bedford-McMullen carpets, while the second property seems to be new. For a self-affine Sierpiński sponge E, we first show that E satisfies the maximal power law if and only if E and all its major projections contain trivial connected components; secondly, we show that E is perfectly disconnected if and only if E and all its major projections are totally disconnected.

A four node quadrilateral shell element for free vibration response of functionally graded spherical shell panels

Abstract The present work involves the free vibration analysis of functionally graded spherical shells using a four-node quadrilateral shell element. This four-node, shell element has seven DOF (Degrees of Freedom) per node namely; three displacements, two rotations of mid-plane, and two transverse shear strain com-ponents. The element is developed by modifying the discrete Kirchhoff quadri-lateral shell element based on Reddy’s third-order theory developed earlier by the authors for the cylindrical shell. By transforming all the degrees of freedom from local to global coordinates using a transformation matrix converts the plate bending element into a flat shell element, resulting in the present formulation being suitable to give results for thin shells as well as for thick shells. In the present work functionally graded spherical shell panels with simply supported as well as clamped boundary condition, with various radius to span ratios and with different volume fraction indices are analyzed for free vibration response. The power law property variation through the thickness is considered in this study. To assess the performance of the developed element, the results, of non-dimen-sionalised frequencies are compared with the results presented in the literature. Comparison of results shows that the developed element yields quite accurate results even with the coarser mesh, which indicates the computational efficiency. It is also seen that the percentage difference between the present results and the other results available in the literature is less than 2 in most of the cases.