Exponential Speed Research Articles

Exponential speed of uniform convergence of the cell density toward equilibrium for subcritical mass in a Patlak–Keller–Segel model

This paper is concerned with a chemotaxis aggregation model for cells, more precisely with a parabolic–elliptic semilinear Patlak–Keller–Segel system in a ball of RN, exhibiting a critical mass phenomenon for N≥2. The main result of this paper is the exponential speed of uniform convergence of radial solutions toward the unique steady state in the subcritical case. We stress that this covers in particular the classical Keller–Segel system with N=2, well known for its critical mass 8π, and that the result improves on the known results even for this most studied problem. A key tool is an associated one-dimensional degenerate parabolic problem. The proof exploits its formal gradient flow structure ut=−∇F[u(t)] on an “infinite dimensional Riemannian manifold”. In particular, we show a new Hardy type inequality, equivalent to the strict convexity of F at any steady state of subcritical mass, which heuristically explains the exponential speed of convergence.

A reduced basis method for microwave semiconductor devices with geometric variations

Purpose – The Reduced Basis Method (RBM) generates low-order models of parametrized PDEs to allow for efficient evaluation of parametrized models in many-query and real-time contexts. The purpose of this paper is to investigate the performance of the RBM in microwave semiconductor devices, governed by Maxwell's equations. Design/methodology/approach – The paper shows the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction under geometry variation. Findings – The RBM reduces model order by a factor of $1,000 and more with guaranteed error bounds. Originality/value – Exponential convergence speed can be observed by numerical experiments, which makes the RBM a suitable method for parametric model reduction (PMOR).

AutoMal: automatic clustering and signature generation for malwares based on the network flow

AbstractThe volume of malwares is growing at an exponential speed nowadays. This huge growth makes it extremely hard to analyse malware manually. Most existing signatures extracting methods are based on string signatures, and string matching is not accurate and time consuming. Therefore, this paper presents AutoMal, a system for automatically extracting signatures from large‐scale malwares. Firstly, the system proposes to represent the network flows by using feature hashing, which can dramatically reduce the high‐dimensional feature spaces that are general in malware analysis. Then, we design a clustering and median filtering method to classify the malware vectors into different types. Finally, it introduces the signature generation algorithm based on Bayesian method. The system can extract both the byte signature and the hash signature of malwares from its network flow with low false positive and zero false negative. Our evaluation shows that AutoMal can generate strongly noise‐resisted signatures that exactly depict the characteristics of malware. Copyright © 2014 John Wiley & Sons, Ltd.

The threshold of effective damping for semilinear wave equations

In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the linear problem. We extend our results to a model with polynomial speed of propagation and to a model with an exponential speed of propagation.

Distributed Concurrent Targeting for Linear Arrays of Point Sources

Motivated by practical applications in satellite formations and antenna arrays etc., the problem of targeting a linear array of point sources at one common point of interest is formulated and then solved using a novel distributed control strategy. These point sources are located collinearly and the two at the two ends orient readily to the target point. The other point sources have to rely on sensing the changes of the relative orientation angles of their nearest neighbors to adjust their own orientations; we rigorously prove that under our control law using only local information, their orientation lines will intersect at the same point of concurrency as the two point sources at the two ends. The crucial idea behind our designed control law is the intuitive argument from plane geometry that reducing the differences between the distances to the baseline of the pairwise intersection points of the orientation lines helps realizing concurrent targeting. This idea is further utilized to construct the key argument in our analysis about the boundedness and the exponential convergence speed of the orientation angles. Numerical simulations are used to validate the effectiveness of our control strategy.

GPU-Meta-Storms: computing the structure similarities among massive amount of microbial community samples using GPU

The number of microbial community samples is increasing with exponential speed. Data-mining among microbial community samples could facilitate the discovery of valuable biological information that is still hidden in the massive data. However, current methods for the comparison among microbial communities are limited by their ability to process large amount of samples each with complex community structure. We have developed an optimized GPU-based software, GPU-Meta-Storms, to efficiently measure the quantitative phylogenetic similarity among massive amount of microbial community samples. Our results have shown that GPU-Meta-Storms would be able to compute the pair-wise similarity scores for 10 240 samples within 20 min, which gained a speed-up of >17 000 times compared with single-core CPU, and >2600 times compared with 16-core CPU. Therefore, the high-performance of GPU-Meta-Storms could facilitate in-depth data mining among massive microbial community samples, and make the real-time analysis and monitoring of temporal or conditional changes for microbial communities possible. GPU-Meta-Storms is implemented by CUDA (Compute Unified Device Architecture) and C++. Source code is available at http://www.computationalbioenergy.org/meta-storms.html.

Mathematical Modeling Suggests That Periodontitis Behaves as a Non‐Linear Chaotic Dynamical Process

This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.

DBI analog of a decaying vacuum cosmology

In this work I discuss the dynamical and thermodynamical equivalence between a general k-essence scalar field cosmology and an arbitrary cosmological model with a decaying vacuum, thus generalizing the approach proposed by Maia and Lima [Phys. Rev. D {\bf 65}, 083513 (2002)]. The formalism obtained is quite general and holds for any non-canonical scalar field model. As a special case I derive a Dirac-Born-Infeld (DBI) model with an exponential potential and constant speed of sound, and show that it is equivalent to a cosmological model with decay law $\Lambda(H) = 3\beta H^2$.

Free-Flow Speed Model Based on Portuguese Roadway Design Features for Two-Lane Highways

Speed is a key performance measure in economic and environmental analyses of two-lane highways. Speed, combined with the percentage of time spent following, is also used in the assessment of level of service. Under free-flow conditions, the circulation of a given vehicle is not constrained by the presence of other vehicles, and the driver's speed choice reflects the driver's response to the geometric features of the road and roadside interference, as well as the driver's perception of risk. Many studies concerned with the effects of road characteristics, design features in particular, on vehicle speed have been conducted in several countries in recent decades. These studies have provided useful tools for modeling speed and evaluating alignment consistency. This paper presents an exponential free-flow speed model, applicable to both curves and tangents, developed for two-lane highways in Portugal. The variables included in the model are representative not only of the road element under consideration (curve or tangent) but also of the preceding road section and of the visual field downstream from the element. The results from this model are compared with other authors’ results and with the guidelines in the Highway Capacity Manual 2010. In addition to the primary influence of the horizontal curvature on speed, the results show that other factors, such as the cross-sectional width, the density of access points, and the downstream visibility, are important.

Exponential speed of mixing for skew-products with singularities

Let f : [0, 1]\\{1/2} × [0, 1] → [0, 1] × [0, 1] be the C∞ endomorphism given by . We prove that f is topologically mixing and if c > 1/4 then f is mixing with respect to the Lebesgue measure. Furthermore the speed of mixing is exponential. This skew-product can be seen as a toy model related to Lorenz-like attractors.

Clinical Applications for Biomarkers of Acute and Chronic Graft-versus-Host Disease

Acute and chronic graft-versus-host disease (aGVHD, cGVHD) are serious complications of allogeneic hematopoietic cell transplantation. The complex pathophysiology of these disease processes is associated with immune system activation, the release of cytokines and chemokines, and alterations in cell populations. The blood levels of specific protein and cellular levels in patients with GVHD have correlated with the development, diagnosis, and prognosis of GVHD. Here, we review the most promising biomarkers for aGVHD and cGVHD with clinical relevance. The utility of GVHD biomarkers in clinical care of allogeneic hematopoietic cell transplantation recipients needs to be proven through clinical trials, and potential approaches to trial design are discussed.

The periodic solution of two-dimensional linear nonstationary systems and estimation of the attraction domain boundary in the problem of control of a wheeled robot

For the problem of control of the plane motion of a wheeled robot the estimate of the attraction domain is set up, which ensures the prescribed exponential speed of asymptotic stability and the absence of overcontrol. This statement of the problem is the generalization of the problems “on the attraction domain,” “on overcontrol,” and “on monotone damping,” which were stated by A.M. Letov in the work [1]. To define the attractive domain estimate, periodic trajectories are considered, which exist at the boundary of the stability domain of twodimensional linear nonstationary systems. Periodic solutions have a finite number of switchings over the period and describe the attraction domain boundary satisfying the preset geometric constraints.

Observer-Based Speed Tracking Control for Sensorless Permanent Magnet Synchronous Motors With Unknown Load Torque

The tracking control problem is addressed for sensorless (nonsalient-pole surface) permanent magnet synchronous motors with unknown constant load torque. Assuming that only stator currents and voltages are available for feedback, a novel sixth order nonlinear adaptive control algorithm is designed, which does not rely on nonrobust open loop integration of motor dynamics and guarantees, under persistency of excitation, local exponential rotor speed tracking.

Software tools and frameworks in High Energy Physics

In many fields of science and industry the computing environment has grown at an exponential speed in the past 30 years. From ad hoc solutions for each problem, the field has evolved gradually to use or reuse systems developed across the years for the same environment or coming from other fields with the same requirements. Several frameworks have emerged to solve common problems. In High Energy Physics (HEP) and Nuclear Physics, we have witnessed the emergence of common tools, packages and libraries that have become gradually the corner stone of the computing in these fields. The emergence of these systems has been complex because the computing field is evolving rapidly, the problems to be solved more and more complex and the size of the experiments now involving several thousand physicists from all over the world. This paper describes the emergence of these frameworks and their evolution from libraries including independent subroutines to task-oriented packages and to general experiments frameworks.

Location-Based Data for Estimated Traffic on Urban Arterial in Heterogeneous Traffic Conditions

Accurate estimation of traffic in intelligent transportation system applications, such as the advanced traveler information system and the advanced traffic management system, requires fixed location-based measurements, vehicle-based measurements, or both. Using both data sources is too expensive for most government agencies, especially in developing countries such as India, and also leads to issues related to installation and maintenance, especially on urban roads. The main drawback of vehicle-based measurements is the potential lack of participation because of privacy concerns; lack of participation would limit data collection to a sample of the population, primarily on public transport vehicles. The study aims to overcome such difficulties by using only location-based flow data for the estimation of spatial parameters, such as density and travel time. These parameters are difficult to measure or estimate on an urban arterial, especially under heterogeneous traffic conditions, because of lack of lane discipline and because of complex interactions among different vehicle types. The Lighthill–Whitham–Richards macroscopic traffic flow model discretized in both space and time was employed in the estimation scheme. The resulting partial differential equations were solved numerically with the finite difference formulation of forward–time backward–space. Both linear and exponential speed–density relationships were considered and incorporated into the macroscopic model. Linear and cubic spline interpolations of input flow values were compared. The estimated density was corroborated with the density obtained from input–output analysis. Estimated travel times were compared with manually observed travel times and travel times obtained from probe vehicles fitted with Global Positioning System devices.

상품정보제공수준과 서비스제공수준에 따른 소비자 태도 차이에 관한 연구

전자상거래의 급속한 발전 속에서 기업들은 세계적 시장에서 경쟁력을 지니기 위해 전자상거래를 이용하여 상품판매, 서비스 제공, 고객과 소통하고자 한다. 그러나, 기존의 연구들은 TAM 모형을 통한 상호관계나 선행관계에만 초점을 맞추고 있기 때문에 좀 더 확장한 모형이 필요하다. 본 연구에서는 상품정보와 서비스 제공수준은 소비자 행동에 영향을 미치는 중요한 요인이지만 연구가 충분치 못한 실정이다. 따라서 본 연구의 목적은 첫째, 상품정보제공수준과 서비스제공수준에 따른 소비자 태도 차이를 조망하고자 한다. 둘째, 기존에 연구가 미약하였던 상품정보제공수준 및 서비스제공수준과 기존에 인지된 가치, 인지된 위험, 구매의도와 구전의도간의 상호인과관계를 조망하고자 한다. 본 연구의 결과는 다음과 같다. 첫째, 상품정보제공수준과 서비스제공수준에 따라 소비자 태도 차이에는 차이가 있었다. 둘째, 상품정보제공수준과 서비스제공수준에 따라 소비자들이 인지된 가치, 인지된 위험, 구매의도, 구전효과에는 차이가 있었다. 셋째, 변수들간에 상호인과관계와 선행관계가 존재하였다. 상품정보제공수준과 서비스 제공수준은 인지된 가치와 인지된 위험에 각각 직접적인 영향을 미쳤다. 뿐만 아니라, 인지된 가치는 인지된 위험, 구매의도, 구전효과에, 인지된 위험은 구매의도와 구전효과에 직접적인 영향을 나타내었다.

Fluid limit theorems for stochastic hybrid systems with application to neuron models

In this paper we establish limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamics coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation, and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to numerically estimate the impact of channel noise both on frequency and spike timing coding.

Fluid limit theorems for stochastic hybrid systems with application to neuron models

In this paper we establish limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamics coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation, and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to numerically estimate the impact of channel noise both on frequency and spike timing coding.

Asymptotically optimal dynamic tree evolution by rapidly mixing random walks on regular networks

Tree-structured computations are among the most popular and important and powerful computing paradigms in computer science. In many such applications, the size and shape of a tree that represents a parallel computation is dynamic and unpredictable at compile time. The tree evolves gradually during the course of the computation. When such an application is executed on a multicomputer system with a static network, the dynamic tree evolution problem is to distribute the tree nodes to the processors of the network such that all the processors receive roughly the same amount of load and that communicating nodes are assigned to neighboring processors. The main contribution of the paper is to conduct a unified study of dynamic tree evolution on regular networks. Our regular networks include d -dimensional torus networks, d -dimensional lattice networks, complete d -partite networks, and random regular networks. These networks include several fundamental networks such as rings, k -ary d -cubes, complete networks, and hypercubes as special cases. We describe a simple random-walk-based asymptotically optimal dynamic tree evolution algorithm on regular networks and analyze the exponential speed at which the performance ratio converges to the optimal. Our strategy is to prove that the Markov chain of a random walk on a regular network is rapidly mixing in the sense that, starting from any initial distribution, the Markov chain converges to its stationary distribution in a small number of steps. We also show that larger dilation results in better tree node distribution.

SUPERPOSITION OF STOCHASTIC PROCESSES AND THE RESULTING PARTICLE DISTRIBUTIONS

Many observations of suprathermal and energetic particles in the solar wind and the inner heliosheath show that distribution functions scale approximately with the inverse of particle speed (v) to the fifth power. Although there are exceptions to this behavior, there is a growing need to understand why this type of distribution function appears so frequently. This paper develops the concept that a superposition of exponential and Gaussian distributions with different characteristic speeds and temperatures show power-law tails. The particular type of distribution function, f ∝ v –5, appears in a number of different ways: (1) a series of Poisson-like processes where entropy is maximized with the rates of individual processes inversely proportional to the characteristic exponential speed, (2) a series of Gaussian distributions where the entropy is maximized with the rates of individual processes inversely proportional to temperature and the density of individual Gaussian distributions proportional to temperature, and (3) a series of different diffusively accelerated energetic particle spectra with individual spectra derived from observations (1997-2002) of a multiplicity of different shocks. Thus, we develop a proof-of-concept for the superposition of stochastic processes that give rise to power-law distribution functions.