1986-02-04
M NRL Memorandum Report 5719 An Examination of Models of Relaxation in Complex Systems 1. Continuous Time Random Walk ( CTRW ) Models K. L. NGAI, R. W...Examination of Models of Relaxation in Complex Systems I. Continuous Time Random Walk ( CTRW ) Models E. PSRSONAL AUTHOR(S) Ntgi, K.L., Rendell. R.W...necessary and idenrify by block number) Models of relaxation in complex systemL based on the continuous time random walk ( CTRW ) formalism are examined on
On the relationship between multiple porosity models and continuous time random walk
Nordbotten, Jan Martin; Vasilyev, Leonid
2010-01-01
We derive a multiple porosity model based on the continuous time random walk model (CTRW). In particular, we show how the parameters of the multiple porosity models relate to the transition probability function which is at the heart of the CTRW formulation. A simple example is included to illustrate the results.
Chemical Continuous Time Random Walks
Aquino, Tomás; Dentz, Marco
2017-12-01
Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The interreaction times are exponentially distributed under the assumption that the system is well mixed. We introduce an arbitrary interreaction time distribution, which may account for the impact of incomplete mixing on chemical reactions, and in general stochastic reaction delay, which may represent the impact of extrinsic noise. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical master equation. This leads naturally to a generalization of the Gillespie algorithm. Based on this formalism, we determine the modified chemical rate laws for different interreaction time distributions. This framework traces Michaelis-Menten-type kinetics back to finite-mean delay times, and predicts time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local nonequilibrium.
Modelling large-particle diffusion in porous media as anisotropic continuous-time random walk
Amitai, Shahar; Blumenfeld, Raphael
We test the fidelity of modelling diffusion of finite-size particles in porous media by continuous-time random walk (CTRW), where the step-size and waiting-time distributions of the former, Pl and Pt, are used as input to the latter. As the particle size is increased, the diffusion undergoes a transition from normal to anomalous. We find that, based only on Pl and Pt, CTRW does not predict correctly this transition. We show that the discrepancy is due to the change in effective connectivity (topology) of the porous media with increasing particle size. We propose a method to capture this within the CTRW model by adding anisotropy. This adjustment yields good agreement with the simulated diffusion process, making it possible to use CTRW, with all its advantages, to model diffusion of any finite size particle in confined geometries.
Solvable continuous-time random walk model of the motion of tracer particles through porous media
Fouxon, Itzhak; Holzner, Markus
2016-08-01
We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015), 10.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ , length l , and velocity v . We solve our model with independent l and v . The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α . Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α , ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ . Universality of tracer diffusion in the porous medium is considered.
Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco
2017-04-01
Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is
A lattice-model representation of continuous-time random walks
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail: daniel.campos@uab.es, E-mail: vicenc.mendez@uab.es
2008-02-29
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.
Natural Organic Matter Transport Modeling with a Continuous Time Random Walk Approach.
McInnis, Daniel P; Bolster, Diogo; Maurice, Patricia A
2014-02-01
In transport experiments through columns packed with naturally Fe/Al oxide-coated quartz sand, breakthrough curves (BTCs) of natural organic matter (NOM) displayed strong and persistent power law tailing that could not be described by the classical advection-dispersion equation. Tailing was not observed in BTCs for a nonreactive tracer (sulforhodamine B); therefore, the anomalous transport is attributed to diverse adsorptive behavior of the polydisperse NOM sample rather than to physical heterogeneity of the porous medium. NOM BTC tailing became more pronounced with decreases in pH and increases in ionic strength, conditions previously shown to be associated with enhanced preferential adsorption of intermediate to high molecular weight NOM components. Drawing from previous work on anomalous solute transport, we develop an approach to model NOM transport within the framework of a continuous time random walk (CTRW) and show that under all conditions examined, the CTRW model is able to capture tailing of NOM BTCs by accounting for differences in transport rates of NOM fractions through a distribution of effective retardation factors. These results demonstrate the importance of considering effects of adsorptive fractionation on NOM mobility, and illustrate the ability of the CTRW model to describe transport of a multicomponent solute.
Uncoupled continuous-time random walk model: Analytical and numerical solutions
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Continuous time random walk model better describes the tailing of atrazine transport in soil.
Deng, Jiancai; Jiang, Xin; Zhang, Xiaoxian; Hu, Weiping; Crawford, John W
2008-05-01
Contaminant transport in soils is complicated and involves some physical and chemical nonequilibrium processes. In this research, the soil column displacement experiments of Cl(-) and atrazine under different flow velocities were carried out. The data sets of Cl(-) transport in sandy loam fitted to the convection dispersion equation (CDE) and the two-region model (TRM) indicated that the effects of physical nonequilibrium process produced by immobile water on the breakthrough curves (BTCs) of Cl(-) and atrazine transport through the repacking soil columns were negligible. The two-site model (TSM) and the continuous time random walk (CTRW) were also used to fit atrazine transport behavior at the flow rate of 19.86 cm h(-1). The CTRW convincingly captured the full evolution of atrazine BTC in the soil column, especially for the part of long tailing. However, the TSM failed to characterize the tailing of atrazine BTC in the soil column. The calculated fraction of equilibrium sorption sites, F, ranging from 0.78 to 0.80 for all flow rates suggested the contribution of nonequilibrium sorption sites to the asymmetry of atrazine BTCs. Furthermore, the data sets for the flow rates of 6.68 cm h(-1) and 32.81 cm h(-1) were predicted by the TSM and the CTRW. As to the flow rate of 6.68 cm h(-1), the CTRW predicted the entire BTC of atrazine transport better than the TSM did. For the flow rate of 32.81 cm h(-1), the CTRW characterized the late part of the tail better, while the TSM failed to predict the tailings of atrazine BTC.
A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management
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Hui-qiang Ma
2015-01-01
Full Text Available We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes. By using the theories of stochastic linear-quadratic (LQ optimal control and backward stochastic differential equations (BSDEs, we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs. We find that the efficient frontier is still a parabola in a market with random parameters. Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem. However, in an incomplete market with random parameters, the liability can not be fully hedged.
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Oliveira, R.; Bijeljic, B.; Blunt, M. J.; Colbourne, A.; Sederman, A. J.; Mantle, M. D.; Gladden, L. F.
2017-12-01
Mixing and reactive processes have a large impact on the viability of enhanced oil and gas recovery projects that involve acid stimulation and CO2 injection. To achieve a successful design of the injection schemes an accurate understanding of the interplay between pore structure, flow and reactive transport is necessary. Dependent on transport and reactive conditions, this complex coupling can also be dependent on initial rock heterogeneity across a variety of scales. To address these issues, we devise a new method to study transport and reactive flow in porous media at multiple scales. The transport model is based on an efficient Particle Tracking Method based on Continuous Time Random Walks (CTRW-PTM) on a lattice. Transport is modelled using an algorithm described in Rhodes and Blunt (2006) and Srinivasan et al. (2010); this model is expanded to enable for reactive flow predictions in subsurface rock undergoing a first-order fluid/solid chemical reaction. The reaction-induced alteration in fluid/solid interface is accommodated in the model through changes in porosity and flow field, leading to time dependent transport characteristics in the form of transit time distributions which account for rock heterogeneity change. This also enables the study of concentration profiles at the scale of interest. Firstly, we validate transport model by comparing the probability of molecular displacement (propagators) measured by Nuclear Magnetic Resonance (NMR) with our modelled predictions for concentration profiles. The experimental propagators for three different porous media of increasing complexity, a beadpack, a Bentheimer sandstone and a Portland carbonate, show a good agreement with the model. Next, we capture the time evolution of the propagators distribution in a reactive flow experiment, where hydrochloric acid is injected into a limestone rock. We analyse the time-evolving non-Fickian signatures for the transport during reactive flow and observe an increase in
Random Graphs Associated to Some Discrete and Continuous Time Preferential Attachment Models
Pachon, Angelica; Polito, Federico; Sacerdote, Laura
2016-03-01
We give a common description of Simon, Barabási-Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barabási-Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter α ) goes to infinity, a portion of them behave as a Yule model with parameters (λ ,β ) = (1-α ,1), and through this relation we explain why asymptotic properties of a random vertex in Simon model, coincide with the asymptotic properties of a random genus in Yule model. As a by-product of our analysis, we prove the explicit expression of the in-degree distribution for the II-PA model, given without proof in Newman (Contemp Phys 46:323-351, 2005). References to traditional and recent applications of the these models are also discussed.
Heterogeneous continuous-time random walks
Grebenkov, Denis S.; Tupikina, Liubov
2018-01-01
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
Olson, Daniel W; Ou, Jia; Tian, Mingwei; Dorfman, Kevin D
2011-02-01
Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Price Formation Modelling by Continuous-Time Random Walk: An Empirical Study
Directory of Open Access Journals (Sweden)
Frédéric Délèze
2015-01-01
Full Text Available Markovian and non-Markovian\tmodels are presented to\tmodel the futures\tmarket price formation.\tWe show that\tthe\twaiting-time\tand\tthe\tsurvival\tprobabilities\thave\ta\tsignificant\timpact\ton\tthe\tprice\tdynamics.\tThis\tstudy tests\tanalytical\tsolutions\tand\tpresent\tnumerical\tresults for the\tprobability\tdensity function\tof the\tcontinuoustime random\twalk\tusing\ttick-by-tick\tquotes\tprices\tfor\tthe\tDAX\t30\tindex\tfutures.
Modeling Continuous-Time Random Processes in Digital Computer Simulations of Physical Systems
1986-08-27
dimensional vector of random variables. All of the information known about X will be embodied in its probability density func- 4 tion ( pdf ) or, if the... pdf is not available, in its proba- bility distribution function.El) For convenience, assume the pdf of X is available and let it be denoted by fK...operation. Therefore, if _(’) - AZ(’) = A-S[x(’)) where A is a constant matrix, then E(L] - E(A7,J - fAA(. VfX (.t)dt - A!( t) f 1(I) dt = AE E(L] (1
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Path probabilities of continuous time random walks
Eule, Stephan; Friedrich, Rudolf
2014-12-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman-Kac formulae.
Liang, Yingjie; Chen, Wen
2018-04-01
The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.
Coupled continuous time-random walks in quenched random environment
Magdziarz, M.; Szczotka, W.
2018-02-01
We introduce a coupled continuous-time random walk with coupling which is characteristic for Lévy walks. Additionally we assume that the walker moves in a quenched random environment, i.e. the site disorder at each lattice point is fixed in time. We analyze the scaling limit of such a random walk. We show that for large times the behaviour of the analyzed process is exactly the same as in the case of uncoupled quenched trap model for Lévy flights.
Parashar, R.; Pickman, L. H.; Reeves, M. D.
2015-12-01
The Continuous Time Random Walk (CTRW) method provides a framework for modeling non-Fickian transport behavior through heterogeneous media by employing probability distributions to generate particle jump lengths and residence times spanning multiple orders of magnitude. In this work, we seek to formulate and parameterize a 2D CTRW directly from attributes of fracture networks with complex geometry. A Discrete Fracture Network (DFN) model is used to produce data on plume evolution over multiple spatial scales by synthetically generating a fracture network based on known fracture characteristics and conducting flow and particle tracking simulations under steady-state boundary conditions and flux-weighted particle migration. DFN Fracture segments, defined as the linear distance between two fracture intersections, are analyzed to define the distribution of jump lengths. The time for particles to migrate along these segments is recorded by the DFN model and is used to define a distribution of waiting times. These distributions provide a basis on which to formulate a CTRW to predict the migration of inert particles on a continuum of scales. The performance of the CTRW in simulating transport at multiple spatial scales is obtained by comparing spatial moments of the DFN plumes with CTRW solutions.
Burnell, Daniel K.; Hansen, Scott K.; Xu, Jie
2017-09-01
Contaminants in groundwater may experience a broad spectrum of velocities and multiple rates of mass transfer between mobile and immobile zones during transport. These conditions may lead to non-Fickian plume evolution which is not well described by the advection-dispersion equation (ADE). Simultaneously, many groundwater contaminants are degraded by processes that may be modeled as first-order decay. It is now known that non-Fickian transport and reaction are intimately coupled, with reaction affecting the transport operator. However, closed-form solutions for these important scenarios have not been published for use in applications. In this paper, we present four new Green's function analytic solutions in the uncoupled, uncorrelated continuous time random walk (CTRW) framework for reactive non-Fickian transport, corresponding to the quartet of conservative tracer solutions presented by Kreft and Zuber (1978) for Fickian transport. These consider pulse injection for both resident and flux concentration combined with detection in both resident and flux concentration. A pair of solutions for resident concentration temporal pulses with detection in both flux and resident concentration is also presented. We also derive the relationship between flux and resident concentration for non-Fickian transport with first-order reaction for this CTRW formulation. An explicit discussion of employment of the new solutions to model transport with arbitrary upgradient boundary conditions as well as mobile-immobile mass transfer is then presented. Using the new solutions, we show that first-order reaction has no effect on the anomalous spatial spreading rate of concentration profiles, but produces breakthrough curves at fixed locations that appear to have been generated by Fickian transport. Under the assumption of a Pareto CTRW transition distribution, we present a variety of numerical simulations including results showing coherence of our analytic solutions and CTRW particle
Comolli, Alessandro; Moussey, Charlie; Dentz, Marco
2016-04-01
Transport processes in groundwater systems are strongly affected by the presence of heterogeneity. The heterogeneity leads to non-Fickian features, that manifest themselves in the heavy-tailed breakthrough curves, as well as in the non-linear growth of the mean squared displacement and in the non-Gaussian plumes of solute particles. The causes of non-Fickian transport can be the heterogeneity in the flow fields and the processes of mass exchange between mobile and immobile phases, such as sorption/desorption reactions and diffusive mass transfer. Here, we present a Continuous Time Random Walk (CTRW) model that describes the transport of solutes in d-dimensional systems by taking into account both heterogeneous advection and mobile-immobile mass transfer. In order to account for these processes in the CTRW, the heterogeneities are mapped onto a distribution of transition times, which can be decomposed into advective transition times and trapping times, the latter being treated as a compound Poisson process. While advective transition times are related to the Eulerian flow velocities and, thus, to the conductivity distribution, trapping times depend on the sorption/desorption time scale, in case of reactive problems, or on the distribution of diffusion times in the immobile zones. Since the trapping time scale is typically much larger than the advective time scale, we observe the existence of two temporal regimes. The pre-asymptotic regime is defined by a characteristic time scale at which the properties of transport are fully determined by the heterogeneity of the advective field. On the other hand, in the asymptotic regime both the heterogeneity and the mass exchange processes play a role in conditioning the behaviour of transport. We consider different scenarios to discuss the relative importance of the advective heterogeneity and the mass transfer for the occurrence of non-Fickian transport. For each case we calculate analytically the scalings of the breakthrough
Application of continuous-time random walk to statistical arbitrage
Directory of Open Access Journals (Sweden)
Sergey Osmekhin
2015-01-01
Full Text Available An analytical statistical arbitrage strategy is proposed, where the distribution of the spread is modelled as a continuous-time random walk. Optimal boundaries, computed as a function of the mean and variance of the firstpassage time ofthe spread,maximises an objective function. The predictability of the trading strategy is analysed and contrasted for two forms of continuous-time random walk processes. We found that the waiting-time distribution has a significant impact on the prediction of the expected profit for intraday trading
Continuous-Time Random Walks at All Times
Kolomeisky, Anatoly B.
2009-01-01
Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach, based on generalized master equations picture, that allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specif...
Continuous Time Random Walks with memory and financial distributions
Montero, Miquel; Masoliver, Jaume
2017-11-01
We study financial distributions from the perspective of Continuous Time Random Walks with memory. We review some of our previous developments and apply them to financial problems. We also present some new models with memory that can be useful in characterizing tendency effects which are inherent in most markets. We also briefly study the effect on return distributions of fractional behaviors in the distribution of pausing times between successive transactions.
Atomic clocks and the continuous-time random-walk
Formichella, Valerio; Camparo, James; Tavella, Patrizia
2017-11-01
Atomic clocks play a fundamental role in many fields, most notably they generate Universal Coordinated Time and are at the heart of all global navigation satellite systems. Notwithstanding their excellent timekeeping performance, their output frequency does vary: it can display deterministic frequency drift; diverse continuous noise processes result in nonstationary clock noise (e.g., random-walk frequency noise, modelled as a Wiener process), and the clock frequency may display sudden changes (i.e., "jumps"). Typically, the clock's frequency instability is evaluated by the Allan or Hadamard variances, whose functional forms can identify the different operative noise processes. Here, we show that the Allan and Hadamard variances of a particular continuous-time random-walk, the compound Poisson process, have the same functional form as for a Wiener process with drift. The compound Poisson process, introduced as a model for observed frequency jumps, is an alternative to the Wiener process for modelling random walk frequency noise. This alternate model fits well the behavior of the rubidium clocks flying on GPS Block-IIR satellites. Further, starting from jump statistics, the model can be improved by considering a more general form of continuous-time random-walk, and this could bring new insights into the physics of atomic clocks.
Continuous-time random walks at all times.
Kolomeisky, Anatoly B
2009-12-21
Continuous-time random walks (CTRW) play an important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on dynamics at long times. We present a new theoretical approach, based on generalized master equations picture, which allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specific calculations are performed for homogeneous, periodic models and for CTRW with irreversible detachments. The approach to stationary states for CTRW is analyzed. Our results are also used to analyze generalized fluctuations theorem.
Energy Technology Data Exchange (ETDEWEB)
Anwar, S.; Cortis, A.; Sukop, M.
2008-10-20
Lattice Boltzmann models simulate solute transport in porous media traversed by conduits. Resulting solute breakthrough curves are fitted with Continuous Time Random Walk models. Porous media are simulated by damping flow inertia and, when the damping is large enough, a Darcy's Law solution instead of the Navier-Stokes solution normally provided by the lattice Boltzmann model is obtained. Anisotropic dispersion is incorporated using a direction-dependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard Advection-Dispersion Equation (ADE) including eddy mixing in conduits. The ADE fails to adequately fit any of these breakthrough curves.
Clustered continuous-time random walks: diffusion and relaxation consequences.
Weron, Karina; Stanislavsky, Aleksander; Jurlewicz, Agnieszka; Meerschaert, Mark M; Scheffler, Hans-Peter
2012-06-08
We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.
International Nuclear Information System (INIS)
Marsan, David; Bean, Christopher J.
2004-01-01
Modeling of earthquake sequences using an epidemic-type aftershock sequence model by Helmstetter and Sornette [Phys. Rev. E 66, 061104 (2002)] has led these authors to conclude that previous analyses of apparent earthquake diffusions were flawed. We show here that diffusion analyses based on spatiotemporal correlation measures for earthquake populations are an appropriate method for capturing the space-time coupling present in earthquake triggering processes
Correlated continuous time random walk and option pricing
Lv, Longjin; Xiao, Jianbin; Fan, Liangzhong; Ren, Fuyao
2016-04-01
In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black-Scholes model, we find the price obtained in this paper is higher than that obtained from the Black-Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.
Continuous time random walks for the evolution of Lagrangian velocities
Dentz, Marco; Kang, Peter K.; Comolli, Alessandro; Le Borgne, Tanguy; Lester, Daniel R.
2016-11-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes the persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model the persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space-continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have nonstationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and nonstationary conditions. We provide explicit expressions for the Lagrangian velocity statistics and determine the behaviors of the mean particle velocity, velocity covariance, and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions that are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.
Subordinated diffusion and continuous time random walk asymptotics.
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2010-12-01
Anomalous transport is usually described either by models of continuous time random walks (CTRWs) or, otherwise, by fractional Fokker-Planck equations (FFPEs). The asymptotic relation between properly scaled CTRW and fractional diffusion process has been worked out via various approaches widely discussed in literature. Here, we focus on a correspondence between CTRWs and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes. One of them is the Monte Carlo simulation of uncoupled CTRW with a Lévy α-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times. The other is based on a discretized form of a subordinated Langevin equation in which the physical time defined via the number of subsequent steps of motion is itself a random variable. Both approaches are tested for their numerical performance and verified with known analytical solutions for the Green function of a space-time fractional diffusion equation. The comparison demonstrates a trade off between precision of constructed solutions and computational costs. The method based on the subordinated Langevin equation leads to a higher accuracy of results, while the CTRW framework with a Mittag-Leffler distribution of waiting times provides efficiently an approximate fundamental solution to the FFPE and converges to the probability density function of the subordinated process in a long-time limit. © 2010 American Institute of Physics.
Anomalous transport in turbulent plasmas and continuous time random walks
Energy Technology Data Exchange (ETDEWEB)
Balescu, R. [Association Euratom-Etat Belge pour la Fusion, Physique Statistique et Plasmas, Universite Libre de Bruxelles, Campus Plaine, Code Postal 231, Boulevard du Triomphe, 1050 Bruxelles (Belgium)
1995-05-01
The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW`s) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW`s is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem: transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to {ital t}{sup 1/2} is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW.
Karaman, M Muge; Sui, Yi; Wang, He; Magin, Richard L; Li, Yuhua; Zhou, Xiaohong Joe
2016-10-01
To demonstrate that a continuous-time random-walk (CTRW) diffusion model can improve diagnostic accuracy of differentiating low- and high-grade pediatric brain tumors. Fifty-four children with histopathologically confirmed brain tumors underwent diffusion MRI scans at 3Twith 12 b-values (0-4000 s/mm(2) ). The diffusion imageswere fit to a simplified CTRW model to extract anomalous diffusion coefficient, Dm , and temporal and spatial heterogeneity parameters, α and β, respectively. Using histopathology results as reference, a k-means clustering algorithm and a receiver operating characteristic (ROC) analysis were employed to determine the sensitivity, specificity, and diagnostic accuracy of the CTRW parameters in differentiating tumor grades. Significant differences between the low- and high-grade tumors were observed in the CTRW parameters (p-valuesCTRW parameters produced higher diagnostic accuracy (85% vs. 75%) and specificity (83% vs. 54%) than the apparent diffusion coefficient (ADC) from a mono-exponential model. The ROC analysis revealed that any combination of the CTRW parameters gave a larger area under the curve (0.90-0.96) than using ADC (0.80). With its sensitivity to intravoxel heterogeneity, the simplified CTRW model is useful for non-invasive grading of pediatric brain tumors, particularly when surgical biopsy is not feasible. Magn Reson Med 76:1149-1157, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
Non-linear continuous time random walk models★
Stage, Helena; Fedotov, Sergei
2017-11-01
A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional equation either for the probability density function of the walker at a certain position and time, or the mean number of walkers. The question arises how one can extend this equation to the non-linear case, where the random walkers interact. The aim of this work is to take into account this interaction under a mean-field approximation where the statistical properties of the random walker depend on the mean number of walkers. The implementation of these non-linear effects within the CTRW integral equations or fractional equations poses difficulties, leading to the alternative methodology we present in this work. We are concerned with non-linear effects which may either inhibit anomalous effects or induce them where they otherwise would not arise. Inhibition of these effects corresponds to a decrease in the waiting times of the random walkers, be this due to overcrowding, competition between walkers or an inherent carrying capacity of the system. Conversely, induced anomalous effects present longer waiting times and are consistent with symbiotic, collaborative or social walkers, or indirect pinpointing of favourable regions by their attractiveness. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Stochastic calculus for uncoupled continuous-time random walks.
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L
2009-06-01
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.
Dynamical continuous time random Lévy flights
Liu, Jian; Chen, Xiaosong
2016-03-01
The Lévy flights' diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton's Second Law while the nonlinear friction f(v) = - γ0v - γ2v3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index μ = 2 case, it is still Brownian motion.
Continuous time random walk in homogeneous porous media.
Jiang, Jianguo; Wu, Jichun
2013-12-01
Continuous time random walk (CTRW) has been successfully applied in the description of anomalous transport in porous media in recent years. We simulate solute transport in randomly packed spheres with the same diameter and use CTRW to analyze the simulated results. From analysis, we find that there exists weak anomalous transport in the approximately homogeneous porous media. The anomaly becomes more apparent with the increase of Pe. This conclusion consists with previous simulations in two-dimensional homogeneous media and experimental data. We also calculate the trapping probabilities of solute particles in stagnant regions, which could give a physically based explanation for this non-Gaussian behavior. © 2013.
A stochastic surplus production model in continuous time
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte
2017-01-01
surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous-time state......Surplus production modelling has a long history as a method for managing data-limited fish stocks. Recent advancements have cast surplus production models as state-space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic...... and improve estimation of reference points relative to discrete-time analysis of aggregated annual data. Finally, subannual data from five North Sea stocks are analysed with particular focus on using residual analysis to diagnose model insufficiencies and identify necessary model extensions such as robust...
Transport behavior of coupled continuous-time random walks.
Dentz, Marco; Scher, Harvey; Holder, Devora; Berkowitz, Brian
2008-10-01
The origin of anomalous or non-Fickian transport in disordered media is the broad spectrum of transition rates intrinsic to these systems. A system that contains within it heterogeneities over multiple length scales is geological formations. The continuous time random walk (CTRW) framework, which has been demonstrated to be an effective means to model non-Fickian transport features in these systems and to have predictive capacities, has at its core this full spectrum represented as a joint probability density psi(s,t) of random space time displacements (s,t) . Transport in a random fracture network (RFN) has been calculated with a coupled psi(s,t) and has subsequently been shown to be approximated well by a decoupled form psi(s,t)=F(s)psi(t) . The latter form has been used extensively to model non-Fickian transport in conjunction with a velocity distribution Phi(xi),xi identical with 1v, where v is the velocity magnitude. The power-law behavior of psi(t) proportional to (-1-beta), which determines non-Fickian transport, derives from the large xi dependence of Phi(xi) . In this study we use numerical CTRW simulations to explore the expanded transport phenomena derived from a coupled psi(s,t) . Specifically, we introduce the features of a power-law dependence in the s distribution with different Phi(xi) distributions (including a constant v) coupled by t=s(xi) . Unlike Lévy flights in this coupled scenario the spatial moments of the plumes are well defined. The shapes of the plumes depend on the entire Phi(xi) distribution, i.e., both small and large xi dependence; there is a competition between long displacements (which depend on the small xi dependence) and large time events (which depend on a power law for large xi). These features give rise to an enhanced range of transport behavior with a broader scope of applications, e.g., to correlated migrations in a RFN and in heterogeneous permeability fields. The approximation to the decoupled case is investigated as a
Continuous-time random walks that alter environmental transport properties.
Angstmann, C; Henry, B I
2011-12-01
We consider continuous-time random walks (CTRWs) in which the walkers have a finite probability to alter the waiting-time and/or step-length transport properties of their environment, resulting in possibly transient anomalous diffusion. We refer to these CTRWs as transmogrifying continuous-time random walks (TCTRWs) to emphasize that they change the form of the transport properties of their environment, and in a possibly strange way. The particular case in which the CTRW waiting-time density has a finite probability to be permanently altered at a given site, following a visitation by a walker, is considered in detail. Master equations for the probability density function of transmogrifying random walkers are derived, and results are compared with Monte Carlo simulations. An interesting finding is that TCTRWs can generate transient subdiffusion or transient superdiffusion without invoking truncated or tempered power law densities for either the waiting times or the step lengths. The transient subdiffusion or transient superdiffusion arises in TCTRWs with Gaussian step-length densities and exponential waiting-time densities when the altered average waiting time is greater than or less than, respectively, the original average waiting time.
Computer Aided Continuous Time Stochastic Process Modelling
DEFF Research Database (Denmark)
Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay
2001-01-01
A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...
Continuous Time Random Walk (CTRW) put to work
Scher, Harvey
2017-12-01
A personal history of the first applications of CTRW to the physics of transport and diffusion in disordered media is presented. The sequence of steps leading to the introduction of novel ψ(t), the probability density of particle-transfer times, without moments is briefly outlined. The key concept that emerged from those early applications is anomalous or non-Fickian transport. The latter involved spatial moments of the particle propagator with completely different time behavior, e.g., the mean ∝ tβ, 0 /σ = constant. With these results many puzzling experimental data were explained. The data ranged from electronic dynamics of amorphous films to chemical migration and interaction in the subsurface of the Earth. These were not anticipated results but a consequence of the CTRW with these special ψ(t). Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Discounting Models for Outcomes over Continuous Time
DEFF Research Database (Denmark)
Harvey, Charles M.; Østerdal, Lars Peter
Events that occur over a period of time can be described either as sequences of outcomes at discrete times or as functions of outcomes in an interval of time. This paper presents discounting models for events of the latter type. Conditions on preferences are shown to be satisfied if and only if t...... if the preferences are represented by a function that is an integral of a discounting function times a scale defined on outcomes at instants of time....
A continuous-time control model on production planning network ...
African Journals Online (AJOL)
A continuous-time control model on production planning network. DEA Omorogbe, MIU Okunsebor. Abstract. In this paper, we give a slightly detailed review of Graves and Hollywood model on constant inventory tactical planning model for a job shop. The limitations of this model are pointed out and a continuous time ...
Continuous-time random walk with correlated waiting times.
Chechkin, Aleksei V; Hofmann, Michael; Sokolov, Igor M
2009-09-01
Based on the Langevin description of the continuous time random walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly decaying persistent power-law correlations between the waiting times as two generic examples and obtain the corresponding mean squared displacements as functions of time. In the case of exponential-type correlations the (sub)diffusion at short times is slower than in the absence of correlations. At long times the behavior of the mean squared displacement is the same as in uncorrelated CTRW. For power-law correlations we find subdiffusion characterized by the same exponent at all times, which appears to be smaller than the one in uncorrelated CTRW. Interestingly, in the limiting case of an extremely long power-law correlations, the (sub)diffusion exponent does not tend to zero, but is bounded from below by the subdiffusion exponent corresponding to a short-time behavior in the case of exponential correlations.
Integral-Value Models for Outcomes over Continuous Time
DEFF Research Database (Denmark)
Harvey, Charles M.; Østerdal, Lars Peter
Models of preferences between outcomes over continuous time are important for individual, corporate, and social decision making, e.g., medical treatment, infrastructure development, and environmental regulation. This paper presents a foundation for such models. It shows that conditions on prefere...... on preferences between real- or vector-valued outcomes over continuous time are satisfied if and only if the preferences are represented by a value function having an integral form......Models of preferences between outcomes over continuous time are important for individual, corporate, and social decision making, e.g., medical treatment, infrastructure development, and environmental regulation. This paper presents a foundation for such models. It shows that conditions...
Continuous Time Structural Equation Modeling with R Package ctsem
Directory of Open Access Journals (Sweden)
Charles C. Driver
2017-04-01
Full Text Available We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1 and time series (N = 1 data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.
Continuous time modeling of panel data by means of SEM
Oud, J.H.L.; Delsing, M.J.M.H.; Montfort, C.A.G.M.; Oud, J.H.L.; Satorra, A.
2010-01-01
After a brief history of continuous time modeling and its implementation in panel analysis by means of structural equation modeling (SEM), the problems of discrete time modeling are discussed in detail. This is done by means of the popular cross-lagged panel design. Next, the exact discrete model
Continuous time structural equation modeling with R package ctsem
Driver, C.C.; Oud, J.H.L.; Völkle, M.C.
2017-01-01
We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1) and time series (N = 1) data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models) in the social and behavioural sciences are discrete time models. An
All-time dynamics of continuous-time random walks on complex networks
Teimouri, Hamid; Kolomeisky, Anatoly B.
2012-01-01
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for...
Continuous-Time Random Walk with multi-step memory: an application to market dynamics
Gubiec, Tomasz; Kutner, Ryszard
2017-11-01
An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Model checking conditional CSL for continuous-time Markov chains
DEFF Research Database (Denmark)
Gao, Yang; Xu, Ming; Zhan, Naijun
2013-01-01
In this paper, we consider the model-checking problem of continuous-time Markov chains (CTMCs) with respect to conditional logic. To the end, we extend Continuous Stochastic Logic introduced in Aziz et al. (2000) [1] to Conditional Continuous Stochastic Logic (CCSL) by introducing a conditional p...
Modeling electricity loads in California: a continuous-time approach
Weron, R.; Kozłowska, B.; Nowicka-Zagrajek, J.
2001-10-01
In this paper we address the issue of modeling electricity loads and prices with diffusion processes. More specifically, we study models which belong to the class of generalized Ornstein-Uhlenbeck processes. After comparing properties of simulated paths with those of deseasonalized data from the California power market and performing out-of-sample forecasts we conclude that, despite certain advantages, the analyzed continuous-time processes are not adequate models of electricity load and price dynamics.
A Stochastic Continuous Time Model for Microgrid Energy Management
Heymann, Benjamin; Frédéric Bonnans, J; Silva, Francisco; Jimenez, Guillermo
2016-01-01
International audience; We propose a novel stochastic control formulation for the microgrid energy management problem and extend previous works on continuous time rolling horizon strategy to uncertain demand. We modelize the demand dynamics with a stochastic differential equation. We decompose this dynamics into three terms: an average drift, a time-dependent mean-reversion term and a Brownian noise. We use BOCOPHJB for the numerical simulations. This optimal control toolbox implements a semi...
Estimation of Continuous Time Models in Economics: an Overview
Clifford R. Wymer
2009-01-01
The dynamics of economic behaviour is often developed in theory as a continuous time system. Rigorous estimation and testing of such systems, and the analysis of some aspects of their properties, is of particular importance in distinguishing between competing hypotheses and the resulting models. The consequences for the international economy during the past eighteen months of failures in the financial sector, and particularly the banking sector, make it essential that the dynamics of financia...
Scaling Properties of Field-Induced Superdiffusion in Continuous Time Random Walks
Burioni, R.; Gradenigo, G.; Sarracino, A.; Vezzani, A.; Vulpiani, A.
2014-10-01
We consider a broad class of Continuous Time Random Walks (CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Lévy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
A Coupled Continuous Time Random Walk Approach For Transport in Highly Heterogeneous Porous Media
Dentz, M.; Scher, H.; Holder, D.; Berkowitz, B.
2008-12-01
We present a coupled continuous time random walk (CTRW) approach as an effective model for transport in highly heterogeneous media. This approach models solute transport by a coupled system of Langevin equations for random movements in the spatial and temporal domains. Motivated by transport in random fracture networks, here we consider a model that is characterized by given distributions of transition lengths (fracture length) and velocities. Thus, transition lengths and times are intrinsically related. Fracture length and velocity define the transition time. A maximum transition time is given by the diffusion time over the fracture length. Diffusion into the matrix can be modeled explicitly by a distribution of retention times. We study spatial distributions, and effective apparent transport coefficients as well as first arrival time distributions for a series of scenarios. The scaling behavior of such a fully coupled walk is different from the one observed in uncoupled walks. We investigate the competition between long jumps and long waiting times in this fully coupled continuous time random walk and determine scaling laws for the spatial moments of concentration.
All-time dynamics of continuous-time random walks on complex networks.
Teimouri, Hamid; Kolomeisky, Anatoly B
2013-02-28
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social, and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.
A Continuous-Time Model for Valuing Foreign Exchange Options
Directory of Open Access Journals (Sweden)
James J. Kung
2013-01-01
Full Text Available This paper makes use of stochastic calculus to develop a continuous-time model for valuing European options on foreign exchange (FX when both domestic and foreign spot rates follow a generalized Wiener process. Using the dollar/euro exchange rate as input for parameter estimation and employing our FX option model as a yardstick, we find that the traditional Garman-Kohlhagen FX option model, which assumes constant spot rates, values incorrectly calls and puts for different values of the ratio of exchange rate to exercise price. Specifically, it undervalues calls when the ratio is between 0.70 and 1.08, and it overvalues calls when the ratio is between 1.18 and 1.30, whereas it overvalues puts when the ratio is between 0.70 and 0.82, and it undervalues puts when the ratio is between 0.86 and 1.30.
Origins and applications of the Montroll-Weiss continuous time random walk
Shlesinger, Michael F.
2017-05-01
The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite. Contribution to the Topical Issue: "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
A continuous-time neural model for sequential action.
Kachergis, George; Wyatte, Dean; O'Reilly, Randall C; de Kleijn, Roy; Hommel, Bernhard
2014-11-05
Action selection, planning and execution are continuous processes that evolve over time, responding to perceptual feedback as well as evolving top-down constraints. Existing models of routine sequential action (e.g. coffee- or pancake-making) generally fall into one of two classes: hierarchical models that include hand-built task representations, or heterarchical models that must learn to represent hierarchy via temporal context, but thus far lack goal-orientedness. We present a biologically motivated model of the latter class that, because it is situated in the Leabra neural architecture, affords an opportunity to include both unsupervised and goal-directed learning mechanisms. Moreover, we embed this neurocomputational model in the theoretical framework of the theory of event coding (TEC), which posits that actions and perceptions share a common representation with bidirectional associations between the two. Thus, in this view, not only does perception select actions (along with task context), but actions are also used to generate perceptions (i.e. intended effects). We propose a neural model that implements TEC to carry out sequential action control in hierarchically structured tasks such as coffee-making. Unlike traditional feedforward discrete-time neural network models, which use static percepts to generate static outputs, our biological model accepts continuous-time inputs and likewise generates non-stationary outputs, making short-timescale dynamic predictions. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Continuous Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations
Pellegrini, Clément
2014-02-01
A new type of quantum random walks, called Open Quantum Random Walks, has been developed and studied in Attal et al. (Open quantum random walks, preprint) and (Central limit theorems for open quantum random walks, preprint). In this article we present a natural continuous time extension of these Open Quantum Random Walks. This continuous time version is obtained by taking a continuous time limit of the discrete time Open Quantum Random Walks. This approximation procedure is based on some adaptation of Repeated Quantum Interactions Theory (Attal and Pautrat in Annales Henri Poincaré Physique Théorique 7:59-104, 2006) coupled with the use of correlated projectors (Breuer in Phys Rev A 75:022103, 2007). The limit evolutions obtained this way give rise to a particular type of quantum master equations. These equations appeared originally in the non-Markovian generalization of the Lindblad theory (Breuer in Phys Rev A 75:022103, 2007). We also investigate the continuous time limits of the quantum trajectories associated with Open Quantum Random Walks. We show that the limit evolutions in this context are described by jump stochastic differential equations. Finally we present a physical example which can be described in terms of Open Quantum Random Walks and their associated continuous time limits.
Path statistics, memory, and coarse-graining of continuous-time random walks on networks
Manhart, Michael; Kion-Crosby, Willow; Morozov, Alexandre V.
2015-12-01
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.
Kolokoltsov, Vassili N.
2007-01-01
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.
Continuous Time Random Walks and the Causes of Non-Fickian Transport in Heterogeneous Media
Dentz, M.; Le Borgne, T.; Kang, P. K.
2015-12-01
Solute transport in heterogeneous porous media is in generalnon-Fickian, this means it shows behaviors that do not conform toadvection-dispersion models characterized by constant equivalent transportparameters. The causes for such behaviors are manifold, while their quantitative relation to large scale non-Fickian transport is often not known. We address the questions of (i) how different heterogeneity and microscale transport mechanisms manifest in large scale transport behavior, (ii) which are their impacts on anomalous solute dispersion, and (iii) how they can be quantified in terms of large scale dynamics. We focus here on the roles of medium and flow heterogeneity, mass transfer between mobile and immobile zones, as well as spatially variable retardation properties on large scale anomalous transport. Starting from the different microscale heterogeneity and transport dynamics, we use a stochastic modeling approach to coarse grain and average particle transport in a Lagrangian modeling framework, and quantify the large scale particle dynamics in terms of continuous time random walks (CTRW). The large scale particle movements are characterized in terms of a random space increment, which can be related to the heterogeneity structure and geometry, and a random time increment, which is quantified in terms of the heterogeneity distribution. We present the CTRW models resulting from the differentheterogeneity scenarios and analyze their transport signatures in terms of solute dispersion and breakthrough curves.
Continuous time random walks for non-local radial solute transport
Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy
2015-08-01
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer
Backward jump continuous-time random walk: An application to market trading
Gubiec, Tomasz; Kutner, Ryszard
2010-10-01
The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.
Occupation times and ergodicity breaking in biased continuous time random walks
Energy Technology Data Exchange (ETDEWEB)
Bel, Golan; Barkai, Eli [Physics Department, Bar-Ilan University, Ramat-Gan 52900 (Israel)
2005-12-14
Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.
Continuous time random walk analysis of solute transport in fractured porous media
Energy Technology Data Exchange (ETDEWEB)
Cortis, Andrea; Cortis, Andrea; Birkholzer, Jens
2008-06-01
The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable interconnected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the 'correct' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains.
Langevin formulation of a subdiffusive continuous-time random walk in physical time
Cairoli, Andrea; Baule, Adrian
2015-07-01
Systems living in complex nonequilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the continuous-time random walk (CTRW). Stochastic trajectories of a CTRW can be described in terms of the subordination of a normal diffusive process by an inverse Lévy-stable process. Here, we propose an equivalent Langevin formulation of a force-free CTRW without subordination. By introducing a different type of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a single Langevin equation in physical time with additive noise. We derive the full multipoint statistics of this noise and compare it with the scaled Brownian motion (SBM), an alternative stochastic model describing subdiffusive dynamics. Interestingly, these two noises are identical up to the second order correlation functions, but different in the higher order statistics. We extend our formalism to general waiting time distributions and force fields and compare our results with those of the SBM. In the presence of external forces, our proposed noise generates a different class of stochastic processes, resembling a CTRW but with forces acting at all times.
Dispersion in porous media, continuous-time random walks, and percolation.
Sahimi, Muhammad
2012-01-01
A promising approach to the modeling of anomalous (non-Gaussian) dispersion in flow through heterogeneous porous media is the continuous-time random walk (CTRW) method. In such a formula on the waiting time distribution ψ(t) is usually assumed to be given by ψ(t)∼t-1-α, with α fitted to the experimental data. The exponent α is also related to the power-law growth of the mean-square displacement of the solute with the time t ∼ tζ. Invoking percolation and using a scaling analysis, we relate α to the geometrical exponents of percolation (ν, β, and βB) as well as the exponents μ and e that characterize the power-law behavior of the effective conductivity and permeability of porous media near the percolation threshold. We then explain the cause of the nonuniversality of α in terms of the nonuniversality of μ and e in continuum systems, and in percolation models with long-range correlations, and propose bounds for it. The results are consistent with the experimental data, both at the laboratory and field scales.
D Fluid Deformation and Mixing via a Continuous Time Random Walk
Lester, D. R.; Dentz, M.; Le Borgne, T.; de Barros, F.
2015-12-01
Fluid stretching and deformation as quantified by the fluid deformation gradient tensor directly controls mixing of diffusive species in both chaotic and non-chaotic, 2D and 3D flows at the pore- and Darcy scales. Indeed, recent advances [LeBorgne et. al. PRL, 110, 204501, 2013] in the prediction of mixing and scalar dissipation require the distribution of fluid deformation rates as quantitative inputs. However, these measures are often difficult to link to medium properties or statistical heterogeneity controls. To advance this problem, we present a novel Continuous Time Random Walk (CTRW) to model stochastic evolution of the 3D fluid deformation tensor in a Protean (streamline) coordinate frame. This approach allows topological constraints imposed by the flow kinematics to be naturally obeyed, and furthermore flow features that generate non-Fickian transport can be clearly elucidated. For simple flows, this framework allows the distribution of deformation rates (and hence mixing) to be expressed in terms of heterogenenity controls, and for more complex flows, this approach clearly identifies what flow features govern anomalous transport and how their statistics can be measured as model inputs.
Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs
International Nuclear Information System (INIS)
Salimi, S.; Jafarizadeh, M. A.
2009-01-01
In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product Cayley graphs (complete cycle, complete K n , charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t → ∞ but for quantum state is not always satisfied. (general)
The continuous time random walk, still trendy: fifty-year history, state of art and outlook
Kutner, Ryszard; Masoliver, Jaume
2017-03-01
In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [ctrw-50-years-on">http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
On properties of continuous-time random walks with non-Poissonian jump-times
Energy Technology Data Exchange (ETDEWEB)
Villarroel, Javier [Facultad de Ciencias, Universidad de Salamanca. Plaza Merced s/n, E-37008 Salamanca (Spain)], E-mail: javier@usal.es; Montero, Miquel [Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)], E-mail: miquel.montero@ub.edu
2009-10-15
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered.
Application of continuous time random walks to transport in porous media
Energy Technology Data Exchange (ETDEWEB)
Margolin, G.; Berkowitz, B.
2000-04-27
The behavior of chemical species as they migrate through heterogeneous porous media is considered. The so-called anomalous transport patterns frequently measured in these materials are quantified in the framework of a continuous time random walk (CTRW) formalism. The physical basis for application of the CTRW is discussed, and new solutions for the first passage time distribution are presented to cover the entire range of transport behaviors. Application of these solutions to analysis of experimental data is also discussed.
Fluid limit of the continuous-time random walk with general Levy jump distribution functions
Energy Technology Data Exchange (ETDEWEB)
Cartea, A. [Birbeck College, University of London; Del-Castillo-Negrete, Diego B [ORNL
2007-01-01
The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x). There are two well-known fluid limits of this model in the uncoupled case. For exponential decaying waiting times and Gaussian jump distribution functions the fluid limit leads to the diffusion equation. On the other hand, for algebraic decaying waiting times psi similar to t(-(1+beta)) and algebraic decaying jump distributions eta similar to x(-(1+alpha)) corresponding to Levy stable processes, the fluid limit leads to the fractional diffusion equation of order alpha in space and order beta in time. However, these are two special cases of a wider class of models. Here we consider the CTRW for the most general Levy stochastic processes in the Levy-Khintchine representation for the jump distribution function and obtain an integrodifferential equation describing the dynamics in the fluid limit. The resulting equation contains as special cases the regular and the fractional diffusion equations. As an application we consider the case of CTRWs with exponentially truncated Levy jump distribution functions. In this case the fluid limit leads to a transport equation with exponentially truncated fractional derivatives which describes the interplay between memory, long jumps, and truncation effects in the intermediate asymptotic regime. The dynamics exhibits a transition from superdiffusion to subdiffusion with the crossover time scaling as tau(c)similar to lambda(-alpha/beta), where 1/lambda is the truncation length scale. The asymptotic behavior of the propagator (Green's function) of the truncated fractional equation exhibits a transition from algebraic decay for t <
A continuous time random walk (CTRW) integro-differential equation with chemical interaction
Ben-Zvi, Rami; Nissan, Alon; Scher, Harvey; Berkowitz, Brian
2018-01-01
A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M ( t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓP A ( s, t) P B ( s, t) is symmetric in the concentrations of A and B (i.e. P A and P B ); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M ( t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.
Energy Technology Data Exchange (ETDEWEB)
Geiger, S.; Cortis, A.; Birkholzer, J.T.
2010-04-01
Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.
Life and Death of Stationary Linear Response in Anomalous Continuous Time Random Walk Dynamics
Igor, Goychuk
2014-10-01
Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description (CTRW) with divergent mean waiting times. The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to systems at thermal equilibrium. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response at thermal equilibrium is absent, in accordance with some recent studies. The absence of such stationary response (or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwise. We show that the absence of stationary response is closely related to the breaking of ergodicity of the corresponding dynamical variable. As an important new result, we derive a generalized Cole-Cole response within ergodic CTRW dynamics with finite waiting time. Moreover, we provide a physically reasonable explanation of the origin and wide presence of 1/f noise in condensed matter for ergodic dynamics close to normal, rather than strongly deviating.
Continuous-time random walk approach to on-off diffusion
Energy Technology Data Exchange (ETDEWEB)
Miyazaki, Syuji; Harada, Tomohiro; Budiyono, Agung [Kyoto Univ., Graduate School of Informatics, Department of Applied Analysis and Complex Dynamical Systems, Kyoto (Japan)
2001-12-01
Statistical properties and scale invariances of on-off diffusion, which is an anomalous transport phenomenon caused by on-off intermittency, are studied on the basis of the continuous-time random walk (CTRW) approach. The anomalous production of heat is also analyzed. Scaling functions of the time evolution of the mean square displacement and the probability density function (PDF) of the position are analytically derived. It is found that there is a characteristic time separating two regimes of time intervals with different scaling laws for the PDF. In the interval that exists at times much smaller than the characteristic time, anomalous subdiffusion appears, which is followed by normal diffusion. In the earlier time interval, aside from the neighborhood of the origin, the PDF takes the form of a power law multiplied by a stretched exponential function, whereas in the later time interval, the PDF becomes a Gaussian. The results are compared with these model simulations. Good agreement between the theory and the simulation is obtained. (author)
Continuous-Time Mean-Variance Portfolio Selection with Random Horizon
International Nuclear Information System (INIS)
Yu, Zhiyong
2013-01-01
This paper examines the continuous-time mean-variance optimal portfolio selection problem with random market parameters and random time horizon. Treating this problem as a linearly constrained stochastic linear-quadratic optimal control problem, I explicitly derive the efficient portfolios and efficient frontier in closed forms based on the solutions of two backward stochastic differential equations. Some related issues such as a minimum variance portfolio and a mutual fund theorem are also addressed. All the results are markedly different from those in the problem with deterministic exit time. A key part of my analysis involves proving the global solvability of a stochastic Riccati equation, which is interesting in its own right
Continuous-Time Mean-Variance Portfolio Selection with Random Horizon
Energy Technology Data Exchange (ETDEWEB)
Yu, Zhiyong, E-mail: yuzhiyong@sdu.edu.cn [Shandong University, School of Mathematics (China)
2013-12-15
This paper examines the continuous-time mean-variance optimal portfolio selection problem with random market parameters and random time horizon. Treating this problem as a linearly constrained stochastic linear-quadratic optimal control problem, I explicitly derive the efficient portfolios and efficient frontier in closed forms based on the solutions of two backward stochastic differential equations. Some related issues such as a minimum variance portfolio and a mutual fund theorem are also addressed. All the results are markedly different from those in the problem with deterministic exit time. A key part of my analysis involves proving the global solvability of a stochastic Riccati equation, which is interesting in its own right.
Parrondo-like behavior in continuous-time random walks with memory.
Montero, Miquel
2011-11-01
The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.
Bisquert, Juan
2003-07-04
We investigate the macroscopic diffusion of carriers in the multiple-trapping (MT) regime, in relation with electron transport in nanoscaled heterogeneous systems, and we describe the differences, as well as the similarities, between MT and the continuous-time random walk (CTRW). Diffusion of free carriers in MT can be expressed as a generalized continuity equation based on fractional time derivatives, while the CTRW model for diffusive transport generalizes the constitutive equation for the carrier flux.
Application of continuous time random walk theory to nonequilibrium transport in soil.
Li, Na; Ren, Li
2009-09-01
Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (upsilon) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (upsilon, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.
Continuous-time random walk and parametric subordination in fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Rudolf [Department of Mathematics and Informatics, Free University of Berlin, Arnimallee 3, D-14195 Berlin (Germany); Mainardi, Francesco [Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna (Italy)]. E-mail: mainardi@bo.infn.it; Vivoli, Alessandro [Department of Physics, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna (Italy)
2007-10-15
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW) is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete operational time. In the continuum limit, we obtain a (generally non-Markovian) diffusion process governed by a space-time fractional diffusion equation. The essential assumption is that the probabilities for waiting times and jump-widths behave asymptotically like powers with negative exponents related to the orders of the fractional derivatives. By what we call parametric subordination, applied to a combination of a Markov process with a positively oriented Levy process, we generate and display sample paths for some special cases.
Multi-point Distribution Function for the Continuous Time Random Walk
Barkai, E.; Sokolov, I. M.
2007-01-01
We derive an explicit expression for the Fourier-Laplace transform of the two-point distribution function $p(x_1,t_1;x_2,t_2)$ of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single point distribution function $p(x_1,t_1)$. The multi-point distribution function has a structure of a convolution of the Montroll-Weiss CTRW and the aging CTRW single point distribution functions. The correlation function $$ for the biased CTRW process is found. T...
Energy Technology Data Exchange (ETDEWEB)
van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT; Calvo, Ivan [CIEMAT, Madrid; Sanchez, Raul [ORNL
2008-01-01
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behavior of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
V-Langevin equations, continuous time random walks and fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Balescu, R. [Association Euratom-Etat Belge, Universite Libre de Bruxelles, CP 231, Campus Plaine ULB, Bd du Triomphe, 1050 Brussels (Belgium)
2007-10-15
The following question is addressed: under what conditions can a strange diffusive process, defined by a semi-dynamical V-Langevin equation or its associated hybrid kinetic equation (HKE), be described by an equivalent purely stochastic process, defined by a continuous time random walk (CTRW) or by a fractional differential equation (FDE)? More specifically, does there exist a class of V-Langevin equations with long-range (algebraic) velocity temporal correlation, that leads to a time-fractional superdiffusive process? The answer is always affirmative in one dimension. It is always negative in two dimensions: any algebraically decaying temporal velocity correlation (with a Gaussian spatial correlation) produces a normal diffusive process. General conditions relating the diffusive nature of the process to the temporal exponent of the Lagrangian velocity correlation (in Corrsin approximation) are derived. It is shown that a bifurcation occurs as the latter parameter is varied. Above that bifurcation value the process is always diffusive.
Energy Technology Data Exchange (ETDEWEB)
Milligen, B Ph van; Calvo, I [Asociacion EURATOM-CIEMAT para Fusion, Avda. Complutense 22, 28040 Madrid (Spain); Sanchez, R [Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)], E-mail: boudewijn.vanmilligen@ciemat.es
2008-05-30
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behaviour of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach
Comolli, Alessandro; Dentz, Marco
2017-09-01
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in
From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets
K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)
2006-01-01
textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with
Transmembrane protein CD93 diffuses by a continuous time random walk.
Goiko, Maria; de Bruyn, John; Heit, Bryan
Molecular motion within the cell membrane is a poorly-defined process. In this study, we characterized the diffusion of the transmembrane protein CD93. By careful analysis of the dependence of the ensemble-averaged mean squared displacement (EA-MSD, r2) on time t and the ensemble-averaged, time-averaged MSD (EA-TAMSD, δ2) on lag time τ and total measurement time T, we showed that the motion of CD93 is well-described by a continuous-time random walk (CTRW). CD93 tracks were acquired using single particle tracking. The tracks were classified as confined or free, and the behavior of the MSD analyzed. EA-MSDs of both populations grew non-linearly with t, indicative of anomalous diffusion. Their EA-TAMSDs were found to depend on both τ and T, indicating non-ergodicity. Free molecules had r2 tα and δ2 (τ /T 1 - α) , with α 0 . 5 , consistent with a CTRW. Mean maximal excursion analysis supported this result. Confined CD93 had r2 t0 and δ2 (τ / T) α , with α 0 . 3 , consistent with a confined CTRW. CTRWs are described by a series of random jumps interspersed with power-law distributed waiting times, and may arise due to the interactions of CD93 with the endocytic machinery. NSERC.
Ageing first passage time density in continuous time random walks and quenched energy landscapes
Krüsemann, Henning; Godec, Aljaž; Metzler, Ralf
2015-07-01
We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function \\psi (t)≃ {t}-1-α (0≤slant α ≤slant 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time ta, the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0\\lt α \\lt 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1\\lt α \\lt 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
Fluctuations around equilibrium laws in ergodic continuous-time random walks.
Schulz, Johannes H P; Barkai, Eli
2015-06-01
We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.
Continuous-time random walk for open systems: fluctuation theorems and counting statistics.
Esposito, Massimiliano; Lindenberg, Katja
2008-05-01
We consider continuous-time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter alpha , which is set to alpha=1 if it decays at least as fast as t{-2} at long times and therefore has a finite first moment. A WTD with alphaCTRW. However, R can be identified as a trajectory entropy change only if the WTDs have alpha=1 and satisfy separability (also called "direction time independence"). For nonseparable WTDs with alpha=1 , R can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with 0
Estimation in continuous-time stochastic| volatility models using nonlinear filters
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
A joint logistic regression and covariate-adjusted continuous-time Markov chain model.
Rubin, Maria Laura; Chan, Wenyaw; Yamal, Jose-Miguel; Robertson, Claudia Sue
2017-12-10
The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross-sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross-sectional response, where the unobserved transition rates of a two-state continuous-time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6-month outcome based on physiological data collected post-injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long-term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, B.; Langner, K. M.; Klösgen-Buchkremer, Beate Maria
2004-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk (CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy...
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, Bozena; Langner, Karol M.; Klösgen, Beate Maria
2005-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk 4CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy...
A continuous-time random-walk approach to the Cole-Davidson dielectric response of dipolar liquids
DEFF Research Database (Denmark)
Szabat, B.; Langner, K. M.; Klösgen-Buchkremer, Beate Maria
2004-01-01
We show how the Cole-Davidson relaxation response, characteristic of alcoholic systems, can be derived within the framework of the continuous-time random walk (CTRW). Using the random-variable formalism, we indicate that the high-frequency power law of dielectric spectra is determined by the heavy......-tailed distribution of quantities that provide the spatio-temporal coupling in the random-walk process. As an illustration, we present the dielectric permittivity spectra of several butanediol isomers....
Abad, E; Yuste, S B; Lindenberg, Katja
2010-03-01
Starting from a continuous-time random-walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integrodifferential equations for the probability density for a particle to be found at point r at time t given that it started its walk from r_{0} at time t=0 . The passage from the CTRW to an integrodifferential equation is well understood when the particles are not evanescent. Depending on the distribution of stepping times and distances, one arrives at standard macroscopic equations that may be "normal" (diffusion) or "anomalous" (subdiffusion and/or superdiffusion). The macroscopic description becomes considerably more complicated and not particularly intuitive if the particles can die during their walk. While such equations have been derived for specific cases, e.g., for location-independent exponential evanescence, we present a more general derivation valid under less stringent constraints than those found in the current literature.
Estimating and Testing Continuous-Time Models in Finance: The Role of Transition Densities
Yacine Aït-Sahalia
2009-01-01
This article surveys recent developments to estimate and test continuous-time models in finance using discrete observations on the underlying asset price or derivative securities' prices. Both parametric and nonparametric methods are described. All these methods share a common focus on the transition density as the central object for inference and testing of the model.
van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F
2013-08-01
Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.
Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.
Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence
2012-01-01
Abstract Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. Background There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real...
Directory of Open Access Journals (Sweden)
Zhi-Ren Tsai
2013-01-01
Full Text Available A tracking problem, time-delay, uncertainty and stability analysis of a predictive control system are considered. The predictive control design is based on the input and output of neural plant model (NPM, and a recursive fuzzy predictive tracker has scaling factors which limit the value zone of measured data and cause the tuned parameters to converge to obtain a robust control performance. To improve the further control performance, the proposed random-local-optimization design (RLO for a model/controller uses offline initialization to obtain a near global optimal model/controller. Other issues are the considerations of modeling error, input-delay, sampling distortion, cost, greater flexibility, and highly reliable digital products of the model-based controller for the continuous-time (CT nonlinear system. They are solved by a recommended two-stage control design with the first-stage (offline RLO and second-stage (online adaptive steps. A theorizing method is then put forward to replace the sensitivity calculation, which reduces the calculation of Jacobin matrices of the back-propagation (BP method. Finally, the feedforward input of reference signals helps the digital fuzzy controller improve the control performance, and the technique works to control the CT systems precisely.
International Nuclear Information System (INIS)
Schulz, Johannes H P; Chechkin, Aleksei V; Metzler, Ralf
2013-01-01
Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Lévy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties. (paper)
A comparison of numerical methods for the solution of continuous-time DSGE models
DEFF Research Database (Denmark)
Parra-Alvarez, Juan Carlos
This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions...... parameters of the model and suggest the use of projection methods when a high degree of accuracy is required....
A continuous time model of the bandwagon effect in collective action
Arieh Gavious; Shlomo Mizrahi
2001-01-01
The paper offers a complex and systematic model of the bandwagon effect in collective action using continuous time equations. The model treats the bandwagon effect as a process influenced by ratio between the mobilization efforts of social activists and the resources invested by the government to counteract this activity. The complex modeling approach makes it possible to identify the conditions for specific types of the bandwagon effect, and determines the scope of that effect. Relying on ce...
Continuous-time quantum walks: Models for coherent transport on complex networks
Energy Technology Data Exchange (ETDEWEB)
Muelken, Oliver, E-mail: muelken@physik.uni-freiburg.de; Blumen, Alexander
2011-05-15
This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the theoretical ideas behind CTQW and of its relation to classical continuous-time random walks (CTRW), implications for the efficiency of the transport are presented. This paper gives an overview of different types of networks on which CTQW have been studied so far. Extensions of CTQW to systems with long-range interactions and with static disorder are also discussed. Systems with traps, i.e., systems in which a walker's probability to remain inside the system is not conserved, are presented. Relations to similar approaches to the transport are studied. This paper closes with an outlook on possible future directions.
Dentz, M.; Kang, P. K.; Comolli, A.; Le Borgne, T.; Lester, D. R.
2016-12-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steadyheterogeneous porous and fractured media flows based on a stochastic relaxation process.This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods,which model persistence over a characteristic time scale.We first establish the relations between Eulerian and Lagrangian velocities for both equidistant and isochronal sampling along streamlines,under transient and stationary conditions. Based on this, we develop the CTRW approach for the spatial and temporaldynamics of Lagrangian velocities. Unlike classical CTRW formulations, the proposed approach quantifies both stationaryand non-stationary Lagrangian velocity statistics, and their evolution from arbitraryinitial velocity distributions. We provide explicit expressions for the Lagrangian velocity distributions,and determine the behaviors of the mean particle velocity, velocity covariance andparticle dispersion. We find strong correlation and anomalous dispersion for velocity distributions which are tailedtoward low velocities. The developed CTRW approach and thus the Lagrangian particle dynamics are fully determined by the Eulerian velocitydistribution and the characteristic correlation scale. The developed framework is applied to particle transport in two-dimensionalrandom fracture networks.
Helfferich, J.; Ziebert, F.; Frey, S.; Meyer, H.; Farago, J.; Blumen, A.; Baschnagel, J.
2014-04-01
The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014), 10.1103/PhysRevE.89.042603], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.
Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy
2015-04-01
Solute transport in heterogeneous porous media is characterized by features that do not conform to advection-dispersion models characterized by equivalent transport parameters. This has been observed in tracer experiments under forced and natural flow conditions. Key questions are (i) how non-Fickian solute transport can be quantified under radial flow conditions, and (ii) how different heterogeneity sources of non-Fickian behavior manifest in non-Fickian radial transport models. In order to approach these questions, we develop a radial continuous time random walk (CTRW) formulation for the quantification and interpretation of non-Fickian solute transport under forced flow conditions and different heterogeneity scenarios. The derived radial CTRW approaches model anomalous behavior induced by heterogeneous flow distributions and mobile-immobile mass transfer processes (matrix diffusion). We start by establishing a general CTRW framework in radial coordinates on the basis of the random walk equations for radial particle positions and times. The evolution of solute concentration is governed by a non-local radial advection-dispersion equation. Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. We then derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile and mass transfer between mobile and immobile regions. We analyze the transport signatures for the distinct CTRW models in terms of solute breakthrough curves and their dependence on the heterogeneity scenarios.
Dentz, M.; Le Borgne, T.; Kang, P. K.; Bolster, D.
2014-12-01
Medium and flow heterogeneities lead to global transport patterns that cannot be captured by large scale transport models that are based on Fickian transport mechanisms. Early and late solute and particle arrivals, and non-linear evolution of dispersion are non-Fickian manifestations of spatial heterogeneity on large scale transport. Such behaviors can be modeled by approaches that are based on time and/or space non-local conservation equations. A key question is the identification and quantification of the heterogeneity controls on global non-Fickian transport patterns. Here, we focus on the roles of broad heterogeneity distribution, and heterogeneity and flow correlation on global non-Fickian transport. We identify the signatures of disorder and correlation dominated large scale transport in the distributions of solute arrival times, solute dispersion and spatial solute distributions. Starting from well-defined small scale stochastic flow and transport descriptions, we quantify large scale transport by ensemble averaging over the Lagrangian particle dynamics, which leads to a global transport model that is given by a coupled continuous time random walk (CTRW) characterized by correlated particle velocities. We formalize this correlated CTRW in terms of an evolution equation for the global particle distribution, and discuss the impact of the correlation of subsequent particle velocitieson the transport behavior, as well as the limits of perfect and no correlation.
Dentz, Marco; Le Borgne, Tanguy; Kang, Peter; Bolster, Diogo
2014-05-01
Medium and flow heterogeneities lead to global transport patterns such as early and late solute and particle arrivals, and non-linear dispersion which cannot be captured by large scale models based on Fickian transport mechanisms. Such behaviors can be modeled by non-Fickian approaches that are based on time and/or space non-local conservation equations. A key question concerns the identification and quantification of the heterogeneity controls on global non-Fickian transport patterns. Anomalous transport can be viewed as a collective phenomenon generated by the complex interaction of small scale fluctuations and mass transfer processes. Here, we focus on the roles of broad heterogeneity distribution, and heterogeneity and flow correlation on global non-Fickian transport. We identify the signatures of disorder and correlation dominated large scale transport in the distributions of solute arrival times, solute dispersion and spatial solute distributions. Starting from well-defined small scale stochastic flow and transport descriptions, we quantify large scale transport by ensemble averaging over the Lagrangian particle dynamics, which leads to a global transport model that is given by a coupled continuous time random walk (CTRW) characterized by correlated particle velocities. We formalize this correlated CTRW in terms of an evolution equation for the global particle distribution, and discuss the impact of the correlation of subsequent particle velocities on the transport behavior, as well as the limits of perfect and no correlation.
Helfferich, J.; Ziebert, F.; Frey, S.; Meyer, H.; Farago, J.; Blumen, A.; Baschnagel, J.
2014-04-01
Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Tc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forward-backward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jump-length and waiting-time distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrhenius-type to a Vogel-Fulcher-type T dependence. We discuss this observation in the context of the bifurcation of the α process and (Johari) β process found in many glass-forming materials to occur near Tc. Our analysis lays the foundation for a study of the jump-length and waiting-time distributions, their temperature and chain-length dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014), 10.1103/PhysRevE.89.042604].
Capasso, Vincenzo
2015-01-01
This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional exercises * Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Editio...
Directory of Open Access Journals (Sweden)
Haroldo Valetin Ribeiro
2012-03-01
Full Text Available We investigate how it is possible to obtain different diffusive regimes from the Continuous Time Random Walk (CTRW approach performing suitable changes for the waiting time and jumping distributions in order to get two or more regimes for the same diffusive process. We also obtain diffusion-like equations related to these processes and investigate the connection of the results with anomalous diffusion.
DEFF Research Database (Denmark)
Andersen, Torben G.; Bollerslev, Tim; Frederiksen, Per Houmann
that might have generated the data. As such, the tests may serve as a useful diagnostic tool in the specification of empirically more realistic asset pricing models. Our results are also directly related to the popular mixture-of-distributions hypoth- esis and the role of the corresponding latent information......We provide an empirical framework for assessing the distributional properties of daily specu- lative returns within the context of the continuous-time modeling paradigm traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures...... and non-parametric jump detection statistics constructed from high-frequency intra- day data. A sequence of relatively simple-to-implement moment-based tests involving various transforms of the daily returns speak directly to the import of different features of the under- lying continuous-time processes...
Stylised facts of financial time series and hidden Markov models in continuous time
DEFF Research Database (Denmark)
Nystrup, Peter; Madsen, Henrik; Lindström, Erik
2015-01-01
Hidden Markov models are often applied in quantitative finance to capture the stylised facts of financial returns. They are usually discrete-time models and the number of states rarely exceeds two because of the quadratic increase in the number of parameters with the number of states. This paper...... presents an extension to continuous time where it is possible to increase the number of states with a linear rather than quadratic growth in the number of parameters. The possibility of increasing the number of states leads to a better fit to both the distributional and temporal properties of daily returns....
Continuous time modelling of dynamical spatial lattice data observed at sparsely distributed times
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl; Møller, Jesper
2007-01-01
, and they exhibit spatial interaction. For specificity we consider a particular dynamical spatial lattice data set which has previously been analysed by a discrete time model involving unknown normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared......Summary. We consider statistical and computational aspects of simulation-based Bayesian inference for a spatial-temporal model based on a multivariate point process which is only observed at sparsely distributed times. The point processes are indexed by the sites of a spatial lattice...
Effective Pore-Scale Dispersion Upscaling with the Correlated Continuous Time Random Walk Approach
Energy Technology Data Exchange (ETDEWEB)
Le Borgne, Tanguy; Bolster, Diogo; Dentz, Marco; de Anna, Pietro; Tartakovsky, Alexandre M.
2011-12-29
We propose a general framework for upscaling dispersion in porous media. A key challenge of the upscaling procedure is to relate the temporal evolution of spreading to the small scale velocity field properties. The representation of the Lagrangian velocity transition process as a Markovian process in space provides a simple way to quantify complex correlation properties, i.e. non-Gaussian velocity distributions. The resulting effective transport model is a correlated CTRW. We use this framework to upscale pore scale dispersion for a periodic pore geometry. The correlated CTRW model is defined by the transit time distribution across one pore and the transition probability density quantifying the correlation between successive transit times. The latter is of central importance since it accounts for incomplete mixing at the pore throats. The predictions of the correlated CTRW model are in good agreement with the pore scale simulations over the pre-asymptotic and asymptotic regimes. We investigate the representation of this effective dispersion model in phase space (position, velocity) in a form similar to a Boltzmann transport equation.
Voelkle, Manuel C; Oud, Johan H L
2013-02-01
When designing longitudinal studies, researchers often aim at equal intervals. In practice, however, this goal is hardly ever met, with different time intervals between assessment waves and different time intervals between individuals being more the rule than the exception. One of the reasons for the introduction of continuous time models by means of structural equation modelling has been to deal with irregularly spaced assessment waves (e.g., Oud & Delsing, 2010). In the present paper we extend the approach to individually varying time intervals for oscillating and non-oscillating processes. In addition, we show not only that equal intervals are unnecessary but also that it can be advantageous to use unequal sampling intervals, in particular when the sampling rate is low. Two examples are provided to support our arguments. In the first example we compare a continuous time model of a bivariate coupled process with varying time intervals to a standard discrete time model to illustrate the importance of accounting for the exact time intervals. In the second example the effect of different sampling intervals on estimating a damped linear oscillator is investigated by means of a Monte Carlo simulation. We conclude that it is important to account for individually varying time intervals, and encourage researchers to conceive of longitudinal studies with different time intervals within and between individuals as an opportunity rather than a problem. © 2012 The British Psychological Society.
Offset-Free Direct Power Control of DFIG Under Continuous-Time Model Predictive Control
DEFF Research Database (Denmark)
Errouissi, Rachid; Al-Durra, Ahmed; Muyeen, S.M.
2017-01-01
This paper presents a robust continuous-time model predictive direct power control for doubly fed induction generator (DFIG). The proposed approach uses Taylor series expansion to predict the stator current in the synchronous reference frame over a finite time horizon. The predicted stator current...... without encompassing the parameters of the machine itself. Hence, no extra power control loop is required in the control structure to ensure smooth operation of the DFIG. The feasibility of the proposed strategy is verified by the experimental results of the grid-connected DFIG and satisfactory...
Rubner, Oliver; Heuer, Andreas
2008-07-01
We show that the dynamics of supercooled liquids, analyzed from computer simulations of the binary mixture Lennard-Jones system, can be described in terms of a continuous-time random walk (CTRW). The required discretization comes from mapping the dynamics on transitions between metabasins. This yields a quantitative link between the elementary step and the full structural relaxation. The analysis involves a verification of the CTRW conditions as well as a quantitative test of the predictions. The wave-vector dependence of the relaxation time and the degree of nonexponentiality can be expressed in terms of the first moments of the waiting time distribution.
Shushin, A I
2008-03-01
Some specific features and extensions of the continuous-time random-walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR, CTRW processes are represented by multidimensional Markovian ones. In this representation the probability density function (PDF) W(t) of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some Markovian controlling process. Within the MR the non-Markovian SLE, which describes the effect of CTRW-like noise on the relaxation of dynamic and stochastic systems, is generalized to take into account the influence of relaxing systems on the statistical properties of noise. Some applications of the generalized non-Markovian SLE are discussed. In particular, it is applied to study two modifications of the CTRW approach. One of them considers cascaded CTRWs in which the controlling process is actually a CTRW-like one controlled by another CTRW process, controlled in turn by a third one, etc. Within the MR a simple expression for the PDF W(t) of the total controlling process is obtained in terms of Markovian variants of controlling PDFs in the cascade. The expression is shown to be especially simple and instructive in the case of anomalous processes determined by the long-time tailed W(t) . The cascaded CTRWs can model the effect of the complexity of a system on the relaxation kinetics (in glasses, fractals, branching media, ultrametric structures, etc.). Another CTRW modification describes the kinetics of processes governed by fluctuating W(t) . Within the MR the problem is analyzed in a general form without restrictive assumptions on the correlations of PDFs of consecutive renewals. The analysis shows that fluctuations of W(t) can strongly affect the kinetics of the process. Possible manifestations of this effect are discussed.
Comolli, A.; Dentz, M.
2015-12-01
Solute transport in geological media is in general non-Fickian as it cannot be explained in terms of equivalent homogeneous media. This anomalous character can be traced back to the existence of multiscale heterogeneity and strong correlations within the medium. Here we investigate the impact of fast heterogeneous mass transfer properties as represented by a spatially varying retardation coefficient (mass exchange between mobile and immobile regions, linear sorption-desorption reactions, variable porosity). In order to estimate the effects of spatial correlation, and disorder distribution on the average transport, we consider 2D media characterized by complex multiscale geometries and point distributions of retardation of increasing heterogeneity. Within a Lagrangian framework, we coarse-grain the Langevin equation for the transport of solute particles due to advection and diffusion in the heterogeneous medium. The large-scale transport properties are derived within a stochastic modeling approach by ensemble averaging of the coarse-grained Langevin equation . This approach shows that the effective particle motion can be described by a coupled CTRW that is fully parametrized by the distribution of the retardation coefficient and the spatial medium organization. This allows for the explicit relation of the heterogeneous medium properties to observed anomalous transport in terms of solute dispersion, breakthrough curves and spatial concentration profiles.
Numerical solution of continuous-time DSGE models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...... then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader...... classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very...
Modeling commodity salam contract between two parties for discrete and continuous time series
Hisham, Azie Farhani Badrol; Jaffar, Maheran Mohd
2017-08-01
In order for Islamic finance to remain competitive as the conventional, there needs a new development of Islamic compliance product such as Islamic derivative that can be used to manage the risk. However, under syariah principles and regulations, all financial instruments must not be conflicting with five syariah elements which are riba (interest paid), rishwah (corruption), gharar (uncertainty or unnecessary risk), maysir (speculation or gambling) and jahl (taking advantage of the counterparty's ignorance). This study has proposed a traditional Islamic contract namely salam that can be built as an Islamic derivative product. Although a lot of studies has been done on discussing and proposing the implementation of salam contract as the Islamic product however they are more into qualitative and law issues. Since there is lack of quantitative study of salam contract being developed, this study introduces mathematical models that can value the appropriate salam price for a commodity salam contract between two parties. In modeling the commodity salam contract, this study has modified the existing conventional derivative model and come out with some adjustments to comply with syariah rules and regulations. The cost of carry model has been chosen as the foundation to develop the commodity salam model between two parties for discrete and continuous time series. However, the conventional time value of money results from the concept of interest that is prohibited in Islam. Therefore, this study has adopted the idea of Islamic time value of money which is known as the positive time preference, in modeling the commodity salam contract between two parties for discrete and continuous time series.
Continuous time boolean modeling for biological signaling: application of Gillespie algorithm
Directory of Open Access Journals (Sweden)
Stoll Gautier
2012-08-01
Full Text Available Abstract Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. Background There exist two major types of mathematical modeling approaches: (1 quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2 and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Results Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be
Continuous-time interval model identification of blood glucose dynamics for type 1 diabetes
Kirchsteiger, Harald; Johansson, Rolf; Renard, Eric; del Re, Luigi
2014-07-01
While good physiological models of the glucose metabolism in type 1 diabetic patients are well known, their parameterisation is difficult. The high intra-patient variability observed is a further major obstacle. This holds for data-based models too, so that no good patient-specific models are available. Against this background, this paper proposes the use of interval models to cover the different metabolic conditions. The control-oriented models contain a carbohydrate and insulin sensitivity factor to be used for insulin bolus calculators directly. Available clinical measurements were sampled on an irregular schedule which prompts the use of continuous-time identification, also for the direct estimation of the clinically interpretable factors mentioned above. An identification method is derived and applied to real data from 28 diabetic patients. Model estimation was done on a clinical data-set, whereas validation results shown were done on an out-of-clinic, everyday life data-set. The results show that the interval model approach allows a much more regular estimation of the parameters and avoids physiologically incompatible parameter estimates.
An approach to the drone fleet survivability assessment based on a stochastic continues-time model
Kharchenko, Vyacheslav; Fesenko, Herman; Doukas, Nikos
2017-09-01
An approach and the algorithm to the drone fleet survivability assessment based on a stochastic continues-time model are proposed. The input data are the number of the drones, the drone fleet redundancy coefficient, the drone stability and restoration rate, the limit deviation from the norms of the drone fleet recovery, the drone fleet operational availability coefficient, the probability of the drone failure-free operation, time needed for performing the required tasks by the drone fleet. The ways for improving the recoverable drone fleet survivability taking into account amazing factors of system accident are suggested. Dependencies of the drone fleet survivability rate both on the drone stability and the number of the drones are analysed.
Discrete- vs. Continuous-Time Modeling of Unequally Spaced Experience Sampling Method Data
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Silvia de Haan-Rietdijk
2017-10-01
Full Text Available The Experience Sampling Method is a common approach in psychological research for collecting intensive longitudinal data with high ecological validity. One characteristic of ESM data is that it is often unequally spaced, because the measurement intervals within a day are deliberately varied, and measurement continues over several days. This poses a problem for discrete-time (DT modeling approaches, which are based on the assumption that all measurements are equally spaced. Nevertheless, DT approaches such as (vector autoregressive modeling are often used to analyze ESM data, for instance in the context of affective dynamics research. There are equivalent continuous-time (CT models, but they are more difficult to implement. In this paper we take a pragmatic approach and evaluate the practical relevance of the violated model assumption in DT AR(1 and VAR(1 models, for the N = 1 case. We use simulated data under an ESM measurement design to investigate the bias in the parameters of interest under four different model implementations, ranging from the true CT model that accounts for all the exact measurement times, to the crudest possible DT model implementation, where even the nighttime is treated as a regular interval. An analysis of empirical affect data illustrates how the differences between DT and CT modeling can play out in practice. We find that the size and the direction of the bias in DT (VAR models for unequally spaced ESM data depend quite strongly on the true parameter in addition to data characteristics. Our recommendation is to use CT modeling whenever possible, especially now that new software implementations have become available.
Learning a Continuous-Time Streaming Video QoE Model.
Ghadiyaram, Deepti; Pan, Janice; Bovik, Alan C
2018-05-01
Over-the-top adaptive video streaming services are frequently impacted by fluctuating network conditions that can lead to rebuffering events (stalling events) and sudden bitrate changes. These events visually impact video consumers' quality of experience (QoE) and can lead to consumer churn. The development of models that can accurately predict viewers' instantaneous subjective QoE under such volatile network conditions could potentially enable the more efficient design of quality-control protocols for media-driven services, such as YouTube, Amazon, Netflix, and so on. However, most existing models only predict a single overall QoE score on a given video and are based on simple global video features, without accounting for relevant aspects of human perception and behavior. We have created a QoE evaluator, called the time-varying QoE Indexer, that accounts for interactions between stalling events, analyzes the spatial and temporal content of a video, predicts the perceptual video quality, models the state of the client-side data buffer, and consequently predicts continuous-time quality scores that agree quite well with human opinion scores. The new QoE predictor also embeds the impact of relevant human cognitive factors, such as memory and recency, and their complex interactions with the video content being viewed. We evaluated the proposed model on three different video databases and attained standout QoE prediction performance.
Fitting and interpreting continuous-time latent Markov models for panel data.
Lange, Jane M; Minin, Vladimir N
2013-11-20
Multistate models characterize disease processes within an individual. Clinical studies often observe the disease status of individuals at discrete time points, making exact times of transitions between disease states unknown. Such panel data pose considerable modeling challenges. Assuming the disease process progresses accordingly, a standard continuous-time Markov chain (CTMC) yields tractable likelihoods, but the assumption of exponential sojourn time distributions is typically unrealistic. More flexible semi-Markov models permit generic sojourn distributions yet yield intractable likelihoods for panel data in the presence of reversible transitions. One attractive alternative is to assume that the disease process is characterized by an underlying latent CTMC, with multiple latent states mapping to each disease state. These models retain analytic tractability due to the CTMC framework but allow for flexible, duration-dependent disease state sojourn distributions. We have developed a robust and efficient expectation-maximization algorithm in this context. Our complete data state space consists of the observed data and the underlying latent trajectory, yielding computationally efficient expectation and maximization steps. Our algorithm outperforms alternative methods measured in terms of time to convergence and robustness. We also examine the frequentist performance of latent CTMC point and interval estimates of disease process functionals based on simulated data. The performance of estimates depends on time, functional, and data-generating scenario. Finally, we illustrate the interpretive power of latent CTMC models for describing disease processes on a dataset of lung transplant patients. We hope our work will encourage wider use of these models in the biomedical setting. Copyright © 2013 John Wiley & Sons, Ltd.
On the gap and time interval between the first two maxima of long continuous time random walks
Mounaix, Philippe; Schehr, Grégory; Majumdar, Satya N.
2016-01-01
We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval T where at each time step the walker waits a random time τ, before performing a jump drawn from a symmetric continuous probability distribution function (PDF) f(η ) , of Lévy index 0μ /2 ). We investigate the joint PDF of the gap g between the first two highest positions of the CTRW and the time t separating these two maxima. We show that this PDF reaches a stationary limiting joint distribution p(g, t) in the limit of long CTRW, T\\to ∞ . Our exact analytical results show a very rich behavior of this joint PDF in the (γ,μ ) plane, which we study in great detail. Our main results are verified by numerical simulations. This work provides a non trivial extension to CTRWs of the recent study in the discrete time setting by Majumdar et al (2014 J. Stat. Mech. P09013).
DEFF Research Database (Denmark)
A methodology is presented that combines modelling based on first principles and data based modelling into a modelling cycle that facilitates fast decision-making based on statistical methods. A strong feature of this methodology is that given a first principles model along with process data......, the corresponding modelling cycle model of the given system for a given purpose. A computer-aided tool, which integrates the elements of the modelling cycle, is also presented, and an example is given of modelling a fed-batch bioreactor....
Transport properties of the continuous-time random walk with a long-tailed waiting-time density
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Weissman, H.; Havlin, S. (BarIlan Univ., Ramat Gan (Israel)); Weiss, G.H. (National Institutes of Health, Bethesda, MD (USA))
1989-10-01
The authors derive asymptotic properties of the propagator p(r, t) of a continuous-time random walk (CTRW) in which the waiting time density has the asymptotic form {psi}(t) {approximately} T{sup {alpha}}/t{sup {alpha}+1} when t >> T and 0 < {alpha} < 1. Several cases are considered; the main ones are those that assume that the variance of the displacement in a single step of the walk is finite. Under this assumption they consider both random walks with and without a bias. The principle results of their analysis is that one needs two forms to characterize p(r, t), depending on whether r is large or small, and that the small-r expansion cannot be characterized by a scaling form, although it is possible to find such a form for large r. Several results can be demonstrated that contrast with the case in which
Michas, Georgios; Vallianatos, Filippos; Karakostas, Vassilios; Papadimitriou, Eleftheria; Sammonds, Peter
2014-05-01
Efpalion aftershock sequence occurred in January 2010, when an M=5.5 earthquake was followed four days later by another strong event (M=5.4) and numerous aftershocks (Karakostas et al., 2012). This activity interrupted a 15 years period of low to moderate earthquake occurrence in Corinth rift, where the last major event was the 1995 Aigion earthquake (M=6.2). Coulomb stress analysis performed in previous studies (Karakostas et al., 2012; Sokos et al., 2012; Ganas et al., 2013) indicated that the second major event and most of the aftershocks were triggered due to stress transfer. The aftershocks production rate decays as a power-law with time according to the modified Omori law (Utsu et al., 1995) with an exponent larger than one for the first four days, while after the occurrence of the second strong event the exponent turns to unity. We consider the earthquake sequence as a point process in time and space and study its spatiotemporal evolution considering a Continuous Time Random Walk (CTRW) model with a joint probability density function of inter-event times and jumps between the successive earthquakes (Metzler and Klafter, 2000). Jump length distribution exhibits finite variance, whereas inter-event times scale as a q-generalized gamma distribution (Michas et al., 2013) with a long power-law tail. These properties are indicative of a subdiffusive process in terms of CTRW. Additionally, the mean square displacement of aftershocks is constant with time after the occurrence of the first event, while it changes to a power-law with exponent close to 0.15 after the second major event, illustrating a slow diffusive process. During the first four days aftershocks cluster around the epicentral area of the second major event, while after that and taking as a reference the second event, the aftershock zone is migrating slowly with time to the west near the epicentral area of the first event. This process is much slower from what would be expected from normal diffusion, a
Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe
Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease
Hofstede, ter F.; Wedel, M.
1998-01-01
This study investigates the effects of time aggregation in discrete and continuous-time hazard models. A Monte Carlo study is conducted in which data are generated according to various continuous and discrete-time processes, and aggregated into daily, weekly and monthly intervals. These data are
Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model
International Nuclear Information System (INIS)
Cvitanic, Jaksa; Wan, Xuhu; Zhang Jianfeng
2009-01-01
We consider a problem of finding optimal contracts in continuous time, when the agent's actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal's utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization
International Nuclear Information System (INIS)
Gill, Wonpyong
2010-01-01
The dependence of the crossing time on the sequence length in the coupled and the decoupled continuous-time mutation-selection models in an asymmetric sharply-peaked landscape with a positive asymmetric parameter, r, was examined for a fixed extension parameter, E, which is defined as the average Hamming distance from the optimal allele of the initial quasispecies divided by the sequence length. Two versions of the coupled mutation-selection model, the continuous-time version and discrete-time version, were found to have the same boundary between the deterministic and the stochastic regions, which is different from the boundary between the deterministic and the stochastic regions in the decoupled continuous-time mutation-selection model. The maximum sequence length for a finite population that can evolve through the fitness barrier, e.g., within 10 6 generations in the decoupled continuous-time mutation-selection model, increased by approximately eight sequence elements with increasing population size by a factor of a thousand when E = 0.1 and r = 0.1. The crossing time for a finite population in the decoupled model in the stochastic region was shorter than the crossing time for a finite population in the coupled model, and the maximum evolvable sequence length for a finite population in the decoupled model was longer than the maximum evolvable sequence length for a finite population in the coupled model. This suggests that a mutation allowed at any time during the life cycle might be more effective than a mutation allowed only at reproduction events when a finite population transits to a higher fitness peak through the fitness barrier in an asymmetric sharply-peaked landscape.
Directory of Open Access Journals (Sweden)
Robert M Dorazio
Full Text Available Several spatial capture-recapture (SCR models have been developed to estimate animal abundance by analyzing the detections of individuals in a spatial array of traps. Most of these models do not use the actual dates and times of detection, even though this information is readily available when using continuous-time recorders, such as microphones or motion-activated cameras. Instead most SCR models either partition the period of trap operation into a set of subjectively chosen discrete intervals and ignore multiple detections of the same individual within each interval, or they simply use the frequency of detections during the period of trap operation and ignore the observed times of detection. Both practices make inefficient use of potentially important information in the data.We developed a hierarchical SCR model to estimate the spatial distribution and abundance of animals detected with continuous-time recorders. Our model includes two kinds of point processes: a spatial process to specify the distribution of latent activity centers of individuals within the region of sampling and a temporal process to specify temporal patterns in the detections of individuals. We illustrated this SCR model by analyzing spatial and temporal patterns evident in the camera-trap detections of tigers living in and around the Nagarahole Tiger Reserve in India. We also conducted a simulation study to examine the performance of our model when analyzing data sets of greater complexity than the tiger data.Our approach provides three important benefits: First, it exploits all of the information in SCR data obtained using continuous-time recorders. Second, it is sufficiently versatile to allow the effects of both space use and behavior of animals to be specified as functions of covariates that vary over space and time. Third, it allows both the spatial distribution and abundance of individuals to be estimated, effectively providing a species distribution model, even in
Flatness-based control and Kalman filtering for a continuous-time macroeconomic model
Rigatos, G.; Siano, P.; Ghosh, T.; Busawon, K.; Binns, R.
2017-11-01
The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.
An SEM Approach to Continuous Time Modeling of Panel Data: Relating Authoritarianism and Anomia
Voelkle, Manuel C.; Oud, Johan H. L.; Davidov, Eldad; Schmidt, Peter
2012-01-01
Panel studies, in which the same subjects are repeatedly observed at multiple time points, are among the most popular longitudinal designs in psychology. Meanwhile, there exists a wide range of different methods to analyze such data, with autoregressive and cross-lagged models being 2 of the most well known representatives. Unfortunately, in these…
H. de Vries (Harwin); A.P.M. Wagelmans (Albert); E.C. Hasker (Epco C.); C. Lumbala (Crispin); P. Lutumba (Pascal); S.J. de Vlas (Sake); J. van de Klundert (Joris)
2016-01-01
textabstractTo eliminate and eradicate gambiense human African trypanosomiasis (HAT), maximizing the effectiveness of active case finding is of key importance. The progression of the epidemic is largely influenced by the planning of these operations. This paper introduces and analyzes five models
Identifcation of a Linear COntinuous Time Stochastic Model of the Heat Dynamics of a Greenhouse
DEFF Research Database (Denmark)
Nielsen, Bjarne; Madsen, Henrik
1998-01-01
The purpose of this paper is to describe the basis for improving the control of air temperature and heat supply in greenhouses using a method which controls the energy supply by a model-based prediction of the air temperature in the greenhouse. Controllers of this type are the minimum variance...... controller, the generalized predictive controller and the proportional-integral-plus(PIP) controller. Prediction-based controllers have proved to be powerful in controlling the supply temperature in a distinct heating system....
Energy Technology Data Exchange (ETDEWEB)
Eaves, B.C.; Rothblum, U.G.
1990-08-01
A discounted-cost, continuous-time, infinite-horizon version of a flexible manufacturing and operator scheduling model is solved. The solution procedure is to convexify the discrete operator-assignment constraints to obtain a linear program, and then to regain the discreteness and obtain an approximate manufacturing schedule by deconvexification of the solution of the linear program over time. The strong features of the model are the accommodation of linear inequality relations among the manufacturing activities and the discrete manufacturing scheduling, whereas the weak features are intra-period relaxation of inventory availability constraints, and the absence of inventory costs, setup times, and setup charges.
International Nuclear Information System (INIS)
Chetoui, Manel; Malti, Rachid; Thomassin, Magalie; Aoun, Mohamed; Najar, Slah; Abdelkrim, Naceur
2011-01-01
This paper deals with continuous-time system identification using fractional models in a noisy input/output context. The third-order cumulants based least squares method (tocls) is extended here to fractional models. The derivatives of the third-order cumulants are computed using a new fractional state variable filter. A numerical example is used to demonstrate the performance of the proposed method called ftocls (fractional third-order cumulants based least squares). The effect of the signal-to-noise ratio and the hyperparameter is studied.
Smolders, K.; Volckaert, M.; Swevers, J.
2008-11-01
This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.
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Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.
2008-01-01
This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiative...... heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated facades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered...... with measurement errors it is also argued that it is important to consider stochastic models. More specifically this paper advocates for using continuous-discrete stochastic state space models in the form of non-linear partially observed stochastic differential equations (SDE's)-with measurement noise...
Liao, Baochao; Liu, Qun; Zhang, Kui; Baset, Abdul; Memon, Aamir Mahmood; Memon, Khadim Hussain; Han, Yanan
2016-09-01
A continuous time delay-diff erence model (CTDDM) has been established that considers continuous time delays of biological processes. The southern Atlantic albacore ( Thunnus alalunga) stock is the one of the commercially important tuna population in the marine world. The age structured production model (ASPM) and the surplus production model (SPM) have already been used to assess the albacore stock. However, the ASPM requires detailed biological information and the SPM lacks the biological realism. In this study, we focus on applying a CTDDM to the southern Atlantic albacore ( T. alalunga) species, which provides an alternative method to assess this fishery. It is the first time that CTDDM has been provided for assessing the Atlantic albacore ( T. alalunga) fishery. CTDDM obtained the 80% confidence interval of MSY (maximum sustainable yield) of (21 510 t, 23 118t). The catch in 2011 (24 100 t) is higher than the MSY values and the relative fishing mortality ratio ( F 2011/ F MSY) is higher than 1.0. The results of CTDDM were analyzed to verify the proposed methodology and provide reference information for the sustainable management of the southern Atlantic albacore stock. The CTDDM treats the recruitment, the growth, and the mortality rates as all varying continuously over time and fills gaps between ASPM and SPM in this stock assessment.
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Mindaugas Snipas
2015-01-01
Full Text Available The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC of voltage gating of gap junction (GJ channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs, which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times.
Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe
2016-01-01
Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity. © The Author(s) 2015.
Angraini, Yenni; Toharudin, Toni; Folmer, Henk; Oud, Johan H L
2014-01-01
This article analyzes the relationships among nationalism (N), individualism (I), ethnocentrism (E), and authoritarianism (A) in continuous time (CT), estimated as a structural equation model. The analysis is based on the General Election Study for Flanders, Belgium, for 1991, 1995, and 1999. We find reciprocal effects between A and E and between E and I as well as a unidirectional effect from A on I. We furthermore find relatively small, but significant, effects from both I and E on N but no effect from A on N or from N on any of the other variables. Because of its central role in the N-I-E-A complex, mitigation of authoritarianism has the largest potential to reduce the spread of nationalism, ethnocentrism, and racism in Flanders.
Walters, Everton St. Patrick
This work was motivated by the need to model a network of natural gas pipelines and its corresponding demand pipeline, in order to make predictions of the pressures at critical junctions in the network Development of such a model amounts to a system identification problem with limited information. In order to solve this problem, we developed a demand model that would provide estimates of the gas usage for the communities serviced by the pipeline network. The parameters of the demand model were estimated using an adaptive genetic algorithm. This new algorithm was first developed and compared with existing genetic algorithms. A discussion of the role played by crossover and mutation operators in the genetic algorithm was also presented. Based on the theory of gas dynamics and the known pipeline network topology, a resistor-capacitor network analog to the pipeline network was developed. The parameters of the resistor-capacitor model were estimated using ordinary least squares techniques. We first studied and developed a number principles and guidelines for a class of system identification problems. One of the main areas studied was the development of a generalized framework for least squares "parameter" identification of continuous-time systems from discrete-time measurements of the states of the continuous-time system. Subsequently, we extended our generalized framework to the least squares parameter identification of a class of resistor-capacitor networks. We also studied the effects on the estimated results of the integration scheme used in the process and the noise levels in the measured data. A demonstration of the benefits of the incorporation of the maximum available structural information of the system being modeled was also presented. Finally, we developed a set of guidelines for the required input signal frequencies and sampling frequencies to provide acceptable identification results for both the plant-model-match and reduced-order modeling problems
Multienergetic continuous time random walk
Energy Technology Data Exchange (ETDEWEB)
Caceres, M.O.; Wio, H.S.
1984-02-01
We have extended the CTRW theory of Montroll and Weiss including the effect of extra variables, like the energy. This MCTRW scheme can be written in a simple matrix notation, that simplifies its solution. As an example of their usefulness we have studied a two-energy-groups neutron diffusion problem. This has shown the peculiarities of the transient behaviour for the variance of the probability distribution, due to the coupling between the groups.
Directory of Open Access Journals (Sweden)
Dandan Su
2017-12-01
Full Text Available This paper proposes an improved continuous-time model predictive control (CTMPC of permanent magnetic synchronous motors (PMSMs for a wide-speed range, including the constant torque region and the flux-weakening (FW region. In the constant torque region, the mathematic models of PMSMs in dq-axes are decoupled without the limitation of DC-link voltage. However, in the FW region, the mathematic models of PMSMs in dq-axes are cross-coupled together with the limitation of DC-link voltage. A nonlinear PMSMs mathematic model in the FW region is presented based on the voltage angle. The solving of the nonlinear mathematic model of PMSMs in FW region will lead to heavy computation load for digital signal processing (DSP. To overcome such a problem, a linearization method of the voltage angle is also proposed to reduce the computation load. The selection of transiting points between the constant torque region and FW regions is researched to improve the performance of the driven system. Compared with the proportional integral (PI controller, the proposed CTMPC has obvious advantages in dealing with systems’ nonlinear constraints and improving system performance by restraining overshoot current under step torque changing. Both simulation and experimental results confirm the effectiveness of the proposed method in achieving good steady-state performance and smooth switching between the constant torque and FW regions.
DEFF Research Database (Denmark)
Pedersen, Jonas Nyvold; Li, Liang; Gradinaru, Cristian
2016-01-01
We provide a tool for data-driven modeling of motility, data being time-lapse recorded trajectories. Several mathematical properties of a model to be found can be gleaned from appropriate model-independent experimental statistics, if one understands how such statistics are distorted by the finite...... of these effects that are valid for any reasonable model for persistent random motion. Our findings are illustrated with experimental data and Monte Carlo simulations....
Pooley, C M; Bishop, S C; Marion, G
2015-06-06
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob-Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed 'model-based proposal' (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2-8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Fontes, Fernando A. C. C.; Paiva, Luís T.
2016-10-01
We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging non-linear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant-spaced time-grid methods, including the ones using discrete-time models. This way, continuous-time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real-time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time-dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC.
Meng, Tianhui; Li, Xiaofan; Zhang, Sha; Zhao, Yubin
2016-09-28
Wireless sensor networks (WSNs) have recently gained popularity for a wide spectrum of applications. Monitoring tasks can be performed in various environments. This may be beneficial in many scenarios, but it certainly exhibits new challenges in terms of security due to increased data transmission over the wireless channel with potentially unknown threats. Among possible security issues are timing attacks, which are not prevented by traditional cryptographic security. Moreover, the limited energy and memory resources prohibit the use of complex security mechanisms in such systems. Therefore, balancing between security and the associated energy consumption becomes a crucial challenge. This paper proposes a secure scheme for WSNs while maintaining the requirement of the security-performance tradeoff. In order to proceed to a quantitative treatment of this problem, a hybrid continuous-time Markov chain (CTMC) and queueing model are put forward, and the tradeoff analysis of the security and performance attributes is carried out. By extending and transforming this model, the mean time to security attributes failure is evaluated. Through tradeoff analysis, we show that our scheme can enhance the security of WSNs, and the optimal rekeying rate of the performance and security tradeoff can be obtained.
Directory of Open Access Journals (Sweden)
Márcio das Chagas Moura
2008-08-01
Full Text Available In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks. This integration results in a hybrid stochastic model that is able to represent the dynamic characteristics of a system as well as to deal with cause-effect relationships among external factors such as environmental and operational conditions. The hybrid model also allows for uncertainty propagation on the system availability. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates. The numerical procedure is based on the application of Laplace transforms that are inverted by the Gauss quadrature method known as Gauss Legendre. The hybrid model and numerical procedure are illustrated by means of an example of application in the context of fault tolerant systems.Neste trabalho, é proposto um modelo baseado na integração entre processos semi-Markovianos e redes Bayesianas para avaliação da disponibilidade de sistemas tolerantes à falha. Esta integração resulta em um modelo estocástico híbrido o qual é capaz de representar as características dinâmicas de um sistema assim como tratar as relações de causa e efeito entre fatores externos tais como condições ambientais e operacionais. Além disso, o modelo híbrido permite avaliar a propagação de incerteza sobre a disponibilidade do sistema. É também proposto um procedimento numérico para a solução das equações de probabilidade de estado de processos semi-Markovianos descritos por taxas de transição. Tal procedimento numérico é baseado na aplicação de transformadas de Laplace que são invertidas pelo método de quadratura Gaussiana conhecido como Gauss Legendre. O modelo híbrido e procedimento numérico são ilustrados por meio de um exemplo de aplicação no contexto de
Distributed synthesis in continuous time
DEFF Research Database (Denmark)
Hermanns, Holger; Krčál, Jan; Vester, Steen
2016-01-01
We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability...
Hansen, Scott K.; Berkowitz, Brian
2015-03-01
We develop continuous-time random walk (CTRW) equations governing the transport of two species that annihilate when in proximity to one another. In comparison with catalytic or spontaneous transformation reactions that have been previously considered in concert with CTRW, both species have spatially variant concentrations that require consideration. We develop two distinct formulations. The first treats transport and reaction microscopically, potentially capturing behavior at sharp fronts, but at the cost of being strongly nonlinear. The second, mesoscopic, formulation relies on a separation-of-scales technique we develop to separate microscopic-scale reaction and upscaled transport. This simplifies the governing equations and allows treatment of more general reaction dynamics, but requires stronger smoothness assumptions of the solution. The mesoscopic formulation is easily tractable using an existing solution from the literature (we also provide an alternative derivation), and the generalized master equation (GME) for particles undergoing A +B →0 reactions is presented. We show that this GME simplifies, under appropriate circumstances, to both the GME for the unreactive CTRW and to the advection-dispersion-reaction equation. An additional major contribution of this work is on the numerical side: to corroborate our development, we develop an indirect particle-tracking-partial-integro-differential-equation (PIDE) hybrid verification technique which could be applicable widely in reactive anomalous transport. Numerical simulations support the mesoscopic analysis.
Voelkle, M.C.; Oud, J.H.L.; Davidov, E.; Schmidt, P.
2012-01-01
Reports an error in "An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia" by Manuel C. Voelkle, Johan H. L. Oud, Eldad Davidov and Peter Schmidt (Psychological Methods, 2012[Jun], Vol 17[2], 176-192). The supplemental materials link was missing. All
2007-03-01
grain particles suspended in a fluid and Norbert Wiener developed the mathematical foundation for this type of random motion [209, 21]. 3-38 Definition...Technology and John Wiley & Sons, Inc., 1949. 209. Wiener , Norbert , et al. Differential Space, Quantum Systems, and Prediction. Cambridge, Massachusetts...space of bounded linear transformations . . . . . . . . 3-6 xvii Symbol Page b(t) Brownian motion (or Wiener ) process . . . . . . . . . 2-10 C([a, b
Ma, Junsheng; Chan, Wenyaw; Tsai, Chu-Lin; Xiong, Momiao; Tilley, Barbara C
2015-11-30
Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state. Copyright © 2015 John Wiley & Sons, Ltd.
Informational and Causal Architecture of Continuous-time Renewal Processes
Marzen, Sarah; Crutchfield, James P.
2017-07-01
We introduce the minimal maximally predictive models (ɛ {-machines }) of processes generated by certain hidden semi-Markov models. Their causal states are either discrete, mixed, or continuous random variables and causal-state transitions are described by partial differential equations. As an application, we present a complete analysis of the ɛ {-machines } of continuous-time renewal processes. This leads to closed-form expressions for their entropy rate, statistical complexity, excess entropy, and differential information anatomy rates.
Song, Youngseok; Ishikawa, Hiroshi; Wu, Mengfei; Liu, Yu-Ying; Lucy, Katie A; Lavinsky, Fabio; Liu, Mengling; Wollstein, Gadi; Schuman, Joel S
2018-03-20
Previously, we introduced a state-based 2-dimensional continuous-time hidden Markov model (2D CT HMM) to model the pattern of detected glaucoma changes using structural and functional information simultaneously. The purpose of this study was to evaluate the detected glaucoma change prediction performance of the model in a real clinical setting using a retrospective longitudinal dataset. Longitudinal, retrospective study. One hundred thirty-four eyes from 134 participants diagnosed with glaucoma or as glaucoma suspects (average follow-up, 4.4±1.2 years; average number of visits, 7.1±1.8). A 2D CT HMM model was trained using OCT (Cirrus HD-OCT; Zeiss, Dublin, CA) average circumpapillary retinal nerve fiber layer (cRNFL) thickness and visual field index (VFI) or mean deviation (MD; Humphrey Field Analyzer; Zeiss). The model was trained using a subset of the data (107 of 134 eyes [80%]) including all visits except for the last visit, which was used to test the prediction performance (training set). Additionally, the remaining 27 eyes were used for secondary performance testing as an independent group (validation set). The 2D CT HMM predicts 1 of 4 possible detected state changes based on 1 input state. Prediction accuracy was assessed as the percentage of correct prediction against the patient's actual recorded state. In addition, deviations of the predicted long-term detected change paths from the actual detected change paths were measured. Baseline mean ± standard deviation age was 61.9±11.4 years, VFI was 90.7±17.4, MD was -3.50±6.04 dB, and cRNFL thickness was 74.9±12.2 μm. The accuracy of detected glaucoma change prediction using the training set was comparable with the validation set (57.0% and 68.0%, respectively). Prediction deviation from the actual detected change path showed stability throughout patient follow-up. The 2D CT HMM demonstrated promising prediction performance in detecting glaucoma change performance in a simulated clinical setting
International Nuclear Information System (INIS)
Qiu-Ye, Sun; Hua-Guang, Zhang; Yan, Zhao
2010-01-01
This paper investigates the chaotification problem of a stable continuous-time T–S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T–S fuzzy system with time-delay and a discrete-time T–S fuzzy system is established. Based on the discrete-time T–S fuzzy system, it proves that the chaos in the discrete-time T–S fuzzy system satisfies the Li–Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example. (general)
International Nuclear Information System (INIS)
Helmstetter, A.; Sornette, D.
2004-01-01
Several methods have been proposed to study the spatiotemporal correlations between earthquakes. Marsan and co-workers proposed a method based on correlations between all earthquake pairs, without distinction between mainshock and aftershocks, and interpreted their results in terms of a space-time coupling in the triggering process between events. In contrast, we studied the diffusion of aftershocks by analyzing the average distance between a triggered event ('aftershock') and a previous large earthquake (the 'mainshock' which initiated the aftershock sequence). We reply to the comments of Marsan and Bean on our previous paper and discuss the applicability of both methods to unravel the spatiotemporal coupling of earthquake triggering processes
Krengel, Annette; Hauth, Jan; Taskinen, Marja-Riitta; Adiels, Martin; Jirstrand, Mats
2013-01-19
When mathematical modelling is applied to many different application areas, a common task is the estimation of states and parameters based on measurements. With this kind of inference making, uncertainties in the time when the measurements have been taken are often neglected, but especially in applications taken from the life sciences, this kind of errors can considerably influence the estimation results. As an example in the context of personalized medicine, the model-based assessment of the effectiveness of drugs is becoming to play an important role. Systems biology may help here by providing good pharmacokinetic and pharmacodynamic (PK/PD) models. Inference on these systems based on data gained from clinical studies with several patient groups becomes a major challenge. Particle filters are a promising approach to tackle these difficulties but are by itself not ready to handle uncertainties in measurement times. In this article, we describe a variant of the standard particle filter (PF) algorithm which allows state and parameter estimation with the inclusion of measurement time uncertainties (MTU). The modified particle filter, which we call MTU-PF, also allows the application of an adaptive stepsize choice in the time-continuous case to avoid degeneracy problems. The modification is based on the model assumption of uncertain measurement times. While the assumption of randomness in the measurements themselves is common, the corresponding measurement times are generally taken as deterministic and exactly known. Especially in cases where the data are gained from measurements on blood or tissue samples, a relatively high uncertainty in the true measurement time seems to be a natural assumption. Our method is appropriate in cases where relatively few data are used from a relatively large number of groups or individuals, which introduce mixed effects in the model. This is a typical setting of clinical studies. We demonstrate the method on a small artificial example
Deviney, Frank A.; Rice, Karen; Brown, Donald E.
2012-01-01
Natural resource managers require information concerning the frequency, duration, and long-term probability of occurrence of water-quality indicator (WQI) violations of defined thresholds. The timing of these threshold crossings often is hidden from the observer, who is restricted to relatively infrequent observations. Here, a model for the hidden process is linked with a model for the observations, and the parameters describing duration, return period, and long-term probability of occurrence are estimated using Bayesian methods. A simulation experiment is performed to evaluate the approach under scenarios based on the equivalent of a total monitoring period of 5-30 years and an observation frequency of 1-50 observations per year. Given constant threshold crossing rate, accuracy and precision of parameter estimates increased with longer total monitoring period and more-frequent observations. Given fixed monitoring period and observation frequency, accuracy and precision of parameter estimates increased with longer times between threshold crossings. For most cases where the long-term probability of being in violation is greater than 0.10, it was determined that at least 600 observations are needed to achieve precise estimates. An application of the approach is presented using 22 years of quasi-weekly observations of acid-neutralizing capacity from Deep Run, a stream in Shenandoah National Park, Virginia. The time series also was sub-sampled to simulate monthly and semi-monthly sampling protocols. Estimates of the long-term probability of violation were unbiased despite sampling frequency; however, the expected duration and return period were over-estimated using the sub-sampled time series with respect to the full quasi-weekly time series.
On Continuous Time Markov Processes in Bargaining
Houba, H.E.D.
2008-01-01
For bilateral stochastic bargaining procedures embedded in stable homogeneous continuous-time Markov processes, we show unusual limit results when time between rounds vanish. Standard convergence results require that some states are instantaneous. © 2008.
Delayed Nondeterminism in Continuous-Time Markov Decision Processes
Neuhausser, M.; Stoelinga, Mariëlle Ida Antoinette; Katoen, Joost P.
2009-01-01
Schedulers in randomly timed games can be classified as to whether they use timing information or not. We consider continuous-time Markov decision processes (CTMDPs) and define a hierarchy of positional (P) and history-dependent (H) schedulers which induce strictly tighter bounds on quantitative
Parameter Estimation in Continuous Time Domain
Directory of Open Access Journals (Sweden)
Gabriela M. ATANASIU
2016-12-01
Full Text Available This paper will aim to presents the applications of a continuous-time parameter estimation method for estimating structural parameters of a real bridge structure. For the purpose of illustrating this method two case studies of a bridge pile located in a highly seismic risk area are considered, for which the structural parameters for the mass, damping and stiffness are estimated. The estimation process is followed by the validation of the analytical results and comparison with them to the measurement data. Further benefits and applications for the continuous-time parameter estimation method in civil engineering are presented in the final part of this paper.
Inverse Ising problem in continuous time: A latent variable approach
Donner, Christian; Opper, Manfred
2017-12-01
We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.
Inverse Ising problem in continuous time: A latent variable approach.
Donner, Christian; Opper, Manfred
2017-12-01
We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.
Continuous-time system identification of a smoking cessation intervention
Timms, Kevin P.; Rivera, Daniel E.; Collins, Linda M.; Piper, Megan E.
2014-07-01
Cigarette smoking is a major global public health issue and the leading cause of preventable death in the United States. Toward a goal of designing better smoking cessation treatments, system identification techniques are applied to intervention data to describe smoking cessation as a process of behaviour change. System identification problems that draw from two modelling paradigms in quantitative psychology (statistical mediation and self-regulation) are considered, consisting of a series of continuous-time estimation problems. A continuous-time dynamic modelling approach is employed to describe the response of craving and smoking rates during a quit attempt, as captured in data from a smoking cessation clinical trial. The use of continuous-time models provide benefits of parsimony, ease of interpretation, and the opportunity to work with uneven or missing data.
Continuous-time capture-recapture in closed populations.
Schofield, Matthew R; Barker, Richard J; Gelling, Nicholas
2017-09-12
The standard approach to fitting capture-recapture data collected in continuous time involves arbitrarily forcing the data into a series of distinct discrete capture sessions. We show how continuous-time models can be fitted as easily as discrete-time alternatives. The likelihood is factored so that efficient Markov chain Monte Carlo algorithms can be implemented for Bayesian estimation, available online in the R package ctime. We consider goodness-of-fit tests for behavior and heterogeneity effects as well as implementing models that allow for such effects. © 2017, The International Biometric Society.
a Continuous-Time Positive Linear System
Directory of Open Access Journals (Sweden)
Kyungsup Kim
2013-01-01
Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.
Inference for Continuous-Time Probabilistic Programming
2017-12-01
Proceedings of the European Conference in Machine Learn- ing and Principals and Practice of Knowledge and Discovery in Databases (ECML- PKDD). Williams , C. K . I...interaction net- works. Journal of the Royal Statistical Society: Series B, 75(5):821–849, 2013. [4] Christopher DuBois, Carter T. Butts, and Padhraic...pages 421–430, 2007. [20] E. Busra Celikkaya, Christian R. Shelton, and William Lam. Factored filtering of continuous- time systems. In Proceedings of
Pseudo-Hermitian continuous-time quantum walks
Energy Technology Data Exchange (ETDEWEB)
Salimi, S; Sorouri, A, E-mail: shsalimi@uok.ac.i, E-mail: a.sorouri@uok.ac.i [Department of Physics, University of Kurdistan, PO Box 66177-15175, Sanandaj (Iran, Islamic Republic of)
2010-07-09
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum-mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system. We observe that the probability distribution on certain vertices increases compared to that of the Hermitian case. This formalism makes the transport process faster and can be useful for search algorithms.
Identification of continuous-time systems from samples of input ...
Indian Academy of Sciences (India)
Abstract. This paper presents an introductory survey ofthe methodsthat have been developed for identification of continuous-time systems from samples of input-output data. The two basic approaches may be described as. the indirect method, where first a discrete-time model is estimated from the sampled data and then an ...
Expectation propagation for continuous time stochastic processes
International Nuclear Information System (INIS)
Cseke, Botond; Schnoerr, David; Sanguinetti, Guido; Opper, Manfred
2016-01-01
We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems. (paper)
Interaction-aided continuous time quantum search
International Nuclear Information System (INIS)
Bae, Joonwoo; Kwon, Younghun; Baek, Inchan; Yoon, Dalsun
2005-01-01
The continuous quantum search algorithm (based on the Farhi-Gutmann Hamiltonian evolution) is known to be analogous to the Grover (or discrete time quantum) algorithm. Any errors introduced in Grover algorithm are fatal to its success. In the same way the Farhi-Gutmann Hamiltonian algorithm has a severe difficulty when the Hamiltonian is perturbed. In this letter we will show that the interaction term in quantum search Hamiltonian (actually which is in the generalized quantum search Hamiltonian) can save the perturbed Farhi-Gutmann Hamiltonian that should otherwise fail. We note that this fact is quite remarkable since it implies that introduction of interaction can be a way to correct some errors on the continuous time quantum search
Transport properties of continuous-time quantum walks on Sierpinski fractals.
Darázs, Zoltán; Anishchenko, Anastasiia; Kiss, Tamás; Blumen, Alexander; Mülken, Oliver
2014-09-01
We model quantum transport, described by continuous-time quantum walks (CTQWs), on deterministic Sierpinski fractals, differentiating between Sierpinski gaskets and Sierpinski carpets, along with their dual structures. The transport efficiencies are defined in terms of the exact and the average return probabilities, as well as by the mean survival probability when absorbing traps are present. In the case of gaskets, localization can be identified already for small networks (generations). For carpets, our numerical results indicate a trend towards localization, but only for relatively large structures. The comparison of gaskets and carpets further implies that, distinct from the corresponding classical continuous-time random walk, the spectral dimension does not fully determine the evolution of the CTQW.
Energy Technology Data Exchange (ETDEWEB)
Huselstein, E.
2003-07-01
This thesis deals with direct identification of linear continuous-time models from experimental data and modeling of municipal solid waste incinerator. The main contributions for system identification consist in the adaptation of the srivc instrumental variable method to multi-input /single-output continuous-time models with different denominators, the adjunction of an approach of model order selection, the extension of the methodology to irregularly sampled data and the implementation of these algorithms in a software toolbox. This developments are applied to the experimental modeling of a municipal solid waste incinerator at Chaumont (France). The main results consist in the perturbation analysis, the determination of static and dynamic models and the proposition of a simple strategy to achieve a 20 % reduction of nitrogen oxide emissions. (author)
Price discovery in a continuous-time setting
DEFF Research Database (Denmark)
Dias, Gustavo Fruet; Fernandes, Marcelo; Scherrer, Cristina
We formulate a continuous-time price discovery model in which the price discovery measure varies (stochastically) at daily frequency. We estimate daily measures of price discovery using a kernel-based OLS estimator instead of running separate daily VECM regressions as standard in the literature. ...... show that our estimator is not only consistent, but also outperforms the standard daily VECM in finite samples. We illustrate our theoretical findings by studying the price discovery process of 10 actively traded stocks in the U.S. from 2007 to 2013.......We formulate a continuous-time price discovery model in which the price discovery measure varies (stochastically) at daily frequency. We estimate daily measures of price discovery using a kernel-based OLS estimator instead of running separate daily VECM regressions as standard in the literature. We...
On Probabilistic Automata in Continuous Time
DEFF Research Database (Denmark)
Eisentraut, Christian; Hermanns, Holger; Zhang, Lijun
2010-01-01
We develop a compositional behavioural model that integrates a variation of probabilistic automata into a conservative extension of interactive Markov chains. The model is rich enough to embody the semantics of generalised stochastic Petri nets. We define strong and weak bisimulations and discuss...
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
A continuous time Cournot duopoly with delays
International Nuclear Information System (INIS)
Gori, Luca; Guerrini, Luca; Sodini, Mauro
2015-01-01
This paper extends the classical repeated duopoly model with quantity-setting firms of Bischi et al. (1998) by assuming that production of goods is subject to some gestation lags but exchanges take place continuously in the market. The model is expressed in the form of differential equations with discrete delays. By using some recent mathematical techniques and numerical experiments, results show some dynamic phenomena that cannot be observed when delays are absent. In addition, depending on the extent of time delays and inertia, synchronisation failure can arise even in the event of homogeneous firms.
Random trinomial tree models and vanilla options
Ganikhodjaev, Nasir; Bayram, Kamola
2013-09-01
In this paper we introduce and study random trinomial model. The usual trinomial model is prescribed by triple of numbers (u, d, m). We call the triple (u, d, m) an environment of the trinomial model. A triple (Un, Dn, Mn), where {Un}, {Dn} and {Mn} are the sequences of independent, identically distributed random variables with 0 < Dn < 1 < Un and Mn = 1 for all n, is called a random environment and trinomial tree model with random environment is called random trinomial model. The random trinomial model is considered to produce more accurate results than the random binomial model or usual trinomial model.
Randomized Local Model Order Reduction
Buhr, Andreas; Smetana, Kathrin
2017-01-01
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation (PDE) with random boundary conditions, yield an approximation
Alternative model of random surfaces
International Nuclear Information System (INIS)
Ambartzumian, R.V.; Sukiasian, G.S.; Savvidy, G.K.; Savvidy, K.G.
1992-01-01
We analyse models of triangulated random surfaces and demand that geometrically nearby configurations of these surfaces must have close actions. The inclusion of this principle drives us to suggest a new action, which is a modified Steiner functional. General arguments, based on the Minkowski inequality, shows that the maximal distribution to the partition function comes from surfaces close to the sphere. (orig.)
Accurate Lithium-ion battery parameter estimation with continuous-time system identification methods
International Nuclear Information System (INIS)
Xia, Bing; Zhao, Xin; Callafon, Raymond de; Garnier, Hugues; Nguyen, Truong; Mi, Chris
2016-01-01
Highlights: • Continuous-time system identification is applied in Lithium-ion battery modeling. • Continuous-time and discrete-time identification methods are compared in detail. • The instrumental variable method is employed to further improve the estimation. • Simulations and experiments validate the advantages of continuous-time methods. - Abstract: The modeling of Lithium-ion batteries usually utilizes discrete-time system identification methods to estimate parameters of discrete models. However, in real applications, there is a fundamental limitation of the discrete-time methods in dealing with sensitivity when the system is stiff and the storage resolutions are limited. To overcome this problem, this paper adopts direct continuous-time system identification methods to estimate the parameters of equivalent circuit models for Lithium-ion batteries. Compared with discrete-time system identification methods, the continuous-time system identification methods provide more accurate estimates to both fast and slow dynamics in battery systems and are less sensitive to disturbances. A case of a 2 nd -order equivalent circuit model is studied which shows that the continuous-time estimates are more robust to high sampling rates, measurement noises and rounding errors. In addition, the estimation by the conventional continuous-time least squares method is further improved in the case of noisy output measurement by introducing the instrumental variable method. Simulation and experiment results validate the analysis and demonstrate the advantages of the continuous-time system identification methods in battery applications.
Continuous-time quantum Monte Carlo impurity solvers
Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias
2011-04-01
Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as
Continuous-time quantum walks on star graphs
International Nuclear Information System (INIS)
Salimi, S.
2009-01-01
In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K 2 graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.
Chaos and unpredictability in evolution of cooperation in continuous time
You, Taekho; Kwon, Minji; Jo, Hang-Hyun; Jung, Woo-Sung; Baek, Seung Ki
2017-12-01
Cooperators benefit others with paying costs. Evolution of cooperation crucially depends on the cost-benefit ratio of cooperation, denoted as c . In this work, we investigate the infinitely repeated prisoner's dilemma for various values of c with four of the representative memory-one strategies, i.e., unconditional cooperation, unconditional defection, tit-for-tat, and win-stay-lose-shift. We consider replicator dynamics which deterministically describes how the fraction of each strategy evolves over time in an infinite-sized well-mixed population in the presence of implementation error and mutation among the four strategies. Our finding is that this three-dimensional continuous-time dynamics exhibits chaos through a bifurcation sequence similar to that of a logistic map as c varies. If mutation occurs with rate μ ≪1 , the position of the bifurcation sequence on the c axis is numerically found to scale as μ0.1, and such sensitivity to μ suggests that mutation may have nonperturbative effects on evolutionary paths. It demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics.
Elliott, Thomas J.; Gu, Mile
2018-03-01
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.
Continuous-time Markov decision processes theory and applications
Guo, Xianping
2009-01-01
This volume provides the first book entirely devoted to recent developments on the theory and applications of continuous-time Markov decision processes (MDPs). The MDPs presented here include most of the cases that arise in applications.
2015-08-17
Control based on Heuristic Dynamic Programming for Nonlinear Continuous-Time Systems In this paper, a novel predictive event-triggered control...method based on heuristic dynamic programming (HDP) algorithm is developed for nonlinear continuous-time systems. A model network is used to estimate...College Road, Suite II Kingston, RI 02881 -1967 ABSTRACT Predictive Event-Triggered Control based on Heuristic Dynamic Programming for Nonlinear
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...
The parabolic Anderson model random walk in random potential
König, Wolfgang
2016-01-01
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
Exploratory Study for Continuous-time Parameter Estimation of Ankle Dynamics
Kukreja, Sunil L.; Boyle, Richard D.
2014-01-01
Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.
A continuous time formulation of the Regge calculus
International Nuclear Information System (INIS)
Brewin, Leo
1988-01-01
A complete continuous time formulation of the Regge calculus is presented by developing the associated continuous time Regge action. It is shown that the time constraint is, by way of the Bianchi identities conserved by the evolution equations. This analysis leads to an explicit first integral for each of the evolution equations. The dynamical equations of the theory are therefore reduced to a set of first-order differential equations. In this formalism the time constraints reduce to a simple sum of the integration constants. This result is unique to the Regge calculus-there does not appear to be a complete set of first integrals available for the vacuum Einstein equations. (author)
A mean-variance frontier in discrete and continuous time
Bekker, Paul A.
2004-01-01
The paper presents a mean-variance frontier based on dynamic frictionless investment strategies in continuous time. The result applies to a finite number of risky assets whose price process is given by multivariate geometric Brownian motion with deterministically varying coefficients. The derivation
Incomplete Continuous-time Securities Markets with Stochastic Income Volatility
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
2014-01-01
We derive closed-form solutions for the equilibrium interest rate and market price of risk processes in an incomplete continuous-time market with uncertainty generated by Brownian motions. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspan...
Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
In an incomplete continuous-time securities market governed by Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and equity premium processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income ...
Reachability in continuous-time Markov reward decision processes
Baier, Christel; Haverkort, Boudewijn R.H.M.; Hermanns, H.; Katoen, Joost P.; Flum, J.; Graedel, E.; Wilke, Th.
Continuous-time Markov decision processes (CTMDPs) are widely used for the control of queueing systems, epidemic and manufacturing processes. Various results on optimal schedulers for discounted and average reward optimality criteria in CTMDPs are known, but the typical game-theoretic winning
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, Pauline; van Doorn, Erik A.
2002-01-01
he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P.; van Doorn, E.A.
2001-01-01
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
Continuous Time Portfolio Selection under Conditional Capital at Risk
Directory of Open Access Journals (Sweden)
Gordana Dmitrasinovic-Vidovic
2010-01-01
Full Text Available Portfolio optimization with respect to different risk measures is of interest to both practitioners and academics. For there to be a well-defined optimal portfolio, it is important that the risk measure be coherent and quasiconvex with respect to the proportion invested in risky assets. In this paper we investigate one such measure—conditional capital at risk—and find the optimal strategies under this measure, in the Black-Scholes continuous time setting, with time dependent coefficients.
Continuous-Time Symmetric Hopfield Nets are Computationally Universal
Czech Academy of Sciences Publication Activity Database
Šíma, Jiří; Orponen, P.
2003-01-01
Roč. 15, č. 3 (2003), s. 693-733 ISSN 0899-7667 R&D Projects: GA AV ČR IAB2030007; GA ČR GA201/02/1456 Institutional research plan: AV0Z1030915 Keywords : continuous-time Hopfield network * Liapunov function * analog computation * computational power * Turing universality Subject RIV: BA - General Mathematics Impact factor: 2.747, year: 2003
Parallel algorithms for simulating continuous time Markov chains
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
The random walk model of intrafraction movement
International Nuclear Information System (INIS)
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-01-01
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction Gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-Gaussian corrections from the random walk model. (paper)
The random walk model of intrafraction movement.
Ballhausen, H; Reiner, M; Kantz, S; Belka, C; Söhn, M
2013-04-07
The purpose of this paper is to understand intrafraction movement as a stochastic process driven by random external forces. The hypothetically proposed three-dimensional random walk model has significant impact on optimal PTV margins and offers a quantitatively correct explanation of experimental findings. Properties of the random walk are calculated from first principles, in particular fraction-average population density distributions for displacements along the principal axes. When substituted into the established optimal margin recipes these fraction-average distributions yield safety margins about 30% smaller as compared to the suggested values from end-of-fraction gaussian fits. Stylized facts of a random walk are identified in clinical data, such as the increase of the standard deviation of displacements with the square root of time. Least squares errors in the comparison to experimental results are reduced by about 50% when accounting for non-gaussian corrections from the random walk model.
Entropy Characterization of Random Network Models
Directory of Open Access Journals (Sweden)
Pedro J. Zufiria
2017-06-01
Full Text Available This paper elaborates on the Random Network Model (RNM as a mathematical framework for modelling and analyzing the generation of complex networks. Such framework allows the analysis of the relationship between several network characterizing features (link density, clustering coefficient, degree distribution, connectivity, etc. and entropy-based complexity measures, providing new insight on the generation and characterization of random networks. Some theoretical and computational results illustrate the utility of the proposed framework.
A Generalized Random Regret Minimization Model
Chorus, C.G.
2013-01-01
This paper presents, discusses and tests a generalized Random Regret Minimization (G-RRM) model. The G-RRM model is created by replacing a fixed constant in the attribute-specific regret functions of the RRM model, by a regret-weight variable. Depending on the value of the regret-weights, the G-RRM
A new model of Random Regret Minimization
Chorus, C.G.
2010-01-01
A new choice model is derived, rooted in the framework of Random Regret Minimization (RRM). The proposed model postulates that when choosing, people anticipate and aim to minimize regret. Whereas previous regret-based discrete choice-models assume that regret is experienced with respect to only the
Bisimulation and Logical Preservation for Continuous-Time Markov Decision Processes
Neuhausser, M.; Katoen, Joost P.
This paper introduces strong bisimulation for continuous-time Markov decision processes (CTMDPs), a stochastic model which allows for a nondeterministic choice between exponential distributions, and shows that bisimulation preserves the validity of CSL. To that end, we interpret the semantics of CSL
Continuous-Time Multiobjective Optimization Problems via Invexity
Directory of Open Access Journals (Sweden)
Valeriano A. De Oliveira
2007-02-01
Full Text Available We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.
Modelling complex networks by random hierarchical graphs
Directory of Open Access Journals (Sweden)
M.Wróbel
2008-06-01
Full Text Available Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erdős-Rényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasket-based graphs with random "decorations". We calculate the important characteristics of these graphs - average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique.
Locally optimal-digital redesign of continuous-time systems
Shieh, Leang-San; Zhao, Xiao-Ming; Zhang, Jian-Liang
1989-01-01
This paper presents a new optimal digital redesign technique for finding a dynamic digital control law from the given continuous-time counterpart by minimizing a local quadratic performance index. The quadratic performance index is chosen as the integral of the weighted squared difference between the states of the original closed-loop system and those of the digitally controlled closed-loop system at any instant between each sampling period. The developed optimal digital redesign control law enables the states of the digitally controlled closed-loop system 10 closely match those of the original closed-loop system at any instant between each sampling period, and it can easily be implemented using microcomputers with a relatively large sampling period.
Two-Stage Modelling Of Random Phenomena
Barańska, Anna
2015-12-01
The main objective of this publication was to present a two-stage algorithm of modelling random phenomena, based on multidimensional function modelling, on the example of modelling the real estate market for the purpose of real estate valuation and estimation of model parameters of foundations vertical displacements. The first stage of the presented algorithm includes a selection of a suitable form of the function model. In the classical algorithms, based on function modelling, prediction of the dependent variable is its value obtained directly from the model. The better the model reflects a relationship between the independent variables and their effect on the dependent variable, the more reliable is the model value. In this paper, an algorithm has been proposed which comprises adjustment of the value obtained from the model with a random correction determined from the residuals of the model for these cases which, in a separate analysis, were considered to be the most similar to the object for which we want to model the dependent variable. The effect of applying the developed quantitative procedures for calculating the corrections and qualitative methods to assess the similarity on the final outcome of the prediction and its accuracy, was examined by statistical methods, mainly using appropriate parametric tests of significance. The idea of the presented algorithm has been designed so as to approximate the value of the dependent variable of the studied phenomenon to its value in reality and, at the same time, to have it "smoothed out" by a well fitted modelling function.
Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion
Energy Technology Data Exchange (ETDEWEB)
Wei, Qingda, E-mail: weiqd@hqu.edu.cn [Huaqiao University, School of Economics and Finance (China); Chen, Xian, E-mail: chenxian@amss.ac.cn [Peking University, School of Mathematical Sciences (China)
2016-10-15
In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.
Random effect selection in generalised linear models
DEFF Research Database (Denmark)
Denwood, Matt; Houe, Hans; Forkman, Björn
We analysed abattoir recordings of meat inspection codes with possible relevance to onfarm animal welfare in cattle. Random effects logistic regression models were used to describe individual-level data obtained from 461,406 cattle slaughtered in Denmark. Our results demonstrate that the largest...
Feedback model predictive control by randomized algorithms
Batina, Ivo; Stoorvogel, Antonie Arij; Weiland, Siep
2001-01-01
In this paper we present a further development of an algorithm for stochastic disturbance rejection in model predictive control with input constraints based on randomized algorithms. The algorithm presented in our work can solve the problem of stochastic disturbance rejection approximately but with
Optimal Allocation in Stratified Randomized Response Model
Directory of Open Access Journals (Sweden)
Javid Shabbir
2005-07-01
Full Text Available A Warner (1965 randomized response model based on stratification is used to determine the allocation of samples. Both linear and log-linear cost functions are discussed under uni and double stratification. It observed that by using a log-linear cost function, one can get better allocations.
Steady states of continuous-time open quantum walks
Liu, Chaobin; Balu, Radhakrishnan
2017-07-01
Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always converges to a steady state regardless of the initial state when a graph is connected. When the graph is both connected and regular, it is shown that the steady state is the maximally mixed state. As shown by the examples in this article, the steady states of CTOQW can be very unusual and complicated even though the underlying graphs are simple. The examples demonstrate that the structure of a graph can affect quantum coherence in CTOQW through a long-time run. Precisely, the quantum coherence persists throughout the evolution of the CTOQW when the underlying topology is certain irregular graphs (such as a path or a star as shown in the examples). In contrast, the quantum coherence will eventually vanish from the open quantum system when the underlying topology is a regular graph (such as a cycle).
Continuous-Time Mean-Variance Portfolio Selection under the CEV Process
Ma, Hui-qiang
2014-01-01
We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance effici...
Wang, Xinghu; Hong, Yiguang; Yi, Peng; Ji, Haibo; Kang, Yu
2017-05-24
In this paper, a distributed optimization problem is studied for continuous-time multiagent systems with unknown-frequency disturbances. A distributed gradient-based control is proposed for the agents to achieve the optimal consensus with estimating unknown frequencies and rejecting the bounded disturbance in the semi-global sense. Based on convex optimization analysis and adaptive internal model approach, the exact optimization solution can be obtained for the multiagent system disturbed by exogenous disturbances with uncertain parameters.
Global dissipativity of continuous-time recurrent neural networks with time delay
International Nuclear Information System (INIS)
Liao Xiaoxin; Wang Jun
2003-01-01
This paper addresses the global dissipativity of a general class of continuous-time recurrent neural networks. First, the concepts of global dissipation and global exponential dissipation are defined and elaborated. Next, the sets of global dissipativity and global exponentially dissipativity are characterized using the parameters of recurrent neural network models. In particular, it is shown that the Hopfield network and cellular neural networks with or without time delays are dissipative systems
A random walk model to evaluate autism
Moura, T. R. S.; Fulco, U. L.; Albuquerque, E. L.
2018-02-01
A common test administered during neurological examination in children is the analysis of their social communication and interaction across multiple contexts, including repetitive patterns of behavior. Poor performance may be associated with neurological conditions characterized by impairments in executive function, such as the so-called pervasive developmental disorders (PDDs), a particular condition of the autism spectrum disorders (ASDs). Inspired in these diagnosis tools, mainly those related to repetitive movements and behaviors, we studied here how the diffusion regimes of two discrete-time random walkers, mimicking the lack of social interaction and restricted interests developed for children with PDDs, are affected. Our model, which is based on the so-called elephant random walk (ERW) approach, consider that one of the random walker can learn and imitate the microscopic behavior of the other with probability f (1 - f otherwise). The diffusion regimes, measured by the Hurst exponent (H), is then obtained, whose changes may indicate a different degree of autism.
Quantum trajectories and measurements in continuous time. The diffusive case
International Nuclear Information System (INIS)
Barchielli, Alberto; Gregoratti, Matteo
2009-01-01
continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output. (orig.)
Echocardiography as an indication of continuous-time cardiac quiescence
Wick, C. A.; Auffermann, W. F.; Shah, A. J.; Inan, O. T.; Bhatti, P. T.; Tridandapani, S.
2016-07-01
Cardiac computed tomography (CT) angiography using prospective gating requires that data be acquired during intervals of minimal cardiac motion to obtain diagnostic images of the coronary vessels free of motion artifacts. This work is intended to assess B-mode echocardiography as a continuous-time indication of these quiescent periods to determine if echocardiography can be used as a cost-efficient, non-ionizing modality to develop new prospective gating techniques for cardiac CT. These new prospective gating approaches will not be based on echocardiography itself but on CT-compatible modalities derived from the mechanics of the heart (e.g. seismocardiography and impedance cardiography), unlike the current standard electrocardiogram. To this end, echocardiography and retrospectively-gated CT data were obtained from ten patients with varied cardiac conditions. CT reconstructions were made throughout the cardiac cycle. Motion of the interventricular septum (IVS) was calculated from both echocardiography and CT reconstructions using correlation-based, deviation techniques. The IVS was chosen because it (1) is visible in echocardiography images, whereas the coronary vessels generally are not, and (2) has been shown to be a suitable indicator of cardiac quiescence. Quiescent phases were calculated as the minima of IVS motion and CT volumes were reconstructed for these phases. The diagnostic quality of the CT reconstructions from phases calculated from echocardiography and CT data was graded on a four-point Likert scale by a board-certified radiologist fellowship-trained in cardiothoracic radiology. Using a Wilcoxon signed-rank test, no significant difference in the diagnostic quality of the coronary vessels was found between CT volumes reconstructed from echocardiography- and CT-selected phases. Additionally, there was a correlation of 0.956 between the echocardiography- and CT-selected phases. This initial work suggests that B-mode echocardiography can be used as a
Random matrix models for phase diagrams
International Nuclear Information System (INIS)
Vanderheyden, B; Jackson, A D
2011-01-01
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from quantum chromodynamics to high-T c materials. Instead of working from specific models, phase diagrams are constructed by averaging over the ensemble of theories that possesses the relevant symmetries of the problem. Although approximate in nature, this approach has a number of advantages. First, it can be useful in distinguishing generic features from model-dependent details. Second, it can help in understanding the 'minimal' number of symmetry constraints required to reproduce specific phase structures. Third, the robustness of predictions can be checked with respect to variations in the detailed description of the interactions. Finally, near critical points, random matrix models bear strong similarities to Ginsburg-Landau theories with the advantage of additional constraints inherited from the symmetries of the underlying interaction. These constraints can be helpful in ruling out certain topologies in the phase diagram. In this Key Issues Review, we illustrate the basic structure of random matrix models, discuss their strengths and weaknesses, and consider the kinds of system to which they can be applied.
i QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
Huang, Li; Wang, Yilin; Meng, Zi Yang; Du, Liang; Werner, Philipp; Dai, Xi
2015-10-01
Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed i QIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantum Monte Carlo algorithm, as well as some essential pre- and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for i QIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of i QIST.
Fermion bag approach to Hamiltonian lattice field theories in continuous time
Huffman, Emilie; Chandrasekharan, Shailesh
2017-12-01
We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.
Summary statistics for end-point conditioned continuous-time Markov chains
DEFF Research Database (Denmark)
Hobolth, Asger; Jensen, Jens Ledet
two states and the distribution of the total number of jumps) for discretely observed continuous time Markov chains. Three alternative methods for calculating properties of summary statistics are described and the pros and cons of the methods are discussed. The methods are based on (i) an eigenvalue...... decomposition of the rate matrix, (ii) the uniformization method, and (iii) integrals of matrix exponentials. In particular we develop a framework that allows for analyses of rather general summary statistics using the uniformization method.......Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behavior and mathematical finance. We consider the problem of calculating properties of summary statistics (e.g. mean time spent in a state, mean number of jumps between...
The impact of conventional space-time aggregation on the dynamics of continuous-time rainfall
Sansom, John; Bulla, Jan; Carey-Smith, Trevor; Thomson, Peter
2017-09-01
Rainfall is a continuous-time phenomenon typically characterized by precipitation states such as rain, showers, and dry whose dependence varies over a variety of space-time scales. Here attention is focused on the effective identification of rain and shower precipitation states over a region where these states have been determined by a hidden semi-Markov model of continuous-time precipitation. The states identified provide an accurate description of precipitation dynamics and can be regarded as close proxies to synoptic weather types of the same name. The stochastic properties and structure of these states (rather than precipitation amounts) are explored and delineated. A primary objective of the paper is to better understand the impact of conventional space-time aggregation on the dynamics of rainfall. What aggregation time scales result in more faithful descriptions of the space-time dynamics of continuous-time rainfall? While rain might be expected to be more spatially coherent than showers and involve longer time scales, dry periods involve much longer time and space scales again than either rain or showers. These issues are discussed and conclusions drawn which provide guidance and insights useful for the development of space-time precipitation models and, more generally, the design of rainfall observation networks and data archives.
On-line parameter and delay estimation of continuous-time dynamic systems
Directory of Open Access Journals (Sweden)
Kozłowski Janusz
2015-06-01
Full Text Available The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.
Random-walk model of precompound decay
International Nuclear Information System (INIS)
Akkermans, J.M.; Gruppelaar, H.
1981-01-01
It is demonstrated that the dynamics of precompound nuclear decay can be formulated, with regard to emission spectra as well as angular distributions, in terms of a simple random walk of the composite nuclear system. In distinction to other preequilibrium models a discrete time parameter is introduced, corresponding to the number of intranuclear interactions. This random-walk description can be employed to analytically calculate several characteristics of the equilibration process, such as the mean time to emission from an exciton state, the mean first passage time, and the attainment of isotropy. Also a simple and compact description of multi-particle emission is obtained. A necessary and sufficient condition is given for the equivalence of the random-walk and the usual exciton models. As an application some neutron emission spectra of neutron-induced reactions on 127 I at E = 15 to 50 MeV have been calculated. The results show that preequilibrium effects are very important in the first particle emission. In the emission of secondary particles preequilibrium effects need to be included at incoming energies above about 25 MeV. Preequilibrium effects in tertiary emission spectra are not significant below E = 50 MeV. (orig.)
The deterministic SIS epidemic model in a Markovian random environment.
Economou, Antonis; Lopez-Herrero, Maria Jesus
2016-07-01
We consider the classical deterministic susceptible-infective-susceptible epidemic model, where the infection and recovery rates depend on a background environmental process that is modeled by a continuous time Markov chain. This framework is able to capture several important characteristics that appear in the evolution of real epidemics in large populations, such as seasonality effects and environmental influences. We propose computational approaches for the determination of various distributions that quantify the evolution of the number of infectives in the population.
Particle filters for random set models
Ristic, Branko
2013-01-01
“Particle Filters for Random Set Models” presents coverage of state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. The resulting algorithms, known as particle filters, in the last decade have become one of the essential tools for stochastic filtering, with applications ranging from navigation and autonomous vehicles to bio-informatics and finance. While particle filters have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. These recent developments have dramatically widened the scope of applications, from single to multiple appearing/disappearing objects, from precise to imprecise measurements and measurement models. This book...
Stability of a Random Walk Model for Fruiting Body Aggregation in M. xanthus
McKenzie-Smith, G. C.; Schüttler, H. B.; Cotter, C.; Shimkets, L.
2015-03-01
Myxococcus xanthus exhibits the social starvation behavior of aggregation into a fruiting body containing myxospores able to survive harsh conditions. During fruiting body aggregation, individual bacteria follow random walk paths determined by randomly selected runtimes, turning angles, and speeds. We have simulated this behavior in terms of a continuous-time random walk (CTRW) model, re-formulated as a system of integral equations, describing the angle-resolved cell density, R(r, t, θ), at position r and cell orientation angle θ at time t, and angle-integrated ambient cell density ρ(r, t). By way of a linear stability analysis, we investigated whether a uniform cell density R0 will be unstable for a small non-uniform density perturbation δR(r, t, θ). Such instability indicates aggregate formation, whereas stability indicates absence of aggregation. We show that a broadening of CTRW distributions of the random speed and/or random runtimes strongly favors aggregation. We also show that, in the limit of slowly-varying (long-wavelength) density perturbations, the time-dependent linear density response can be approximated by a drift-diffusion model for which we calculate diffusion and drift coefficients as functions of the CTRW model parameters. Funded by the Fungal Genomics and Computational Biology REU at UGA.
Modeling superhydrophobic surfaces comprised of random roughness
Samaha, M. A.; Tafreshi, H. Vahedi; Gad-El-Hak, M.
2011-11-01
We model the performance of superhydrophobic surfaces comprised of randomly distributed roughness that resembles natural surfaces, or those produced via random deposition of hydrophobic particles. Such a fabrication method is far less expensive than ordered-microstructured fabrication. The present numerical simulations are aimed at improving our understanding of the drag reduction effect and the stability of the air-water interface in terms of the microstructure parameters. For comparison and validation, we have also simulated the flow over superhydrophobic surfaces made up of aligned or staggered microposts for channel flows as well as streamwise or spanwise ridge configurations for pipe flows. The present results are compared with other theoretical and experimental studies. The numerical simulations indicate that the random distribution of surface roughness has a favorable effect on drag reduction, as long as the gas fraction is kept the same. The stability of the meniscus, however, is strongly influenced by the average spacing between the roughness peaks, which needs to be carefully examined before a surface can be recommended for fabrication. Financial support from DARPA, contract number W91CRB-10-1-0003, is acknowledged.
Connectivity ranking of heterogeneous random conductivity models
Rizzo, C. B.; de Barros, F.
2017-12-01
To overcome the challenges associated with hydrogeological data scarcity, the hydraulic conductivity (K) field is often represented by a spatial random process. The state-of-the-art provides several methods to generate 2D or 3D random K-fields, such as the classic multi-Gaussian fields or non-Gaussian fields, training image-based fields and object-based fields. We provide a systematic comparison of these models based on their connectivity. We use the minimum hydraulic resistance as a connectivity measure, which it has been found to be strictly correlated with early time arrival of dissolved contaminants. A computationally efficient graph-based algorithm is employed, allowing a stochastic treatment of the minimum hydraulic resistance through a Monte-Carlo approach and therefore enabling the computation of its uncertainty. The results show the impact of geostatistical parameters on the connectivity for each group of random fields, being able to rank the fields according to their minimum hydraulic resistance.
Identification of continuous-time systems from samples of input ...
Indian Academy of Sciences (India)
Identification of process parameters for control purposes must often be done using a digital computer, from samples of input±output observations. On the other hand, the .... As stated earlier, it is convenient to divide the problem into two subproblems. The first of these is the determination of a suitable discrete-time model from ...
Applying Mean-Field Approximation to Continuous Time Markov Chains
Kolesnichenko, A.V.; Senni, Valerio; Pourranjabar, Alireza; Remke, A.K.I.; Stoelinga, M.I.A.
2014-01-01
The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found
On Discrete Time Control of Continuous Time Systems
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
This report is meant as a supplement or an extension to the material used in connection to or after the courses Stochastic Adaptive Control (02421) and Static and Dynamic Optimization (02711) given at the department Department of Informatics and Mathematical Modelling, The Technical University...
Forecasting the Global Mean Sea Level, a Continuous-Time State-Space Approach
DEFF Research Database (Denmark)
Boldrini, Lorenzo
) and the temperature reconstruction from Hansen et al. (2010). We compare the forecasting performance of the proposed specification to the procedures developed in Rahmstorf (2007b) and Vermeer and Rahmstorf (2009). Finally, we compute projections for the sea-level rise conditional on the 21st century SRES temperature......In this paper we propose a continuous-time, Gaussian, linear, state-space system to model the relation between global mean sea level (GMSL) and the global mean temperature (GMT), with the aim of making long-term projections for the GMSL. We provide a justification for the model specification based...... on popular semi-empirical methods present in the literature and on zero-dimensional energy balance models. We show that some of the models developed in the literature on semi-empirical models can be analysed within this framework. We use the sea-level data reconstruction developed in Church and White (2011...
Adaptive control of chaotic continuous-time systems with delay
Tian, Yu-Chu; Gao, Furong
1998-06-01
A simple delay system governed by a first-order differential-delay equation may behave chaotically, but the conditions for the system to have such behaviors have not been well recognized. In this paper, a set of rules is postulated first for the conditions for the delay system to display chaos. A model-reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters. Numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme.
DEFF Research Database (Denmark)
Hobolth, Asger; Stone, Eric
2009-01-01
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from...... computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete...
Random matrix model of adiabatic quantum computing
International Nuclear Information System (INIS)
Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2005-01-01
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size
Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework
International Nuclear Information System (INIS)
Zhou, X.Y.; Li, D.
2000-01-01
This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be 'embedded' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem
Simulation of a directed random-walk model: the effect of pseudo-random-number correlations
Shchur, L. N.; Heringa, J. R.; Blöte, H. W. J.
1996-01-01
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms.
Dynamics of the Random Field Ising Model
Xu, Jian
The Random Field Ising Model (RFIM) is a general tool to study disordered systems. Crackling noise is generated when disordered systems are driven by external forces, spanning a broad range of sizes. Systems with different microscopic structures such as disordered mag- nets and Earth's crust have been studied under the RFIM. In this thesis, we investigated the domain dynamics and critical behavior in two dipole-coupled Ising ferromagnets Nd2Fe14B and LiHoxY 1-xF4. With Tc well above room temperature, Nd2Fe14B has shown reversible disorder when exposed to an external transverse field and crosses between two universality classes in the strong and weak disorder limits. Besides tunable disorder, LiHoxY1-xF4 has shown quantum tunneling effects arising from quantum fluctuations, providing another mechanism for domain reversal. Universality within and beyond power law dependence on avalanche size and energy were studied in LiHo0.65Y0.35 F4.
Spectra of Anderson type models with decaying randomness
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
There have been but few models in higher dimensional random operators of the Anderson model type in which presence ... The models we consider in this paper are related to the discrete Laplacian ( u)(n) = ∑. |i|=1 u(n + i) on l2( ν). .... identically distributed real valued random variables with distribution µ. The operator H0.
A continuous-time/discrete-time mixed audio-band sigma delta ADC
Yan, Liu; Siliang, Hua; Donghui, Wang; Chaohuan, Hou
2011-01-01
This paper introduces a mixed continuous-time/discrete-time, single-loop, fourth-order, 4-bit audio-band sigma delta ADC that combines the benefits of continuous-time and discrete-time circuits, while mitigating the challenges associated with continuous-time design. Measurement results show that the peak SNR of this ADC reaches 100 dB and the total power consumption is less than 30 mW.
A continuous-time/discrete-time mixed audio-band sigma delta ADC
International Nuclear Information System (INIS)
Liu Yan; Hua Siliang; Wang Donghui; Hou Chaohuan
2011-01-01
This paper introduces a mixed continuous-time/discrete-time, single-loop, fourth-order, 4-bit audio-band sigma delta ADC that combines the benefits of continuous-time and discrete-time circuits, while mitigating the challenges associated with continuous-time design. Measurement results show that the peak SNR of this ADC reaches 100 dB and the total power consumption is less than 30 mW. (semiconductor integrated circuits)
Continuous-Time Mean-Variance Portfolio Selection under the CEV Process
Directory of Open Access Journals (Sweden)
Hui-qiang Ma
2014-01-01
Full Text Available We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.
A coverage metric to evaluate tests for continuous-time dynamic systems
Skruch, Paweł
2011-06-01
We present a test quality measure that allows for quantifying the completeness of black-box tests for continuous-time dynamic systems. The measure is based on a state space model of the system under test. The metric has been called the state space coverage. The classical coverage metrics, such as statement, branch, and path coverage, are not appropriate for dynamic systems because such systems are defined by differential equations and usually have an infinite number of states. The objective of the paper is to develop a necessary foundation for the metric as well as to present guidance on its application to software systems that incorporate dynamic behavior. The purpose of the proposed solution is to better assure the test engineer that a given test set is sufficient and to indicate where additional testing is required. An application example is presented to illustrate theoretical analysis and mathematical formulation.
Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Dufour, F., E-mail: dufour@math.u-bordeaux1.fr [Bordeaux INP, IMB, UMR CNRS 5251 (France); Piunovskiy, A. B., E-mail: piunov@liv.ac.uk [University of Liverpool, Department of Mathematical Sciences (United Kingdom)
2016-08-15
In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.
Single passband microwave photonic filter using continuous-time impulse response.
Huang, Thomas X H; Yi, Xiaoke; Minasian, Robert A
2011-03-28
A single passband microwave photonic signal processor based on continuous time impulse response that has high resolution, multiple-taps and baseband-free response as well as exhibiting a square-top passband and tunability, is presented. The design and synthesis of the frequency response are based on a full systematic model for single passband microwave photonic filters to account for arbitrary spectrum slice shapes, which for the first time investigates the combined effects from both the dispersion-induced carrier suppression effect and the RF decay effect due to the spectrum slice width, to enable the optimum design to be realized by utilizing the carrier suppression effect to improve the filter performance. Experimental results demonstrate a high order microwave filter showing high resolution single passband filtering as well as exhibiting reconfiguration, square-top passband and tunability, for the first time to our best knowledge.
Continuous-Time Discrete-Distribution Theory for Activity-Driven Networks
Zino, Lorenzo; Rizzo, Alessandro; Porfiri, Maurizio
2016-11-01
Activity-driven networks are a powerful paradigm to study epidemic spreading over time-varying networks. Despite significant advances, most of the current understanding relies on discrete-time computer simulations, in which each node is assigned an activity potential from a continuous distribution. Here, we establish a continuous-time discrete-distribution framework toward an analytical treatment of the epidemic spreading, from its onset to the endemic equilibrium. In the thermodynamic limit, we derive a nonlinear dynamical system to accurately model the epidemic spreading and leverage techniques from the fields of differential inclusions and adaptive estimation to inform short- and long-term predictions. We demonstrate our framework through the analysis of two real-world case studies, exemplifying different physical phenomena and time scales.
Modeling of Random Delays in Networked Control Systems
Directory of Open Access Journals (Sweden)
Yuan Ge
2013-01-01
Full Text Available In networked control systems (NCSs, the presence of communication networks in control loops causes many imperfections such as random delays, packet losses, multipacket transmission, and packet disordering. In fact, random delays are usually the most important problems and challenges in NCSs because, to some extent, other problems are often caused by random delays. In order to compensate for random delays which may lead to performance degradation and instability of NCSs, it is necessary to establish the mathematical model of random delays before compensation. In this paper, four major delay models are surveyed including constant delay model, mutually independent stochastic delay model, Markov chain model, and hidden Markov model. In each delay model, some promising compensation methods of delays are also addressed.
Jensen, K; Baier, Christel; Haverkort, Boudewijn R.H.M.; Podelski, A.; Hermanns, H.; Katoen, Joost P.
2004-01-01
A continuous-time Markov decision process (CTMDP) is a generalization of a continuous-time Markov chain in which both probabilistic and nondeterministic choices co-exist. This paper presents an efficient algorithm to compute the maximum (or minimum) probability to reach a set of goal states within a
Baier, Christel; Hermanns, H.; Katoen, Joost P.; Haverkort, Boudewijn R.H.M.
2005-01-01
A continuous-time Markov decision process (CTMDP) is a generalization of a continuous-time Markov chain in which both probabilistic and nondeterministic choices co-exist. This paper presents an efficient algorithm to compute the maximum (or minimum) probability to reach a set of goal states within a
A Note on the Correlated Random Coefficient Model
DEFF Research Database (Denmark)
Kolodziejczyk, Christophe
In this note we derive the bias of the OLS estimator for a correlated random coefficient model with one random coefficient, but which is correlated with a binary variable. We provide set-identification to the parameters of interest of the model. We also show how to reduce the bias of the estimator...
A random energy model for size dependence : recurrence vs. transience
Külske, Christof
1998-01-01
We investigate the size dependence of disordered spin models having an infinite number of Gibbs measures in the framework of a simplified 'random energy model for size dependence'. We introduce two versions (involving either independent random walks or branching processes), that can be seen as
Some random models in traffic science
Energy Technology Data Exchange (ETDEWEB)
Hjorth, U.
1996-06-01
We give an overview of stochastic models for the following traffic phenomena. Models for traffic flow including gaps and capacities for lanes, crossings and roundabouts. Models for wanted and achieved speed distributions. Mode selection models including dispersed equilibrium models and traffic accident models. Also some statistical questions are discussed. 60 refs, 1 tab
International Nuclear Information System (INIS)
Schuetz, G.; Sandow, S.
1993-05-01
We consider systems of particles hopping stochastically on d-dimensional lattices with space-dependent probabilities. We map the master equation in a Fock space where the dynamics are given by a quantum Hamiltonian (continuous time) or a transfer matrix resp. (discrete time). We show that under certain conditions the time-dependent two-point density correlation function in N-particle steady state can be computed from the probability distribution of a single particle moving in the same environment. Focussing on exclusion models where the lattice site can be occupied by at most one particle we discuss as an example for such a stochastic process a generalized Heisenberg antiferromagnet where the strength of the spin-spin coupling in space-dependent. In discrete time one obtains for one dimensional systems the diagonal-to-diagonal transfer matrix of the two dimensional six vertex model with space dependent vertex weights. For a random distribution of the vertex weights one obtains a version of the random barrier model describing diffusion of particles in disordered media. We derive exact expressions for the average two-point density correlation function in the presence of weak, correlated disorder. (authors)
A Model for Random Student Drug Testing
Nelson, Judith A.; Rose, Nancy L.; Lutz, Danielle
2011-01-01
The purpose of this case study was to examine random student drug testing in one school district relevant to: (a) the perceptions of students participating in competitive extracurricular activities regarding drug use and abuse; (b) the attitudes and perceptions of parents, school staff, and community members regarding student drug involvement; (c)…
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
We present a random matrix ensemble where real, positive semi-deﬁnite matrix elements, , are log-normal distributed, exp [ − log 2 ( x ) ] . We show that the level density varies with energy, , as 2/(1 + ) for large , in the unitary family, consistent with the expectation for disordered conductors. The two-level ...
Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time
Kelly, D. T B
2014-09-22
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so for small ensemble size. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with respect to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz \\'63 and \\'96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise.
Critical thresholds for eventual extinction in randomly disturbed population growth models.
Peckham, Scott D; Waymire, Edward C; De Leenheer, Patrick
2018-02-16
This paper considers several single species growth models featuring a carrying capacity, which are subject to random disturbances that lead to instantaneous population reduction at the disturbance times. This is motivated in part by growing concerns about the impacts of climate change. Our main goal is to understand whether or not the species can persist in the long run. We consider the discrete-time stochastic process obtained by sampling the system immediately after the disturbances, and find various thresholds for several modes of convergence of this discrete process, including thresholds for the absence or existence of a positively supported invariant distribution. These thresholds are given explicitly in terms of the intensity and frequency of the disturbances on the one hand, and the population's growth characteristics on the other. We also perform a similar threshold analysis for the original continuous-time stochastic process, and obtain a formula that allows us to express the invariant distribution for this continuous-time process in terms of the invariant distribution of the discrete-time process, and vice versa. Examples illustrate that these distributions can differ, and this sends a cautionary message to practitioners who wish to parameterize these and related models using field data. Our analysis relies heavily on a particular feature shared by all the deterministic growth models considered here, namely that their solutions exhibit an exponentially weighted averaging property between a function of the initial condition, and the same function applied to the carrying capacity. This property is due to the fact that these systems can be transformed into affine systems.
Xu, Jason; Minin, Vladimir N
2015-07-01
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.
Directory of Open Access Journals (Sweden)
Tataru Paula
2011-12-01
Full Text Available Abstract Background Continuous time Markov chains (CTMCs is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications past evolutionary events (exact times and types of changes are unaccessible and the past must be inferred from DNA sequence data observed in the present. Results We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned on the end-points of the chain, and compare their performance with respect to accuracy and running time. The first algorithm is based on an eigenvalue decomposition of the rate matrix (EVD, the second on uniformization (UNI, and the third on integrals of matrix exponentials (EXPM. The implementation in R of the algorithms is available at http://www.birc.au.dk/~paula/. Conclusions We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually faster than EVD.
Event-Triggered Fault Detection Filter Design for a Continuous-Time Networked Control System.
Wang, Yu-Long; Shi, Peng; Lim, Cheng-Chew; Liu, Yuan
2016-12-01
This paper studies the problem of event-triggered fault detection filter (FDF) and controller coordinated design for a continuous-time networked control system (NCS) with biased sensor faults. By considering sensor-to-FDF network-induced delays and packet dropouts, which do not impose a constraint on the event-triggering mechanism, and proposing the simultaneous network bandwidth utilization ratio and fault occurrence probability-based event-triggering mechanism, a new closed-loop model for the considered NCS is established. Based on the established model, the event-triggered H ∞ performance analysis, and FDF and controller coordinated design are presented. The combined mutually exclusive distribution and Wirtinger-based integral inequality approach is proposed for the first time to deal with integral inequalities for products of vectors. This approach is proved to be less conservative than the existing Wirtinger-based integral inequality approach. The designed FDF and controller can guarantee the sensitivity of the residual signal to faults and the robustness of the NCS to external disturbances. The simulation results verify the effectiveness of the proposed event-triggering mechanism, and the FDF and controller coordinated design.
The general critical analysis for continuous-time UPPAM recurrent neural networks.
Qiao, Chen; Jing, Wen-Feng; Fang, Jian; Wang, Yu-Ping
2016-01-29
The uniformly pseudo-projection-anti-monotone (UPPAM) neural network model, which can be considered as the unified continuous-time neural networks (CNNs), includes almost all of the known CNNs individuals. Recently, studies on the critical dynamics behaviors of CNNs have drawn special attentions due to its importance in both theory and applications. In this paper, we will present the analysis of the UPPAM network under the general critical conditions. It is shown that the UPPAM network possesses the global convergence and asymptotical stability under the general critical conditions if the network satisfies one quasi-symmetric requirement on the connective matrices, which is easy to be verified and applied. The general critical dynamics have rarely been studied before, and this work is an attempt to gain an meaningful assurance of general critical convergence and stability of CNNs. Since UPPAM network is the unified model for CNNs, the results obtained here can generalize and extend the existing critical conclusions for CNNs individuals, let alone those non-critical cases. Moreover, the easily verified conditions for general critical convergence and stability can further promote the applications of CNNs.
CMOS continuous-time adaptive equalizers for high-speed serial links
Gimeno Gasca, Cecilia; Aldea Chagoyen, Concepción
2015-01-01
This book introduces readers to the design of adaptive equalization solutions integrated in standard CMOS technology for high-speed serial links. Since continuous-time equalizers offer various advantages as an alternative to discrete-time equalizers at multi-gigabit rates, this book provides a detailed description of continuous-time adaptive equalizers design - both at transistor and system levels-, their main characteristics and performances. The authors begin with a complete review and analysis of the state of the art of equalizers for wireline applications, describing why they are necessary, their types, and their main applications. Next, theoretical fundamentals of continuous-time adaptive equalizers are explored. Then, new structures are proposed to implement the different building blocks of the adaptive equalizer: line equalizer, loop-filters, power comparator, etc. The authors demonstrate the design of a complete low-power, low-voltage, high-speed, continuous-time adaptive equalizer. Finally, a cost-...
Conditional Monte Carlo randomization tests for regression models.
Parhat, Parwen; Rosenberger, William F; Diao, Guoqing
2014-08-15
We discuss the computation of randomization tests for clinical trials of two treatments when the primary outcome is based on a regression model. We begin by revisiting the seminal paper of Gail, Tan, and Piantadosi (1988), and then describe a method based on Monte Carlo generation of randomization sequences. The tests based on this Monte Carlo procedure are design based, in that they incorporate the particular randomization procedure used. We discuss permuted block designs, complete randomization, and biased coin designs. We also use a new technique by Plamadeala and Rosenberger (2012) for simple computation of conditional randomization tests. Like Gail, Tan, and Piantadosi, we focus on residuals from generalized linear models and martingale residuals from survival models. Such techniques do not apply to longitudinal data analysis, and we introduce a method for computation of randomization tests based on the predicted rate of change from a generalized linear mixed model when outcomes are longitudinal. We show, by simulation, that these randomization tests preserve the size and power well under model misspecification. Copyright © 2014 John Wiley & Sons, Ltd.
Approximating prediction uncertainty for random forest regression models
John W. Coulston; Christine E. Blinn; Valerie A. Thomas; Randolph H. Wynne
2016-01-01
Machine learning approaches such as random forest haveÂ increased for the spatial modeling and mapping of continuousÂ variables. Random forest is a non-parametric ensembleÂ approach, and unlike traditional regression approaches thereÂ is no direct quantification of prediction error. UnderstandingÂ prediction uncertainty is important when using model-basedÂ continuous maps as...
A random spatial network model based on elementary postulates
Karlinger, Michael R.; Troutman, Brent M.
1989-01-01
A model for generating random spatial networks that is based on elementary postulates comparable to those of the random topology model is proposed. In contrast to the random topology model, this model ascribes a unique spatial specification to generated drainage networks, a distinguishing property of some network growth models. The simplicity of the postulates creates an opportunity for potential analytic investigations of the probabilistic structure of the drainage networks, while the spatial specification enables analyses of spatially dependent network properties. In the random topology model all drainage networks, conditioned on magnitude (number of first-order streams), are equally likely, whereas in this model all spanning trees of a grid, conditioned on area and drainage density, are equally likely. As a result, link lengths in the generated networks are not independent, as usually assumed in the random topology model. For a preliminary model evaluation, scale-dependent network characteristics, such as geometric diameter and link length properties, and topologic characteristics, such as bifurcation ratio, are computed for sets of drainage networks generated on square and rectangular grids. Statistics of the bifurcation and length ratios fall within the range of values reported for natural drainage networks, but geometric diameters tend to be relatively longer than those for natural networks.
Application of random regression models to the genetic evaluation ...
African Journals Online (AJOL)
The model included fixed regression on AM (range from 30 to 138 mo) and the effect of herd-measurement date concatenation. Random parts of the model were RRM coefficients for additive and permanent environmental effects, while residual effects were modelled to account for heterogeneity of variance by AY. Estimates ...
The Random Walk Drainage Simulation Model as a Teaching Exercise
High, Colin; Richards, Paul
1972-01-01
Practical instructions about using the random walk drainage network simulation model as a teaching excercise are given and the results discussed. A source of directional bias in the resulting simulated drainage patterns is identified and given an interpretation in the terms of the model. Three points of educational value concerning the model are…
Rumor spreading models with random denials
Giorno, Virginia; Spina, Serena
2016-11-01
The concept of denial is introduced on rumor spreading processes. The denials occur with a certain rate and they reset to start the initial situation. A population of N individuals is subdivided into ignorants, spreaders and stiflers; at the initial time there is only one spreader and the rest of the population is ignorant. The denials are introduced in the classic DK model and in its generalization, in which a spreader can transmit the rumor at most to k ignorants. The steady state densities are analyzed for these models. Finally, a numerical analysis is performed to study the rule of the involved parameters and to compare the proposed models.
Directory of Open Access Journals (Sweden)
Botond Molnár
Full Text Available There has been a long history of using neural networks for combinatorial optimization and constraint satisfaction problems. Symmetric Hopfield networks and similar approaches use steepest descent dynamics, and they always converge to the closest local minimum of the energy landscape. For finding global minima additional parameter-sensitive techniques are used, such as classical simulated annealing or the so-called chaotic simulated annealing, which induces chaotic dynamics by addition of extra terms to the energy landscape. Here we show that asymmetric continuous-time neural networks can solve constraint satisfaction problems without getting trapped in non-solution attractors. We concentrate on a model solving Boolean satisfiability (k-SAT, which is a quintessential NP-complete problem. There is a one-to-one correspondence between the stable fixed points of the neural network and the k-SAT solutions and we present numerical evidence that limit cycles may also be avoided by appropriately choosing the parameters of the model. This optimal parameter region is fairly independent of the size and hardness of instances, this way parameters can be chosen independently of the properties of problems and no tuning is required during the dynamical process. The model is similar to cellular neural networks already used in CNN computers. On an analog device solving a SAT problem would take a single operation: the connection weights are determined by the k-SAT instance and starting from any initial condition the system searches until finding a solution. In this new approach transient chaotic behavior appears as a natural consequence of optimization hardness and not as an externally induced effect.
A generalized model via random walks for information filtering
Energy Technology Data Exchange (ETDEWEB)
Ren, Zhuo-Ming, E-mail: zhuomingren@gmail.com [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Kong, Yixiu [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland); Shang, Ming-Sheng, E-mail: msshang@cigit.ac.cn [Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, ChongQing, 400714 (China); Zhang, Yi-Cheng [Department of Physics, University of Fribourg, Chemin du Musée 3, CH-1700, Fribourg (Switzerland)
2016-08-06
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
A generalized model via random walks for information filtering
International Nuclear Information System (INIS)
Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng
2016-01-01
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation. - Highlights: • We propose a generalized recommendation model employing the random walk dynamics. • The proposed model with single and hybrid of degree information is analyzed. • A strategy with the hybrid degree information improves precision of recommendation.
Money creation in a random matching model
Alexei Deviatov
2004-01-01
I study money creation in versions of the Trejos-Wright (1995) and Shi (1995) models with indivisible money and individual holdings bounded at two units. I work with the same class of policies as in Deviatov and Wallace (2001), who study money creation in that model. However, I consider an alternative notion of implementability–the ex ante pairwise core. I compute a set of numerical examples to determine whether money creation is beneficial. I find beneficial e?ects of money creation if indiv...
Directory of Open Access Journals (Sweden)
François Niragire
2017-05-01
Full Text Available Child survival programmes are efficient when they target the most significant and area-specific factors. This study aimed to assess the key determinants and spatial variation of child mortality at the district level in Rwanda. Data from the 2010 Rwanda Demographic and Health Survey were analysed for 8817 live births that occurred during five years preceding the survey. Out of the children born, 433 had died before survey interviews were carried out. A full Bayesian geo-additive continuous-time hazard model enabled us to maximise data utilisation and hence improve the accuracy of our estimates. The results showed substantial district- level spatial variation in childhood mortality in Rwanda. District-specific spatial characteristics were particularly associated with higher death hazards in two districts: Musanze and Nyabihu. The model estimates showed that there were lower death rates among children from households of medium and high economic status compared to those from low-economic status households. Factors, such as four antenatal care visits, delivery at a health facility, prolonged breastfeeding and mothers younger than 31 years were associated with lower child death rates. Long preceding birth intervals were also associated with fewer hazards. For these reasons, programmes aimed at reducing child mortality gaps between districts in Rwanda should target maternal factors and take into consideration district-specific spatial characteristics. Further, child survival gains require strengthening or scaling-up of existing programmes pertaining to access to, and utilisation of maternal and child health care services as well as reduction of the household gap in the economic status.
Dutta, Samrat; Patchaikani, Prem Kumar; Behera, Laxmidhar
2016-07-01
This paper presents a single-network adaptive critic-based controller for continuous-time systems with unknown dynamics in a policy iteration (PI) framework. It is assumed that the unknown dynamics can be estimated using the Takagi-Sugeno-Kang fuzzy model with arbitrary precision. The successful implementation of a PI scheme depends on the effective learning of critic network parameters. Network parameters must stabilize the system in each iteration in addition to approximating the critic and the cost. It is found that the critic updates according to the Hamilton-Jacobi-Bellman formulation sometimes lead to the instability of the closed-loop systems. In the proposed work, a novel critic network parameter update scheme is adopted, which not only approximates the critic at current iteration but also provides feasible solutions that keep the policy stable in the next step of training by combining a Lyapunov-based linear matrix inequalities approach with PI. The critic modeling technique presented here is the first of its kind to address this issue. Though multiple literature exists discussing the convergence of PI, however, to the best of our knowledge, there exists no literature, which focuses on the effect of critic network parameters on the convergence. Computational complexity in the proposed algorithm is reduced to the order of (Fz)(n-1) , where n is the fuzzy state dimensionality and Fz is the number of fuzzy zones in the states space. A genetic algorithm toolbox of MATLAB is used for searching stable parameters while minimizing the training error. The proposed algorithm also provides a way to solve for the initial stable control policy in the PI scheme. The algorithm is validated through real-time experiment on a commercial robotic manipulator. Results show that the algorithm successfully finds stable critic network parameters in real time for a highly nonlinear system.
Casabán, M.-C.; Cortés, J.-C.; Romero, J.-V.; Roselló, M.-D.
2015-07-01
This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.
Money creation process in a random redistribution model
Chen, Siyan; Wang, Yougui; Li, Keqiang; Wu, Jinshan
2014-01-01
In this paper, the dynamical process of money creation in a random exchange model with debt is investigated. The money creation kinetics are analyzed by both the money-transfer matrix method and the diffusion method. From both approaches, we attain the same conclusion: the source of money creation in the case of random exchange is the agents with neither money nor debt. These analytical results are demonstrated by computer simulations.
Simulating intrafraction prostate motion with a random walk model
Directory of Open Access Journals (Sweden)
Tobias Pommer, PhD
2017-07-01
Conclusions: Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.
Shape Modelling Using Markov Random Field Restoration of Point Correspondences
DEFF Research Database (Denmark)
Paulsen, Rasmus Reinhold; Hilger, Klaus Baggesen
2003-01-01
A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized...
Single-cluster dynamics for the random-cluster model
Deng, Y.; Qian, X.; Blöte, H.W.J.
2009-01-01
We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the q-state Potts model to noninteger values q>1. Its results for static quantities are in a satisfactory agreement with those
Using convex quadratic programming to model random media with Gaussian random fields
International Nuclear Information System (INIS)
Quintanilla, John A.; Jones, W. Max
2007-01-01
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented
The random field Blume-Capel model revisited
Santos, P. V.; da Costa, F. A.; de Araújo, J. M.
2018-04-01
We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner (1990). The magnetic field (H) versus temperature (T) phase diagrams for given values of the crystal field D were recovered in accordance to Kaufman and Kanner original work. However, our main goal in the present work was to investigate the distinct structures of the crystal field versus temperature phase diagrams as the random magnetic field is varied because similar models have presented reentrant phenomenon due to randomness. Following previous works we have classified the distinct phase diagrams according to five different topologies. The topological structure of the phase diagrams is maintained for both H - T and D - T cases. Although the phase diagrams exhibit a richness of multicritical phenomena we did not found any reentrant effect as have been seen in similar models.
Some Limits Using Random Slope Models to Measure Academic Growth
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Daniel B. Wright
2017-11-01
Full Text Available Academic growth is often estimated using a random slope multilevel model with several years of data. However, if there are few time points, the estimates can be unreliable. While using random slope multilevel models can lower the variance of the estimates, these procedures can produce more highly erroneous estimates—zero and negative correlations with the true underlying growth—than using ordinary least squares estimates calculated for each student or school individually. An example is provided where schools with increasing graduation rates are estimated to have negative growth and vice versa. The estimation is worse when the underlying data are skewed. It is recommended that there are at least six time points for estimating growth if using a random slope model. A combination of methods can be used to avoid some of the aberrant results if it is not possible to have six or more time points.
A 10 MHz Bandwidth Continuous-Time Delta-Sigma Modulator for Portable Ultrasound Scanners
DEFF Research Database (Denmark)
Llimos Muntal, Pere; Jørgensen, Ivan Harald Holger; Bruun, Erik
2016-01-01
A fourth-order 1-bit continuous-time delta-sigma modulator designed in a 65 nm process for portable ultrasound scanners is presented in this paper. The loop filter consists of RCintegrators, with programmable capacitor arrays and resistors, and the quantizer is implemented with a high-speed clocked...
Robustness of quantized continuous-time nonlinear systems to encoder/decoder mismatch
Persis, Claudio De
2009-01-01
The robustness of quantized continuous-time nonlinear systems with respect to the discrepancy (mismatch) between the ranges of the encoder and the decoder quantizers is investigated. A condition which guarantees asymptotic stability and which describes the interplay between quantization density and
Delsing, M.J.M.H.; Oud, J.H.L.; Bruyn, E.E.J. De
2005-01-01
In family research, bidirectional influences between the family and the individual are usually analyzed in discrete time. Results from discrete time analysis, however, have been shown to be highly dependent on the length of the observation interval. Continuous time analysis using stochastic
A Corrigendum to "Games with Imperfectly Observable Actions in Continuous Time"
Hashimoto, Tadashi
2007-01-01
Sannikov (2007) investigates properties of perfect public equilibria in continuous time repeated games. This note points out that the proof of Lemma 6, required for the proof of the main theorem (Theorem 2), contains an error in computing a Hessian matrix. A correct proof of Lemma 6 is provided using an additional innocuous assumption and a generalized version of Lemma 5.
Limit Properties of Transition Functions of Continuous-Time Markov Branching Processes
Directory of Open Access Journals (Sweden)
Azam A. Imomov
2014-01-01
Full Text Available Consider the Markov Branching Process with continuous time. Our focus is on the limit properties of transition functions of this process. Using differential analogue of the Basic Lemma we prove local limit theorems for all cases and observe invariant properties of considering process.
Effects of random noise in a dynamical model of love
International Nuclear Information System (INIS)
Xu Yong; Gu Rencai; Zhang Huiqing
2011-01-01
Highlights: → We model the complexity and unpredictability of psychology as Gaussian white noise. → The stochastic system of love is considered including bifurcation and chaos. → We show that noise can both suppress and induce chaos in dynamical models of love. - Abstract: This paper aims to investigate the stochastic model of love and the effects of random noise. We first revisit the deterministic model of love and some basic properties are presented such as: symmetry, dissipation, fixed points (equilibrium), chaotic behaviors and chaotic attractors. Then we construct a stochastic love-triangle model with parametric random excitation due to the complexity and unpredictability of the psychological system, where the randomness is modeled as the standard Gaussian noise. Stochastic dynamics under different three cases of 'Romeo's romantic style', are examined and two kinds of bifurcations versus the noise intensity parameter are observed by the criteria of changes of top Lyapunov exponent and shape of stationary probability density function (PDF) respectively. The phase portraits and time history are carried out to verify the proposed results, and the good agreement can be found. And also the dual roles of the random noise, namely suppressing and inducing chaos are revealed.
Effects of random noise in a dynamical model of love
Energy Technology Data Exchange (ETDEWEB)
Xu Yong, E-mail: hsux3@nwpu.edu.cn [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Gu Rencai; Zhang Huiqing [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2011-07-15
Highlights: > We model the complexity and unpredictability of psychology as Gaussian white noise. > The stochastic system of love is considered including bifurcation and chaos. > We show that noise can both suppress and induce chaos in dynamical models of love. - Abstract: This paper aims to investigate the stochastic model of love and the effects of random noise. We first revisit the deterministic model of love and some basic properties are presented such as: symmetry, dissipation, fixed points (equilibrium), chaotic behaviors and chaotic attractors. Then we construct a stochastic love-triangle model with parametric random excitation due to the complexity and unpredictability of the psychological system, where the randomness is modeled as the standard Gaussian noise. Stochastic dynamics under different three cases of 'Romeo's romantic style', are examined and two kinds of bifurcations versus the noise intensity parameter are observed by the criteria of changes of top Lyapunov exponent and shape of stationary probability density function (PDF) respectively. The phase portraits and time history are carried out to verify the proposed results, and the good agreement can be found. And also the dual roles of the random noise, namely suppressing and inducing chaos are revealed.
Using Random Forest Models to Predict Organizational Violence
Levine, Burton; Bobashev, Georgly
2012-01-01
We present a methodology to access the proclivity of an organization to commit violence against nongovernment personnel. We fitted a Random Forest model using the Minority at Risk Organizational Behavior (MAROS) dataset. The MAROS data is longitudinal; so, individual observations are not independent. We propose a modification to the standard Random Forest methodology to account for the violation of the independence assumption. We present the results of the model fit, an example of predicting violence for an organization; and finally, we present a summary of the forest in a "meta-tree,"
Buffalos milk yield analysis using random regression models
Directory of Open Access Journals (Sweden)
A.S. Schierholt
2010-02-01
Full Text Available Data comprising 1,719 milk yield records from 357 females (predominantly Murrah breed, daughters of 110 sires, with births from 1974 to 2004, obtained from the Programa de Melhoramento Genético de Bubalinos (PROMEBUL and from records of EMBRAPA Amazônia Oriental - EAO herd, located in Belém, Pará, Brazil, were used to compare random regression models for estimating variance components and predicting breeding values of the sires. The data were analyzed by different models using the Legendre’s polynomial functions from second to fourth orders. The random regression models included the effects of herd-year, month of parity date of the control; regression coefficients for age of females (in order to describe the fixed part of the lactation curve and random regression coefficients related to the direct genetic and permanent environment effects. The comparisons among the models were based on the Akaike Infromation Criterion. The random effects regression model using third order Legendre’s polynomials with four classes of the environmental effect were the one that best described the additive genetic variation in milk yield. The heritability estimates varied from 0.08 to 0.40. The genetic correlation between milk yields in younger ages was close to the unit, but in older ages it was low.
Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models.
Lock, Eric F; Kohli, Nidhi; Bose, Maitreyee
2017-11-17
Piecewise growth mixture models are a flexible and useful class of methods for analyzing segmented trends in individual growth trajectory over time, where the individuals come from a mixture of two or more latent classes. These models allow each segment of the overall developmental process within each class to have a different functional form; examples include two linear phases of growth, or a quadratic phase followed by a linear phase. The changepoint (knot) is the time of transition from one developmental phase (segment) to another. Inferring the location of the changepoint(s) is often of practical interest, along with inference for other model parameters. A random changepoint allows for individual differences in the transition time within each class. The primary objectives of our study are as follows: (1) to develop a PGMM using a Bayesian inference approach that allows the estimation of multiple random changepoints within each class; (2) to develop a procedure to empirically detect the number of random changepoints within each class; and (3) to empirically investigate the bias and precision of the estimation of the model parameters, including the random changepoints, via a simulation study. We have developed the user-friendly package BayesianPGMM for R to facilitate the adoption of this methodology in practice, which is available at https://github.com/lockEF/BayesianPGMM . We describe an application to mouse-tracking data for a visual recognition task.
The Abelian Sandpile Model on a Random Binary Tree
Redig, F.; Ruszel, W.M.; Saada, E.
2012-01-01
We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar and Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process survives with positive probability) exponential decay of
The dilute random field Ising model by finite cluster approximation
International Nuclear Information System (INIS)
Benyoussef, A.; Saber, M.
1987-09-01
Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs
Unifying model for random matrix theory in arbitrary space dimensions
Cicuta, Giovanni M.; Krausser, Johannes; Milkus, Rico; Zaccone, Alessio
2018-03-01
A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the eigenvalue spectrum of this model in different limits of space dimension d , and for arbitrary values of the lattice coordination number Z , are shown and discussed. As a function of these two parameters (and their ratio Z /d ), the most studied models in random matrix theory (Erdos-Renyi graphs, effective medium, and replicas) can be reproduced in the various limits of block dimensionality d . Remarkably, the Marchenko-Pastur spectral density (which is recovered by replica calculations for the Laplacian matrix) is reproduced exactly in the limit of infinite size of the blocks, or d →∞ , which clarifies the physical meaning of space dimension in these models. We feel that the approximate results for d =3 provided by our method may have many potential applications in the future, from the vibrational spectrum of glasses and elastic networks to wave localization, disordered conductors, random resistor networks, and random walks.
Asthma Self-Management Model: Randomized Controlled Trial
Olivera, Carolina M. X.; Vianna, Elcio Oliveira; Bonizio, Roni C.; de Menezes, Marcelo B.; Ferraz, Erica; Cetlin, Andrea A.; Valdevite, Laura M.; Almeida, Gustavo A.; Araujo, Ana S.; Simoneti, Christian S.; de Freitas, Amanda; Lizzi, Elisangela A.; Borges, Marcos C.; de Freitas, Osvaldo
2016-01-01
Information for patients provided by the pharmacist is reflected in adhesion to treatment, clinical results and patient quality of life. The objective of this study was to assess an asthma self-management model for rational medicine use. This was a randomized controlled trial with 60 asthmatic patients assigned to attend five modules presented by…
Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
Hafermann, Hartmut; Werner, Philipp; Gull, Emanuel
2013-04-01
Strongly correlated quantum impurity problems appear in a wide variety of contexts ranging from nanoscience and surface physics to material science and the theory of strongly correlated lattice models, where they appear as auxiliary systems within dynamical mean-field theory. Accurate and unbiased solutions must usually be obtained numerically, and continuous-time quantum Monte Carlo algorithms, a family of algorithms based on the stochastic sampling of partition function expansions, perform well for such systems. With the present paper we provide an efficient and generic implementation of the hybridization expansion quantum impurity solver, based on the segment representation. We provide a complete implementation featuring most of the recently developed extensions and optimizations. Our implementation allows one to treat retarded interactions and provides generalized measurement routines based on improved estimators for the self-energy and for vertex functions. The solver is embedded in the ALPS-DMFT application package. Catalogue identifier: AEOL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Use of the hybridization expansion impurity solvers requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. No. of lines in distributed program, including test data, etc.: 650044 No. of bytes in distributed program, including test data, etc.: 20553265 Distribution format: tar.gz Programming language: C++/Python. Computer: Desktop PC, high-performance computers. Operating system: Unix, Linux, OSX, Windows. Has the code been vectorized or parallelized?: Yes, MPI parallelized. RAM: 1 GB Classification: 7.3. External routines: ALPS [1, 2, 3], BLAS [4, 5], LAPACK [6], HDF5 [7] Nature of problem: Quantum impurity models were originally introduced to describe a magnetic transition metal ion in a non
Continuous time sigma delta ADC design and non-idealities analysis
International Nuclear Information System (INIS)
Yuan Jun; Chen Zhenhai; Yang Yintang; Zhang Zhaofeng; Wu Jun; Wang Chao; Qian Wenrong
2011-01-01
A wide bandwidth continuous time sigma delta ADC is implemented in 130 nm CMOS. A detailed non-idealities analysis (excess loop delay, clock jitter, finite gain and GBW, comparator offset and DAC mismatch) is performed developed in Matlab/Simulink. This design is targeted for wide bandwidth applications such as video or wireless base-stations. Athird-order continuous time sigma delta modulator comprises a third-order RC operational-amplifier-based loop filter and 3-bit internal quantizer operated at 512 MHz clock frequency. The sigma delta ADC achieves 60 dB SNR and 59.3 dB SNDR over a 16-MHz signal band at an OSR of 16. The power consumption of the CT sigma delta modulator is 22 mW from the 1.2-V supply. (semiconductor integrated circuits)
Optimization of Modulator and Circuits for Low Power Continuous-Time Delta-Sigma ADC
DEFF Research Database (Denmark)
Marker-Villumsen, Niels; Bruun, Erik
2014-01-01
This paper presents a new optimization method for achieving a minimum current consumption in a continuous-time Delta-Sigma analog-to-digital converter (ADC). The method is applied to a continuous-time modulator realised with active-RC integrators and with a folded-cascode operational transconduc......- tance amplifier (OTA). Based on a detailed circuit analysis of the integrator and the OTA, key expression are derived relating the biasing current of the OTA to the noise requirements of the integrator. In the optimization the corner frequency of the modulator loop filter and the number of quantizer...... levels are swept. Based on the results of the circuit analysis, for each modulator combination the summed current consumption of the 1st integrator and quantizer of the ADC is determined. By also sweeping the partitioning of the noise power for the different circuit parts, the optimum modulator...
International Nuclear Information System (INIS)
Bachschmid-Romano, Ludovica; Opper, Manfred
2015-01-01
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the nontrivial equal time correlations between spins induced by the dynamics for the speed of learning. These correlations become more important as the spin’s stochasticity is decreased. We also analyse the deviation of the estimation error (paper)
Mean-variance Optimal Reinsurance-investment Strategy in Continuous Time
Daheng Peng; Fang Zhang
2017-01-01
In this paper, Lagrange method is used to solve the continuous-time mean-variance reinsurance-investment problem. Proportional reinsurance, multiple risky assets and risk-free asset are considered synthetically in the optimal strategy for insurers. By solving the backward stochastic differential equation for the Lagrange multiplier, we get the mean-variance optimal reinsurance-investment strategy and its effective frontier in explicit forms.
Mean-variance Optimal Reinsurance-investment Strategy in Continuous Time
Directory of Open Access Journals (Sweden)
Daheng Peng
2017-10-01
Full Text Available In this paper, Lagrange method is used to solve the continuous-time mean-variance reinsurance-investment problem. Proportional reinsurance, multiple risky assets and risk-free asset are considered synthetically in the optimal strategy for insurers. By solving the backward stochastic differential equation for the Lagrange multiplier, we get the mean-variance optimal reinsurance-investment strategy and its effective frontier in explicit forms.
Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays
Directory of Open Access Journals (Sweden)
Tadeusz Kaczorek
2013-06-01
Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.
Choi, Han-Lim
2013-01-01
This paper presents expression of mutual information that defines the information gain in planning of sensing resources, when the goal is to reduce the forecast uncertainty of some quantities of interest and the system dynamics is described as a continuous-time linear system. The method extends the smoother approach in [5] to handle more general notion of verification entity - continuous sequence of variables over some finite time window in the future. The expression of mutual information for...
Value Function and Optimal Rule on the Optimal Stopping Problem for Continuous-Time Markov Processes
Directory of Open Access Journals (Sweden)
Lu Ye
2017-01-01
Full Text Available This paper considers the optimal stopping problem for continuous-time Markov processes. We describe the methodology and solve the optimal stopping problem for a broad class of reward functions. Moreover, we illustrate the outcomes by some typical Markov processes including diffusion and Lévy processes with jumps. For each of the processes, the explicit formula for value function and optimal stopping time is derived. Furthermore, we relate the derived optimal rules to some other optimal problems.
Directory of Open Access Journals (Sweden)
Hajnalka Péics
2016-08-01
Full Text Available The asymptotic behavior of solutions of the system of difference equations with continuous time and lag function between two known real functions is studied. The cases when the lag function is between two linear delay functions, between two power delay functions and between two constant delay functions are observed and illustrated by examples. The asymptotic estimates of solutions of the considered system are obtained.
Power comparator for continuous-time adaptive equalization in Ethernet-based instrumentation
Guerrero, E.; Gimeno, C.; Sánchez-Azqueta, C.; Celma, S.
2014-08-01
Recently, Ethernet has been chosen as a replacement for standard-based instrumentation. Its performance is increasing, thanks to speeds of 1 Gbps, 10 Gbps and beyond on backplanes, which expands the instrumentation and measurement potential. However, these high-speed serial links need to be able to retain the integrity of the data stream through some type of equalization. This paper proposes a new differential power comparator, to be used in continuous-time adaptive equalizers inside these Ethernet-based instruments.
Hobolth, Asger; Stone, Eric A
2009-09-01
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length T. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix Q of the CTMC, its beginning and ending states, and the length of sampling time T. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given Q, T, and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.
A new continuous-time formulation for scheduling crude oil operations
International Nuclear Information System (INIS)
Reddy, P. Chandra Prakash; Karimi, I.A.; Srinivasan, R.
2004-01-01
In today's competitive business climate characterized by uncertain oil markets, responding effectively and speedily to market forces, while maintaining reliable operations, is crucial to a refinery's bottom line. Optimal crude oil scheduling enables cost reduction by using cheaper crudes intelligently, minimizing crude changeovers, and avoiding ship demurrage. So far, only discrete-time formulations have stood up to the challenge of this important, nonlinear problem. A continuous-time formulation would portend numerous advantages, however, existing work in this area has just begun to scratch the surface. In this paper, we present the first complete continuous-time mixed integer linear programming (MILP) formulation for the short-term scheduling of operations in a refinery that receives crude from very large crude carriers via a high-volume single buoy mooring pipeline. This novel formulation accounts for real-world operational practices. We use an iterative algorithm to eliminate the crude composition discrepancy that has proven to be the Achilles heel for existing formulations. While it does not guarantee global optimality, the algorithm needs only MILP solutions and obtains excellent maximum-profit schedules for industrial problems with up to 7 days of scheduling horizon. We also report the first comparison of discrete- vs. continuous-time formulations for this complex problem. (Author)
Investigation of continuous-time quantum walk via modules of Bose-Mesner and Terwilliger algebras
International Nuclear Information System (INIS)
Jafarizadeh, M A; Salimi, S
2006-01-01
The continuous-time quantum walk on the underlying graphs of association schemes has been studied, via the algebraic combinatorics structures of association schemes, namely semi-simple modules of their Bose-Mesner and Terwilliger algebras. It is shown that the Terwilliger algebra stratifies the graph into a (d + 1) disjoint union of strata which is different from the stratification based on distance, except for distance regular graphs. In underlying graphs of association schemes, the probability amplitudes and average probabilities are given in terms of dual eigenvalues of association schemes, such that the amplitudes of observing the continuous-time quantum walk on all sites belonging to a given stratum are the same, therefore there are at most (d + 1) different observing probabilities. The importance of association scheme in continuous-time quantum walk is shown by some worked out examples such as arbitrary finite group association schemes followed by symmetric S n , Dihedral D 2m and cyclic groups. At the end it is shown that the highest irreducible representations of Terwilliger algebras pave the way to use the spectral distributions method of Jafarizadeh and Salimi (2005 Preprint quant-ph/0510174) in studying quantum walk on some rather important graphs called distance regular graphs
Simulating intrafraction prostate motion with a random walk model.
Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O
2017-01-01
Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during
A generalized model via random walks for information filtering
Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng
2016-08-01
There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation.
Directory of Open Access Journals (Sweden)
Gabriele Tosadori
2017-11-01
Full Text Available Biological networks are becoming a fundamental tool for the investigation of high-throughput data in several fields of biology and biotechnology. With the increasing amount of information, network-based models are gaining more and more interest and new techniques are required in order to mine the information and to validate the results. To fill the validation gap we present an app, for the Cytoscape platform, which aims at creating randomised networks and randomising existing, real networks. Since there is a lack of tools that allow performing such operations, our app aims at enabling researchers to exploit different, well known random network models that could be used as a benchmark for validating real, biological datasets. We also propose a novel methodology for creating random weighted networks, i.e. the multiplication algorithm, starting from real, quantitative data. Finally, the app provides a statistical tool that compares real versus randomly computed attributes, in order to validate the numerical findings. In summary, our app aims at creating a standardised methodology for the validation of the results in the context of the Cytoscape platform.
An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia
Voelkle, M.C.; Oud, J.H.L.; Davidov, E.; Schmidt, P.
2012-01-01
[Correction Notice: An Erratum for this article was reported in Vol 17(3) of Psychological Methods (see record 2012-24038-005). The supplemental materials link was missing. All versions of this article have been corrected.] Panel studies, in which the same subjects are repeatedly observed at
A Fay-Herriot Model with Different Random Effect Variances
Czech Academy of Sciences Publication Activity Database
Hobza, Tomáš; Morales, D.; Herrador, M.; Esteban, M.D.
2011-01-01
Roč. 40, č. 5 (2011), s. 785-797 ISSN 0361-0926 R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : small area estimation * Fay-Herriot model * Linear mixed model * Labor Force Survey Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.274, year: 2011 http://library.utia.cas.cz/separaty/2011/SI/hobza-a%20fay-herriot%20model%20with%20different%20random%20effect%20variances.pdf
Inference of random walk models to describe leukocyte migration
Jones, Phoebe J. M.; Sim, Aaron; Taylor, Harriet B.; Bugeon, Laurence; Dallman, Magaret J.; Pereira, Bernard; Stumpf, Michael P. H.; Liepe, Juliane
2015-12-01
While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding.
Scaling of coercivity in a 3d random anisotropy model
Energy Technology Data Exchange (ETDEWEB)
Proctor, T.C., E-mail: proctortc@gmail.com; Chudnovsky, E.M., E-mail: EUGENE.CHUDNOVSKY@lehman.cuny.edu; Garanin, D.A.
2015-06-15
The random-anisotropy Heisenberg model is numerically studied on lattices containing over ten million spins. The study is focused on hysteresis and metastability due to topological defects, and is relevant to magnetic properties of amorphous and sintered magnets. We are interested in the limit when ferromagnetic correlations extend beyond the size of the grain inside which the magnetic anisotropy axes are correlated. In that limit the coercive field computed numerically roughly scales as the fourth power of the random anisotropy strength and as the sixth power of the grain size. Theoretical arguments are presented that provide an explanation of numerical results. Our findings should be helpful for designing amorphous and nanosintered materials with desired magnetic properties. - Highlights: • We study the random-anisotropy model on lattices containing up to ten million spins. • Irreversible behavior due to topological defects (hedgehogs) is elucidated. • Hysteresis loop area scales as the fourth power of the random anisotropy strength. • In nanosintered magnets the coercivity scales as the six power of the grain size.
Avanzi, Francesco; Caruso, Marco; Jommi, Cristina; De Michele, Carlo; Ghezzi, Antonio
2014-06-01
Liquid water in snowpacks rules wet snow avalanche formation, surface albedo and snowmelt runoff timing. By now, volumetric liquid water content (LWC) measurements are collected mainly with destructive methods, while continuous-time and non-invasive measurements would be preferable to track its time dynamics. Here, we assess the feasibility of continuous-time monitoring of LWC using EnviroSMART® capacitance sensors. These were conceived to track liquid water dynamics in soils, and their use in snow is evaluated here for the first time, as far as we know. A field case study was settled up in April 2013 within an Italian Alpine valley. An instrumental set up with eight capacitance sensors was installed. Two time-domain reflectrometers were added to the aim of comparison. To assist in interpreting the signal of the capacitance sensors, two laboratory tests were run, and a FEM model was implemented. This preliminary study demonstrates that capacitance sensors are sensitive to increasing LWC, although their long-term installation in snow entails the development of an air gap around them, due to localized melting, air turbulence and solar radiation absorption, which hinders following LWC variations. As a result, capacitance sensors readings are challenging to be interpreted quantitatively. Perspectives on future investigation are discussed to bring the proposed procedure towards long-term applications in snowpacks.
Belkhatir, Zehor
2017-05-31
This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.
Zhao, Tao; Dian, Songyi
2017-09-01
This paper addresses a fuzzy dynamic output feedback H ∞ control design problem for continuous-time nonlinear systems via T-S fuzzy model. The stability of the fuzzy closed-loop system which is formed by a T-S fuzzy model and a fuzzy dynamic output feedback H ∞ controller connected in a closed loop is investigated with Lyapunov stability theory. The proposed fuzzy controller does not share the same membership functions and number of rules with T-S fuzzy systems, which can enhance design flexibility. A line-integral fuzzy Lyapunov function is utilized to derive the stability conditions in the form of linear matrix inequalities (LMIs). The boundary information of membership functions is considered in the stability analysis to reduce the conservativeness of the imperfect premise matching design technique. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
The transverse spin-1 Ising model with random interactions
Energy Technology Data Exchange (ETDEWEB)
Bouziane, Touria [Department of Physics, Faculty of Sciences, University of Moulay Ismail, B.P. 11201 Meknes (Morocco)], E-mail: touria582004@yahoo.fr; Saber, Mohammed [Department of Physics, Faculty of Sciences, University of Moulay Ismail, B.P. 11201 Meknes (Morocco); Dpto. Fisica Aplicada I, EUPDS (EUPDS), Plaza Europa, 1, San Sebastian 20018 (Spain)
2009-01-15
The phase diagrams of the transverse spin-1 Ising model with random interactions are investigated using a new technique in the effective field theory that employs a probability distribution within the framework of the single-site cluster theory based on the use of exact Ising spin identities. A model is adopted in which the nearest-neighbor exchange couplings are independent random variables distributed according to the law P(J{sub ij})=p{delta}(J{sub ij}-J)+(1-p){delta}(J{sub ij}-{alpha}J). General formulae, applicable to lattices with coordination number N, are given. Numerical results are presented for a simple cubic lattice. The possible reentrant phenomenon displayed by the system due to the competitive effects between exchange interactions occurs for the appropriate range of the parameter {alpha}.
Social aggregation in pea aphids: experiment and random walk modeling.
Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J; Topaz, Chad M
2013-01-01
From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.
Random resistor network model of minimal conductivity in graphene.
Cheianov, Vadim V; Fal'ko, Vladimir I; Altshuler, Boris L; Aleiner, Igor L
2007-10-26
Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.
Levy Random Bridges and the Modelling of Financial Information
Hoyle, Edward; Hughston, Lane P.; Macrina, Andrea
2009-01-01
The information-based asset-pricing framework of Brody, Hughston and Macrina (BHM) is extended to include a wider class of models for market information. In the BHM framework, each asset is associated with a collection of random cash flows. The price of the asset is the sum of the discounted conditional expectations of the cash flows. The conditional expectations are taken with respect to a filtration generated by a set of "information processes". The information processes carry imperfect inf...
Policy Iteration for Continuous-Time Average Reward Markov Decision Processes in Polish Spaces
Directory of Open Access Journals (Sweden)
Quanxin Zhu
2009-01-01
Full Text Available We study the policy iteration algorithm (PIA for continuous-time jump Markov decision processes in general state and action spaces. The corresponding transition rates are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. The criterion that we are concerned with is expected average reward. We propose a set of conditions under which we first establish the average reward optimality equation and present the PIA. Then under two slightly different sets of conditions we show that the PIA yields the optimal (maximum reward, an average optimal stationary policy, and a solution to the average reward optimality equation.
Directory of Open Access Journals (Sweden)
A. Baddou
2006-01-01
Full Text Available This paper solves the problem of controlling linear continuous-time systems subject to control signals constrained in magnitude (maybe asymmetrically. A controller design methodology is proposed, based on using an asymmetric Lyapunov function, that avoids the discontinuities in the control vector components resulting from the application of a piecewise linear control law previously proposed. The proposed method gives improved speed of convergence without discontinuities of the control vector components, respecting always the imposed asymmetric constraints. An example illustrates the approach.
Convergence of discrete-time Kalman filter estimate to continuous time estimate
Aalto, Atte
2016-04-01
This article is concerned with the convergence of the state estimate obtained from the discrete-time Kalman filter to the continuous time estimate as the temporal discretisation is refined. The convergence follows from Martingale convergence theorem as demonstrated below; however, surprisingly, no results exist on the rate of convergence. We derive convergence rate estimates for the discrete-time Kalman filter estimate for finite and infinite dimensional systems. The proofs are based on applying the discrete-time Kalman filter on a dense numerable subset of a certain time interval [0, T].
Random walks and diffusion on networks
Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud
2017-11-01
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.
High-temperature series expansions for random Potts models
Directory of Open Access Journals (Sweden)
M.Hellmund
2005-01-01
Full Text Available We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique, quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2 and 4-state Potts model in three dimensions up to the order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.
Continuous-time digital front-ends for multistandard wireless transmission
Nuyts, Pieter A J; Dehaene, Wim
2014-01-01
This book describes the design of fully digital multistandard transmitter front-ends which can directly drive one or more switching power amplifiers, thus eliminating all other analog components. After reviewing different architectures, the authors focus on polar architectures using pulse width modulation (PWM), which are entirely based on unclocked delay lines and other continuous-time digital hardware. As a result, readers are enabled to shift accuracy concerns from the voltage domain to the time domain, to coincide with submicron CMOS technology scaling. The authors present different architectural options and compare them, based on their effect on the signal and spectrum quality. Next, a high-level theoretical analysis of two different PWM-based architectures – baseband PWM and RF PWM – is made. On the circuit level, traditional digital components and design techniques are revisited from the point of view of continuous-time digital circuits. Important design criteria are identified and diff...
A new phase of disordered phonons modelled by random matrices
Schmittner, Sebastian; Zirnbauer, Martin
2015-03-01
Starting from the clean harmonic crystal and not invoking two-level systems, we propose a model for phonons in a disordered solid. In this model the strength of mass and spring constant disorder can be increased separately. Both types of disorder are modelled by random matrices that couple the degrees of freedom locally. Treated in coherent potential approximation (CPA), the speed of sound decreases with increasing disorder until it reaches zero at finite disorder strength. There, a critical transition to a strong disorder phase occurs. In this novel phase, we find the density of states at zero energy in three dimensions to be finite, leading to a linear temperature dependence of the heat capacity, as observed experimentally for vitreous systems. For any disorder strength, our model is stable, i.e. masses and spring constants are positive, and there are no runaway dynamics. This is ensured by using appropriate probability distributions, inspired by Wishart ensembles, for the random matrices. The CPA self-consistency equations are derived in a very accessible way using planar diagrams. The talk focuses on the model and the results. The first author acknowledges financial support by the Deutsche Telekom Stiftung.
Marginal and Random Intercepts Models for Longitudinal Binary Data with Examples from Criminology
Long, Jeffrey D.; Loeber, Rolf; Farrington, David P.
2009-01-01
Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides…
Random matrices and the six-vertex model
Bleher, Pavel
2013-01-01
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wa...
Energy Technology Data Exchange (ETDEWEB)
Salimi, S; Radgohar, R, E-mail: shsalimi@uok.ac.i, E-mail: r.radgohar@uok.ac.i [Faculty of Science, Department of Physics, University of Kurdistan, Pasdaran Ave, Sanandaj (Iran, Islamic Republic of)
2010-01-28
In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point-contact induced by the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the square of the distance parameter (m). This shows that the mixing time decreases with increasing range of interaction. Also, what we obtain for m = 0 is in agreement with Fedichkin, Solenov and Tamon's results [48] for cycle, and we see that the mixing time of CTQWs on cycle improves with adding interacting edges.
iQIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit
Huang, Li
2017-12-01
In this paper, we present a new version of the iQIST software package, which is capable of solving various quantum impurity models by using the hybridization expansion (or strong coupling expansion) continuous-time quantum Monte Carlo algorithm. In the revised version, the software architecture is completely redesigned. New basis (intermediate representation or singular value decomposition representation) for the single-particle and two-particle Green's functions is introduced. A lot of useful physical observables are added, such as the charge susceptibility, fidelity susceptibility, Binder cumulant, and autocorrelation time. Especially, we optimize measurement for the two-particle Green's functions. Both the particle-hole and particle-particle channels are supported. In addition, the block structure of the two-particle Green's functions is exploited to accelerate the calculation. Finally, we fix some known bugs and limitations. The computational efficiency of the code is greatly enhanced.
Prediction of Geological Subsurfaces Based on Gaussian Random Field Models
Energy Technology Data Exchange (ETDEWEB)
Abrahamsen, Petter
1997-12-31
During the sixties, random functions became practical tools for predicting ore reserves with associated precision measures in the mining industry. This was the start of the geostatistical methods called kriging. These methods are used, for example, in petroleum exploration. This thesis reviews the possibilities for using Gaussian random functions in modelling of geological subsurfaces. It develops methods for including many sources of information and observations for precise prediction of the depth of geological subsurfaces. The simple properties of Gaussian distributions make it possible to calculate optimal predictors in the mean square sense. This is done in a discussion of kriging predictors. These predictors are then extended to deal with several subsurfaces simultaneously. It is shown how additional velocity observations can be used to improve predictions. The use of gradient data and even higher order derivatives are also considered and gradient data are used in an example. 130 refs., 44 figs., 12 tabs.
Universality of correlation functions in random matrix models of QCD
International Nuclear Information System (INIS)
Jackson, A.D.; Sener, M.K.; Verbaarschot, J.J.M.
1997-01-01
We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a schematic temperature dependence. We calculate the correlation functions analytically using the technique of Itzykson-Zuber integrals for arbitrary complex supermatrices. An alternative exact calculation for arbitrary matrix size is given for the special case of zero temperature, and we reproduce the well-known Laguerre kernel. At finite temperature, the microscopic limit of the correlation functions are calculated in the saddle-point approximation. The main result of this paper is that the microscopic universality of correlation functions is maintained even though unitary invariance is broken by the addition of a deterministic matrix to the ensemble. (orig.)
Ising Models on Power-Law Random Graphs
Dommers, Sander; Giardinà, Cristian; van der Hofstad, Remco
2010-11-01
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent τ>2), for which the random graph has a tree-like structure. For this, we closely follow the analysis by Dembo and Montanari (Ann. Appl. Probab. 20(2):565-592, 2010) which assumes finite variance degrees ( τ>3), adapting it when necessary and also simplifying it when possible. Our results also apply in cases where the degree distribution does not obey a power law. We further identify the thermodynamic limits of various physical quantities, such as the magnetization and the internal energy.
Scaling of coercivity in a 3d random anisotropy model
Proctor, T. C.; Chudnovsky, E. M.; Garanin, D. A.
2015-06-01
The random-anisotropy Heisenberg model is numerically studied on lattices containing over ten million spins. The study is focused on hysteresis and metastability due to topological defects, and is relevant to magnetic properties of amorphous and sintered magnets. We are interested in the limit when ferromagnetic correlations extend beyond the size of the grain inside which the magnetic anisotropy axes are correlated. In that limit the coercive field computed numerically roughly scales as the fourth power of the random anisotropy strength and as the sixth power of the grain size. Theoretical arguments are presented that provide an explanation of numerical results. Our findings should be helpful for designing amorphous and nanosintered materials with desired magnetic properties.
Nonparametric Estimation of Distributions in Random Effects Models
Hart, Jeffrey D.
2011-01-01
We propose using minimum distance to obtain nonparametric estimates of the distributions of components in random effects models. A main setting considered is equivalent to having a large number of small datasets whose locations, and perhaps scales, vary randomly, but which otherwise have a common distribution. Interest focuses on estimating the distribution that is common to all datasets, knowledge of which is crucial in multiple testing problems where a location/scale invariant test is applied to every small dataset. A detailed algorithm for computing minimum distance estimates is proposed, and the usefulness of our methodology is illustrated by a simulation study and an analysis of microarray data. Supplemental materials for the article, including R-code and a dataset, are available online. © 2011 American Statistical Association.
Genetic evaluation of European quails by random regression models
Directory of Open Access Journals (Sweden)
Flaviana Miranda Gonçalves
2012-09-01
Full Text Available The objective of this study was to compare different random regression models, defined from different classes of heterogeneity of variance combined with different Legendre polynomial orders for the estimate of (covariance of quails. The data came from 28,076 observations of 4,507 female meat quails of the LF1 lineage. Quail body weights were determined at birth and 1, 14, 21, 28, 35 and 42 days of age. Six different classes of residual variance were fitted to Legendre polynomial functions (orders ranging from 2 to 6 to determine which model had the best fit to describe the (covariance structures as a function of time. According to the evaluated criteria (AIC, BIC and LRT, the model with six classes of residual variances and of sixth-order Legendre polynomial was the best fit. The estimated additive genetic variance increased from birth to 28 days of age, and dropped slightly from 35 to 42 days. The heritability estimates decreased along the growth curve and changed from 0.51 (1 day to 0.16 (42 days. Animal genetic and permanent environmental correlation estimates between weights and age classes were always high and positive, except for birth weight. The sixth order Legendre polynomial, along with the residual variance divided into six classes was the best fit for the growth rate curve of meat quails; therefore, they should be considered for breeding evaluation processes by random regression models.
Donier, J.; Bouchaud, J.-P.
2016-12-01
In standard Walrasian auctions, the price of a good is defined as the point where the supply and demand curves intersect. Since both curves are generically regular, the response to small perturbations is linearly small. However, a crucial ingredient is absent of the theory, namely transactions themselves. What happens after they occur? To answer the question, we develop a dynamic theory for supply and demand based on agents with heterogeneous beliefs. When the inter-auction time is infinitely long, the Walrasian mechanism is recovered. When transactions are allowed to happen in continuous time, a peculiar property emerges: close to the price, supply and demand vanish quadratically, which we empirically confirm on the Bitcoin. This explains why price impact in financial markets is universally observed to behave as the square root of the excess volume. The consequences are important, as they imply that the very fact of clearing the market makes prices hypersensitive to small fluctuations.
Low Power Continuous-Time Delta-Sigma ADC with Current Output DAC
DEFF Research Database (Denmark)
Marker-Villumsen, Niels; Jørgensen, Ivan Harald Holger; Bruun, Erik
2015-01-01
CT ∆Σ ADC for audio applications, designed in a 0.18 µm CMOS process, with active-RC integrators, a 7-level Flash ADC quantizer and current output DAC for the feedback. From simulations the ADC achieves a dynamic range of 95.0 dB in the audio band, with a current consumption of 284 µA for a 1.7 V......The paper presents a continuous-time (CT) DeltaSigma (∆Σ) analog-to-digital converter (ADC) using a current output digital-to-analog converter (DAC) for the feedback. From circuit analysis it is shown that using a current output DAC makes it possible to relax the noise requirements of the 1st...
A toolbox for safety instrumented system evaluation based on improved continuous-time Markov chain
Wardana, Awang N. I.; Kurniady, Rahman; Pambudi, Galih; Purnama, Jaka; Suryopratomo, Kutut
2017-08-01
Safety instrumented system (SIS) is designed to restore a plant into a safe condition when pre-hazardous event is occur. It has a vital role especially in process industries. A SIS shall be meet with safety requirement specifications. To confirm it, SIS shall be evaluated. Typically, the evaluation is calculated by hand. This paper presents a toolbox for SIS evaluation. It is developed based on improved continuous-time Markov chain. The toolbox supports to detailed approach of evaluation. This paper also illustrates an industrial application of the toolbox to evaluate arch burner safety system of primary reformer. The results of the case study demonstrates that the toolbox can be used to evaluate industrial SIS in detail and to plan the maintenance strategy.
Xue, Xiaoxiao; Zheng, Xiaoping; Zhang, Hanyi; Zhou, Bingkun
2012-11-19
We propose a novel structure of complex-tap microwave photonic filter (MPF) employing an incoherent broadband optical source (BOS) and a programmable optical spectrum processor. By tailoring the optical spectral amplitude and phase, arbitrary complex continuous-time impulse responses of the MPF can be constructed. Frequency responses with a single flat-top, highly chirped, or arbitrary-shape passband are demonstrated, respectively. The passband center can also be tuned in a wide range only limited by the opto-electrical devices. To the best of our knowledge, it is the first demonstration of an incoherent-BOS-based MPF which is single-bandpass, widely tunable, and highly reconfigurable with complex taps.
Deng, Zhenhua; Liang, Shu; Hong, Yiguang
2017-10-17
In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms.In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms.
Estimating the continuous-time dynamics of energy and fat metabolism in mice.
Directory of Open Access Journals (Sweden)
Juen Guo
2009-09-01
Full Text Available The mouse has become the most popular organism for investigating molecular mechanisms of body weight regulation. But understanding the physiological context by which a molecule exerts its effect on body weight requires knowledge of energy intake, energy expenditure, and fuel selection. Furthermore, measurements of these variables made at an isolated time point cannot explain why body weight has its present value since body weight is determined by the past history of energy and macronutrient imbalance. While food intake and body weight changes can be frequently measured over several weeks (the relevant time scale for mice, correspondingly frequent measurements of energy expenditure and fuel selection are not currently feasible. To address this issue, we developed a mathematical method based on the law of energy conservation that uses the measured time course of body weight and food intake to estimate the underlying continuous-time dynamics of energy output and net fat oxidation. We applied our methodology to male C57BL/6 mice consuming various ad libitum diets during weight gain and loss over several weeks and present the first continuous-time estimates of energy output and net fat oxidation rates underlying the observed body composition changes. We show that transient energy and fat imbalances in the first several days following a diet switch can account for a significant fraction of the total body weight change. We also discovered a time-invariant curve relating body fat and fat-free masses in male C57BL/6 mice, and the shape of this curve determines how diet, fuel selection, and body composition are interrelated.
The Little-Hopfield model on a sparse random graph
International Nuclear Information System (INIS)
Castillo, I Perez; Skantzos, N S
2004-01-01
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model). We solve this model within replica symmetry, and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetic transition lines of our phase diagram are identical to those of sequential dynamics. The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement
The Little Hopfield model on a sparse random graph
Pérez Castillo, I.; Skantzos, N. S.
2004-10-01
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model). We solve this model within replica symmetry, and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetic transition lines of our phase diagram are identical to those of sequential dynamics. The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement.
Exponential random graph models for networks with community structure.
Fronczak, Piotr; Fronczak, Agata; Bujok, Maksymilian
2013-09-01
Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.
Zero temperature landscape of the random sine-Gordon model
International Nuclear Information System (INIS)
Sanchez, A.; Bishop, A.R.; Cai, D.
1997-01-01
We present a preliminary summary of the zero temperature properties of the two-dimensional random sine-Gordon model of surface growth on disordered substrates. We found that the properties of this model can be accurately computed by using lattices of moderate size as the behavior of the model turns out to be independent of the size above certain length (∼ 128 x 128 lattices). Subsequently, we show that the behavior of the height difference correlation function is of (log r) 2 type up to a certain correlation length (ξ ∼ 20), which rules out predictions of log r behavior for all temperatures obtained by replica-variational techniques. Our results open the way to a better understanding of the complex landscape presented by this system, which has been the subject of very many (contradictory) analysis
Heidergott, B.F.; Hordijk, A.; Leder, N.
2010-01-01
We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q* through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm
Critical behavior of the Ising model on random fractals.
Monceau, Pascal
2011-11-01
We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d(f) is approximately equal to 1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
Universality in random-walk models with birth and death
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1995-01-01
Models of random walks are considered in which walkers are born at one site and die at all other sites. Steady-state distributions of walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D≠2, 4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. This work elucidates the adsorption transition of polymers at curved interfaces. copyright 1995 The American Physical Society
Traffic data reconstruction based on Markov random field modeling
International Nuclear Information System (INIS)
Kataoka, Shun; Tanaka, Kazuyuki; Yasuda, Muneki; Furtlehner, Cyril
2014-01-01
We consider the traffic data reconstruction problem. Suppose we have the traffic data of an entire city that are incomplete because some road data are unobserved. The problem is to reconstruct the unobserved parts of the data. In this paper, we propose a new method to reconstruct incomplete traffic data collected from various sensors. Our approach is based on Markov random field modeling of road traffic. The reconstruction is achieved by using a mean-field method and a machine learning method. We numerically verify the performance of our method using realistic simulated traffic data for the real road network of Sendai, Japan. (paper)
Geometric Models for Isotropic Random Porous Media: A Review
Directory of Open Access Journals (Sweden)
Helmut Hermann
2014-01-01
Full Text Available Models for random porous media are considered. The models are isotropic both from the local and the macroscopic point of view; that is, the pores have spherical shape or their surface shows piecewise spherical curvature, and there is no macroscopic gradient of any geometrical feature. Both closed-pore and open-pore systems are discussed. The Poisson grain model, the model of hard spheres packing, and the penetrable sphere model are used; variable size distribution of the pores is included. A parameter is introduced which controls the degree of open-porosity. Besides systems built up by a single solid phase, models for porous media with the internal surface coated by a second phase are treated. Volume fraction, surface area, and correlation functions are given explicitly where applicable; otherwise numerical methods for determination are described. Effective medium theory is applied to calculate physical properties for the models such as isotropic elastic moduli, thermal and electrical conductivity, and static dielectric constant. The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.
Boyce, Lola; Lovelace, Thomas B.
1989-01-01
FORTRAN programs RANDOM3 and RANDOM4 are documented in the form of a user's manual. Both programs are based on fatigue strength reduction, using a probabilistic constitutive model. The programs predict the random lifetime of an engine component to reach a given fatigue strength. The theoretical backgrounds, input data instructions, and sample problems illustrating the use of the programs are included.
Interpreting parameters in the logistic regression model with random effects
DEFF Research Database (Denmark)
Larsen, Klaus; Petersen, Jørgen Holm; Budtz-Jørgensen, Esben
2000-01-01
interpretation, interval odds ratio, logistic regression, median odds ratio, normally distributed random effects......interpretation, interval odds ratio, logistic regression, median odds ratio, normally distributed random effects...
RIM: A Random Item Mixture Model to Detect Differential Item Functioning
Frederickx, Sofie; Tuerlinckx, Francis; De Boeck, Paul; Magis, David
2010-01-01
In this paper we present a new methodology for detecting differential item functioning (DIF). We introduce a DIF model, called the random item mixture (RIM), that is based on a Rasch model with random item difficulties (besides the common random person abilities). In addition, a mixture model is assumed for the item difficulties such that the…
RIM: A random item mixture model to detect Differential Item Functioning
Frederickx, S.; Tuerlinckx, T.; de Boeck, P.; Magis, D.
2010-01-01
In this paper we present a new methodology for detecting differential item functioning (DIF). We introduce a DIF model, called the random item mixture (RIM), that is based on a Rasch model with random item difficulties (besides the common random person abilities). In addition, a mixture model is
Gaussian random bridges and a geometric model for information equilibrium
Mengütürk, Levent Ali
2018-03-01
The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.
Monotonic entropy growth for a nonlinear model of random exchanges.
Apenko, S M
2013-02-01
We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.
Joint modeling of ChIP-seq data via a Markov random field model
Bao, Yanchun; Vinciotti, Veronica; Wit, Ernst; 't Hoen, Peter A C
Chromatin ImmunoPrecipitation-sequencing (ChIP-seq) experiments have now become routine in biology for the detection of protein-binding sites. In this paper, we present a Markov random field model for the joint analysis of multiple ChIP-seq experiments. The proposed model naturally accounts for
Evaluating Continuous-Time Slam Using a Predefined Trajectory Provided by a Robotic Arm
Koch, B.; Leblebici, R.; Martell, A.; Jörissen, S.; Schilling, K.; Nüchter, A.
2017-09-01
Recently published approaches to SLAM algorithms process laser sensor measurements and output a map as a point cloud of the environment. Often the actual precision of the map remains unclear, since SLAMalgorithms apply local improvements to the resulting map. Unfortunately, it is not trivial to compare the performance of SLAMalgorithms objectively, especially without an accurate ground truth. This paper presents a novel benchmarking technique that allows to compare a precise map generated with an accurate ground truth trajectory to a map with a manipulated trajectory which was distorted by different forms of noise. The accurate ground truth is acquired by mounting a laser scanner on an industrial robotic arm. The robotic arm is moved on a predefined path while the position and orientation of the end-effector tool are monitored. During this process the 2D profile measurements of the laser scanner are recorded in six degrees of freedom and afterwards used to generate a precise point cloud of the test environment. For benchmarking, an offline continuous-time SLAM algorithm is subsequently applied to remove the inserted distortions. Finally, it is shown that the manipulated point cloud is reversible to its previous state and is slightly improved compared to the original version, since small errors that came into account by imprecise assumptions, sensor noise and calibration errors are removed as well.
Yang, Xiong; He, Haibo
2018-03-01
This paper presents a novel adaptive dynamic programming(ADP)-based self-learning robust optimal control scheme for input-affine continuous-time nonlinear systems with mismatched disturbances. First, the stabilizing feedback controller for original nonlinear systems is designed by modifying the optimal control law of the auxiliary system. It is also demonstrated that this feedback controller can optimize a specified value function. Then, within the framework of ADP, a single critic network is constructed to solve the Hamilton-Jacobi-Bellman equation associated with the auxiliary system optimal control law. To update the critic network weights, an indicator function and a concurrent learning technique are employed. By using the proposed update law for the critic network, the restrictive conditions including the initial admissible control and the persistence of excitation condition are relaxed. Moreover, the stability of the closed-loop auxiliary system is guaranteed in the sense that all the signals are uniformly ultimately bounded. Finally, the applicability of the developed control strategy is illustrated through simulations for an unstable nonlinear plant and a power system. Copyright © 2017 Elsevier Ltd. All rights reserved.
Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach
International Nuclear Information System (INIS)
Ferrari, Giorgio; Riedel, Frank; Steg, Jan-Henrik
2017-01-01
In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochastic Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.
A low power CMOS 3.3 Gbps continuous-time adaptive equalizer for serial link
International Nuclear Information System (INIS)
Ju Hao; Zhou Yumei; Zhao Jianzhong
2011-01-01
This paper describes using a high-speed continuous-time analog adaptive equalizer as the front-end of a receiver for a high-speed serial interface, which is compliant with many serial communication specifications such as USB2.0, PCI-E2.0 and Rapid IO. The low and high frequency loops are merged to decrease the effect of delay between the two paths, in addition, the infinite input impedance facilitates the cascade stages in order to improve the high frequency boosting gain. The implemented circuit architecture could facilitate the wide frequency range from 1 to 3.3 Gbps with different length FR4-PCB traces, which brings as much as 25 dB loss. The replica control circuits are injected to provide a convenient way to regulate common-mode voltage for full differential operation. In addition, AC coupling is adopted to suppress the common input from the forward stage. A prototype chip was fabricated in 0.18-μm 1P6M mixed-signal CMOS technology. The actual area is 0.6 x 0.57 mm 2 and the analog equalizer operates up to 3.3 Gbps over FR4-PCB trace with 25 dB loss. The overall power dissipation is approximately 23.4 mW. (semiconductor integrated circuits)
A low power CMOS 3.3 Gbps continuous-time adaptive equalizer for serial link
Hao, Ju; Yumei, Zhou; Jianzhong, Zhao
2011-09-01
This paper describes using a high-speed continuous-time analog adaptive equalizer as the front-end of a receiver for a high-speed serial interface, which is compliant with many serial communication specifications such as USB2.0, PCI-E2.0 and Rapid IO. The low and high frequency loops are merged to decrease the effect of delay between the two paths, in addition, the infinite input impedance facilitates the cascade stages in order to improve the high frequency boosting gain. The implemented circuit architecture could facilitate the wide frequency range from 1 to 3.3 Gbps with different length FR4-PCB traces, which brings as much as 25 dB loss. The replica control circuits are injected to provide a convenient way to regulate common-mode voltage for full differential operation. In addition, AC coupling is adopted to suppress the common input from the forward stage. A prototype chip was fabricated in 0.18-μm 1P6M mixed-signal CMOS technology. The actual area is 0.6 × 0.57 mm2 and the analog equalizer operates up to 3.3 Gbps over FR4-PCB trace with 25 dB loss. The overall power dissipation is approximately 23.4 mW.
Continuous-time ΣΔ ADC with implicit variable gain amplifier for CMOS image sensor.
Tang, Fang; Bermak, Amine; Abbes, Amira; Benammar, Mohieddine Amor
2014-01-01
This paper presents a column-parallel continuous-time sigma delta (CTSD) ADC for mega-pixel resolution CMOS image sensor (CIS). The sigma delta modulator is implemented with a 2nd order resistor/capacitor-based loop filter. The first integrator uses a conventional operational transconductance amplifier (OTA), for the concern of a high power noise rejection. The second integrator is realized with a single-ended inverter-based amplifier, instead of a standard OTA. As a result, the power consumption is reduced, without sacrificing the noise performance. Moreover, the variable gain amplifier in the traditional column-parallel read-out circuit is merged into the front-end of the CTSD modulator. By programming the input resistance, the amplitude range of the input current can be tuned with 8 scales, which is equivalent to a traditional 2-bit preamplification function without consuming extra power and chip area. The test chip prototype is fabricated using 0.18 μm CMOS process and the measurement result shows an ADC power consumption lower than 63.5 μW under 1.4 V power supply and 50 MHz clock frequency.
Gain-Scheduled ℋ2 Controller Synthesis for Continuous-Time Polytopic LPV Systems
Directory of Open Access Journals (Sweden)
Guangbin Cai
2014-01-01
Full Text Available This paper is concerned with the problem of gain-scheduled ℋ2 controller synthesis for continuous-time linear parameter-varying systems. In this problem, the system matrices in the state-space form are polytopic and patameterized and the admissible values of the parameters are assumed to be measurable on-line in a polytope space. By employing a basis-parameter-dependent Lyapunov function and introducing some slack variables to the well-established performance conditions, sufficient conditions for the existence of the desired gain-scheduled ℋ2 state feedback and dynamic output feedback controllers are established in terms of parameterized linear matrix inequalities. Based on the polytopic characteristic of the dependent parameters and a convexification method, the corresponding controller synthesis problem is then cast into finite-dimensional convex optimization problem which can be efficiently solved by using standard numerical softwares. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.
Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions
Izaac, J. A.; Wang, J. B.
2017-09-01
To extend the continuous-time quantum walk (CTQW) to simulate P distinguishable particles on a graph G composed of N vertices, the Hamiltonian of the system is expanded to act on an NP-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph G via a single-particle CTQW propagating on the Cartesian graph product G□P. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated NP state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure G□P in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing "redundant" and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed N .
Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach
Energy Technology Data Exchange (ETDEWEB)
Ferrari, Giorgio, E-mail: giorgio.ferrari@uni-bielefeld.de; Riedel, Frank, E-mail: frank.riedel@uni-bielefeld.de; Steg, Jan-Henrik, E-mail: jsteg@uni-bielefeld.de [Bielefeld University, Center for Mathematical Economics (Germany)
2017-06-15
In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochastic Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.
Hedonic travel cost and random utility models of recreation
Energy Technology Data Exchange (ETDEWEB)
Pendleton, L. [Univ. of Southern California, Los Angeles, CA (United States); Mendelsohn, R.; Davis, E.W. [Yale Univ., New Haven, CT (United States). School of Forestry and Environmental Studies
1998-07-09
Micro-economic theory began as an attempt to describe, predict and value the demand and supply of consumption goods. Quality was largely ignored at first, but economists have started to address quality within the theory of demand and specifically the question of site quality, which is an important component of land management. This paper demonstrates that hedonic and random utility models emanate from the same utility theoretical foundation, although they make different estimation assumptions. Using a theoretically consistent comparison, both approaches are applied to examine the quality of wilderness areas in the Southeastern US. Data were collected on 4778 visits to 46 trails in 20 different forest areas near the Smoky Mountains. Visitor data came from permits and an independent survey. The authors limited the data set to visitors from within 300 miles of the North Carolina and Tennessee border in order to focus the analysis on single purpose trips. When consistently applied, both models lead to results with similar signs but different magnitudes. Because the two models are equally valid, recreation studies should continue to use both models to value site quality. Further, practitioners should be careful not to make simplifying a priori assumptions which limit the effectiveness of both techniques.
Macroscopic damping model for structural dynamics with random polycrystalline configurations
Yang, Yantao; Cui, Junzhi; Yu, Yifan; Xiang, Meizhen
2017-12-01
In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro-nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro-nano scales is set up.
Fractal planetary rings: Energy inequalities and random field model
Malyarenko, Anatoliy; Ostoja-Starzewski, Martin
2017-12-01
This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square F2 of the radial cross-section F of the rings, where F is a fat fractal.
[Critical of the additive model of the randomized controlled trial].
Boussageon, Rémy; Gueyffier, François; Bejan-Angoulvant, Theodora; Felden-Dominiak, Géraldine
2008-01-01
Randomized, double-blind, placebo-controlled clinical trials are currently the best way to demonstrate the clinical effectiveness of drugs. Its methodology relies on the method of difference (John Stuart Mill), through which the observed difference between two groups (drug vs placebo) can be attributed to the pharmacological effect of the drug being tested. However, this additive model can be questioned in the event of statistical interactions between the pharmacological and the placebo effects. Evidence in different domains has shown that the placebo effect can influence the effect of the active principle. This article evaluates the methodological, clinical and epistemological consequences of this phenomenon. Topics treated include extrapolating results, accounting for heterogeneous results, demonstrating the existence of several factors in the placebo effect, the necessity to take these factors into account for given symptoms or pathologies, as well as the problem of the "specific" effect.
Droplet localization in the random XXZ model and its manifestations
Elgart, A.; Klein, A.; Stolz, G.
2018-01-01
We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- \\frac 1 2 XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal. (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb-Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.
Measurement model choice influenced randomized controlled trial results.
Gorter, Rosalie; Fox, Jean-Paul; Apeldoorn, Adri; Twisk, Jos
2016-11-01
In randomized controlled trials (RCTs), outcome variables are often patient-reported outcomes measured with questionnaires. Ideally, all available item information is used for score construction, which requires an item response theory (IRT) measurement model. However, in practice, the classical test theory measurement model (sum scores) is mostly used, and differences between response patterns leading to the same sum score are ignored. The enhanced differentiation between scores with IRT enables more precise estimation of individual trajectories over time and group effects. The objective of this study was to show the advantages of using IRT scores instead of sum scores when analyzing RCTs. Two studies are presented, a real-life RCT, and a simulation study. Both IRT and sum scores are used to measure the construct and are subsequently used as outcomes for effect calculation. The bias in RCT results is conditional on the measurement model that was used to construct the scores. A bias in estimated trend of around one standard deviation was found when sum scores were used, where IRT showed negligible bias. Accurate statistical inferences are made from an RCT study when using IRT to estimate construct measurements. The use of sum scores leads to incorrect RCT results. Copyright Â© 2016 Elsevier Inc. All rights reserved.
Franz, Silvio; Gradenigo, Giacomo; Spigler, Stefano
2016-03-01
We study how the thermodynamic properties of the triangular plaquette model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in kinetically constrained models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model the random-diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "random first-order" kind. Finally, we give support to our conjectures studying the finite-temperature phase diagram of the random-diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free energy and configurational entropy can be computed by means of the cavity equations.
Discriminative Random Field Models for Subsurface Contamination Uncertainty Quantification
Arshadi, M.; Abriola, L. M.; Miller, E. L.; De Paolis Kaluza, C.
2017-12-01
Application of flow and transport simulators for prediction of the release, entrapment, and persistence of dense non-aqueous phase liquids (DNAPLs) and associated contaminant plumes is a computationally intensive process that requires specification of a large number of material properties and hydrologic/chemical parameters. Given its computational burden, this direct simulation approach is particularly ill-suited for quantifying both the expected performance and uncertainty associated with candidate remediation strategies under real field conditions. Prediction uncertainties primarily arise from limited information about contaminant mass distributions, as well as the spatial distribution of subsurface hydrologic properties. Application of direct simulation to quantify uncertainty would, thus, typically require simulating multiphase flow and transport for a large number of permeability and release scenarios to collect statistics associated with remedial effectiveness, a computationally prohibitive process. The primary objective of this work is to develop and demonstrate a methodology that employs measured field data to produce equi-probable stochastic representations of a subsurface source zone that capture the spatial distribution and uncertainty associated with key features that control remediation performance (i.e., permeability and contamination mass). Here we employ probabilistic models known as discriminative random fields (DRFs) to synthesize stochastic realizations of initial mass distributions consistent with known, and typically limited, site characterization data. Using a limited number of full scale simulations as training data, a statistical model is developed for predicting the distribution of contaminant mass (e.g., DNAPL saturation and aqueous concentration) across a heterogeneous domain. Monte-Carlo sampling methods are then employed, in conjunction with the trained statistical model, to generate realizations conditioned on measured borehole data
Conditional random field modelling of interactions between findings in mammography
Kooi, Thijs; Mordang, Jan-Jurre; Karssemeijer, Nico
2017-03-01
Recent breakthroughs in training deep neural network architectures, in particular deep Convolutional Neural Networks (CNNs), made a big impact on vision research and are increasingly responsible for advances in Computer Aided Diagnosis (CAD). Since many natural scenes and medical images vary in size and are too large to feed to the networks as a whole, two stage systems are typically employed, where in the first stage, small regions of interest in the image are located and presented to the network as training and test data. These systems allow us to harness accurate region based annotations, making the problem easier to learn. However, information is processed purely locally and context is not taken into account. In this paper, we present preliminary work on the employment of a Conditional Random Field (CRF) that is trained on top the CNN to model contextual interactions such as the presence of other suspicious regions, for mammography CAD. The model can easily be extended to incorporate other sources of information, such as symmetry, temporal change and various patient covariates and is general in the sense that it can have application in other CAD problems.
Casabán, M.-C.; Cortés, J.-C.; Navarro-Quiles, A.; Romero, J.-V.; Roselló, M.-D.; Villanueva, R.-J.
2016-03-01
This paper provides a complete probabilistic description of SIS-type epidemiological models where all the input parameters (contagion rate, recovery rate and initial conditions) are assumed to be random variables. By applying the Random Variable Transformation technique, the first probability density function, the mean and the variance functions, as well as confidence intervals associated with the solution of SIS-type epidemiological models, are determined. It is done under the general hypothesis that model random inputs have any joint probability density function. The distributions to describe the time until a given proportion of the population remains susceptible and infected are also determined. Finally, a probabilistic description of the so-called basic reproductive number is included. The theoretical results are applied to an illustrative example showing good fitting.
Random geometry model in criticality calculations of solutions containing Raschig rings
International Nuclear Information System (INIS)
Teng, S.P.; Lindstrom, D.G.
1979-01-01
The criticality constants of fissile solutions containing borated Raschig rings are evaluated using the Monte Carlo code KENO IV with various geometry models. In addition to those used by other investigators, a new geometry model, the random geometry model, is presented to simulate the system of randomly oriented Raschig rings in solution. A technique to obtain the material thickness distribution functions of solution and rings for use in the random geometry model is also presented. Comparison between the experimental data and the calculated results using Monte Carlo method with various geometry models indicates that the random geometry model is a reasonable alternative to models previously used in describing the system of Raschig-ring-filled solution. The random geometry model also provides a solution to the problem of describing an array containing Raschig-ring-filled tanks that is not available to techniques using other models
Estimating a DIF decomposition model using a random-weights linear logistic test model approach.
Paek, Insu; Fukuhara, Hirotaka
2015-09-01
A differential item functioning (DIF) decomposition model separates a testlet item DIF into two sources: item-specific differential functioning and testlet-specific differential functioning. This article provides an alternative model-building framework and estimation approach for a DIF decomposition model that was proposed by Beretvas and Walker (2012). Although their model is formulated under multilevel modeling with the restricted pseudolikelihood estimation method, our approach illustrates DIF decomposition modeling that is directly built upon the random-weights linear logistic test model framework with the marginal maximum likelihood estimation method. In addition to demonstrating our approach's performance, we provide detailed information on how to implement this new DIF decomposition model using an item response theory software program; using DIF decomposition may be challenging for practitioners, yet practical information on how to implement it has previously been unavailable in the measurement literature.
DEFF Research Database (Denmark)
Holst, René; Jørgensen, Bent
2015-01-01
The paper proposes a versatile class of multiplicative generalized linear longitudinal mixed models (GLLMM) with additive dispersion components, based on explicit modelling of the covariance structure. The class incorporates a longitudinal structure into the random effects models and retains...
Force Limited Random Vibration Test of TESS Camera Mass Model
Karlicek, Alexandra; Hwang, James Ho-Jin; Rey, Justin J.
2015-01-01
The Transiting Exoplanet Survey Satellite (TESS) is a spaceborne instrument consisting of four wide field-of-view-CCD cameras dedicated to the discovery of exoplanets around the brightest stars. As part of the environmental testing campaign, force limiting was used to simulate a realistic random vibration launch environment. While the force limit vibration test method is a standard approach used at multiple institutions including Jet Propulsion Laboratory (JPL), NASA Goddard Space Flight Center (GSFC), European Space Research and Technology Center (ESTEC), and Japan Aerospace Exploration Agency (JAXA), it is still difficult to find an actual implementation process in the literature. This paper describes the step-by-step process on how the force limit method was developed and applied on the TESS camera mass model. The process description includes the design of special fixtures to mount the test article for properly installing force transducers, development of the force spectral density using the semi-empirical method, estimation of the fuzzy factor (C2) based on the mass ratio between the supporting structure and the test article, subsequent validating of the C2 factor during the vibration test, and calculation of the C.G. accelerations using the Root Mean Square (RMS) reaction force in the spectral domain and the peak reaction force in the time domain.
Mendelian Randomization versus Path Models: Making Causal Inferences in Genetic Epidemiology.
Ziegler, Andreas; Mwambi, Henry; König, Inke R
2015-01-01
The term Mendelian randomization is popular in the current literature. The first aim of this work is to describe the idea of Mendelian randomization studies and the assumptions required for drawing valid conclusions. The second aim is to contrast Mendelian randomization and path modeling when different 'omics' levels are considered jointly. We define Mendelian randomization as introduced by Katan in 1986, and review its crucial assumptions. We introduce path models as the relevant additional component to the current use of Mendelian randomization studies in 'omics'. Real data examples for the association between lipid levels and coronary artery disease illustrate the use of path models. Numerous assumptions underlie Mendelian randomization, and they are difficult to be fulfilled in applications. Path models are suitable for investigating causality, and they should not be mixed up with the term Mendelian randomization. In many applications, path modeling would be the appropriate analysis in addition to a simple Mendelian randomization analysis. Mendelian randomization and path models use different concepts for causal inference. Path modeling but not simple Mendelian randomization analysis is well suited to study causality with different levels of 'omics' data. 2015 S. Karger AG, Basel.
Wang, Jinling; Jiang, Haijun; Ma, Tianlong; Hu, Cheng
2018-05-01
This paper considers the delay-dependent stability of memristive complex-valued neural networks (MCVNNs). A novel linear mapping function is presented to transform the complex-valued system into the real-valued system. Under such mapping function, both continuous-time and discrete-time MCVNNs are analyzed in this paper. Firstly, when activation functions are continuous but not Lipschitz continuous, an extended matrix inequality is proved to ensure the stability of continuous-time MCVNNs. Furthermore, if activation functions are discontinuous, a discontinuous adaptive controller is designed to acquire its stability by applying Lyapunov-Krasovskii functionals. Secondly, compared with techniques in continuous-time MCVNNs, the Halanay-type inequality and comparison principle are firstly used to exploit the dynamical behaviors of discrete-time MCVNNs. Finally, the effectiveness of theoretical results is illustrated through numerical examples. Copyright © 2018 Elsevier Ltd. All rights reserved.
Genetic Analysis of Daily Maximum Milking Speed by a Random Walk Model in Dairy Cows
DEFF Research Database (Denmark)
Karacaören, Burak; Janss, Luc; Kadarmideen, Haja
Data were obtained from dairy cows stationed at research farm ETH Zurich for maximum milking speed. The main aims of this paper are a) to evaluate if the Wood curve is suitable to model mean lactation curve b) to predict longitudinal breeding values by random regression and random walk models...... of maximum milking speed. Wood curve did not provide a good fit to the data set. Quadratic random regressions gave better predictions compared with the random walk model. However random walk model does not need to be evaluated for different orders of regression coefficients. In addition with the Kalman...... filter applications: random walk model could give online prediction of breeding values. Hence without waiting for whole lactation records, genetic evaluation could be made when the daily or monthly data is available...
Energy Technology Data Exchange (ETDEWEB)
Dmitriev, Alexander S.; Yemelyanov, Ruslan Yu. [V.A. Kotelnikov Institute of Radio Engineering and Electronics of the RAS Mokhovaya 11-7, Moscow, 125009 (Russian Federation); Moscow Institute of Physics and Technology (State University) 9 Institutskiy per., Dolgoprudny, Moscow, 141700 (Russian Federation); Gerasimov, Mark Yu. [V.A. Kotelnikov Institute of Radio Engineering and Electronics of the RAS Mokhovaya 11-7, Moscow, 125009 (Russian Federation); Itskov, Vadim V. [Moscow Institute of Physics and Technology (State University) 9 Institutskiy per., Dolgoprudny, Moscow, 141700 (Russian Federation)
2016-06-08
The paper deals with a new multi-element processor platform assigned for modelling the behaviour of interacting dynamical systems, i.e., active wireless network. Experimentally, this ensemble is implemented in an active network, the active nodes of which include direct chaotic transceivers and special actuator boards containing microcontrollers for modelling the dynamical systems and an information display unit (colored LEDs). The modelling technique and experimental results are described and analyzed.
MODELING URBAN DYNAMICS USING RANDOM FOREST: IMPLEMENTING ROC AND TOC FOR MODEL EVALUATION
Directory of Open Access Journals (Sweden)
M. Ahmadlou
2016-06-01
Full Text Available The importance of spatial accuracy of land use/cover change maps necessitates the use of high performance models. To reach this goal, calibrating machine learning (ML approaches to model land use/cover conversions have received increasing interest among the scholars. This originates from the strength of these techniques as they powerfully account for the complex relationships underlying urban dynamics. Compared to other ML techniques, random forest has rarely been used for modeling urban growth. This paper, drawing on information from the multi-temporal Landsat satellite images of 1985, 2000 and 2015, calibrates a random forest regression (RFR model to quantify the variable importance and simulation of urban change spatial patterns. The results and performance of RFR model were evaluated using two complementary tools, relative operating characteristics (ROC and total operating characteristics (TOC, by overlaying the map of observed change and the modeled suitability map for land use change (error map. The suitability map produced by RFR model showed 82.48% area under curve for the ROC model which indicates a very good performance and highlights its appropriateness for simulating urban growth.
Drikvandi, Reza
2017-06-01
Nonlinear mixed-effects models are frequently used for pharmacokinetic data analysis, and they account for inter-subject variability in pharmacokinetic parameters by incorporating subject-specific random effects into the model. The random effects are often assumed to follow a (multivariate) normal distribution. However, many articles have shown that misspecifying the random-effects distribution can introduce bias in the estimates of parameters and affect inferences about the random effects themselves, such as estimation of the inter-subject variability. Because random effects are unobservable latent variables, it is difficult to assess their distribution. In a recent paper we developed a diagnostic tool based on the so-called gradient function to assess the random-effects distribution in mixed models. There we evaluated the gradient function for generalized liner mixed models and in the presence of a single random effect. However, assessing the random-effects distribution in nonlinear mixed-effects models is more challenging, especially when multiple random effects are present, and therefore the results from linear and generalized linear mixed models may not be valid for such nonlinear models. In this paper, we further investigate the gradient function and evaluate its performance for such nonlinear mixed-effects models which are common in pharmacokinetics and pharmacodynamics. We use simulations as well as real data from an intensive pharmacokinetic study to illustrate the proposed diagnostic tool.
A Design Methodology for Power-efficient Continuous-time Sigma-Delta A/D Converters
DEFF Research Database (Denmark)
Nielsen, Jannik Hammel; Bruun, Erik
2003-01-01
In this paper we present a design methodology for optimizing the power consumption of continuous-time (CT) ΣΔ A/D converters. A method for performance prediction for ΣΔ A/D converters is presented. Estimation of analog and digital power consumption is derived and employed to predict the most power...
Pan, Shin-Liang; Chen, Hsiu-Hsi
2010-09-01
The rates of functional recovery after stroke tend to decrease with time. Time-varying Markov processes (TVMP) may be more biologically plausible than time-invariant Markov process for modeling such data. However, analysis of such stochastic processes, particularly tackling reversible transitions and the incorporation of random effects into models, can be analytically intractable. We make use of ordinary differential equations to solve continuous-time TVMP with reversible transitions. The proportional hazard form was used to assess the effects of an individual's covariates on multi-state transitions with the incorporation of random effects that capture the residual variation after being explained by measured covariates under the concept of generalized linear model. We further built up Bayesian directed acyclic graphic model to obtain full joint posterior distribution. Markov chain Monte Carlo (MCMC) with Gibbs sampling was applied to estimate parameters based on posterior marginal distributions with multiple integrands. The proposed method was illustrated with empirical data from a study on the functional recovery after stroke. Copyright 2010 Elsevier Inc. All rights reserved.
Modeling and optimizing of the random atomic spin gyroscope drift based on the atomic spin gyroscope
Energy Technology Data Exchange (ETDEWEB)
Quan, Wei; Lv, Lin, E-mail: lvlinlch1990@163.com; Liu, Baiqi [School of Instrument Science and Opto-Electronics Engineering, Beihang University, Beijing 100191 (China)
2014-11-15
In order to improve the atom spin gyroscope's operational accuracy and compensate the random error caused by the nonlinear and weak-stability characteristic of the random atomic spin gyroscope (ASG) drift, the hybrid random drift error model based on autoregressive (AR) and genetic programming (GP) + genetic algorithm (GA) technique is established. The time series of random ASG drift is taken as the study object. The time series of random ASG drift is acquired by analyzing and preprocessing the measured data of ASG. The linear section model is established based on AR technique. After that, the nonlinear section model is built based on GP technique and GA is used to optimize the coefficients of the mathematic expression acquired by GP in order to obtain a more accurate model. The simulation result indicates that this hybrid model can effectively reflect the characteristics of the ASG's random drift. The square error of the ASG's random drift is reduced by 92.40%. Comparing with the AR technique and the GP + GA technique, the random drift is reduced by 9.34% and 5.06%, respectively. The hybrid modeling method can effectively compensate the ASG's random drift and improve the stability of the system.
Random regression models in the evaluation of the growth curve of Simbrasil beef cattle
Mota, M.; Marques, F.A.; Lopes, P.S.; Hidalgo, A.M.
2013-01-01
Random regression models were used to estimate the types and orders of random effects of (co)variance functions in the description of the growth trajectory of the Simbrasil cattle breed. Records for 7049 animals totaling 18,677 individual weighings were submitted to 15 models from the third to the
Technology diffusion in hospitals : A log odds random effects regression model
Blank, J.L.T.; Valdmanis, V.G.
2013-01-01
This study identifies the factors that affect the diffusion of hospital innovations. We apply a log odds random effects regression model on hospital micro data. We introduce the concept of clustering innovations and the application of a log odds random effects regression model to describe the
Technology diffusion in hospitals: A log odds random effects regression model
J.L.T. Blank (Jos); V.G. Valdmanis (Vivian G.)
2015-01-01
textabstractThis study identifies the factors that affect the diffusion of hospital innovations. We apply a log odds random effects regression model on hospital micro data. We introduce the concept of clustering innovations and the application of a log odds random effects regression model to
Random forest (RF) modeling has emerged as an important statistical learning method in ecology due to its exceptional predictive performance. However, for large and complex ecological datasets there is limited guidance on variable selection methods for RF modeling. Typically, e...
International Nuclear Information System (INIS)
Kang, Li; Tang, Sanyi
2016-01-01
Highlights: • The discrete single species and multiple species models with random perturbation are proposed. • The complex dynamics and interesting bifurcation behavior have been investigated. • The reverse effects of random perturbation on discrete systems have been discussed and revealed. • The main results can be applied for pest control and resources management. - Abstract: The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.
Quenched Central Limit Theorems for the Ising Model on Random Graphs
Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
2015-09-01
The main goal of the paper is to prove central limit theorems for the magnetization rescaled by for the Ising model on random graphs with N vertices. Both random quenched and averaged quenched measures are considered. We work in the uniqueness regime or and , where is the inverse temperature, is the critical inverse temperature and B is the external magnetic field. In the random quenched setting our results apply to general tree-like random graphs (as introduced by Dembo, Montanari and further studied by Dommers and the first and third author) and our proof follows that of Ellis in . For the averaged quenched setting, we specialize to two particular random graph models, namely the 2-regular configuration model and the configuration model with degrees 1 and 2. In these cases our proofs are based on explicit computations relying on the solution of the one dimensional Ising models.
Soundness of Timed-Arc Workflow Nets in Discrete and Continuous-Time Semantics
DEFF Research Database (Denmark)
Mateo, Jose Antonio; Srba, Jiri; Sørensen, Mathias Grund
2015-01-01
Analysis of workflow processes with quantitative aspectslike timing is of interest in numerous time-critical applications. We suggest a workflow model based on timed-arc Petri nets and studythe foundational problems of soundness and strong (time-bounded) soundness.We first consider the discrete......-time semantics (integer delays)and explore the decidability of the soundness problemsand show, among others, that soundness is decidable for monotonic workflow nets while reachability is undecidable.For general timed-arc workflow nets soundness andstrong soundness become undecidable, though we can design......, and a blood transfusion workflow.The implementation of the algorithms is freely available as a part of the model checker TAPAAL (www.tapaal.net)....
Random Modeling of Daily Rainfall and Runoff Using a Seasonal Model and Wavelet Denoising
Directory of Open Access Journals (Sweden)
Chien-ming Chou
2014-01-01
Full Text Available Instead of Fourier smoothing, this study applied wavelet denoising to acquire the smooth seasonal mean and corresponding perturbation term from daily rainfall and runoff data in traditional seasonal models, which use seasonal means for hydrological time series forecasting. The denoised rainfall and runoff time series data were regarded as the smooth seasonal mean. The probability distribution of the percentage coefficients can be obtained from calibrated daily rainfall and runoff data. For validated daily rainfall and runoff data, percentage coefficients were randomly generated according to the probability distribution and the law of linear proportion. Multiplying the generated percentage coefficient by the smooth seasonal mean resulted in the corresponding perturbation term. Random modeling of daily rainfall and runoff can be obtained by adding the perturbation term to the smooth seasonal mean. To verify the accuracy of the proposed method, daily rainfall and runoff data for the Wu-Tu watershed were analyzed. The analytical results demonstrate that wavelet denoising enhances the precision of daily rainfall and runoff modeling of the seasonal model. In addition, the wavelet denoising technique proposed in this study can obtain the smooth seasonal mean of rainfall and runoff processes and is suitable for modeling actual daily rainfall and runoff processes.
Directory of Open Access Journals (Sweden)
Jaime Araujo Cobuci
2012-09-01
Full Text Available Milk yield test-day records on the first three lactations of 25,500 Holstein cows were used to estimate genetic parameters and predict breeding values for nine measures of persistency and 305-d milk yield in a random regression animal model using two criteria to define the fixed regression. Legendre polynomials of fourth and fifth orders were used to model the fixed and random regressions of lactation curves. The fixed regressions were adjusted for average milk yield on populations (single or subpopulations (multiple formed by cows that calved at the same age and in the same season. Akaike Information (AIC and Bayesian Information (BIC criteria indicated that models with multiple regression lactation curves had the best fit to test-day milk records of first lactations, while models with a single regression curve had the best fit for the second and third lactations. Heritability and genetic correlation estimates between persistency and milk yield differed significantly depending on the lactation order and the measures of persistency used. These parameters did not differ significantly depending on the criteria used for defining the fixed regressions for lactation curves. In general, the heritability estimates were higher for first (0.07 to 0.43, followed by the second (0.08 to 0.21 and third (0.04 to 0.10 lactation. The rank of sires resulting from the processes of genetic evaluation for milk yield or persistency using random regression models differed according to the criteria used for determining the fixed regression of lactation curve.
Wave propagation modeling in composites reinforced by randomly oriented fibers
Kudela, Pawel; Radzienski, Maciej; Ostachowicz, Wieslaw
2018-02-01
A new method for prediction of elastic constants in randomly oriented fiber composites is proposed. It is based on mechanics of composites, the rule of mixtures and total mass balance tailored to the spectral element mesh composed of 3D brick elements. Selected elastic properties predicted by the proposed method are compared with values obtained by another theoretical method. The proposed method is applied for simulation of Lamb waves in glass-epoxy composite plate reinforced by randomly oriented fibers. Full wavefield measurements conducted by the scanning laser Doppler vibrometer are in good agreement with simulations performed by using the time domain spectral element method.
Event Triggered Reinforcement Learning Approach for Unknown Nonlinear Continuous Time System
2014-07-06
unknown system functions . Assume that f(x(t)) + g(x(t))u(t) is Lipschitz continuous on a set Ω ⊆ Rn, and f(0) = 0, g(0) = 0. In order to save resources...feedback controller γ(x̂j), which maps the sampled state onto a control vector. Assume that γ(x̂j) is a Lipschitz continuous function . The obtained...Currently, the event- triggered control methods are based on the accurate system function or model [6], [7]. In many cases, the complete knowledge of
Positive random fields for modeling material stiffness and compliance
DEFF Research Database (Denmark)
Hasofer, Abraham Michael; Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1998-01-01
Positive random fields with known marginal properties and known correlation function are not numerous in the literature. The most prominent example is the log\\-normal field for which the complete distribution is known and for which the reciprocal field is also lognormal. It is of interest to supp...
Least squares estimation in a simple random coefficient autoregressive model
DEFF Research Database (Denmark)
Johansen, S; Lange, T
2013-01-01
we prove the curious result that View the MathML source. The proof applies the notion of a tail index of sums of positive random variables with infinite variance to find the order of magnitude of View the MathML source and View the MathML source and hence the limit of View the MathML source...
Symmetry in stochasticity: Random walk models of large-scale ...
Indian Academy of Sciences (India)
This paper describes the insights gained from the excursion set approach, in which various questions about the phenomenology of large-scale structure formation can be mapped to problems associated with the ﬁrst crossing distribution of appropriately deﬁned barriers by random walks. Much of this is summarized in R K ...
Scale-free random graphs and Potts model
Indian Academy of Sciences (India)
We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertex has a prescribed weight − (0 < < 1) and an edge can connect vertices and with rate . Corresponding equilibrium ensemble is identified and the problem is solved by the → 1 limit of the -state Potts ...
Modeling Grade IV Gas Emboli using a Limited Failure Population Model with Random Effects
Thompson, Laura A.; Conkin, Johnny; Chhikara, Raj S.; Powell, Michael R.
2002-05-01
Venous gas emboli (VGE) (gas bubbles in venous blood) are associated with an increased risk of decompression sickness (DCS) in hypobaric environments. A high grade of VGE can be a precursor to serious DCS. In this paper, we model time to Grade IV VGE considering a subset of individuals assumed to be immune from experiencing VGE. Our data contain monitoring test results from subjects undergoing up to 13 denitrogenation test procedures prior to exposure to a hypobaric environment. The onset time of Grade IV VGE is recorded as contained within certain time intervals. We fit a parametric (lognormal) mixture survival model to the interval-and right-censored data to account for the possibility of a subset of "cured" individuals who are immune to the event. Our model contains random subject effects to account for correlations between repeated measurements on a single individual. Model assessments and cross-validation indicate that this limited failure population mixture model is an improvement over a model that does not account for the potential of a fraction of cured individuals. We also evaluated some alternative mixture models. Predictions from the best fitted mixture model indicate that the actual process is reasonably approximated by a limited failure population model.
Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition
Yalouz, Saad; Pouthier, Vincent
2018-02-01
A tight-binding model is introduced for describing the dynamics of an exciton on an extended star graph whose central node is occupied by a trap. On this graph, the exciton dynamics is governed by two kinds of eigenstates: many eigenstates are associated with degenerate real eigenvalues insensitive to the trap, whereas three decaying eigenstates characterized by complex energies contribute to the trapping process. It is shown that the excitonic population absorbed by the trap depends on the size of the graph, only. By contrast, both the size parameters and the absorption rate control the dynamics of the trapping. When these parameters are judiciously chosen, the efficiency of the transfer is optimized resulting in the minimization of the absorption time. Analysis of the eigenstates reveals that such a feature arises around the superradiance transition. Moreover, depending on the size of the network, two situations are highlighted where the transport efficiency is either superoptimized or suboptimized.
Marginal and Random Intercepts Models for Longitudinal Binary Data With Examples From Criminology.
Long, Jeffrey D; Loeber, Rolf; Farrington, David P
2009-01-01
Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides individual-level information including information about heterogeneity of growth. It is shown how a type of numerical averaging can be used with the random intercepts model to obtain group-level information, thus approximating individual and marginal aspects of the LMM. The types of inferences associated with each model are illustrated with longitudinal criminal offending data based on N = 506 males followed over a 22-year period. Violent offending indexed by official records and self-report were analyzed, with the marginal model estimated using generalized estimating equations and the random intercepts model estimated using maximum likelihood. The results show that the numerical averaging based on the random intercepts can produce prediction curves almost identical to those obtained directly from the marginal model parameter estimates. The results provide a basis for contrasting the models and the estimation procedures and key features are discussed to aid in selecting a method for empirical analysis.
Denial-of-Service Security Attack in the Continuous-Time World
DEFF Research Database (Denmark)
Wang, Shuling; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
Hybrid systems are integrations of discrete computation and continuous physical evolution. The physical components of such systems introduce safety requirements, the achievement of which asks for the correct monitoring and control from the discrete controllers. However, due to denial-of-service s......Hybrid systems are integrations of discrete computation and continuous physical evolution. The physical components of such systems introduce safety requirements, the achievement of which asks for the correct monitoring and control from the discrete controllers. However, due to denial......-of-service security attack, the expected information from the controllers is not received and as a consequence the physical systems may fail to behave as expected. This paper proposes a formal framework for expressing denial-of-service security attack in hybrid systems. As a virtue, a physical system is able to plan...... for reasonable behavior in case the ideal control fails due to unreliable communication, in such a way that the safety of the system upon denial-of-service is still guaranteed. In the context of the modeling language, we develop an inference system for verifying safety of hybrid systems, without putting any...
Activated aging dynamics and effective trap model description in the random energy model
Baity-Jesi, M.; Biroli, G.; Cammarota, C.
2018-01-01
We study the out-of-equilibrium aging dynamics of the random energy model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.
A Markov Chain Model for evaluating the effectiveness of randomized surveillance procedures
Energy Technology Data Exchange (ETDEWEB)
Edmunds, T.A.
1994-01-01
A Markov Chain Model has been developed to evaluate the effectiveness of randomized surveillance procedures. The model is applicable for surveillance systems that monitor a collection of assets by randomly selecting and inspecting the assets. The model provides an estimate of the detection probability as a function of the amount of time that an adversary would require to steal or sabotage the asset. An interactive computer code has been written to perform the necessary computations.
Efficient cache oblivious algorithms for randomized divide-and-conquer on the multicore model
Sharma, Neeraj; Sen, Sandeep
2012-01-01
In this paper we present randomized algorithms for sorting and convex hull that achieves optimal performance (for speed-up and cache misses) on the multicore model with private cache model. Our algorithms are cache oblivious and generalize the randomized divide and conquer strategy given by Reischuk and Reif and Sen. Although the approach yielded optimal speed-up in the PRAM model, we require additional techniques to optimize cache-misses in an oblivious setting. Under a mild assumption on in...
Random Matching Models and Money : The Global Structure and Approximation of Stationary Equilibria
Kamiya, K.; Talman, A.J.J.
2003-01-01
Random matching models with different states are an important class of dynamic games; for example, money search models, job search models, and some games in biology are special cases.In this paper, we investigate the basic structure of the models: the existence of equilibria, the global structure of
Asking Sensitive Questions: A Statistical Power Analysis of Randomized Response Models
Ulrich, Rolf; Schroter, Hannes; Striegel, Heiko; Simon, Perikles
2012-01-01
This article derives the power curves for a Wald test that can be applied to randomized response models when small prevalence rates must be assessed (e.g., detecting doping behavior among elite athletes). These curves enable the assessment of the statistical power that is associated with each model (e.g., Warner's model, crosswise model, unrelated…
Numerical Simulation of Entropy Growth for a Nonlinear Evolutionary Model of Random Markets
Directory of Open Access Journals (Sweden)
Mahdi Keshtkar
2016-01-01
Full Text Available In this communication, the generalized continuous economic model for random markets is revisited. In this model for random markets, agents trade by pairs and exchange their money in a random and conservative way. They display the exponential wealth distribution as asymptotic equilibrium, independently of the effectiveness of the transactions and of the limitation of the total wealth. In the current work, entropy of mentioned model is defined and then some theorems on entropy growth of this evolutionary problem are given. Furthermore, the entropy increasing by simulation on some numerical examples is verified.
A Random Pattern Mixture Model for Ordinal Outcomes with Informative Dropouts
Liu, Chengcheng; Ratcliffe, Sarah J.; Guo, Wensheng
2016-01-01
We extend a random pattern mixture joint model for longitudinal ordinal outcomes and informative dropouts. The patients are generalized to ”pattern” groups based on known covariates that are potential surrogated for the severity of the underlying condition. The random pattern effects are defined as the latent effects linking the dropout process and the ordinal longitudinal outcome. Conditional on the random pattern effects, the longitudinal outcome and the dropout times are assumed independent. Estimates are obtained via the EM algorithm. We applied the model to the end-stage renal disease (ESRD) data. Anemia was found to be significantly affected by baseline iron treatment when the dropout information was adjusted via the study model; as opposed to an independent or shared parameter model. Simulations were performed to evaluate the performance of the random pattern mixture model under various assumptions. PMID:25894456
Local Hidden Variable Models for Entangled Quantum States Using Finite Shared Randomness
Bowles, Joseph; Hirsch, Flavien; Quintino, Marco Túlio; Brunner, Nicolas
2015-03-01
The statistics of local measurements performed on certain entangled states can be reproduced using a local hidden variable (LHV) model. While all known models make use of an infinite amount of shared randomness, we show that essentially all entangled states admitting a LHV model can be simulated with finite shared randomness. Our most economical model simulates noisy two-qubit Werner states using only log2(12 )≃3.58 bits of shared randomness. We also discuss the case of positive operator valued measures, and the simulation of nonlocal states with finite shared randomness and finite communication. Our work represents a first step towards quantifying the cost of LHV models for entangled quantum states.
Absence of Replica Symmetry Breaking in the Transverse and Longitudinal Random Field Ising Model
Itoi, C.
2018-02-01
It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant space in the infinite volume limit. The weak Fortuin-Kasteleyn-Ginibre property in this model and the Ghirlanda-Guerra identities in artificial models in a path integral representation based on the Lie-Trotter-Suzuki formula enable us to extend Chatterjee's proof for the random field Ising model to the quantum model.
Process of random distributions : classification and prediction ...
African Journals Online (AJOL)
Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case. We give an application in ...
DEFF Research Database (Denmark)
Strathe, Anders B; Mark, Thomas; Nielsen, Bjarne
2014-01-01
Random regression models were used to estimate covariance functions between cumulated feed intake (CFI) and body weight (BW) in 8424 Danish Duroc pigs. Random regressions on second order Legendre polynomials of age were used to describe genetic and permanent environmental curves in BW and CFI...
Cizek, Pavel; Lei, Jinghua
The identification in a nonseparable single-index models with correlated random effects is considered in panel data with a fixed number of time periods. The identification assumption is based on the correlated random effects structure. Under this assumption, the parameters of interest are identified
Cizek, P.; Lei, J.
2013-01-01
Abstract: The identification of parameters in a nonseparable single-index models with correlated random effects is considered in the context of panel data with a fixed number of time periods. The identification assumption is based on the correlated random-effect structure: the distribution of
DEFF Research Database (Denmark)
Ruban, Andrei; Simak, S.I.; Shallcross, S.
2003-01-01
We present a simple effective tetrahedron model for local lattice relaxation effects in random metallic alloys on simple primitive lattices. A comparison with direct ab initio calculations for supercells representing random Ni0.50Pt0.50 and Cu0.25Au0.75 alloys as well as the dilute limit of Au...
Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees
Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; Hofstad, Remco van der
2018-04-01
We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.
A note on moving average models for Gaussian random fields
DEFF Research Database (Denmark)
Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.
basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result...
The Random Walk Model Based on Bipartite Network
Directory of Open Access Journals (Sweden)
Zhang Man-Dun
2016-01-01
Full Text Available With the continuing development of the electronic commerce and growth of network information, there is a growing possibility for citizens to be confused by the information. Though the traditional technology of information retrieval have the ability to relieve the overload of information in some extent, it can not offer a targeted personality service based on user’s interests and activities. In this context, the recommendation algorithm arose. In this paper, on the basis of conventional recommendation, we studied the scheme of random walk based on bipartite network and the application of it. We put forward a similarity measurement based on implicit feedback. In this method, a uneven character vector is imported(the weight of item in the system. We put forward a improved random walk pattern which make use of partial or incomplete neighbor information to create recommendation information. In the end, there is an experiment in the real data set, the recommendation accuracy and practicality are improved. We promise the reality of the result of the experiment
Exact probability distribution function for multifractal random walk models of stocks
Saakian, D. B.; Martirosyan, A.; Hu, Chin-Kun; Struzik, Z. R.
2011-07-01
We investigate the multifractal random walk (MRW) model, popular in the modelling of stock fluctuations in the financial market. The exact probability distribution function (PDF) is derived by employing methods proposed in the derivation of correlation functions in string theory, including the analytical extension of Selberg integrals. We show that the recent results by Y. V. Fyodorov, P. Le Doussal and A. Rosso obtained with the logarithmic Random Energy Model (REM) model are sufficient to derive exact formulas for the PDF of the log returns in the MRW model.
Directory of Open Access Journals (Sweden)
Hongqiang Liu
2016-06-01
Full Text Available A Bayesian random effects modeling approach was used to examine the influence of neighborhood characteristics on burglary risks in Jianghan District, Wuhan, China. This random effects model is essentially spatial; a spatially structured random effects term and an unstructured random effects term are added to the traditional non-spatial Poisson regression model. Based on social disorganization and routine activity theories, five covariates extracted from the available data at the neighborhood level were used in the modeling. Three regression models were fitted and compared by the deviance information criterion to identify which model best fit our data. A comparison of the results from the three models indicates that the Bayesian random effects model is superior to the non-spatial models in fitting the data and estimating regression coefficients. Our results also show that neighborhoods with above average bar density and department store density have higher burglary risks. Neighborhood-specific burglary risks and posterior probabilities of neighborhoods having a burglary risk greater than 1.0 were mapped, indicating the neighborhoods that should warrant more attention and be prioritized for crime intervention and reduction. Implications and limitations of the study are discussed in our concluding section.
Parametric level correlations in random-matrix models
International Nuclear Information System (INIS)
Weidenmueller, Hans A
2005-01-01
We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle-point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications
Random phase mask as a model of a rough surface
International Nuclear Information System (INIS)
Svitasheva, S.N.
2011-01-01
Artificial roughness was created on sample surfaces by etching through a two-dimensional orthogonal grating with a stochastic distribution of square 'defects' of size. 'Defects' depth was varied from 0.02 μm up to 1.005 μm. The experimental dependences of the scattering of polarized light were studied on four types of surface roughness for two materials: quartz and aluminum. The defect sizes of the random phase mask were 25 x 25 μm and 2.5 x 2.5 μm. The impacts of the sizes and density of artificial defects of rough surfaces on the polarization of reflected light were investigated by multiple-angle-of-incidence (MAI) ellipsometry at a wavelength of 0.63 μm.
Statistical shape model with random walks for inner ear segmentation
DEFF Research Database (Denmark)
Pujadas, Esmeralda Ruiz; Kjer, Hans Martin; Piella, Gemma
2016-01-01
Cochlear implants can restore hearing to completely or partially deaf patients. The intervention planning can be aided by providing a patient-specific model of the inner ear. Such a model has to be built from high resolution images with accurate segmentations. Thus, a precise segmentation is requ...
International Nuclear Information System (INIS)
Wang Shen-Quan; Feng Jian; Zhao Qing
2012-01-01
In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks (CRNNs) with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique (the reciprocally convex combination method), less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Two numerical examples show that our results are better than the existing ones. (general)
Simulation of random set models for unions of discs and the use of power tessellations
DEFF Research Database (Denmark)
Møller, Jesper; Helisová, Katerina
The power tessellation (or power diagram or Laguerre diagram) turns out to be particular useful in connection to a certain class of stochastic models for a disc process used for generating a random set model. We discuss how to simulate these models and calculate various characteristics of power t...
A spatial error model with continuous random effects and an application to growth convergence
Laurini, Márcio Poletti
2017-10-01
We propose a spatial error model with continuous random effects based on Matérn covariance functions and apply this model for the analysis of income convergence processes (β -convergence). The use of a model with continuous random effects permits a clearer visualization and interpretation of the spatial dependency patterns, avoids the problems of defining neighborhoods in spatial econometrics models, and allows projecting the spatial effects for every possible location in the continuous space, circumventing the existing aggregations in discrete lattice representations. We apply this model approach to analyze the economic growth of Brazilian municipalities between 1991 and 2010 using unconditional and conditional formulations and a spatiotemporal model of convergence. The results indicate that the estimated spatial random effects are consistent with the existence of income convergence clubs for Brazilian municipalities in this period.
Xu, Lei; Zhai, Wanming
2017-10-01
This paper devotes to develop a computational model for stochastic analysis and reliability assessment of vehicle-track systems subject to earthquakes and track random irregularities. In this model, the earthquake is expressed as non-stationary random process simulated by spectral representation and random function, and the track random irregularities with ergodic properties on amplitudes, wavelengths and probabilities are characterized by a track irregularity probabilistic model, and then the number theoretical method (NTM) is applied to effectively select representative samples of earthquakes and track random irregularities. Furthermore, a vehicle-track coupled model is presented to obtain the dynamic responses of vehicle-track systems due to the earthquakes and track random irregularities at time-domain, and the probability density evolution method (PDEM) is introduced to describe the evolutionary process of probability from excitation input to response output by assuming the vehicle-track system as a probabilistic conservative system, which lays the foundation on reliability assessment of vehicle-track systems. The effectiveness of the proposed model is validated by comparing to the results of Monte-Carlo method from statistical viewpoint. As an illustrative example, the random vibrations of a high-speed railway vehicle running on the track slabs excited by lateral seismic waves and track random irregularities are analyzed, from which some significant conclusions can be drawn, e.g., track irregularities will additionally promote the dynamic influence of earthquakes especially on maximum values and dispersion degree of responses; the characteristic frequencies or frequency ranges respectively governed by earthquakes and track random irregularities are greatly different, moreover, the lateral seismic waves will dominate or even change the characteristic frequencies of system responses of some lateral dynamic indices at low frequency.
Spectral and Dynamical Properties of Random Models with Nonlocal and Singular Interactions
Hislop, P D; Krishna, M G
2002-01-01
We give a spectral and dynamical description of certain models of random Schr\\"odinger operators on $L^2 ( \\R^d)$ for which a modified version of the small moment method of Aizenman and Molchanov \\cite{[AizenmanMolchanov]} can be applied. One family of models includes includes \\Schr\\ operators with random, nonlocal interactions constructed from a wavelet basis. The second family includes \\Schr\\ operators with random singular interactions randomly located on sublattices of $\\Z^d$, for $d = 1 , 2, 3$. We prove that these models are amenable to Aizenman-Molchanov-type analysis of the Green's function, thereby eliminating the use of multiscale analysis. The basic technical result is an estimate on the expectation of small moments of the Green's function. Among our results, we prove a good Wegner estimate and the H\\"older continuity of the integrated density of states, and spectral and dynamical localization at negative energies.
The limiting behavior of the estimated parameters in a misspecified random field regression model
DEFF Research Database (Denmark)
Dahl, Christian Møller; Qin, Yu
This paper examines the limiting properties of the estimated parameters in the random field regression model recently proposed by Hamilton (Econometrica, 2001). Though the model is parametric, it enjoys the flexibility of the nonparametric approach since it can approximate a large collection...... convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully...
A random-walk model for pore pressure accumulation in marine soils
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Cheng, Niang-Sheng
1999-01-01
A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous to the concentra......A numerical random-walk model has been developed for the pore-water pressure. The model is based on the analogy between the variation of the pore pressure and the diffusion process of any passive quantity such as concentration. The pore pressure in the former process is analogous...
Restoration of dimensional reduction in the random-field Ising model at five dimensions
Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2017-04-01
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.
Gilthorpe, M S; Dahly, D L; Tu, Y K; Kubzansky, L D; Goodman, E
2014-06-01
Lifecourse trajectories of clinical or anthropological attributes are useful for identifying how our early-life experiences influence later-life morbidity and mortality. Researchers often use growth mixture models (GMMs) to estimate such phenomena. It is common to place constrains on the random part of the GMM to improve parsimony or to aid convergence, but this can lead to an autoregressive structure that distorts the nature of the mixtures and subsequent model interpretation. This is especially true if changes in the outcome within individuals are gradual compared with the magnitude of differences between individuals. This is not widely appreciated, nor is its impact well understood. Using repeat measures of body mass index (BMI) for 1528 US adolescents, we estimated GMMs that required variance-covariance constraints to attain convergence. We contrasted constrained models with and without an autocorrelation structure to assess the impact this had on the ideal number of latent classes, their size and composition. We also contrasted model options using simulations. When the GMM variance-covariance structure was constrained, a within-class autocorrelation structure emerged. When not modelled explicitly, this led to poorer model fit and models that differed substantially in the ideal number of latent classes, as well as class size and composition. Failure to carefully consider the random structure of data within a GMM framework may lead to erroneous model inferences, especially for outcomes with greater within-person than between-person homogeneity, such as BMI. It is crucial to reflect on the underlying data generation processes when building such models.
Perugini, G.; Ricci-Tersenghi, F.
2018-01-01
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of extremal solutions for the BP equations, and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the extremal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other hand we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions about the physics of this class of models.
A cellular automata model of traffic flow with variable probability of randomization
International Nuclear Information System (INIS)
Zheng Wei-Fan; Zhang Ji-Ye
2015-01-01
Research on the stochastic behavior of traffic flow is important to understand the intrinsic evolution rules of a traffic system. By introducing an interactional potential of vehicles into the randomization step, an improved cellular automata traffic flow model with variable probability of randomization is proposed in this paper. In the proposed model, the driver is affected by the interactional potential of vehicles before him, and his decision-making process is related to the interactional potential. Compared with the traditional cellular automata model, the modeling is more suitable for the driver’s random decision-making process based on the vehicle and traffic situations in front of him in actual traffic. From the improved model, the fundamental diagram (flow–density relationship) is obtained, and the detailed high-density traffic phenomenon is reproduced through numerical simulation. (paper)
Directory of Open Access Journals (Sweden)
Gabriel Recchia
2015-01-01
Full Text Available Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, “noisy” permutations in which units are mapped to other units arbitrarily (no one-to-one mapping perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.
Recchia, Gabriel; Sahlgren, Magnus; Kanerva, Pentti; Jones, Michael N
2015-01-01
Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, "noisy" permutations in which units are mapped to other units arbitrarily (no one-to-one mapping) perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.
Multilevel random effect and marginal models for longitudinal data ...
African Journals Online (AJOL)
The models were applied to data obtained from a phase-III clinical trial on a new meningococcal vaccine. The goal is to investigate whether children injected by the candidate vaccine have a lower or higher risk for the occurrence of specific adverse events than children injected with licensed vaccine, and if so, to quantify the ...
Modeling species distribution and change using random forest [Chapter 8
Jeffrey S. Evans; Melanie A. Murphy; Zachary A. Holden; Samuel A. Cushman
2011-01-01
Although inference is a critical component in ecological modeling, the balance between accurate predictions and inference is the ultimate goal in ecological studies (Peters 1991; Deâath 2007). Practical applications of ecology in conservation planning, ecosystem assessment, and bio-diversity are highly dependent on very accurate spatial predictions of...
Stochastic disturbance rejection in model predictive control by randomized algorithms
Batina, Ivo; Stoorvogel, Antonie Arij; Weiland, Siep
2001-01-01
In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into
Gale, Ella M; Johns, Marcus A; Wirawan, Remigius H; Scott, Janet L
2017-07-21
Polysaccharides, such as cellulose, are often processed by dissolution in solvent mixtures, e.g. an ionic liquid (IL) combined with a dipolar aprotic co-solvent (CS) that the polymer does not dissolve in. A multi-walker, discrete-time, discrete-space 1-dimensional random walk can be applied to model solvation of a polymer in a multi-component solvent mixture. The number of IL pairs in a solvent mixture and the number of solvent shells formable, x, is associated with n, the model time-step, and N, the number of random walkers. The mean number of distinct sites visited is proportional to the amount of polymer soluble in a solution. By also fitting a polynomial regression model to the data, we can associate the random walk terms with chemical interactions between components and probe where the system deviates from a 1-D random walk. The 'frustration' between solvents shells is given as ln x in the random walk model and as a negative IL:IL interaction term in the regression model. This frustration appears in regime II of the random walk model (high volume fractions of IL) where walkers interfere with each other, and the system tends to its limiting behaviour. In the low concentration regime, (regime I) the solvent shells do not interact, and the system depends only on IL and CS terms. In both models (and both regimes), the system is almost entirely controlled by the volume available to solvation shells, and thus is a counting/space-filling problem, where the molar volume of the CS is important. Small deviations are observed when there is an IL-CS interaction. The use of two models, built on separate approaches, confirm these findings, demonstrating that this is a real effect and offering a route to identifying such systems. Specifically, the majority of CSs - such as dimethylformide - follow the random walk model, whilst 1-methylimidazole, dimethyl sulfoxide, 1,3-dimethyl-2-imidazolidinone and tetramethylurea offer a CS-mediated improvement and propylene carbonate
Validity of tests under covariate-adaptive biased coin randomization and generalized linear models.
Shao, Jun; Yu, Xinxin
2013-12-01
Some covariate-adaptive randomization methods have been used in clinical trials for a long time, but little theoretical work has been done about testing hypotheses under covariate-adaptive randomization until Shao et al. (2010) who provided a theory with detailed discussion for responses under linear models. In this article, we establish some asymptotic results for covariate-adaptive biased coin randomization under generalized linear models with possibly unknown link functions. We show that the simple t-test without using any covariate is conservative under covariate-adaptive biased coin randomization in terms of its Type I error rate, and that a valid test using the bootstrap can be constructed. This bootstrap test, utilizing covariates in the randomization scheme, is shown to be asymptotically as efficient as Wald's test correctly using covariates in the analysis. Thus, the efficiency loss due to not using covariates in the analysis can be recovered by utilizing covariates in covariate-adaptive biased coin randomization. Our theory is illustrated with two most popular types of discrete outcomes, binary responses and event counts under the Poisson model, and exponentially distributed continuous responses. We also show that an alternative simple test without using any covariate under the Poisson model has an inflated Type I error rate under simple randomization, but is valid under covariate-adaptive biased coin randomization. Effects on the validity of tests due to model misspecification is also discussed. Simulation studies about the Type I errors and powers of several tests are presented for both discrete and continuous responses. © 2013, The International Biometric Society.
A single-level random-effects cross-lagged panel model for longitudinal mediation analysis.
Wu, Wei; Carroll, Ian A; Chen, Po-Yi
2017-12-06
Cross-lagged panel models (CLPMs) are widely used to test mediation with longitudinal panel data. One major limitation of the CLPMs is that the model effects are assumed to be fixed across individuals. This assumption is likely to be violated (i.e., the model effects are random across individuals) in practice. When this happens, the CLPMs can potentially yield biased parameter estimates and misleading statistical inferences. This article proposes a model named a random-effects cross-lagged panel model (RE-CLPM) to account for random effects in CLPMs. Simulation studies show that the RE-CLPM outperforms the CLPM in recovering the mean indirect and direct effects in a longitudinal mediation analysis when random effects exist in the population. The performance of the RE-CLPM is robust to a certain degree, even when the random effects are not normally distributed. In addition, the RE-CLPM does not produce harmful results when the model effects are in fact fixed in the population. Implications of the simulation studies and potential directions for future research are discussed.
Entropy, complexity, and Markov diagrams for random walk cancer models.
Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter
2014-12-19
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.
Solvable random-decimation model of cluster scaling
Fraser, Simon J.
1988-07-01
A percolation model of critical-cluster scaling is studied. The model allows the generation of configurations of strongly self-similar clusters by stochastic decimation on a tree. Tree traversal is controlled by a probability parameter p. At p=0 or 1, the configuration is deterministic, but, for 0decimation algorithm uses the Sierpinski carpet and Vicsek snowflake generators, so that the treelike character (connectedness) of the clusters can be changed continuously. Various dimensions of the (fractal) percolation cluster are calculated using boundary conditions that give correct values at the deterministic limits. The usual cluster distribution law, ns~s-τ with τ=d/D+1, is obeyed for stationary p in (0,1), although τ=d/D, the deterministic value at p=0 or 1. Here d is the space dimension, and D the fractal dimension of the percolation cluster. The sensitivity of τ to changes in p near p=0 or 1 allows anomalous cluster scaling, so that τ may be fixed between d/D and d/D+1, without affecting D. Possible applications of the model are discussed.
Directory of Open Access Journals (Sweden)
Hyungsuk Tak
2017-06-01
Full Text Available Rgbp is an R package that provides estimates and verifiable confidence intervals for random effects in two-level conjugate hierarchical models for overdispersed Gaussian, Poisson, and binomial data. Rgbp models aggregate data from k independent groups summarized by observed sufficient statistics for each random effect, such as sample means, possibly with covariates. Rgbp uses approximate Bayesian machinery with unique improper priors for the hyper-parameters, which leads to good repeated sampling coverage properties for random effects. A special feature of Rgbp is an option that generates synthetic data sets to check whether the interval estimates for random effects actually meet the nominal confidence levels. Additionally, Rgbp provides inference statistics for the hyper-parameters, e.g., regression coefficients.
Evolution models with lethal mutations on symmetric or random fitness landscapes.
Kirakosyan, Zara; Saakian, David B; Hu, Chin-Kun
2010-07-01
We calculate the mean fitness for evolution models, when the fitness is a function of the Hamming distance from a reference sequence, and there is a probability that this fitness is nullified (Eigen model case) or tends to the negative infinity (Crow-Kimura model case). We calculate the mean fitness of these models. The mean fitness is calculated also for the random fitnesses with logarithmic-normal distribution, reasonably describing sometimes the situation with RNA viruses.
Janssen, Hans-Karl; Stenull, Olaf
2004-02-01
We investigate corrections to scaling induced by irrelevant operators in randomly diluted systems near the percolation threshold. The specific systems that we consider are the random resistor network and a class of continuous spin systems, such as the x-y model. We focus on a family of least irrelevant operators and determine the corrections to scaling that originate from this family. Our field theoretic analysis carefully takes into account that irrelevant operators mix under renormalization. It turns out that long standing results on corrections to scaling are respectively incorrect (random resistor networks) or incomplete (continuous spin systems).
Directory of Open Access Journals (Sweden)
Hideki Katagiri
2017-10-01
Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.
A new neural network model for solving random interval linear programming problems.
Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza
2017-05-01
This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.
Random generalized linear model: a highly accurate and interpretable ensemble predictor.
Song, Lin; Langfelder, Peter; Horvath, Steve
2013-01-16
Ensemble predictors such as the random forest are known to have superior accuracy but their black-box predictions are difficult to interpret. In contrast, a generalized linear model (GLM) is very interpretable especially when forward feature selection is used to construct the model. However, forward feature selection tends to overfit the data and leads to low predictive accuracy. Therefore, it remains an important research goal to combine the advantages of ensemble predictors (high accuracy) with the advantages of forward regression modeling (interpretability). To address this goal several articles have explored GLM based ensemble predictors. Since limited evaluations suggested that these ensemble predictors were less accurate than alternative predictors, they have found little attention in the literature. Comprehensive evaluations involving hundreds of genomic data sets, the UCI machine learning benchmark data, and simulations are used to give GLM based ensemble predictors a new and careful look. A novel bootstrap aggregated (bagged) GLM predictor that incorporates several elements of randomness and instability (random subspace method, optional interaction terms, forward variable selection) often outperforms a host of alternative prediction methods including random forests and penalized regression models (ridge regression, elastic net, lasso). This random generalized linear model (RGLM) predictor provides variable importance measures that can be used to define a "thinned" ensemble predictor (involving few features) that retains excellent predictive accuracy. RGLM is a state of the art predictor that shares the advantages of a random forest (excellent predictive accuracy, feature importance measures, out-of-bag estimates of accuracy) with those of a forward selected generalized linear model (interpretability). These methods are implemented in the freely available R software package randomGLM.
Silkworm cocoons inspire models for random fiber and particulate composites
Chen, Fujia; Porter, David; Vollrath, Fritz
2010-10-01
The bioengineering design principles evolved in silkworm cocoons make them ideal natural prototypes and models for structural composites. Cocoons depend for their stiffness and strength on the connectivity of bonding between their constituent materials of silk fibers and sericin binder. Strain-activated mechanisms for loss of bonding connectivity in cocoons can be translated directly into a surprisingly simple yet universal set of physically realistic as well as predictive quantitative structure-property relations for a wide range of technologically important fiber and particulate composite materials.
Scale-free random graphs and Potts model
Indian Academy of Sciences (India)
(esrh0 + re−sh0 )nG(s),. (14) where nG(s) is the number of s-clusters, a cluster with s vertices in a given graph. G. In particular, ZN (q, 0) = (qC), where C = ∑ s nG(s) is the total number of clusters in graph G. Thus ZN (q, 0) is the generating function of C. The magnetization of the Potts model at q = 1 is m(1,h0) = lim q→1. 1.
A random effects meta-analysis model with Box-Cox transformation.
Yamaguchi, Yusuke; Maruo, Kazushi; Partlett, Christopher; Riley, Richard D
2017-07-19
In a random effects meta-analysis model, true treatment effects for each study are routinely assumed to follow a normal distribution. However, normality is a restrictive assumption and the misspecification of the random effects distribution may result in a misleading estimate of overall mean for the treatment effect, an inappropriate quantification of heterogeneity across studies and a wrongly symmetric prediction interval. We focus on problems caused by an inappropriate normality assumption of the random effects distribution, and propose a novel random effects meta-analysis model where a Box-Cox transformation is applied to the observed treatment effect estimates. The proposed model aims to normalise an overall distribution of observed treatment effect estimates, which is sum of the within-study sampling distributions and the random effects distribution. When sampling distributions are approximately normal, non-normality in the overall distribution will be mainly due to the random effects distribution, especially when the between-study variation is large relative to the within-study variation. The Box-Cox transformation addresses this flexibly according to the observed departure from normality. We use a Bayesian approach for estimating parameters in the proposed model, and suggest summarising the meta-analysis results by an overall median, an interquartile range and a prediction interval. The model can be applied for any kind of variables once the treatment effect estimate is defined from the variable. A simulation study suggested that when the overall distribution of treatment effect estimates are skewed, the overall mean and conventional I 2 from the normal random effects model could be inappropriate summaries, and the proposed model helped reduce this issue. We illustrated the proposed model using two examples, which revealed some important differences on summary results, heterogeneity measures and prediction intervals from the normal random effects model. The
A binomial random sum of present value models in investment analysis
Βουδούρη, Αγγελική; Ντζιαχρήστος, Ευάγγελος
1997-01-01
Stochastic present value models have been widely adopted in financial theory and practice and play a very important role in capital budgeting and profit planning. The purpose of this paper is to introduce a binomial random sum of stochastic present value models and offer an application in investment analysis.
B. Li (Bayoue); B. Roozenbeek (Bob); E.W. Steyerberg (Ewout); E.M.E.H. Lesaffre (Emmanuel)
2011-01-01
textabstractBackground: Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. Methods. We used individual patient data from 8509
Simulation of random set models for unions of discs and the use of power tessellations
DEFF Research Database (Denmark)
Møller, Jesper; Helisova, Katerina
2009-01-01
The power tessellation (or power diagram or Laguerre diagram) turns out to be particularly useful in connection to a flexible class of random set models specified by an underlying process of interacting discs. We discuss how to simulate these models and calculate various geometric characteristics...
Examples of mixed-effects modeling with crossed random effects and with binomial data
Quené, H.; van den Bergh, H.
2008-01-01
Psycholinguistic data are often analyzed with repeated-measures analyses of variance (ANOVA), but this paper argues that mixed-effects (multilevel) models provide a better alternative method. First, models are discussed in which the two random factors of participants and items are crossed, and not
Potts Model with Invisible Colors : Random-Cluster Representation and Pirogov–Sinai Analysis
Enter, Aernout C.D. van; Iacobelli, Giulio; Taati, Siamak
We study a recently introduced variant of the ferromagnetic Potts model consisting of a ferromagnetic interaction among q “visible” colors along with the presence of r non-interacting “invisible” colors. We introduce a random-cluster representation for the model, for which we prove the existence of
93-106, 2015 93 Multilevel random effect and marginal models
African Journals Online (AJOL)
But, this higher in number of parameter cannot be considered as a disadvantage in a situation when model (5) better fits the data. Relationship between marginal and random effect model parameters. Zeger et al. (1988) derived an approximate relation- ship for the population averaged parameters (from. GEE) and subject ...