Random Walk Process Research Articles

Simulation of <i>In Vitro</i>-Like Electrical Activities in Urinary Bladder Smooth Muscle Cells

Urinary bladder smooth muscle (UBSM) generates spontaneous electrical activities due to stochastic nature of purinergic neurotransmitter release from the parasympathetic nerve. The stochastic nature of the purinergic neurotransmitter release was represented by a simplified ‘point-conductance’ model to mimic in vitro-like electrical activities in UBSM cell. The point-conductance was represented by the independent synaptic conductance described by the stochastic random-walk processes and injected into a single-compartment model of mouse UBSM cell. This model successfully evoked irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) as the properties of in vitro-like electrical activities in UBSM cells. The model mimics the T- and L-type Ca2+ ion channel blocker by setting their respective conductance to zero. We also found that the point-conductance model modulates the sAP properties by adding background activity.

Foreign Exchange Market Efficiency In Botswana

AbstractThe random walk behaviour of exchange rates in Botswana’s foreign exchange market is explored by employing unit root tests. The unit root tests employed include the ADF, PP and the KPSS. This paper uses monthly data for the period 2000:01 to 2015:12. The conclusive evidence based on the unit roots tests indicates that the behaviour of the Pula against the South African Rand, Japanese Yen and the American Dollar exchange rates is consistent with the random walk process and the weak form efficiency market hypothesis. However, the Pula against the British Pound is inconsistent with the weak form efficiency market hypothesis. These results compliment those from Namibia (Mabakeng and Sheefeni, 2014). Furthermore, there is no evidence of the semi-strong form level of efficiency as revealed by the cointegration results obtained. These results corroborates with those found by Wickremasinghe (2008) and Çiçek (2014) in which weak form was found to exist whilst the semi-strong form was found not to exist. This paper has filled an important gap as it is the first study to investigate the efficiency of the foreign exchange market in Botswana.

The energy landscape underpinning module dynamics in the human brain connectome

Human brain dynamics can be viewed through the lens of statistical mechanics, where neurophysiological activity evolves around and between local attractors representing mental states. Many physically-inspired models of these dynamics define brain states based on instantaneous measurements of regional activity. Yet, recent work in network neuroscience has provided evidence that the brain might also be well-characterized by time-varying states composed of locally coherent activity or functional modules. We study this network-based notion of brain state to understand how functional modules dynamically interact with one another to perform cognitive functions. We estimate the functional relationships between regions of interest (ROIs) by fitting a pair-wise maximum entropy model to each ROI's pattern of allegiance to functional modules. This process uses an information theoretic notion of energy (as opposed to a metabolic one) to produce an energy landscape in which local minima represent attractor states characterized by specific patterns of modular structure. The clustering of local minima highlights three classes of ROIs with similar patterns of allegiance to community states. Visual, attention, sensorimotor, and subcortical ROIs are well-characterized by a single functional community. The remaining ROIs affiliate with a putative executive control community or a putative default mode and salience community. We simulate the brain's dynamic transitions between these community states using a random walk process. We observe that simulated transition probabilities between basins are statistically consistent with empirically observed transitions in resting state fMRI data. These results offer a view of the brain as a dynamical system that transitions between basins of attraction characterized by coherent activity in groups of brain regions, and that the strength of these attractors depends on the ongoing cognitive computations.

Logarithmic scaling of planar random walk’s local times

We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the M1 topology and fails to hold in the J1 topology.

Random walks on activity-driven networks with attractiveness.

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here, we present a time-varying network model where each node and the dynamical formation of ties are characterized by these two features. We study how these properties affect random-walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable. We derive analytical solutions for the stationary state and the mean first-passage time of the process, and we study cases informed by empirical observations of social networks. Our work shows that previously disregarded properties of real social systems, such as heterogeneous distributions of activity and attractiveness as well as the correlations between them, substantially affect the dynamical process unfolding on the network.

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams.

A generalized approach to Wang-Landau simulations, macroscopically constrained Wang-Landau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional random-walk process in phase space into many separate, one-dimensional random-walk processes in well-defined subspaces. Each of these random walks is constrained to a different set of values of the macroscopic order parameters. When the multivariable density of states is obtained for one set of values of fieldlike model parameters, the density of states for any other values of these parameters can be obtained by a simple transformation of the total system energy. All thermodynamic quantities of the system can then be rapidly calculated at any point in the phase diagram. We demonstrate how to use the multivariable density of states to draw the phase diagram, as well as order-parameter probability distributions at specific phase points, for a model spin-crossover material: an antiferromagnetic Ising model with ferromagnetic long-range interactions. The fieldlike parameters in this model are an effective magnetic field and the strength of the long-range interaction.

Precise real-time navigation of LEO satellites using a single-frequency GPS receiver and ultra-rapid ephemerides

Precise (sub-meter level) real-time navigation using a space-capable single-frequency global positioning system (GPS) receiver and ultra-rapid (real-time) ephemerides from the international global navigation satellite systems service is proposed for low-Earth-orbiting (LEO) satellites. The C/A code and L1 carrier phase measurements are combined and single-differenced to eliminate first-order ionospheric effects and receiver clock offsets. A random-walk process is employed to model the phase ambiguities in order to absorb the time-varying and satellite-specific higher-order measurement errors as well as the GPS clock correction errors. A sequential Kalman filter which incorporates the known orbital dynamic model is developed to estimate orbital states and phase ambiguities without matrix inversion. Real flight data from the single-frequency GPS receiver onboard China's SJ-9A small satellite are processed to evaluate the orbit determination accuracy. Statistics from internal orbit assessments indicate that three-dimensional accuracies better than 0.50 m and 0.55 mm/s are achieved for position and velocity, respectively.

Glaubers Ising chain between two thermostats

We consider a one-dimensional Ising model with N spins, each in contact with two thermostats of distinct temperatures, T1 and T2. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an effective intermediate temperature . The system nevertheless carries a nontrivial energy current between the thermostats. By means of the fermionization technique, for a chain initially in equilibrium at an arbitrary temperature T0 we calculate the Fourier transform of the probability for the time-integrated energy current during a finite time interval τ. In the long time limit we determine the corresponding generating function for the cumulants per site and unit of time, , and explicitly give those with n = 1, 2, 3, 4. We exhibit various phenomena in specific regimes: kinetic mean-field effects when one thermostat flips any spin less often than the other one, as well as dissipation towards a thermostat at zero temperature. Moreover, when the system size N goes to infinity while the effective temperature T vanishes, the cumulants of per unit of time grow linearly with N and are equal to those of a random walk process. In two adequate scaling regimes involving T and N we exhibit the dependence of the first correction upon the ratio of the spin–spin correlation length and the size N.

Random walk in nonhomogeneous environments: A possible approach to human and animal mobility.

The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.

Reconstruction and signal propagation analysis of the Syk signaling network in breast cancer cells.

The ability to build in-depth cell signaling networks from vast experimental data is a key objective of computational biology. The spleen tyrosine kinase (Syk) protein, a well-characterized key player in immune cell signaling, was surprisingly first shown by our group to exhibit an onco-suppressive function in mammary epithelial cells and corroborated by many other studies, but the molecular mechanisms of this function remain largely unsolved. Based on existing proteomic data, we report here the generation of an interaction-based network of signaling pathways controlled by Syk in breast cancer cells. Pathway enrichment of the Syk targets previously identified by quantitative phospho-proteomics indicated that Syk is engaged in cell adhesion, motility, growth and death. Using the components and interactions of these pathways, we bootstrapped the reconstruction of a comprehensive network covering Syk signaling in breast cancer cells. To generate in silico hypotheses on Syk signaling propagation, we developed a method allowing to rank paths between Syk and its targets. We first annotated the network according to experimental datasets. We then combined shortest path computation with random walk processes to estimate the importance of individual interactions and selected biologically relevant pathways in the network. Molecular and cell biology experiments allowed to distinguish candidate mechanisms that underlie the impact of Syk on the regulation of cortactin and ezrin, both involved in actin-mediated cell adhesion and motility. The Syk network was further completed with the results of our biological validation experiments. The resulting Syk signaling sub-networks can be explored via an online visualization platform.

What Has Caused Global Business Cycle Decoupling: Smaller Shocks or Reduced Sensitivity?

According to a growing body of empirical literature, global shocks have become less important for business cycles in industrialized countries and emerging market economies since the mid-1980s. In this paper, we analyze the question of what might have caused a decoupling from the global business cycle: the smaller size of the global shocks or a reduced sensitivity of national business cycles to these shocks? To this end, we employ a large scale hierarchical dynamic factor model that decomposes the growth rates of GDP, consumption, and investment for 106 countries over 1961–2014 into a global, a group-, and a country-specific factor, as well as an idiosyncratic component. The factor loadings and conditional variances are allowed to vary over time according to random walk processes. Instead of assuming that the parameters change, we test for time variation using a Bayesian stochastic model specification search. Our results confirm a reduction in the importance of the global business cycle for the vast majority of our countries. However, the sensitivity of most countries to global or group-specific shocks as measured by the factor loadings has not changed over time. Instead, the magnitude of the global shocks relative to group-specific and country-specific shocks has decreased, resulting in a lower relevance of global shocks for national cycles.

Exchange rate prediction using monetary policy rules in Taiwan

This study examines exchange rate predictability based on different types of monetary policy rules in Taiwan. The out-of-sample exchange rate predictive accuracy is compared based on the Taylor rule fundamentals to a naïve random walk model. We find that both short-horizon and long-horizon out-of-sample exchange rate predictive power outperform the random walk process in many cases. The stronger evidence relates to the Taylor rule models with interest rate smoothing. The strongest evidence comes from the specifications which involve higher-order interest rate smoothing in the trade-weighted Taiwan Dollar rate. The findings are confirmed by the contemporaneous Taylor rules, the homogeneous coefficients, and the examinations of the nonlinear least squares approaches.

Infrared Investigations of the Neutral-Ionic Phase Transition in TTF-CA and Its Dynamics

The neutral-ionic phase transition in TTF-CA was investigated by steady-state and time-resolved infrared spectroscopy. We describe the growth of high-quality single crystals and their characterization. Extended theoretical calculations were performed in order to obtain the band structure, the molecular vibrational modes and the optical spectra along all crystallographic axes. The theoretical results are compared to polarization-dependent infrared reflection experiments. The temperature-dependent optical conductivity is discussed in detail. We study the photo-induced phase transition in the vicinity of thermally-induced neutral-ionic transition. The observed temporal dynamics of the photo-induced states is attributed to the random-walk of neutral-ionic domain walls. We simulate the random-walk annihilation process of domain walls on a one-dimensional chain.

Testing the Efficient Market Hypothesis in an Emerging Market: Evidence from Forex Market in Mauritius

The present study investigates the efficiency of the forex market based on the theory of the Efficient Market Hypothesis in Mauritius, a well-diversified and emerging economy in the African region. Hence, this study considers the case of Mauritian forex market nominal spot rate daily data namely EUR/MUR, USD/ MUR, GBP/ MUR and JPY/ MUR over a time period of 5 years ranging from 2012 to 2016. The technique used for analysis is firstly concentrated on the use of Augmented-Dickey Fuller (ADF) and Philips Peron (PP) unit root to test the weak-form of efficiency and secondly, the Johansen Cointegration Test, the Granger Causality Test and Variance Decomposition are utilized to examine the existence of semi-strong form efficiency in the Mauritian foreign exchange market. Results indicated that the unit root test tested by ADF and PP unit root test support the weak form market as it follows a random walk process. Secondly, the Johansen Cointegration test reveals that there is no long run relationships among foreign exchange variables. However, the Granger causality test confirmed the existence of unidirectional and bidirectional relationships among the various exchange rates. Moreover, the Variance Decomposition confirmed the presence of long run co-movements among the exchange rates. Therefore, both tests fail to support the semi-strong form market. This means that one exchange rate can predict one or more exchange rates which is against the semi-strong form market hypothesis. Therefore, it is deduced that the foreign market is efficient in the weak-form but is inefficient in the semi-strong form in Mauritius.

Hybrid Stochastic Local Unit Roots

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n→∞. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit root (LSTUR) specification that has both LUR and STUR components and allows for endogeneity in the time-varying coefficient that introduces structural elements to the autoregression. This hybrid model generates trajectories that, upon normalization, have non-linear diffusion limit processes that link closely to models that have been studied in mathematical finance, particularly with respect to option pricing. It is shown that some LSTUR parameterizations have a mean and variance which are the same as a random walk process but with a kurtosis exceeding 3, a feature which is consistent with much financial data. We develop limit theory and asymptotic expansions for the process and document how inference in LUR and STUR autoregressions is affected asymptotically by ignoring one or the other component in the more general hybrid generating mechanism. In particular, we show how confidence belts constructed from the LUR model are affected by the presence of a STUR component in the generating mechanism. The import of these findings for empirical research are explored in an application to the spreads on US investment grade corporate debt.

Testing the Random Walk Behavior in the Damascus Securities Exchange Using Unit Root Tests with Structural Breaks

This study aims to test whether stock prices on the Damascus Securities Exchange (DSE) follow a random walk process, using weekly data during the period from January 2010 to Mars 2017. For that purpose, in addition to the ADF test, which does not account for structural breaks in the data, the Zivot and Andrews test with one break, the Lumsdaine and Papell test with two breaks and the Lee and Strazicich tests with one and two endogenously determined structural breaks are applied. The findings of the study provide evidence in favor of random walk hypothesis in the DSE despite considering up to structural breaks in the data. Moreover, the dates of endogenously captured structural breaks in the majority of models tested coincide with the political instability that erupted in 2011 in Syria.

Performance Study of Monte Carlo Codes on Xeon Phi Coprocessors — Testing MCNP 6.1 and Profiling ARCHER Geometry Module on the FS7ONNi Problem

This paper contains two parts revolving around Monte Carlo transport simulation on Intel Many Integrated Core coprocessors (MIC, also known as Xeon Phi). (1) MCNP 6.1 was recompiled into multithreading (OpenMP) and multiprocessing (MPI) forms respectively without modification to the source code. The new codes were tested on a 60-core 5110P MIC. The test case was FS7ONNi, a radiation shielding problem used in MCNP’s verification and validation suite. It was observed that both codes became slower on the MIC than on a 6-core X5650 CPU, by a factor of ~4 for the MPI code and, abnormally, ~20 for the OpenMP code, and both exhibited limited capability of strong scaling. (2) We have recently added a Constructive Solid Geometry (CSG) module to our ARCHER code to provide better support for geometry modelling in radiation shielding simulation. The functions of this module are frequently called in the particle random walk process. To identify the performance bottleneck we developed a CSG proxy application and profiled the code using the geometry data from FS7ONNi. The profiling data showed that the code was primarily memory latency bound on the MIC. This study suggests that despite low initial porting e_ort, Monte Carlo codes do not naturally lend themselves to the MIC platform — just like to the GPUs, and that the memory latency problem needs to be addressed in order to achieve decent performance gain.

Global industrial impact coefficient based on random walk process and inter-country input–output table

Input–output table is very comprehensive and detailed in describing the national economic system with lots of economic relationships, which contains supply and demand information among industrial sectors. The complex network, a theory and method for measuring the structure of complex system, can describe the structural characteristics of the internal structure of the research object by measuring the structural indicators of the social and economic system, revealing the complex relationship between the inner hierarchy and the external economic function. This paper builds up GIVCN-WIOT models based on World Input–Output Database in order to depict the topological structure of Global Value Chain (GVC), and assumes the competitive advantage of nations is equal to the overall performance of its domestic sectors’ impact on the GVC. Under the perspective of econophysics, Global Industrial Impact Coefficient (GIIC) is proposed to measure the national competitiveness in gaining information superiority and intermediate interests. Analysis of GIVCN-WIOT models yields several insights including the following: (1) sectors with higher Random Walk Centrality contribute more to transmitting value streams within the global economic system; (2) Half-Value Ratio can be used to measure robustness of open-economy macroeconomics in the process of globalization; (3) the positive correlation between GIIC and GDP indicates that one country’s global industrial impact could reveal its international competitive advantage.

Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time

In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with sufficient accuracy, zenith wet delay (ZWD) has to be estimated, which is usually done in a random walk process. Since ZWD temporal variation depends on the water vapor content in the atmosphere, it seems to be reasonable that ZWD constraints in GNSS processing should be geographically and/or time dependent. We propose to take benefit from numerical weather prediction models to define optimum random walk process noise. In the first approach, we used archived VMF1-G data to calculate a grid of yearly and monthly means of the difference of ZWD between two consecutive epochs divided by the root square of the time lapsed, which can be considered as a random walk process noise. Alternatively, we used the Global Forecast System model from National Centres for Environmental Prediction to calculate random walk process noise dynamically in real-time. We performed two representative experimental campaigns with 20 globally distributed International GNSS Service (IGS) stations and compared real-time ZTD estimates with the official ZTD product from the IGS. With both our approaches, we obtained an improvement of up to 10% in accuracy of the ZTD estimates compared to any uniformly fixed random walk process noise applied for all stations.

A New Continuous Rotation IMU Alignment Algorithm Based on Stochastic Modeling for Cost Effective North-Finding Applications

Based on stochastic modeling of Coriolis vibration gyros by the Allan variance technique, this paper discusses Angle Random Walk (ARW), Rate Random Walk (RRW) and Markov process gyroscope noises which have significant impacts on the North-finding accuracy. A new continuous rotation alignment algorithm for a Coriolis vibration gyroscope Inertial Measurement Unit (IMU) is proposed in this paper, in which the extended observation equations are used for the Kalman filter to enhance the estimation of gyro drift errors, thus improving the north-finding accuracy. Theoretical and numerical comparisons between the proposed algorithm and the traditional ones are presented. The experimental results show that the new continuous rotation alignment algorithm using the extended observation equations in the Kalman filter is more efficient than the traditional two-position alignment method. Using Coriolis vibration gyros with bias instability of 0.1°/h, a north-finding accuracy of 0.1° (1σ) is achieved by the new continuous rotation alignment algorithm, compared with 0.6° (1σ) north-finding accuracy for the two-position alignment and 1° (1σ) for the fixed-position alignment.