Occupation Densities Research Articles

Unified approach to reset processes and application to coupling between process and reset.

Processes under reset, where realizations are interrupted according to some stochastic rule and restarted from the initial state, find broad application in modeling physical, chemical, and biological phenomena and in designing search strategies. While a wealth of theoretical results has been recently obtained, current derivations tend to focus on specific processes, obscuring the general principles and preventing broad applicability. We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive general solutions, and determine the conditions for existence and equality of stationary values with and without reset. For intermittent (i.e., broadlydistributed) reset times, we derive exact asymptotic expressions for observables that vary asymptotically as a power of time. We illustrate the general approach with results for occupation densities and moments of subdiffusive processes. We focus on subdiffusion-decay processes with microscopic dependence between transport and decay, where the probability of a random walker to be removed and subsequently restarted depends on the local transit times. In contrast to the uncoupled case, restarting the particle upon decay does not produce a probability current associated with restart equal to the decay rate, but instead drastically alters the time dependence of the decay rate and the resulting current due to memory effects associated with ageing. Our framework shows that such effects are independent of the specific microscopic details, uncovering the general impact of restart on occupation densities, spatial moments, and other quantities.

The application of direct ridership models in the evaluation of the expansion of the Porto Light Rail Transit

The main purpose of this paper is to show how a direct demand ride model coupled with a transfer model was able to support the choice of alternative routes for the expansion of the light rail system serving the Porto Metropolitan Area. After an overview of the literature on direct ridership models, emphasizing some key issues such as the need for a systematic assessment of their forecasting performance, the issues related to the definition of the pedestrian catchment area and the limitations of the simultaneous consideration of demand and supply effects, the paper moves into the case study, providing some background information on current occupation densities, land uses and mobility patterns, as well as on the performance of the existing LRT in the Metropolitan Area of Porto. The development of the direct ridership model, measuring the potential attractiveness of each station, and the transfer model, measuring the number of transfers at each station, are presented in detail. A justification is provided why, in this case, a two-step modelling approach was necessary. Further details about the statistical tests for model validation are also provided. After a brief characterization of the alternative routes under analysis for the expansion of the network, the modelling results are presented enabling a comparative assessment of the potential performance of each proposed route. The paper ends with a discussion of the relevance of this modelling results vis a vis the actual final decisions on investment priorities taken jointly by the Metropolitan Council and the Metro Company.

RECONSTRUCTING HUMAN−ENVIRONMENTAL RELATIONSHIP IN THE SIBERIAN ARCTIC AND SUB-ARCTIC: A HOLOCENE OVERVIEW

ABSTRACTThis paper examines patterns of human–environmental interactions across northern Asia during the Holocene, in order to summarize current knowledge and identify key areas for future research. To achieve these goals, currently available chronological, cultural, and paleoenvironmental datasets from the east Russian Arctic for the last 10,000 14C years were integrated. Study regions include the Taymyr Peninsula, Lena River basin (except its southern part), northeastern Siberia, and Kamchatka Peninsula. Several broad-scale correlations between climatic fluctuations and cultural responses (e.g., subsistence strategies and occupation densities) were identified; however, these are not straightforward. For example, the increase of occupations during the warm periods in the Early–Middle Holocene are notable while the most pronounced rises coincide with a cooling trend in the Late Holocene. This shows that the human–environmental relationships in the Holocene were not linear; more interdisciplinary research will be needed to construct higher resolution data for understanding prehistoric cultural responses to past environmental changes in the Asian Arctic.

On the existence and the Hölder regularity of the local time of the Brownian bridge

Abstract In this paper, we will establish the existence and the Hölder regularity of the local time of the Brownian bridge. Our results are obtained by using a result on Malliavin calculus in [K. Es-Sebaiy, D. Nualart, Y. Ouknine and C. A. Tudor, Occupation densities for certain processes related to fractional Brownian motion, Stochastics 82 2010, 1–3, 133–147] for a Gaussian process with an absolutely continuous random drift, jointly with the classical approach based on the concept of local nondeterminism for Gaussian processes introduced by Berman [S. M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 1973/74, 69–94].

Interfacial hetero‐phase construction in nickel/molybdenum selenide hybrids to promote the water splitting performance

In this work, a novel hetero-phase interface structure (NiMoSe/NF-2), consisting of crystalline (NiSe) and amorphous (MoSex), was constructed by annealing Ni0.85Se/MoSex hybrid (NiMoSe/NF-1), synthesized through hydrothermal and selenylation steps. For hydrogen evolution and oxygen evolution reaction, the NiMoSe/NF-2 exhibited an overpotential of 91 mV (10 mA cm−2) and 307 mV (100 mA cm−2) with the Tafel slope of 48.1 mV dec−1 and 30.9 mV dec−1, respectively, superior to NiMoSe/NF-1. Meanwhile, much higher stability with 10 and 14 h tests was also respectively achieved for HER and OER. Using the NiMoSe/NF-2 as anode and cathode, the electrolyzer showed a long-time stability up to 14 h with the current density of 100 mA cm−2 at the potential of 1.91 V for overall water splitting. The density functional theory calculation validates that the crystalline/amorphous hetero-phase structure remarkably reduces the Gibbs free energy difference for both HER/OER and the increased occupation densities of electronic states near Fermi level accelerated charge transfer rate during electrocatalytic process. The hydrogen and oxygen intermediates desorption are facilitated by the downshift of Ni d-band center. The proposed crystalline/amorphous hetero-phase structure is prospective for designing bifunctional catalysts for water splitting.

Density distribution functions of random sequential adsorption on a [formula omitted] lattice

Random sequential adsorption (RSA) is an irreversible random deposition process with short range exclusion interaction. It is shown that the distribution function of the occupation densities at the jamming limit of a RSA process on a 2×n lattice converges for n→∞ to a Gaussian around an average density. The second moment decreases like 1∕n.

Occupation density estimation for noisy high-frequency data

This paper studies the nonparametric estimation of occupation densities for semimartingale processes observed with noise. As leading examples we consider the stochastic volatility of a latent efficient price process, the volatility of the latent noise that separates the efficient price from the actually observed price, and nonlinear transformations of these processes. Our estimation methods are decidedly nonparametric and consist of two steps: the estimation of the spot price and noise volatility processes based on pre-averaging techniques and in-fill asymptotic arguments, followed by a kernel-type estimation of the occupation densities. Our spot volatility estimates attain the optimal rate of convergence, and are robust to leverage effects, price and volatility jumps, general forms of serial dependence in the noise, and random irregular sampling. The convergence rates of our occupation density estimates are directly related to that of the estimated spot volatilities and the smoothness of the true occupation densities. An empirical application involving high-frequency equity data illustrates the usefulness of the new methods in illuminating time-varying risks, market liquidity, and informational asymmetries across time and assets.

Occupation densities of ensembles of branching random walks

We study the limiting occupation density process for a large number of critical and driftless branching random walks. We show that the rescaled occupation densities of $\lfloor sN\rfloor$ branching random walks, viewed as a function-valued, increasing process $\{g_{s}^{N}\}_{s\ge 0}$, converges weakly to a pure jump process in the Skorohod space $\mathbb D([0, +\infty), \mathcal C_{0}(\mathbb R))$, as $N\to\infty$. Moreover, the jumps of the limiting process consist of i.i.d. copies of an Integrated super-Brownian Excursion (ISE) density, rescaled and weighted by the jump sizes in a real-valued stable-1/2 subordinator.

Coherent Energy Transfer Dynamics and Photoluminescence of Coupled Quantum Dots: Fully Analytical Approach

We theoretically studied coherent excitation energy transfer between self-growth semiconductor quantum dots (QDs) by solving Heisenberg’s equations of motion for density matrix elements in second quantization regime. In a local excitation condition where only one QD electron is optically excited by the pump laser field, coherent excitation energy transfer to the other QD electron can be achieved through Coulomb (Forster) and electron-photon (radiation field) interactions. We calculated three diagonal and one off-diagonal Coulomb coupling constants, which are responsible for the biexcitonic frequency renormalization and the coherent energy transfer between QDs, respectively, and radiation field coupling coefficients by using electron and hole wave functions derived from eight-band kp-theorem, whose validity has already been tested by comparison with experiment. In linear optical regime where the occupation densities of electrons at higher energy level are negligibly small, we could successfully derive fully analytical behaviors of temporal dynamics of the interband polarizations and level occupation densities of both QDs by using Hartree-Fock approximation (HFA), in eventual, the stationary photoluminescence of the coupled QDs in an analytical form. Additionally, the validity of the HFA was examined by comparing the numerical results with those obtained from the exact correlation expansion model for different values of the pump field intensity.

Point defects patterning in irradiated α-zirconium: numerical study in the framework of the rate theory

ABSTRACTWe study point defects patterning in irradiated α-zirconium numerically. In our consideration, we exploit reaction-rate theory by taking into account sink density dynamics and a change in internal stress fields due to the presence of defects. Dynamics of defect populations are studied at different irradiation conditions. It is found that point defects patterning is accompanied by a formation of vacancy clusters; their morphology change is governed by irradiation temperature and damage rate. By using statistical analysis of spatially distributed vacancy clusters, it was shown that the characteristic size of these clusters is of several nanometers. Vacancy clusters' occupation densities and distributions over their sizes are studied in detail.

Condensate characteristics of bosons in a tilted optical lattice

In this work we study the properties of interacting bosons in a tilted triple well optical lattice potential. A tilted optical lattice is possible to create in an experiment with charged bosons in presence of an electric field. The ground state energy, occupation densities in each well and first order correlation function of occupation densities as a function of the tilt parameter for N = 90 bosons using recently developed Multiconfigurational time-dependent Hartree method for bosons (MCTDHB) are studied. The ground state energy falls off with the tilt parameter for a given value of the barrier height and interparticle interaction. Also the tilt parameter is observed to restrict the fragmentation of the occupation densities in each well and thus promote condensation. Further the correlation between the bosons in different wells enhances with the tilt parameter and at large values the bosons in the first and the third wells are correlated apart from the correlation among the bosons in the same well, while the occupancy in the middle one seems to be uncorrelated with the other two. Such correlation between different wells is not observed in absence of the tilt effect for the same barrier height of the potential and interparticle interaction strength.

Disorder, three body interaction and Bose glass phase in a spinor atomic gas in an optical lattice

We study the effects of disorder on the spin dependent interaction term of a spinor Bose Hubbard model with a three body interaction potential. The signature of the Bose glass (BG) phase is observed by computing the fraction of the lattice sites having finite superfluid (SF) order parameter and non integer occupation densities. We obtain the phase diagram both for the antiferromagnetic (AF) and ferromagnetic (F) cases via a percolation analysis. In the AF case, the BG phase intervenes between the odd-even Mott insulating (MI) lobes (for example, the lobes corresponding to occupation densities, n=1 and (n=2) but not between the even-odd MI lobes. In the ferromagnetic case, the presence of the BG phase is observed between all the MI lobes irrespective of them being even or odd. The BG phase almost destroys the first MI lobe while the MI phase looks more stable than the SF phase both in the AF and F cases due to the presence of the three body interactions.

Black holes as random particles: entanglement dynamics in infinite range and matrix models

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-$\mathcal{N}$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-$\mathcal{N}$ matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.

Occupation densities for certain processes related to subfractional Brownian motion

Occupation densities for certain processes related to subfractional Brownian motion

Local times for functions with finite variation: two versions of Stieltjes change-of-variables formula

We introduce two natural notions for the occupation measure of a function V with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show that both measures are absolutely continuous with respect to the Lebesgue measure. Occupation densities can be thought of as local times of V, and are described by a Meyer–Tanaka like formula. As an example of applications, we derive an extension of Banach's indicatrix theorem.

Thermodynamic Modeling of Variations in the Rate of RNA Chain Elongation of E. coli rrn Operons

Previous electron-microscopic imaging has shown high RNA polymerase occupation densities in the 16S and 23S encoding regions and low occupation densities in the noncoding leader, spacer, and trailer regions of the rRNA (rrn) operons in E. coli. This indicates slower transcript elongation within the coding regions and faster elongation within the noncoding regions of the operon. Inactivation of four of the seven rrn operons increases the transcript initiation frequency at the promoters of the three intact operons and reduces the time for RNA polymerase to traverse the operon. We have used the DNA sequence-dependent standard free energy variation of the transcription complex to model the experimentally observed changes in the elongation rate along the rrnB operon. We also model the stimulation of the average transcription rate over the whole operon by increasing rate of transcript initiation. Monte Carlo simulations, taking into account initiation of transcription, translocation, and backward and forward tracking of RNA polymerase, partially reproduce the observed transcript elongation rate variations along the rrn operon and fully account for the increased average rate in response to increased frequency of transcript initiation.

Proposta de classificação das fontes potenciais de contaminação da água subterrânea

Identificar as atividades que têm potencial de contaminar a água subterrânea auxilia na priorização de ações de proteção dos recursos hídricos, especialmente nas regiões com expressivo crescimento urbano e econômico. Nesse sentido, este trabalho apresenta o levantamento das fontes potenciais de contaminação nos municípios de Capivari, Elias Fausto, Indaiatuba, Monte Mor, Rafard e Salto (SP) e propõe uma classificação da carga contaminante associada, de forma a auxiliar na identificação de áreas com maior perigo de contaminação da água subterrânea. A metodologia para classificação é aqui denominada de POSH-IG e foi adaptada do consagrado método POSH (Pollutant Origin, Surcharge Hydraulically), que classifica a carga contaminante das fontes potenciais de contaminação em três níveis qualitativos (reduzido, moderado e elevado), com base na origem do contaminante e na existência de sobrecarga hidráulica que promova o transporte advectivo do contaminante ao aquífero. No método POSH-IG foram efetuadas adequações, como a inserção de parâmetros disponíveis no Sistema Paulista de Licenciamento Ambiental para a classificação da carga potencial contaminante das fontes pontuais e a integração de informações obtidas pelo mapeamento do uso e cobertura da terra, da tipologia e do padrão da ocupação para a classificação das fontes difusas, associadas aos sistemas de saneamento na área urbana e às atividades agropastoris na área rural. Além da avaliação das áreas de expansão urbana, foi também considerado como critério de classificação das fontes difusas relacionadas aos sistemas de saneamento, a densidade de ocupação das áreas de uso Residencial/Comercial/Serviços, como indicador indireto da densidade populacional. Foram cadastradas 1918 fontes pontuais de contaminação, sendo que os empreendimentos geradores de maior carga contaminante são as indústrias de produtos químicos, metalurgia, produtos metálicos, eletroeletrônicos e de engenharia mecânica, o comércio de produtos perigosos e a disposição inadequada de resíduos. A maior carga potencial de contaminação por fontes difusas nas áreas urbanas está concentrada nas porções mais antigas das cidades, onde ocorrem elevadas densidades de ocupação. A maior expressão em área ocorre nos municípios de Indaiatuba e Salto, onde houve intensa urbanização, e em Monte Mor, onde menos de 45% da cidade possui rede coletora de esgoto. Nas áreas rurais, a canavicultura, predominante nos municípios de Capivari e Rafard, destaca-se pelo elevado potencial de contaminação da água subterrânea.

The Limits of Mean-Field Heterozygosity Estimates under Spatial Extension in Simulated Plant Populations

Computational models of evolutionary processes are increasingly required to incorporate multiple and diverse sources of data. A popular feature to include in population genetics models is spatial extension, which reflects more accurately natural populations than does a mean field approach. However, such models necessarily violate the mean field assumptions of classical population genetics, as do natural populations in the real world. Recently, it has been questioned whether classical approaches are truly applicable to the real world. Individual based models (IBM) are a powerful and versatile approach to achieve integration in models. In this study an IBM was used to examine how populations of plants deviate from classical expectations under spatial extension. Populations of plants that used three different mating strategies were placed in a range of arena sizes giving crowded to sparse occupation densities. Using a measure of population density, the pollen communication distance (Pcd), the deviation exhibited by outbreeding populations differed from classical mean field expectations by less than 5% when Pcd was less than 1, and over this threshold value the deviation significantly increased. Populations with an intermediate mating strategy did not have such a threshold and deviated directly with increasing isolation between individuals. Populations with a selfing strategy were influenced more by the mating strategy than by increased isolation. In all cases pollen dispersal was more influential than seed dispersal. The IBM model showed that mean field calculations can be reasonably applied to natural outbreeding plant populations that occur at a density in which individuals are less than the average pollen dispersal distance from their neighbors.

Occupation densities in solving exit problems for Markov additive processes and their reflections

This paper solves exit problems for spectrally negative Markov additive processes and their reflections. So-called scale matrix, which is a generalization of the scale function of a spectrally negative Lévy process, plays the central role in the study of the exit problems. Existence of the scale matrix was shown by Kyprianou and Palmowski (2008) [32, Thm. 3]. We provide the probabilistic construction of the scale matrix, and identify its transform. In addition, we generalize to the MAP setting the relation between the scale function and the excursion (height) measure. The main technique is based on the occupation density formula and even in the context of fluctuations of spectrally negative Lévy processes this idea seems to be new. Our representation of the scale matrix W(x)=e−ΛxL(x) in terms of nice probabilistic objects opens up possibilities for further investigation of its properties.

Work and settlement locations of immigrants: how are they connected? The case of the Oporto Metropolitan Area

The research reported in this article aims to explain the residential and work location patterns of different groups of immigrants living in a particular metropolitan area, based on the following underlying causes: socio-spatial differentiation resulting from the characteristics of urban economies, the performance of housing and labour markets, spatial and socioeconomic/professional mobility, and immigrants’ own characteristics. Within this scope, census data are analysed and cartographically displayed, and classification trees are applied in order to understand the relationship between the residential and work locations of the different population groups and their respective demographic, economic and professional characteristics, on the one hand, and land occupation densities, on the other. Although this methodology is applied to the Oporto Metropolitan Area (Portugal), it can easily be used in other urban and metropolitan areas.