Poissonian Process Research Articles

Anomalous spin-dependent tunneling statistics in Fe/MgO/Fe junctions induced by disorder at the interface

We present first-principles analysis of interfacial disorder effects on spin-dependent tunneling statistics in thin Fe/MgO/Fe magnetic tunnel junctions. We find that interfacial disorder scattering can significantly modulate the tunneling statistics in the minority spin of the parallel configuration (PC) while all other spin channels remain dominated by the Poissonian process. For the minority-spin channel of PC, interfacial disorder scattering favors the formation of resonant tunneling channels by lifting the limitation of symmetry conservation at low concentration, presenting an important sub-Poissonian process in PC, but is destructive to the open channels at high concentration. We find that the important modulation of tunneling statistics is independent of the type of interfacial disorder. A bimodal distribution function of transmission with disorder dependence is introduced and fits very well our first-principles results. The increase of MgO thickness can quickly change the tunneling from a sub-Poissonian to Poissonian dominated process in the minority spin of PC with disorder. Our results provide a sensitive detection method of an ultralow concentration of interfacial defects.

Length distributions of Au-catalyzed III-V nanowires in different regimes of the diffusion-induced growth

We present a model for kinetic broadening effects on the length distributions of Au-catalyzed III-V nanowires obtained in the growth regime with adatom diffusion from the substrate and the nanowire sidewalls to the top. We observe three different regimes for the length distribution evolution with time. For short growth times, the length distribution is sub-Poissonian, converting to broader than Poissonian with increasing the mean length above a certain threshold value. After the diffusion flux from the nanowire sidewalls has stabilized, the length distribution variance increases linearly with the mean length, as in the Poissonian process.

Testing stress shadowing effects at the South American subduction zone

The seismic gap hypothesis assumes that a characteristic earthquake is followed by a long period with a reduced occurrence probability for the next large event on the same fault segment, as a consequence of the induced stress shadow. The gap model is commonly accepted by geologists and is often used for time-dependent seismic hazard estimations. However, systematic and rigorous tests to verify the seismic gap model have often failed so far, which might be partially related to limited data and too tight model assumptions. In this study, we relax the assumption of a characteristic size and location of repeating earthquakes and analyse one of the best available data sets, namely the historical record of major earthquakes along a 3000 km long linear segment of the South American subduction zone. To test whether a stress shadow effect is observable, we compiled a comprehensive catalogue of mega-thrust earthquakes along this plate boundary from 1520 to 2015 containing 174 earthquakes with Mw > 6.5. In our new testing approach, we analyse the time span between an earthquake and the last event that ruptured the epicentre location, where we consider the impact of the uncertainties of epicentres and rupture extensions. Assuming uniform boundary conditions along the trench, we compare the distribution of these recurrence times with simple recurrence models. We find that the distribution is in all cases almost exponentially distributed corresponding to a random (Poissonian) process; despite some tendencies for clustering of the Mw ≥ 7 events and a weak quasi-periodicity of the Mw ≥ 8 earthquakes, respectively. To verify whether the absence of a clear stress shadow signal is related to physical assumptions or data uncertainties, we perform simulations of a physics-based stochastic earthquake model considering rate and state-dependent earthquake nucleation, which are adapted to the observations with regard to the number of events, spatial extend, size distribution and involved uncertainties. Our simulations show that the catalogue uncertainties lead to a significant blurring of the theoretically peaked distribution, but the distribution would be still distinguishable from the observed one for Mw ≥ 7 events. However, considering the stress transfer to adjacent fault segments and heterogeneous instead of constant stress drop within the rupture zone can explain the observed recurrence time distribution. We conclude that simplified recurrence models, ignoring the complexity of the underlying physical process, cannot be applied for forecasting the Mw ≥ 7 earthquake occurrence at this plate boundary.

Pseudo-Poissonian processes with stochastic intensity and a class of processes generalizing the Ornstein–Uhlenbeck process

The definition of pseudo-Poissonian processes is given in the famous monograph of William Feller (1971, Vol. II, Chapter X). The contemporary development of the theory of information flows generates new interest in the detailed analysis of behavior and characteristics of pseudo-Poissonian processes. Formally, a pseudo-Poissonian process is a Poissonian subordination of the mathematical time of an independent random sequence (the time randomization of a random sequence). We consider a sequence consisting of independent identically distributed random variables with second moments. In this case, pseudo-Poissonian processes do not have independent increments, but it is possible to calculate the autocovariance function, and it turns out that it exponentially decreases. Appropriately normed sums of independent copies of such pseudo-Poissonian processes tend to the Ornstein–Uhlenbeck process. A generalization of driving Poissonian processes to the case where the intensity is random is considered and it is shown that, under this generalization, the autocovariance function of the corresponding pseudo-Poissonian process is the Laplace transform of the distribution of that random intensity. Stochastic choice principles for the distribution of the random intensity are shortly discussed and they are illustrated by two detailed examples.

Prediction in a mixed Poisson cluster model

ABSTRACTMotivated by insurance applications, a mixed Poisson cluster model is considered, where the cluster center process is a mixed Poisson process and descendant processes are additive processes. Each point of the center process represents a claim’s reported time and descendant processes are interpreted as processes of the corresponding payments or number of payments. In this study, we focus on the process aggregating all separate claim’s payment processes. Given the past observations, we study prediction of future increments and their mean-squared errors, also revealing the dependency between future increments from non-reported (IBNR) claims and the past available information. In the existing literature, they are independent since models were considered with a purely Poissonian center process. We derive computationally reasonable expressions for predictors and their variances.

Análisis de los goles conseguidos en 13 temporadas (2000/01-2012/13) correspondientes a la Primera División de la Liga Española de Fútbol Profesional

ObjectiveThe aim of this study is to analyze, 2000/01season through 2012/13season, the goal scored distribution by game and team; as its behavior in time. We also analyze the relationship with the league competitiveness degree. MethodWe used the Poisson and the Negative Binomial distributions in order to study the goals distribution; and the Normalized Shannon Entropy for calculating the leagues uncertainty. ResultsThe Spaniard league has lost competitiveness in the seasons evaluated as the entropy and index of dispersion (team-game) display, especially in the last seasons analyzed. From the perspective of teams, it is not Poisson anymore, above all beyond 2008/09 season. From the perspective of games it does not take place the same phenomenon, specially the last seasons studied (a=0.0099±0.0097; b=0.9622±0.077; R2=0.316; p=0.045 vs. a=0.0162±0.009; b=0.9952±0.0715; R2=0.588; p=0.002). Regarding time differences between each goal, the behavior is different from 200minutes, where the process follows an exponential distribution, and can be considered as a Poissonian process. This modification points out a possible memory effect that can be understood as a Mathew effect, which explains that the less powerful teams are unable to overcome the situation. ConclusionsThe superiority of most powerful teams seems to be more clear, perhaps excessive, compared to the rest of participating teams, as well as the probability that a lot of goals take place (>5 goals) in a single game.

Distribution of tunnelling times for quantum electron transport.

In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a practical approach for calculating it, where the environment is described by the general Markovian master equation. We illustrate the theory by using the rate equation to compute the tunnelling time distribution for electron transport through a molecular junction. The tunnelling time distribution is exponential, which indicates that Markovian quantum tunnelling is a Poissonian statistical process. The tunnelling time distribution is used not only to study the quantum statistics of tunnelling along the average electric current but also to analyse extreme quantum events where an electron jumps against the applied voltage bias. The average tunnelling time shows distinctly different temperature dependence for p- and n-type molecular junctions and therefore provides a sensitive tool to probe the alignment of molecular orbitals relative to the electrode Fermi energy.

Edge-state blockade of transport in quantum dot arrays

We propose a transport blockade mechanism in quantum dot arrays and conducting molecules based on an interplay of Coulomb repulsion and the formation of edge states. As a model we employ a dimer chain that exhibits a topological phase transition. The connection to a strongly biased electron source and drain enables transport. We show that the related emergence of edge states is manifest in the shot noise properties as it is accompanied by a crossover from bunched electron transport to a Poissonian process. For both regions we develop a scenario that can be captured by a rate equation. The resulting analytical expressions for the Fano factor agree well with the numerical solution of a full quantum master equation.

Quantum filtering for multiple diffusive and Poissonian measurements

We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations of diffusive and Poissonian processes. This covers the standard cases from quantum optics, where homodyne detection may be described as a diffusive process and photon counting may be described as a Poissonian process. We obtain a necessary and sufficient condition for any pair of such measurements taken at different output channels to satisfy a commutation relationship. Then, we derive a general, multiple-measurement quantum filter as an extension of a single-measurement quantum filter. As an application we explicitly obtain the quantum filter corresponding to homodyne detection and photon counting at the output ports of a beam splitter.

Correlated bursts and the role of memory range.

Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of heavy-tailed interevent time distributions, higher-order correlations between interevent times, called correlated bursts, have been studied only recently. As the underlying mechanism behind such correlated bursts is far from being fully understood, we devise a simple model for correlated bursts using a self-exciting point process with a variable range of memory. Whether a new event occurs is stochastically determined by a memory function that is the sum of decaying memories of past events. In order to incorporate the noise and/or limited memory capacity of systems, we apply two memory loss mechanisms: a fixed number or a variable number of memories. By analysis and numerical simulations, we find that too much memory effect may lead to a Poissonian process, implying that there exists an intermediate range of memory effect to generate correlated bursts comparable to empirical findings. Our conclusions provide a deeper understanding of how long-range memory affects correlated bursts.

The Main Statistical Properties of the Background Activity of Cortical Neurons in Cats During Slow-Wave Sleep

The statistical properties of neuron spike activity during slow-wave sleep were studied by recording the background activity of 62 cells in the cerebral cortex of two cats. Three groups of neurons were identified. In group 1, deviations from random (event) Poissonian process were small and were apparent as fragments of increased excitability immediately following a refractory period. Neurons of group 2 showed a positive correlation between neighboring intervals, due to slow changes in the mean spike frequency. The number of spikes in volleys decreased after intervals of random durations. Neurons of group 3 was characterized by a larger number of spikes in volleys (>15%) and decreases in the number of volleys of most cells after random intervals. The intravolley intervals of some neurons of this group were constant, while others showed monotonic increases. Only some neurons showed the maximum autocorrelation of the function corresponding to the frequencies of EEG delta activity.

Current Fluctuations in a Semiconductor Quantum Dot with Large Energy Spacing

We report on the measurements of the current noise properties of electron tunneling through a split-gate GaAs quantum dot with large energy level spacing and a small number of electrons. Shot noise is full Poissonian or suppressed in the Coulomb-blockaded regime, while it is enhanced to show as super-Poissonian when an excited energy level is involved by finite source-drain bias. The results can be explained by multiple Poissonian processes through multilevel sequential tunneling.

Simulation‐based estimation: a case study in oncology (SIMEST) and a case study in portfolio selection (SIMUGRAM)

Since the time of Poisson, stochastic processes have been axiomatized in the temporally forward direction. Yet for nearly a century, estimation of parameters and even forecasts have been based on likelihood approaches that start with temporally indexed data and then look backward in time. I shall be using the philosophy of Karl Pearson [Scott DW, Tapia RA, Thompson JR. Karl Pearson was right. Computer Science and Statistics: Tenth Annual Symposium on the Interface; 1978, 179–183] in this article where I create, using a forward model, a large virtual universe of happenings based on the assumption of four parameters characterizing an oncological process based on four Poissonian processes. Bins will be formed in the real time space based on the actual data of real world system of times of discovery of primary and secondary tumors and use bin boundaries that enclose roughly 5% of the actual tumor discover data and compare the bin proportions of virtual data with the proportions of actual data in each of the bins. This will enable us to use Karl Pearson's goodness‐of‐fit criterion as the objective function for a Nelder–Mead optimization. We present here an oncological example where the objective is to estimate four parameters relevant to the progression of beast cancer. This procedure is termed the SIMEST paradigm.Then we briefly describe the patented SIMUGRAM for estimating the distribution of portfolio values using daily resampling strategies. This procedure makes minimal model assumptions and is completely based on data. WIREs Comput Stat 2014, 6:379–385. doi: 10.1002/wics.1320This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model

We consider a generalized Malthus-Verhulst model with a fluctuating carrying capacity and we study its effects on population growth. The carrying capacity fluctuations are described by a Poissonian process with an exponential correlation function. We will find an analytical expression for the average of a number of individuals and show that even in presence of a fluctuating carrying capacity the average tends asymptotically to a constant quantity.

Temporal and Spatial Evolution of Bursts in a Fiber Bundle Model of Creep Rupture

We present a theoretical study of the creep rupture of heterogeneous materials based on a fiber bundle model which provides a direct connection between the microscopic fracture mechanisms and the macroscopic time evolution. In the model, material elements fail either due to immediate breaking or undergo a damage accumulating ageing process. We found that on the micro-level the competition of the two failure modes gives rise to bursts of breakings with power law distributed size and waiting time between events. We demonstrate that approaching macroscopic failure the system accelerates which can be fully described as a non-homogeneous Poissonian process for long range load sharing, however, when localization occurs breaking events get clustered. Bursts are composed of sub-avalanches which lead to a non-trivial temporal shape comparable to measurements. The pulse shape proved to be sensitive to the range of load sharing.

Creep rupture as a non-homogeneous Poissonian process

Creep rupture of heterogeneous materials occurring under constant sub-critical external loads is responsible for the collapse of engineering constructions and for natural catastrophes. Acoustic monitoring of crackling bursts provides microscopic insight into the failure process. Based on a fiber bundle model, we show that the accelerating bursting activity when approaching failure can be described by the Omori law. For long range load redistribution the time series of bursts proved to be a non-homogeneous Poissonian process with power law distributed burst sizes and waiting times. We demonstrate that limitations of experiments such as finite detection threshold and time resolution have striking effects on the characteristic exponents, which have to be taken into account when comparing model calculations with experiments. Recording events solely within the Omori time to failure the size distribution of bursts has a crossover to a lower exponent which is promising for forecasting the imminent catastrophic failure.

Impact of induced bandgaps on sub-Poissonian shot noise in graphene armchair-edge nanoribbons

The impact of the bandgap induced by transversal constriction on the sub-Poissonian properties of graphene armchair-edge nanoribbons (GANRs) has been investigated in a theoretical perspective. For a typical GANR with a bandgap, the minimal conductivity at the Dirac point becomes more suppressed than that of the gapless case 4e2/πh, and the Fano factor becomes more enhanced than the originally predicted value 1/3. The amplitudes of conductivity suppression and Fano factor enhancement will grow large as the nanoribbon width decreases. And the variance of Fano factor is qualitatively consistent with the reported experimental data. The carriers of GANRs with gaps behave like counterparticles in a semiconductor, and the transition from the sub-Poissonian to a Poissonian process takes place gradually with the reduction of the nanoribbon width. For the low aspect ratio (the sample width over its length) limit, the shot noise property at the Dirac point is no longer sensitive to the boundary edges. For the high limit, it requires a larger aspect ratio for the minimal conductivity and maximal Fano factor to achieve stationary values than that of the gapless case.

Coherent quantum ratchets driven by tunnel oscillations: Fluctuations and correlations

We study two capacitively coupled double quantum dots focusing on the regime in which one double dot is strongly biased, while no voltage is applied to the other. Then the latter experiences an effective driving force which induces a ratchet current, i.e., a dc current in the absence of a bias voltage. Its current noise is investigated with a quantum master equation in terms of the full-counting statistics. This reveals, that whenever the ratchet current is large, it also exhibits some features of a Poissonian process. By eliminating the drive circuit, we obtain a reduced master equation which provides analytical results for the Fano factor.

Can we trust earthquake cluster detection tests?

Testing the global earthquake catalogue for indications of non‐Poissonian attributes has been an area of intense research, especially since the 2011 Tohoku earthquake. The usual approach is to test statistically the hypothesis that the global earthquake catalogue is well explained by a Poissonian process. In this paper we analyse one aspect of this problem which has been disregarded by the literature: the power of such tests to detect non‐Poissonian features if they exist; that is, the probability of type II statistical errors. We argue in this article that the low frequency of large events and the brevity of our earthquake catalogues reduce the power of the statistical tests and render them unable to provide an unequivocal answer to this question. We do this using a counter example of a stochastic process that is clustered by construction and by analysing the resulting distribution of p‐values given by a selection of statistical tests related to those found in the literature.

Study on the Long-Period source mechanism at Campi Flegrei (Italy) by a multi-parametric analysis

The source properties of the Long-Period events that occurred at Campi Flegrei Caldera (Italy) during the 2004–2006 ground uplift episode are investigated by analyzing the temporal release of seismic energy, amplitude distribution and inter-event occurrence time. Moreover, an entropy-based decomposition method is applied to identify the simpler waveforms thought to be representative of the source mechanism of Long-Period events. On the basis of the outcomes, we propose that the main part of these events is the result of a source process triggered by a mechanism of fluid charge/discharge, which causes pressure drop in a main branch of a dentritic network of the hydrothermal system. In this model, the rate of the Poissonian process (about 15min), which drives the occurrence of the Long-Period events, provides the average recharge time of the system up to the critical condition. A partial shunting of the fluid flow away from the main conduit activates the ”resonance” of a second branch, spatially separated from the first one. This is a process that occurs whenever the fluid pressure exceeds a critical value and produces less energetic Long-Period events. The mechanism of pressure variation in the two conduits generates signals with preferred amplitude scales, described by a bi-lognormal distribution. From a dynamical point of view, Long-Period events result well described by a low-dimensional dynamical system. Finally, the time pattern of the energy release and its correlation with the diurnal solid earth tide suggest that the whole mechanism of fluid charge/discharge is likely modulated by tidal stress variation.