Finite Probability Research Articles

Activation instanton in real-time formalism

In this paper, we study the dynamics of the activation of a Brownian particle using the path integral formalism in real time. Along with the construction of the saddle-point (instanton) solutions, we develop the formalism allowing to calculate the effect of the fluctuations near this solution in detail. In particular, it is shown that there is a soft mode for which the integration is not Gaussian and just this mode is responsible for the finite probability flux.

Performance Prediction of Matched Filter and Adaptive Cosine Estimator Hyperspectral Target Detectors

Many applications of hyperspectral remote sensing involve the detection of subpixel targets for search and rescue or defense and intelligence operations. The design and potential capabilities of these systems depends on their target detection performance. Therefore, it is important to have tools that reliably predict the performance of target detection systems under different realistic situations. The purpose of this paper is to present a hyperspectral target performance prediction model for the widely used matched filter (MF) and adaptive cosine estimator (ACE) detectors. We use a replacement signal model for resolved and subpixel targets and a finite probability mixture of t-elliptically contoured distributions ( t-ECDs) for the background. A major contribution of this paper is the development of a robust analytical and numerical approach to determine the output distribution of ACE for mixtures of t-ECDs. The proposed technique can be a very useful tool for evaluating target detection performance for highly complex backgrounds.

The Bivariate Erlang and its Application in Modeling Recurrence Times of Kidney Dialysis Data

Recent advances in computer modeling allows us to find closer fits to data. Our emphasis is on the interdependence between occurrence at kidney dialysis. The interdependence between kidney dialysis occurrences is modelled by a bivariate exponential that we propose in this article. The application is shown on the McGilchrist and Aisbett kidney data set with the use of the exponential distribution. The proposed bivariate exponential model has exponential marginal densities, correlated via a latent random variables and with finite probability of simultaneous occurrence. Extension of the model to a bivariate Erlang type distribution with same shape parameter is presented.

Minimizing Upper Bound of Ruin Probability Under Discrete Risk Model with Markov Chain Interest Rate

This article focuses on minimal upper bound of ruin probability for a discrete time risk model with Markov chain interest rate and stochastic investment return. The interest rate of bond market is assumed to be a stationary Markov chain, and the return process of a stock market can be negative. This article presents two kinds of methods for minimizing the upper bound of ruin probability. One method relies on recursive equations for finite time ruin probabilities and inductive approach, the other one depends on martingale approach. Numerical examples show that the martingale approach is better than the inductive one.

Jamming transition in a driven lattice gas

We study a two-lane driven lattice gas model with oppositely directed species of particles moving on two periodic lanes with correlated lane switching processes. While the overall density of individual species of particles is conserved in this system, the particles are allowed to switch lanes with finite probability only when oppositely directed species meet on the same lane. This system exhibits a unique behavior, wherein phase transition is observed between a homogeneous absorbing phase, characterized by complete segregation of oppositely directed particles between the two lanes, and a jammed phase. The transition is accompanied by a finite drop of current in the lattice, emergence of a cluster comprised of both species of particles in the jammed phase, and is determined by the interplay of the relative rates of translation of particles on the same lane and their lane switching rates. These findings may have interesting implications for understanding the phenomenon of jamming in microtubule filaments observed in the context of axonal transport.

Completion of the Causal Completability Problem

We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces (Hofer-Szabó et al. [1999]; Gyenis and Rédei [2004]). We prove that (i) any classical probability space has a causally closed extension; (ii) any finite classical probability space with positive rational probabilities on the atoms of the event algebra can be extended to a causally up-to-three-closed finite space; and (iii) any classical probability space can be extended to a space in which all correlations between events that are logically independent modulo measure zero event have a countably infinite common-cause system. Collectively, these results show that it is surprisingly easy to find Reichenbach-style ‘explanations' for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality. 1 Introduction2 Basic Definitions and Results in the Literature3 Causal Completability the Easy Way: ‘Splitting the Atom’4 Causal Completability of Classical Probability Spaces: The General Case5 Infinite Statistical Common-Cause Systems for Arbitrary Pairs6 Conclusion Appendix A

Molecular dynamics simulations of organic crystal dissolution: The lifetime and stability of the polymorphic forms of para-amino benzoic acid in aqueous environment

Para-amino benzoic acid (PABA) manifests crystalline solid-state properties that are typical of a class of chemical compounds with important industrial applications. Hence, it is particularly worthwhile to investigate the lifetime and stability of representative molecular-clusters of two polymorphic forms of PABA in aqueous solution using molecular dynamics simulations. Simulations of 5ns duration in the isothermal–isobaric ensemble (constant particle number, pressure and temperature (NPT) ensemble) were performed for the two polymorphic forms at three different temperatures 0°C, 50°C and 100°C. The simulations revealed that at 0°C the representative molecular-clusters of the two polymorphic forms remain ordered while at 50°C the molecular packing within the clusters becomes partially disordered for both polymorphic forms and at 100°C the clusters lose long-range order rapidly and come to resemble liquid drops. Care should be taken when assessing the relative stability of polymorphic forms, as a function of temperature, from such computational experiments which explore the dissolution of nano-scale crystals. The long range order of the clusters of the α-form at 50°C and 100°C was, respectively, partially and completely lost after 5ns which merits further investigation given that the α-form is the high-temperature stable polymorph. Importantly, the initial shape of clusters, as well as the number of solute molecules they contained, affected the extent to which order was lost and how rapidly the loss occurred. Given that the classical nucleation theory predicts a finite probability that clusters significantly larger than the critical size, in terms of number of molecules, may dissolve, building clusters containing a greater number of molecules could improve the simulated stability of the α polymorph at 50°C and 100°C. Furthermore, the simulations revealed that the selection of a suitable electrostatic potential is very important for the description of the dissolution process of the nano-sized crystals.

Asymptotics for ruin probabilities in a discrete-time risk model with dependent financial and insurance risks

Let us consider a discrete-time insurance risk model with insurance and financial risks, where the insurance net loss within period and the stochastic discount factor over the interval follow a certain dependence structure for each fixed . Under the assumption that the distribution of net insurance loss within one time period is consistently varying-tailed, precise estimates for finite and infinite time ruin probabilities are derived. Furthermore, these estimates are uniform on the time horizon.

ALTERNATIVE ANALYSIS OF FINITE-TIME PROBABILITY DISTRIBUTIONS OF RENEWAL THEORY

We introduce a level-crossing analysis of the finite time-t probability distributions of the excess life, age, total life, and related quantities of renewal processes. The technique embeds the renewal process as one cycle of a regenerative process with a barrier at level t, whose limiting probability density function leads directly to the time-t quantities. The new method connects the analysis of renewal processes with the analysis of a large class of stochastic models of Operations Research. Examples are given.

INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY-INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 1: BAYESIAN INFERENCE OF FIXED MODEL FORMS

Uncertainty quantification techniques have the potential to play an important role in constructing constitutive relationships applicable to nanoscale physics. At these small scales, deviations from laws appropriate at the macroscale arise due to insufficient scale separation between the atomic and continuum length scales, as well as fluctuations due to thermal processes. In this work, we consider the problem of inferring the coefficients of an assumed constitutive model form using atomistic information and propagation of the associated uncertainty. A nanoscale heat transfer problem is taken as the model, and we use a polynomial chaos expansion to represent the thermal conductivity with a linear temperature dependence. A Bayesian inference method is developed to extract the coefficients in this expansion from molecular dynamics (MD) samples at prescribed temperatures. Importantly, the atomistic data are incompatible with the continuum model because of the finite probability of heat flowing in the opposite direction of the temperature gradient; we present a method to account for this in the model. The fidelity and uncertainty in these techniques are then examined. Validation is provided by comparing a continuum Fourier model against a larger all MD simulation representing the true solution.

Timing variation aware dynamic digital phase detector for low‐latency clock domain crossing

This study presents a digital phase detector-based approach for estimating and synchronising phase variations between clock domains. Instead of waiting for the resolution of metastability (with finite probability of failure), the authors propose a metastability avoidance algorithm, based on a sampling method for asynchronous signals. The results, using 90 nm inovation for high performance microelectronics (IHP) technology, show that the proposed design is about 1.5 times faster and provides a 35% improvement in Energy-Delay Product compared with the state-of-the-art approaches. Moreover, it completely prevents metastability failures.

Probabilistic Analysis of Power Tower Systems to Achieve Sunshot Goals

The U.S. Department of Energy's (DOE) SunShot goal seeks to reduce the levelized cost of energy (LCOE) for solar energy technologies to $0.06/kWh. A number of cost and technical performance targets for various concentrating solar power (CSP) components have been issued by the DOE to meet the SunShot goals for CSP. This paper presents probabilistic analyses of the LCOE for a 100 MWe power tower system with inherent cost and performance uncertainties. Previous results show that while CSP systems are likely to meet the cost target necessary to compete broadly in U.S. markets, there is a very low probability of reaching an LCOE of $0.06/kWh if parameter uncertainty distributions are used that range from current cost and performance values to the current DOE targets. This work investigates additional parameter distributions using new cost and technical targets to determine performance and cost scenarios for power tower systems that yield finite probabilities of achieving $0.06/kWh. Starting with the “baseline” uncertainty distributions, the minimum (or maximum) value for each uncertain parameter was “improved” by ∼50% and ∼75%. Results show that the probability of achieving an LCOE of $0.06/kWh increases to 15% and 46%, respectively, with these new cost and technical targets.

Learning experiences and the value of knowledge

Generalized probabilistic learning takes place in a black-box where present probabilities lead to future probabilities by way of a hidden learning process. The idea that generalized learning can be partially characterized by saying that it doesn’t foreseeably lead to harmful decisions is explored. It is shown that a martingale principle follows for finite probability spaces.

Upper Bounds for Ruin Probability in a Generalized Risk Process under Rates of Interest with Homogenous Markov Chain Claims

This paper explores recursive and integral equations for ruin probability of a controlled risk process under rates of interest with homogenous Markov chains. We assume that claim and rates of interest are homogenous Markov chains, take a countable number of non – negative values. Generalized Lundberg inequalities for ruin probability of this process are derived via a recursive technique. Recursive equations for finite time ruin probability and an integral equation for ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.Mathematics Subject Classification: 62P05, 60G40, 12E05Keywords: ruin probability, homogenous Markov chain, controlled risk process

Second Order Corrections for the Limits of Normalized Ruin Times in the Presence of Heavy Tails

In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [4] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In this paper we derive the rate of convergence for this finite time ruin probability when the claims are regularly varying with a finite second moment.

Revisiting the physico-chemical hypothesis of code origin: an analysis based on code-sequence coevolution in a finite population.

The origin of the genetic code marked a major transition from a plausible RNA world to the world of DNA and proteins and is an important milestone in our understanding of the origin of life. We examine the efficacy of the physico-chemical hypothesis of code origin by carrying out simulations of code-sequence coevolution in finite populations in stages, leading first to the emergence of ten amino acid code(s) and subsequently to 14 amino acid code(s). We explore two different scenarios of primordial code evolution. In one scenario, competition occurs between populations of equilibrated code-sequence sets while in another scenario; new codes compete with existing codes as they are gradually introduced into the population with a finite probability. In either case, we find that natural selection between competing codes distinguished by differences in the degree of physico-chemical optimization is unable to explain the structure of the standard genetic code. The code whose structure is most consistent with the standard genetic code is often not among the codes that have a high fixation probability. However, we find that the composition of the code population affects the code fixation probability. A physico-chemically optimized code gets fixed with a significantly higher probability if it competes against a set of randomly generated codes. Our results suggest that physico-chemical optimization may not be the sole driving force in ensuring the emergence of the standard genetic code.

Resonance mass spectra of gravity and fermion on Bloch branes

In this paper, by presenting the potentials of Kaluza-Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and resonances of gravity and fermion on the symmetric and asymmetric Bloch {branes}. We find that the localization properties of zero modes for gravity and fermion in the symmetric brane case are the same, whereas, for the asymmetric brane case, the fermion zero mode is localized on one of the sub-branes, while the gravity zero mode is localized on another sub-brane. The spectra of the gravity and the left- or right-handed fermion are composed of a bound zero mode and a series of gapless continuous massive KK modes. Among the continuous massive KK modes, we obtain some discrete gravity and fermion resonant (quasilocalized) KK states on the brane, which have a finite probability of escaping into the bulk. The KK states with lower resonant masses have a longer lifetime on the brane. And the number of the resonant KK states increases linearly with the width of the brane and the scalar-fermion coupling constant, {but it decreases with the asymmetric factor $\beta$}. The structure of the resonance spectrum is investigated in detail.

Measurement of a Reaction-Diffusion Crossover in Exciton-Exciton Recombination inside Carbon Nanotubes Using Femtosecond Optical Absorption

Exciton-exciton recombination in isolated semiconducting single-walled carbon nanotubes was studied using femtosecond transient absorption. Under sufficient excitation to saturate the optical absorption, we observed an abrupt transition between reaction- and diffusion-limited kinetics, arising from reactions between incoherent localized excitons with a finite probability of ~0.2 per encounter. This represents the first experimental observation of a crossover between classical and critical kinetics in a 1D coalescing random walk, which is a paradigm for the study of nonequilibrium systems.

Dynamic forces on agglomerated particles caused by high-intensity ultrasound

In this paper the acoustic forces on particles and agglomerates caused by high-intensity ultrasound in gaseous atmosphere are derived by means of computational fluid dynamics (CFD). Sound induced forces cause an oscillating stress scenario where the primary particles of an agglomerate are alternatingly pressed together and torn apart with the frequency of the applied wave. A comparison of the calculated acoustic forces with respect to the inter particle adhesion forces from Van-der-Waals and liquid bridge interactions reveals that the separation forces may reach the same order of magnitude for 80μm sized SiO2-particles. Hence, with finite probability acoustically agitated gases may de-agglomerate/disperse solid agglomerate structures. This effect is confirmed by dispersion experiments in an acoustic particle levitation setup.

TURBULENT DISKS ARE NEVER STABLE: FRAGMENTATION AND TURBULENCE-PROMOTED PLANET FORMATION

A fundamental assumption in our understanding of disks is that when the Toomre Q>>1, the disk is stable against fragmentation into self-gravitating objects (and so cannot form planets via direct collapse). But if disks are turbulent, this neglects a spectrum of stochastic density fluctuations that can produce rare, high-density mass concentrations. Here, we use a recently-developed analytic framework to predict the statistics of these fluctuations, i.e. the rate of fragmentation and mass spectrum of fragments formed in a turbulent Keplerian disk. Turbulent disks are never completely stable: we calculate the (always finite) probability of forming self-gravitating structures via stochastic turbulent density fluctuations in such disks. Modest sub-sonic turbulence above Mach number ~0.1 can produce a few stochastic fragmentation or 'direct collapse' events over ~Myr timescales, even if Q>>1 and cooling is slow (t_cool>>t_orbit). In trans-sonic turbulence this extends to Q~100. We derive the true Q-criterion needed to suppress such events, which scales exponentially with Mach number. We specify to turbulence driven by MRI, convection, or spiral waves, and derive equivalent criteria in terms of Q and the cooling time. Cooling times >~50*t_dyn may be required to completely suppress fragmentation. These gravoturbulent events produce mass spectra peaked near ~M_disk*(Q*M_disk/M_star)^2 (rocky-to-giant planet masses, increasing with distance from the star). We apply this to protoplanetary disk models and show that even minimum mass solar nebulae could experience stochastic collapse events, provided a source of turbulence.