Decay Probability Research Articles

Second-Order Asymptotically Optimal Outlier Hypothesis Testing

We revisit the outlier hypothesis testing framework of Li <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task is to discern the set of outlying sequences that are generated from anomalous distributions. The nominal and anomalous distributions are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unknown</i> . We study the tradeoff among the probabilities of misclassification error, false alarm and false reject for tests that satisfy weak conditions on the rate of decrease of these error probabilities as a function of sequence length. Specifically, we propose a threshold-based test that ensures exponential decay of misclassification error and false alarm probabilities. We study two constraints on the false reject probability, with one constraint being that it is a non-vanishing constant and the other being that it has an exponential decay rate. For both cases, we characterize bounds on the false reject probability, as a function of the threshold, for each pair of nominal and anomalous distributions and demonstrate the optimality of our test under the generalized Neyman-Pearson criterion. We first consider the case of at most one outlying sequence and then generalize our results to the case of multiple outlying sequences where the number of outlying sequences is unknown and each outlying sequence can follow a different anomalous distribution.

Dissipation Effects Induced by Internal Relative Motion Between Two Nonlinear σ-Models

We studied the dissipation effect induced by the internal relative motion between two nonlinear [Formula: see text]-models (NLSMs). The internal degrees of freedom (DOF) of the two NLSMs coupled to each other via an interface potential. We performed the path integral of the vacuum persistence amplitude (VPA) and got the quantum action. Then we introduced the relative motion via a boost transformation with velocity parameter [Formula: see text]. Furthermore, we calculated the imaginary part of the boosted quantum action which was proportional to the vacuum decay probability. At last, we calculated the frictional force. The numerical results gave the velocity [Formula: see text] dependency of the vacuum decay probability, and the velocity [Formula: see text] dependency of the frictional force. There was a threshold of relative velocity [Formula: see text] for the vacuum decay probability and the frictional force. We gave a classical argument of the existence of the threshold, and the argument matched the mathematical results.

Multichannel decay law

It is well known, both theoretically and experimentally, that the survival probability for an unstable quantum state, formed at t=0, is not a simple exponential function, even if the latter is a good approximation for intermediate times. Typically, unstable quantum states/particles can decay in more than a single decay channel. In this work, the general expression for the probability that an unstable state decays into a certain i-th channel between the initial time t=0 and an arbitrary t>0 is provided, both for nonrelativistic quantum states and for relativistic particles. These partial decay probabilities are also not exponential and their ratio turns out to be not a simple constant, as it would be in the exponential limit. Quite remarkably, these deviations may last relatively long, thus making them potentially interesting in applications. Thus, multichannel decays represent a promising and yet unexplored framework to search for deviations from the exponential decay law in quantum mechanical systems, such as quantum tunneling, and in the context of particle decays.

First-passage times to anisotropic partially reactive targets

We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three- and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with mixed Robin-Neumann boundary conditions. This approximation involves the harmonic capacity and the surface area of the target, the volume of the confining domain, the diffusion coefficient, and the reactivity. The accuracy of the approximation is checked by using a finite-elements method. The proposed approximation determines also the mean first-reaction time, the long-time decay of the survival probability, and the overall reaction rate on that target. We identify the relevant lengthscale of the target, which determines its trapping capacity, and we investigate its relation to the target shape. In particular, we study the effect of target anisotropy on the principal eigenvalue by computing the harmonic capacity of prolate and oblate spheroids in various space dimensions. Some implications of these results in chemical physics and biophysics are briefly discussed.

Functional Peaks-Over-Threshold Analysis

AbstractPeaks-over-threshold analysis using the generalised Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results. In this paper, we extend peaks-over-threshold analysis to extremes of functional data. Threshold exceedances defined using a functional r are modelled by the generalised r-Pareto process, a functional generalisation of the generalised Pareto distribution that covers the three classical regimes for the decay of tail probabilities, and that is the only possible continuous limit for r-exceedances of a properly rescaled process. We give construction rules, simulation algorithms and inference procedures for generalised r-Pareto processes, discuss model validation and apply the new methodology to extreme European windstorms and heavy spatial rainfall.

Minimal energy thresholds for sustained turbulent bands in channel flow

In this work, nonlinear variational optimization is used for obtaining minimal seeds for the formation of turbulent bands in channel flow. Using nonlinear optimization together with energy bisection, we have found that the minimal energy threshold for obtaining spatially patterned turbulence scales with$Re^{-8.5}$for$Re&gt;1000$. The minimal seed, which is different to that found in a much smaller domain, is characterized by a spot-like structure surrounded by a low-amplitude large-scale quadrupolar flow filling the whole domain. This minimal-energy perturbation of the laminar flow has dominant wavelengths close to$4$in the streamwise direction and$1$in the spanwise direction, and is characterized by a spatial localization increasing with the Reynolds number. At$Re \lesssim 1200$, the minimal seed evolves in time, creating an isolated oblique band, whereas for$Re\gtrsim 1200$, a quasi-spanwise-symmetric evolution is observed, giving rise to two distinct bands. A similar evolution is found also at low$Re$for non-minimal optimal perturbations. This highlights two different mechanisms of formation of turbulent bands in channel flow, depending on the Reynolds number and initial energy of the perturbation. The selection of one of these two mechanisms appears to be dependent on the probability of decay of the newly created stripe, which increases with time, but decreases with the Reynolds number.

Relevance of artefacts in 99mTc-MAA SPECT scans on pre-therapy patient-specific 90Y TARE internal dosimetry: a GATE Monte Carlo study

Objective. The direct Monte Carlo (MC) simulation of radiation transport exploiting morphological and functional tomographic imaging as input data is considered the gold standard for internal dosimetry in nuclear medicine, and it is increasingly used in studies regarding trans-arterial radio-embolization (TARE). However, artefacts affecting the functional scans, such as reconstruction artefacts and motion blurring, decrease the accuracy in defining the radionuclide distribution in the simulations and consequently lead to errors in absorbed dose estimations. In this study, the relevance of such artefacts in patient-specific three-dimensional MC dosimetry was investigated in three cases of 90Y TARE. Approach. The pre-therapy 99mTc MacroAggregate Albumin (Tc-MAA) SPECTs and CTs of patients were used as input for simulations performed with the GEANT4-based toolkit GATE. Several pre-simulation SPECT-masking techniques were implemented, with the aim of zeroing the decay probability in air, in lungs, or in the whole volume outside the liver. Main results. Increments in absorbed dose up to about +40% with respect to the native-SPECT simulations were found in liver-related volumes of interest (VOIs), depending on the masking procedure adopted. Regarding lungs-related VOIs, decrements in absorbed doses in right lung as high as −90% were retrieved. Significance. These results highlight the relevant influence of SPECT artefacts, if not properly treated, on dosimetric outcomes for 90Y TARE cases. Well-designed SPECT-masking techniques appear to be a promising way to correct for such misestimations.

Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation

The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest curve, the Airy 2 _2 process, describes after the subtraction of a parabola the limiting law of the scaled energy of a geodesic running from the origin to a variable point on an anti-diagonal line in such problems as Poissonian last passage percolation. The ensemble of curves resulting from the Airy line ensemble after the subtraction of the same parabola enjoys a simple and explicit spatial Markov property, the Brownian Gibbs property. In this paper, we employ the Brownian Gibbs property to make a close comparison between the Airy line ensemble’s curves after affine shift and Brownian bridge, proving the finiteness of a superpolynomially growing moment bound on Radon-Nikodym derivatives. We also determine the value of a natural exponent describing in Brownian last passage percolation the decay in probability for the existence of several near geodesics that are disjoint except for their common endpoints, where the notion of ‘near’ refers to a small deficit in scaled geodesic energy, with the parameter specifying this nearness tending to zero. To prove both results, we introduce a technique that may be useful elsewhere for finding upper bounds on probabilities of events concerning random systems of curves enjoying the Brownian Gibbs property. Several results in this article play a fundamental role in a further study of Brownian last passage percolation in three companion papers (Hammond 2017a,b,c), in which geodesic coalescence and geodesic energy profiles are investigated in scaled coordinates.

First-encounter time of two diffusing particles in two- and three-dimensional confinement.

The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two- and three-dimensional domains with reflecting boundaries. Based on the outcome of the simulations, we give a comprehensive overview of the behavior of the survival probability S(t) and the associated first-encounter time probability density H(t) over a broad time range spanning several decades. In addition, we provide numerical estimates and empirical formulas for the mean first-encounter time 〈T〉, as well as for the decay time T characterizing the monoexponential long-time decay of the survival probability. Based on the distance between the boundary and the center of mass of two particles, we obtain an empirical lower bound t_{B} for the time at which S(t) starts to significantly deviate from its counterpart for the no boundary case. Surprisingly, for small-sized particles, the dominant contribution to T depends only on the total diffusivity D=D_{1}+D_{2}, in sharp contrast to the one-dimensional case. This contribution can be related to the Wiener sausage generated by a fictitious Brownian particle with diffusivity D. In two dimensions, the first subleading contribution to T is found to depend weakly on the ratio D_{1}/D_{2}. We also investigate the slow-diffusion limit when D_{2}≪D_{1}, and we discuss the transition to the limit when one particle is a fixed target. Finally, we give some indications to anticipate when T can be expected to be a good approximation for 〈T〉.

Immigrant Status and Ethnic Inequities in Dental Caries in Children: Bilbao, Spain.

This study examined the migratory status/ethnic inequities in dental caries in school children aged 4–9 years (n = 1388) and the impact of the Children’s Oral Health Program in the Municipality of Bilbao in the Basque Country Region, Spain. Using the 2017 Children’s Oral Health Survey, log binomial regression was used to quantify the association of parental immigration status/ethnicity with tooth decay for (1) the primary and the permanent dentitions, separately, in children 4–9 years old; and (2) for the permanent dentition in children aged 7–9 years. Compared with Spanish children, Spanish Roma and immigrant children had a higher probability of tooth decay in primary and permanent teeth after adjustment. Similarly, Spanish Roma and immigrant children had a higher probability of caries experience in primary and permanent teeth. In children aged 7–9 years, Spanish Roma children had a greater probability of tooth decay and caries experience (DMFT index ≥ 1; PR: 6.20; 95% CI: 3.18, 12.12; and PR: 4.52; 95% CI: 2.46, 8.32; respectively) compared with Spanish Children. These associations were not observed in immigrant children. This study shows that parental immigration status and/or ethnicity affect caries outcomes in immigrant and Roma children in both primary and permanent dentition.

On the stability of superheavy nuclei

Potential energy surfaces of even–even superheavy nuclei are evaluated within the macroscopic-microscopic approximation. A very rapidly converging analytical Fourier-type shape parametrization is used to describe nuclear shapes throughout the periodic table, including those of fissioning nuclei. The Lublin Strasbourg Drop and another effective liquid-drop type mass formula are used to determine the macroscopic part of nuclear energy. The Yukawa-folded single-particle potential, the Strutinsky shell-correction method, and the BCS approximation for including pairing correlations are used to obtain microscopic energy corrections. The evaluated nuclear binding energies, fission-barrier heights, and \(Q_\alpha \) energies show a relatively good agreement with the experimental data. A simple one-dimensional WKB model à la Świa̧tecki is used to estimate spontaneous fission lifetimes, while \(\alpha \) decay probabilities are obtained within a Gamow-type model.

Age‐Specific differences in Asian elephant defecation, dung decay, detection and their implication for dung count

AbstractIn vertebrate population estimation, converting faecal density into animal density requires information on the faecal production rate, decay rate and faecal density. Differences in the above factors for long‐lived species across age classes were not evaluated. We have evaluated these factors associated with the dung count of Asian elephants (Elephas maximus) in the tropical forest of southern India.The defecation rate of elephants was determined in semi‐wild elephants at the Mudumalai elephant camp. The relationship between dung bolus diameter and age was determined to estimate the age of the elephant. The total and age‐specific elephant density based on dung bolus diameter was estimated. A total of 24 transect lines of 2–4 km (125 km) were sampled in the study area. An experiment was conducted to assess the detection probability across the age classes of dung piles. The dung decay rates across age classes and seasons were determined by marking fresh dung piles (n = 1551). The dung‐based age structure assessment and its limitations were evaluated.The mean defecation rate was 13.51 ± 0.51 per day. The defecation rate was significantly lower for the younger age class and increased with the age of elephants. Defecation rates were significantly lower in the wet season than in the dry. The dung bolus diameter positively increased with the age of elephants, and the growth curve can be used to predict the age and age structure of elephant populations.The disparity in the dung production rate results in the lower availability of younger age class (juvenile and calf) dung in the transect for counting, which results in lower dung abundance. The detection probability of dung piles of younger age classes was low (0.58). The survival rates of dung piles of younger age classes were lower and increased with the age of elephants in the wet season. Hence, the demographic assessment of the population based on dung needs to consider age‐specific differences in dung production, decay and detection probability. Although the demographic assessment using dung provides insight into population age structure, it has limitations in predicting age structure for young elephants.

Spin inhibition in γ -decay probabilities for states above Sn in Sm and Dy nuclei

When a compound nucleus is formed at an excitation energy above the neutron-separation threshold, it is assumed that its de-excitation will proceed via neutron emission. However, if the excited nucleus is in a high-spin state, but does not have enough excitation energy to conserve angular momentum by either photon emission after neutron emission or relative angular momentum carried off by the neutron, the nucleus will de-excite via $\ensuremath{\gamma}$-emission instead. This effect, the spin inhibition, provides an insight into the structure of the compound nuclei and can aid the understanding of the distribution of the populated spin states in a compound nuclear reaction. In this work, the effects of spin inhibition on the $\ensuremath{\gamma}$-decay probabilities from states in $^{146,147}\mathrm{Sm}$ and $^{160}\mathrm{Dy}$ are presented. For high-spin states above the ${S}_{n}$, spin inhibition is able to suppress neutron emission, and de-excitation via $\ensuremath{\gamma}$-ray emission is observed for states up to 3 MeV above the ${S}_{n}$.

Probable decay modes of even–even superheavy nuclei

Cluster-decay half-lives () of even–even nuclei are calculated employing interaction potential involving Coulomb and proximity potentials and, the obtained results are compared with the experimental ones. In order to study cluster radioactivity in even–even superheavy nuclei (SHN), we evaluate the required disintegration energies (Q c -values) utilizing periodic-orbit theory within microscopic-macroscopic formalism and hence, predict the logarithmic values of 's for even–even 298−312Og and 296−310120 nuclei. Among various isotopes of daughter nuclei, products produced with minimum value of Gibbs free energy are chosen for our investigation. Also, an analysis of the branching ratios enables us to determine the dominant mode of decay among α − decay, spontaneous fission (SF) and cluster-decay in these SHN. The emissions of 90Kr from 298Og and 94Sr cluster from 296,298120 SHN are found to be the dominant mode of decay. Our results are in agreement with those obtained using UDL method except for few cases. We believe that this work can play a significant role in the experiments leading to identification of exotic nuclei.

Quantum random walk and tight-binding model subject to projective measurements at random times

What happens when a quantum system undergoing unitary evolution in time is subject to repeated projective measurements to the initial state at random times? A question of general interest is: how does the survival probability S m , namely, the probability that an initial state survives even after m number of measurements, behave as a function of m? We address these issues in the context of two paradigmatic quantum systems, one, the quantum random walk evolving in discrete time, and the other, the tight-binding model evolving in continuous time, with both defined on a one-dimensional periodic lattice with a finite number of sites N. For these two models, we present several numerical and analytical results that hint at the curious nature of quantum measurement dynamics. In particular, we unveil that when evolution after every projective measurement continues with the projected component of the instantaneous state, the average and the typical survival probability decay as an exponential in m for large m. By contrast, if the evolution continues with the leftover component, namely, what remains of the instantaneous state after a measurement has been performed, the survival probability exhibits two characteristic m values, namely, and with δ > 1. These scales are such that (i) for m large and satisfying , the decay of the survival probability is as m −2, (ii) for m satisfying , the decay is as m −3/2, while (iii) for , the decay is as an exponential. The results for the dynamics with the leftover component, already known for the case of measurements at regular intervals, are being extended here to the case of measurements at random intervals. We find that our results hold independently of the choice of the distribution of times between successive measurements, as have been corroborated by our results for a wide range of distributions including exponential and power-law distributions as well as for the case of measurements at regular intervals. This fact hints at robustness and ubiquity of our derived results.

Motion induced excitation and radiation from an atom facing a mirror

We study quantum dissipative effects due to the nonrelativistic, bounded, accelerated motion of a single neutral atom in the presence of a planar perfect mirror, i.e., a perfect conductor at all frequencies. We consider a simplified model whereby a moving ``scalar atom'' is coupled to a quantum real scalar field, subjected to either Dirichlet or Neumann boundary conditions on the plane. We use an expansion in powers of the departure of the atom with respect to a static average position to compute the vacuum persistence amplitude and the resulting vacuum decay probability. We evaluate transition amplitudes corresponding to the excitation of the atom plus the emission of a particle, and show explicitly that the vacuum decay probabilities match the results obtained by integrating the transition amplitudes over the directions of the emitted particle. We also compute the spontaneous emission rate of an oscillating atom that is initially in an excited state.

Puzzle on isomeric configurations in and around N=126 closed shell

The puzzle of finding consistent nuclear configurations to explain both the decay probabilities and moments of the ${9/2}^{\ensuremath{-}}, {8}^{+}$, and ${21/2}^{\ensuremath{-}}$ isomers in and around the $N=126$ closed shell has been approached in the generalized seniority scheme. Though ${h}_{9/2}$ is the dominant orbital near Fermi energy, the role of configuration mixing from the surrounding ${f}_{7/2}$ and ${i}_{13/2}$ orbitals is found to be very important for the consistent explanation of all the isomeric properties such as the $B(E2)$ rates, $Q\phantom{\rule{0.28em}{0ex}}\mathrm{moments},$ and $g\phantom{\rule{0.28em}{0ex}}\mathrm{factors}$. The structural behavior of the closed shell $N=126$ isotonic isomers turns out to be very similar to that of the $N=124$ and $N=128$ isotonic isomers, which have two neutron holes and two neutron particles, respectively. This is due to the pairing symmetries of nuclear many-body Hamiltonian. As confirmation, the microscopic shell model occupancies are also calculated for these isomers in the $N=126$ chain which support the generalized seniority results. Additional arguments using the systematics of odd-proton ${9/2}^{\ensuremath{-}}$ states in Tl ($Z=81$), Bi ($Z=83$), At ($Z=85$), and Fr ($Z=87$) isotopes are also presented.

Abstract WP43: Modeling The Decay In Probability Of Receiving Endovascular Thrombectomy Based On Time From Stroke Onset

Introduction: Large-vessel occlusion (LVO) stroke patients with infarct core volumes greater than 70 mL do not meet current AHA guidelines for thrombectomy eligibility. Therefore, it is important to understand how time-dependent infarct core growth translates to a patient’s declining probability of thrombectomy eligibility. Modeling the probability that a suspected LVO patient would qualify for thrombectomy can help inform the optimal prehospital emergency transport strategy which maximizes the likelihood of an excellent patient outcome. Methods: We determined the time from stroke onset required for an infarct core to grow to 70 mL as a function of penumbra volume and collateral score. After applying a series of numerical interpolations, our framework outputted the probability a suspected LVO patient qualifies for thrombectomy (based on core volume threshold) as a function of time from stroke onset to imaging. We then incorporated this function into an existing model of prehospital emergency transport, which previously assumed all patients were thrombectomy-eligible, in order to assess the impact that considering treatment eligibility had on optimal transport decisions. Results: An exponential decay curve best fit the numerically-generated probability function. We found that after integrating this eligibility model into the emergency transport decision tool the optimal transport strategy changed from drip and ship to mothership in 8.5% of possible patient pickup locations in Alberta, Canada. Conclusions: This methodology provides a novel, mechanistic approach to deriving a thrombectomy eligibility curve. As a result, we are able to better optimize prehospital transport decisions to improve outcomes of suspected LVO patients.

Which App is Going to Die? A Framework for App Survival Prediction With Multitask Learning

App survival prediction is a significant task in mobile service development. It differs from existing prediction tasks in two aspects. First, rather than the traditional survival prediction in bioinformatics where all the patients' survival probabilities decay in a similar way, apps' survival pattern varies from each other. Second, affected by multiple factors, an app's popularity is time-varying and sequence-dependent, which makes existing short-term prediction methods not applicable due to error accumulation. These characteristics bring great difficulties in app survival prediction. In this paper, we propose AppLife, a framework that fuses multi-source influence factors and utilizes Multi-Task Learning (MTL) to combine the state information of mobile app for survival prediction. First, we analyze how the app survival is affected by multi-source factors, including download history, ratings, and reviews. Second, to overcome error accumulation in long-term prediction, we propose a novel MTL based approach. The approach estimates whether an app is surviving at each time interval during the life cycle of apps and leverages relatedness among tasks to improve the prediction performance. Last, we collect a large-scale dataset with more than 35,000 apps, based on which we evaluate our proposed framework and results show that it outperforms the seven state-of-the-art methods.

Investigation of Weisskopf-Ewing approximation for the determination of ( n,p ) cross sections using the surrogate reaction technique

The present study explores the limitations of the surrogate reaction method for determining the $(n,p)$ cross sections for the target nuclei in the mass region $A\ensuremath{\approx}50$ for the neutron energies 1--20 MeV. In the past few years there have been several experimental attempts for determining the $(n,p)$ and $(n,xp)$ cross sections using the surrogate reaction method. But this method has not been benchmarked with the experimentally well-known $(n,p)$ cross sections. The surrogate reaction method with Weisskopf-Ewing approximation may help in providing good constraints for the cross-section data, but this approximation has not been validated yet for $(n,p)$ reactions. In this paper, we have examined the validity of the Weisskopf-Ewing approximation for the $(n,p)$ reactions and also check the sensitivity of the surrogate reaction results with respect to the compound nucleus spin distribution. We have simulated the cross sections obtained through the surrogate reaction method for $n+^{48}\mathrm{Ti}, n+^{53}\mathrm{Cr}, n+^{56}\mathrm{Fe}$, and $n+^{59}\mathrm{Co}$ reactions for the different schematic spin distributions of the compound nucleus and studied the effect of assuming the validity of the Weisskopf-Ewing approximation. It has been observed that the proton decay probabilities of the compound nucleus for the $(n,p)$ channel are strongly spin dependent, therefore the Weisskopf-Ewing approximation is violated. We have also observed that the cross sections obtained using the Weisskopf-Ewing approximation show clear dependence on the spin distribution of the compound nucleus. It has also been observed that, due to the large pre-equilibrium contributions in the $(n,p)$ reactions at higher neutron energies, the use of the surrogate reaction method for the neutron energies greater than $\ensuremath{\approx}15$ MeV may not be suitable. It is concluded that the surrogate reaction method relying solely on the Weisskopf-Ewing approximation is not sufficient for determining the $(n,p)$ cross sections for the target nuclei in mass range $A\ensuremath{\approx}50$ and further development and exploration of the surrogate technique is required.