Time-independent Probabilities Research Articles

Time-Independent Grid-Based Forecast Model for M ≥6.0 Earthquakes in Southeastern Tibetan Plateau Using GNSS Strain Rates and Seismicity

ABSTRACT Earthquake forecasting models play a vital role in earthquake occurrence assessment. Despite improved availability of seismic and geodetic data and processing techniques to produce high-resolution catalogs and deformation history, the implementation of earthquake forecasting models with seismic and geodetic data remains a challenge. In this study, we utilize seismicity and Global Navigation Satellite Systems (GNSS) data to propose time-independent grid-based regional earthquake likelihood models for southeastern Tibetan plateau (RELM-TibetSE). First, we solve the GNSS velocity field and strain rates from 1999 to 2017, deriving geodetic moment rates and introducing empirical correction coefficients to balance them with historical seismic moment rate. Subsequently, we employ a truncated Gutenberg–Richter law and Poisson process to calculate time-independent probabilities for M ≥ 6 earthquakes in 0.2° × 0.2° cells. The grid-based forecasting models indicate that the 30-year probability for M ≥ 6 earthquakes exceeds 1% in more than one-third of the entire study area, highlighting prominently higher earthquake occurrence in these regions. Probability distribution exhibits significant spatial variations. Finally, the predictive performance of the forecasting models is validated based on historical seismicity. The validation indicates that all RELM-TibetSE exhibit good predictive capability relative to a spatially uniform model. The RELM-TibetSE incorporating principal strain rates outperforms those involving maximum shear strain rate in forecasting seismicity. And the differences in forecasting performance between the RELM-TibetSE accounting for spatially varied seismogenic thickness and rigidity and those with uniform thickness and rigidity are not significant. The forecasting models also exhibit better predictive performance for seismic source areas than for epicenters. Moreover, the optimal model highlights zones with higher earthquake occurrence, including the zones about 50 km wide across the Ninglang fault, the zones across the southwestern segment of the Lijiang–Xiaojinhe fault, the China–Myanmar borderland north of the Nantinghe fault, and so on. Therefore, it is justified to conduct multidisciplinary rigorous observations to capture the potential nucleation process of future large earthquakes in these zones.

Sudden excitations of harmonic normal modes

The N-harmonium boson system, i.e., a completely integrable model of N particles where both the external confinement and the two-particle interaction are harmonic, is investigated under the action of sudden time-dependent perturbation. This quench-like external perturbation of confinement has a quadrupolar space-character. The time-independent transition probabilities, which characterize the impact of quench as average occupation numbers, form a complete distribution in the sense of probability theory. The quench-generated energy shift Delta E in the correlated many-body system, and a purity-type Rényi entropy S_{alpha =2} are calculated. Challenging reinterpretations of such an energy change in terms of variables of a classical thermodynamical system of N(N-1)/2 pairs are given as well. As in the case of the ground-state correlated system, an entropy could characterize a global link to energetically optimized independent-particle models.

Comparison of the collapse frequency and the probability of failure of bridges

In this paper, the collapse frequencies of bridges are summarised and compared with target values of probabilities of failure and with calculated failure probabilities for real bridges. The determination of the collapse frequencies is based on various publications in the sense of a meta-analysis. First, the various studies are summarised graphically, discussed and examined for a trend. The results show that the collapse frequencies decrease over time and that today they have reached a minimum. In the next step, the observed collapse frequencies, the target failure probabilities and the calculated failure probabilities are compared. There is a good agreement between the collapse frequencies and failure probabilities for real bridges. The collapse frequencies fulfil the current safety targets for time-dependent target probabilities as well as for time-independent target probabilities for dead and traffic loads. Subsequently, the causes of bridge collapses are assessed regarding loads. The main cause for bridge collapses is accidental loads, such as hydraulic events. Such loads can be controlled if they are considered in the correct order of magnitude. The probabilities of failure can be extended regarding further factors and thus the matching between probabilities and frequencies can be further improved.

Cohort versus patient level simulation for the economic evaluation of single versus combination immuno-oncology therapies in metastatic melanoma

Background: Model structure, despite being a key source of uncertainty in economic evaluations, is often not treated as a priority for model development. In oncology, partitioned survival models (PSMs) and Markov models, both types of cohort model, are commonly used, but patient responses to newer immuno-oncology (I-O) agents suggest that more innovative model frameworks should be explored.Objective: A discussion of the theoretical pros and cons of cohort level vs patient level simulation (PLS) models provides the background for an illustrative comparison of I-O therapies, namely nivolumab/ipilimumab combination and ipilimumab alone using patient level data from the CheckMate 067 trial in metastatic melanoma. PSM, Markov, and PLS models were compared on the basis of coherence with short-term clinical trial endpoints and long-term cost per QALY outcomes reported.Methods: The PSM was based on Kaplan-Meier curves from CheckMate 067 with 3-year data on progression free survival (PFS) and overall survival (OS). The Markov model used time independent transition probabilities based on the average trajectory of PFS and OS over the trial period. The PLS model was developed based on baseline characteristics hypothesized to be associated with disease as well as significant mortality and disease progression risk factors identified through a proportional hazards model.Results: The short-term Markov model outputs matched the 1–3 year clinical trial results approximately as well as the PSMs for OS but not PFS. The fixed (average) cohort PLS results corresponded as well as the PSMs for OS in the combination therapy arm and PFS in the monotherapy arm. Over the lifetime horizon, the PLS produced an additional 5.95 quality adjusted life years (QALYs) associated with combination therapy relative to ipilimumab alone, resulting in an incremental cost-effectiveness ratio (ICER) of £6,474 per QALY, compared with £14,194 for the PSMs which gave an incremental benefit of between 2.2 and 2.4 QALYs. The Markov model was an outlier (∼ £49,000 per QALY in the base case).Conclusions: The 4- and 5-state versions of the PSM cohort model estimated in this study deviate from the standard 3-state approach to better capture I-O response patterns. Markov and PLS approaches, by modeling state transitions explicitly, could be more informative in understanding I-O immune response, the PLS particularly so by reflecting heterogeneity in treatment response. However, both require a number of assumptions to capture the immune response effectively. Better I-O representation with surrogate endpoints in future clinical trials could yield greater model validity across all models.

Time-dependent versus time-independent probabilities of transmission and reflection of a quantum particle incident upon a step potential and a square potential well

We investigate the transmission and reflection of a quantum particle incident upon a step potential decrease and a square well. The probabilities of transmission and reflection using the time-independent Schrödinger equation and also the time-dependent Schrödinger equation are in excellent agreement. We explain why the probabilities agree so well. In doing so, we make use of an exact analytical expression for the square well for time-dependent transmission and reflection, which reveals additional interesting and unexpected results. One such result is that transmission of a wave packet can occur with the probability of transmission depending weakly on the initial spread of the packet. The explanations and the additional results will be of interest to instructors of and students in upper year undergraduate quantum mechanics courses.

Time-dependent versus time-independent probabilities of transmission and reflection of a quantum particle incident upon potentials with large changes

We investigate the transmission and reflection of a quantum particle incident upon a step potential increase, a step potential decrease, a square well, and a square barrier, all well studied in undergraduate quantum mechanics. We are especially interested in the extreme where the change in the potential is arbitrarily large, but with the difference in the energy of the particle and the potential held fixed, if possible. We obtain the probabilities of transmission and reflection using the time-independent Schrödinger equation and also the time-dependent Schrödinger equation. In the time-dependent case, we have the particle initially in a Gaussian wave packet or a similar localized state. We obtain results that fall into three categories: results that are not surprising, results where time-dependent and time-independent agree surprisingly well, and results that are very different. We discuss the unexpected results. Our work may be of interest to instructors of and students in upper year undergraduate quantum mechanics courses.

Multi‐scale modeling of GMP differentiation based on single‐cell genealogies

Hematopoiesis is often pictured as a hierarchy of branching decisions, giving rise to all mature blood cell types from stepwise differentiation of a single cell, the hematopoietic stem cell. Various aspects of this process have been modeled using various experimental and theoretical techniques on different scales. Here we integrate the more common population-based approach with a single-cell resolved molecular differentiation model to study the possibility of inferring mechanistic knowledge of the differentiation process. We focus on a sub-module of hematopoiesis: differentiation of granulocyte-monocyte progenitors (GMPs) to granulocytes or monocytes. Within a branching process model, we infer the differentiation probability of GMPs from the experimentally quantified heterogeneity of colony assays under permissive conditions where both granulocytes and monocytes can emerge. We compare the predictions with the differentiation probability in genealogies determined from single-cell time-lapse microscopy. In contrast to the branching process model, we found that the differentiation probability as determined by differentiation marker onset increases with the generation of the cell within the genealogy. To study this feature from a molecular perspective, we established a stochastic toggle switch model, in which the intrinsic lineage decision is executed using two antagonistic transcription factors. We identified parameter regimes that allow for both time-dependent and time-independent differentiation probabilities. Finally, we infer parameters for which the model matches experimentally observed differentiation probabilities via approximate Bayesian computing. These parameters suggest different timescales in the dynamics of granulocyte and monocyte differentiation. Thus we provide a multi-scale picture of cell differentiation in murine GMPs, and illustrate the need for single-cell time-resolved observations of cellular decisions.

Equivalent constant rates for performance-based seismic assessment of ageing structures

Analytical, closed-form solutions are derived for the computation of equivalent constant rates of limit-state exceedance for structures under seismic loads whose capacity is degrading with time. Seismic guidelines currently designate constant, time-independent probabilities or mean annual frequencies of exceedance that are assumed to remain invariable for the entire design life. These are at odds with the time-dependent, ever-increasing exceedance rates of ageing structures. Based on the concept of social equity and discounting of societal investments, the equivalent constant rate provides a basis for judging the safety of structures with time-dependent capacity by allowing comparisons with the code-mandated rates of limit-state exceedance. Starting from the simple SAC/FEMA solution and assuming a power-law degradation of capacity with time and a linear change in the combined epistemic and aleatory variability of capacity, we provide general solutions for the equivalent constant rate and for the limiting case of the average rate over the design life of the structure. The solutions are formulated both in the demand-based and in the intensity-based format, the latter being suitable for all limit-states, even close to global collapse. By using a 7-story reinforced concrete building as an example, we demonstrate the accuracy and the practicality of these approximations for the assessment of an existing structure.

Dinâmica do emprego e custos de ajustamento na indústria do Rio Grande do Sul

O presente estudo tem como propósito fazer uma análise empírica da estrutura dos custos de ajustamento do emprego industrial usando dados do Brasil. As estruturas teóricas para custos de ajustamento do emprego encontradas na literatura podem ser agrupadas em custos convexos (que incluem a popular função quadrática) e não-convexos (como custos fixos). Seguindo o trabalho de Varejão e Portugal (2007), empregamos metodologias complementares para a identificação da estrutura de custos de ajustamento de modo inovador no Brasil. Primeiro, usando matrizes de transição entre regimes de emprego. Segundo, empregando modelos de sobrevivência, que são mais gerais que os modelos de matriz de transição Markoviana. Os resultados obtidos sugerem que os custos de ajustamento não-convexos têm mais apoio nos dados do que o modelo usual de custos de ajustamentos quadráticos.

Scattering by a time-dependent target

The scattering of a particle by a target with periodic time dependence is usually formulated in Floquet extended space. This leads to time-independent transition probabilities which correspond to the scattering of wave packets that are close to being monoenergetic. Because of the wide space extension of such packets, many oscillations take place during the time particle and target interact. The purpose of this study consists in showing that the scattering amplitudes can also be used to describe the way the particle feels the instantaneous configuration of the target at the time of the collision. The application is made to an oscillating barrier in one dimension. Several tests of the formalism validate the analysis, by changing either the initial position of the wave packet, or the phase of the particle–target interaction. Two equivalent necessary conditions can be formulated to recover the results of standard scattering theory. One is that no energies differing by at least one quantum are present in the energy range effectively covered by the initial wave packet. The other is that there is appreciable self-overlapping of the wave packet after one period of oscillation.

Reciprocity relations for time-independent transition probabilities of time-dependent Hamiltonians

Reciprocity relations are derived between time-independent transition probabilities for absorption and emission of photons within a system governed by a time-dependent Hamiltonian. The proof combines the use of absorbing boundary conditions to express the probabilities and the (t ,t8) formalism. The case of a particle incident on an asymmetric double-barrier potential and interacting with an oscillatory field is given for illustration. @S1050-2947~98!04711-8#

Proof by Certainty Equivalents That Diversification-Across-Time Does Worse, Risk Corrected, Than Diversification-Throughout-Time

For those with constant relative-risk-aversion, one can calculate an easy and exact measurement of their risk-corrected total return per period by use of an appropriate "power mean". For them, this approach can dramatize the inefficiency of being (say) half the time in each of two independent and identically distributed securities; 100% is then lost of the benefit from being all the time 50-50 in each; actually, being half the time in each is as bad as being all the time in either one, which is equivalent to being completely undiversified. More generally, there is proved here that, for any risk-averse U(W) and time-independent probabilities, optimal diversification within each time period outperforms generically any and all patterns of across-time diversification. The variety of proposed risk-corrected returns can give useful approximations for different classes of investors–widows and orphans, pension fiduciaries, high-flying plungers, and so forth–to replace or extend Markowitz, Sharpe, Treynor, or Modigliani-Modigliani measures of corrected performance.

The recombination-induced temperature change of non-equilibrium charge carriers

A novel mechanism changing the temperature of a non-equilibrium gas of charge carriers is shown to exist: recombination of a proportion of the carriers. The rate of temperature change thus induced is proportional to the recombination probability 1/ tau . If recombination heating occurs it can compensate carrier-acoustic-phonon-mediated energy relaxation. For density- and time-independent recombination probabilities the minimum temperature Tmin that carriers can reach is defined. The sign, size and temperature dependence of the 'recombination heating' depend on the type of statistics obeyed by the carriers and on the details of the energy dependence of the recombination probability. For Maxwell-Boltzmann statistics heating, nothing or cooling occurs if the recombination probability decreases with, does not depend on or increases with energy, respectively. If the Fermi statistics applies to an electron-hole plasma the remaining carriers always heat upon recombination. The results of this theory are compared with experimental findings on the temperature relaxation of free electrons trapped by impurities, excitons in quantum wells and electron-hole drops.

M.T.T.F. and availability evaluation of a two-unit, two-state, standby redundant complex system with constant human failure

In this paper, the investigation have been carried out for the evaluation of availability and M.T.T.F. of a standby redundant complex system incorporating the concept of human failure in two states, viz. good and failed. Single service facility is available for the service of unit failure. Using the supplementary variable technique, Laplace transforms of various state probabilities have been obtained. Making use of Abel's Theorem, various time independent probabilities have been further evaluated. To make the system more applicable to practical life problems, M.T.T.F. for the system has also been computed and various graphs have been plotted to highlight the utility of the model.

Cost analysis of a two-unit electronic parallel redundant system with overloading effect

A two-unit parallel redundant repairable electronic system with exponential failure-time distribution and overloading effect is considered. The system is to be in any of the three states: good, degraded and failed. One repair facility is available when the system is either in degraded or failed state. The repair for the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and operational availability of the system at any time. Using supplementary variable technique, Laplace transforms of various state probabilities have been evaluated. Making use of Abel's theorem, various time independent probabilities have been computed. Also the overloading effect for the expected profit on the operational availability of the complex system has been studied.

Hardware approach for generating spanning trees in reliability studies: V. K. Bansal and K. B. Misra. Microelectron. Reliab.21 (2) 243 (1981)

A two-unit parallel redundant repairable electronic system with exponential failure-time distribution and overloading effect is considered. The system is to be in any of the three states: good, degraded and failed. One repair facility is available when the system is either in degraded or failed state. The repair for the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and operational availability of the system at any time. Using supplementary variable technique, Laplace transforms of various state probabilities have been evaluated. Making use of Abel's theorem, various time independent probabilities have been computed. Also the overloading effect for the expected profit on the operational availability of the complex system has been studied.

A stochastic model for a two-compartment reversible system

This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.

Futures research scenarios and time succession

The possibility of introducing time-succession into a type of scenario approach used in futures research is examined, starting from Duperrin and Godet's SMIC-74 method, which deals with sets of nondated binary events and requires as input data the individual probabilities of these events and their time-independent conditional probabilities, taken by pairs. Time succession is then considered successively at two levels: 1)as a means used just to make conditional probabilities more accessible to intuition, following a proposal of Mitchell and Tydeman, to which a simplification is suggested; and 2) as a characteristic to be kept in the time-succession dependent scenarios that are finally dealt with. In the second the investigated period is split into q time “scenes,” as suggested by Olaf Helmer, and a method is proposed using the same algorithm as is used in SMIC-74, but in which binary events, as basic elements, are replaced by “boxed-events.” A boxed-event consists in the couple formed by an event and a “box” that represents either one of the q time scenes or the nonoccurrence of the event. The procedure by which experts can be consulted about the individual and conditional probability data required is described in some detail.

The distribution of sojourn times in finite absorbing Markov chains

The distribution of the time spent before absorption in various states of finite Markov chains with time-independent transition probabilities is derived. All the moments of this distribution are calculated. The problem is of interest in population genetics.

Breakdown of local equilibrium in coupled relaxation processes: Translational nonequilibrium during vibrational relaxation

Coupled relaxation processes involving several variables are examined using the theory of Markov Processes. This leads naturally to a relaxation equation for one of the variables which has the form of a master equation, but involves time dependent transition probabilities. The equation agrees with usual theories based on local equilibrium and time independent transition probabilities when both the correlations between the variables and the distribution function of the suppressed variables reach their equilibrium form more rapidly than the variable of interest. In order to test the relevance of deviations from local equilibrium, a model which mimics many of the properties of the coupled relaxation of translation and vibration for V−T energy exchange in a thermal reservoir is proposed and solved. Using cross sections which are like those for energy transfer in diatomic molecules, it is shown that important nonequilibrium correlations persist on the transient time scale of the relaxation of the translational degrees of freedom. These correlations can be large when the preponderance of molecules are initially in the ground state and are the order of magnitude of the enhancement of vibrational relaxation times observed at low temperatures.