Probability Distribution & Applications

The depth-duration-frequency curves and isopluvial maps for the region encompassing South Carolina, North Carolina, and Georgia were developed using the available rainfall data. The aim was to update the existing intensity-duration-frequency curves in the region and obtain these curves at ungauged sites throughout the region using the newly developed rainfall frequency analysis techniques. A total of 17 durations ranging from 15 minutes to 120 hours for return periods of 2, 10, 25, 50, and 100 years were analyzed. The L-moment method with X-10 test was used to search for homogeneous regions within the study area. It was found that the method was either unable to homogeneous regions that were geographically contiguous or too many stations had to be eliminated before a region could be considered homogenous. Finally, at-site statistics were calculated to develop frequency relationships. Normal, lognormal, generalized extreme value, Pearson type III, and log Pearson type III probability distribution functions were used to fit the maximum annual precipitation data at each gauging site for each duration. The chi-squared goodness-of-fit test was used to determine the best fit probability distribution. The new intensity-duration-frequency curves were found to be lower than the existing curves developed in 1986. The difference between the two set of curves was found to be due to the removal of the outliers in the present study and the existence of the post 1986 drought conditions in the region. The spatial interpolation of the rainfall intensity from the depthduration-frequency curves was found to yield accurate intensity-duration-frequency curves and could be used to develop these curves at ungauged sites in the study area.

We propose a new algorithm in the two-sided marriage market wherein both sides of the market propose in each round. The algorithm always yields a stable matching. Moreover, the outcome is often a non-extremal matching, and in fact, is a Rawlsian stable matching if the matching market is "balanced." Lastly, the algorithm can be computed in polynomial time and, hence, from a practical standpoint, can be used in markets in which fairness considerations are important.

A distributed asynchronous algorithm for minimizing a function with a nonstationary minimum over a constraint set is considered. The communication delays among the processors are assumed to be stochastic with Markovian character. Conditions which guarantee the mean square and almost sure convergence to the sought solution are presented. We also present an optimal routing application for a network that connects various U.S. cities. Results of the extensive simulation that we implemented assert the practical applicability of distributed asynchronous algorithms with stochastic delays. Comparison results for varying the probability distribution of these delays are provided. The impact of varying the communication delay bound and the stepsize is also assessed.

Demand Assigned Multiple Access (DAMA) schemes in which requests for communication channels are transmitted over collision type channels to a master controller and in which messages of different priorities are present is analyzed. Priority use of the request channels is achieved by having users select among those channels according to a priority dependent probability distribution. Two important schemes of this class are considered. Additionally, three schemes for priority assignment of message channels are treated; two are nonpreemptive and one is preemptive. Trade offs among bandwidth utilization and delay are considered as well as optimization of system parameters. i.

The relativistic Ornstein-Uhlenbeck Process (ROUP), which is a toy-model of relativistic irreversible phenomena, is studied statistically in an explicitly covariant manner. An 8-dimensional phase space is introduced (four dimensions for space-time coordinates, and four dimensions for the 4-momentum coordinates), on which 'extended' probability distributions are defined (the usual probability distribution is recovered as their restriction to the mass shell). An explicitly covariant Kolmogorov equation is derived for these 'extended' probability distributions. The whole formalism is used to introduce a 4-current of conditional entropy and prove that the 4-divergence of this 4-current is always positive. This constitutes an H-theorem for the ROUP.

For random percolation at p c , the probability distribution P (n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with P (n) ∼ exp(-an 2 ) for all dimensions. We also study the variation of the average size (mass) of the spanning clusters when there are more than one spanning cluster. While the average size of the spanning clusters scales as usual with L D where D = dβ/ν for any number of clusters, it shows a smooth decrease as the number of spanning clusters increases.

Scalar transport by turbulent flows is best described in terms of Lagrangian parcel motions. Here we measure the Eulerian distance travel along Lagrangian trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared Eulerian displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the Eulerian integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the Lagrangian integral time and times longer than the Eulerian integral time. The very short-time enhancement reflects the underlying Lagrangian velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of Lagrangian tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.

We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a "best" approximation from within a family of trial distributions, and (b) to quantify the extent to which non-optimal trial distributions are ruled out. The Bogoliuvob variational method is shown to be included as a special case. As an illustration we apply our method to simple fluids. In a first use of the ME method the "exact" canonical distribution is approximated by that of a fluid of hard spheres and ME is used to select the optimal value of the hard-sphere diameter. A second, more refined application of the ME method approximates the "exact" distribution by a suitably weighed average over different hard-sphere diameters and leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a specific example, the radial distribution function and the equation of state for a Lennard-Jones fluid (Argon) are compared with results from molecular dynamics simulations.

We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

We prove the following infinite-case theorem. If the Riemann Hypothesis is false, then the set of nontrivial zeros of the Riemann zeta function off the critical line ℜ(s) = 1/2 cannot be infinite. The proof is self-contained. The main ingredients are: (i) a Hadamard-type summability argument excluding the escape λ_m → +∞; (ii) a corrected near/far analysis excluding the escape λ_m → 0; (iii) a shell-counting proof that the theta-limit F_∞(λ) is strictly positive for every λ > 0 under infinitely many off-critical zeros; and (iv) a shell-counted proof of the compact-uniform convergence F_m → F_∞ with explicit rate O(1/m).

The response excitation theory, introduced in Athanassoulis & Sapsis (2006) and , is a new powerful method that can be used for treating nonlinear systems with arbitrary polynomial non-linearities excited by colored, Gaussian or non Gaussian, stochastic processes. Since the assumption of delta-correlated excitation is overcome, this formulation is appropriate for macroscopic stochastic dynamical systems, where the excitation correlation time is comparable with the system's relaxation time. In these cases, the response is not Markovian and, thus, a reduction to Fokker-Planck-Kolmogorov equations is not generally possible. Besides, the filtering approach, is not generally applicable for non Gaussian excitation. The joint Response-Excitation Probability Density Function (REPDF) evolution equation is derived by finite dimensional projection of a Functional Differential Equation for the joint, response-excitation characteristic functional. However, it is a peculiar equation, involving two times and two probability arguments (one for the excitation and one for the response), and partial derivatives only with respect to one (excitation) time and one (excitation) probability argument. This equation alone is a necessary differential constraint, that cannot provide a unique joint REPDF. However, if it is further supplemented by the marginal compatibility constraints, and analytically solved, local, linearized problems, accounting for the local, response-excitation, correlation structure, becomes uniquely solvable. In this paper we present, for the first time, a numerical solution to this equation, in the long time, based on an appropriate Kernel Density (KD) representation of the REPDF, and a Galerkin-type numerical scheme to calculate the KD coefficients. This scheme is used to derive the probabilistic characteristics of the responses of a half oscillator, subject to asymptotically stationary, strongly colored, Gaussian excitation. The obtained PDF is favorably compared with results from a Monte Carlo simulation.

In study of the statistical packages, simulation from probability distributions is one of the important aspects. This paper is based on simulation study from Bernoulli distribution conducted by various popular statistical packages like R, SAS, Minitab, MS Excel and PASW. The accuracy of generated random data is tested through Chi-Square goodness of fit test. This simulation study based on 8685000 random numbers and 27000 tests of significance shows that ability to simulate random data from Bernoulli distribution is best in SAS and is closely followed by R Language, while Minitab showed the worst performance among compared packages.

A Decision Guidance Management System (DGMS) is a productivity platform for fast development of applications that require a closed-loop data acquisition, learning, prediction, and decision optimization. This paper introduces the DGMS concept, and the first DGMS data model with its query language, DG-SQL. The DGMS data model is an extension of the relational model with probability distributions over a set of attributes as random variables. DG-SQL supports a seamless integration of (1) querying the data collection and construction of learning sets, (2) learning from the learning sets, using parameterized transformers and optionally defining an estimation utility, such as sum of squares of errors, to be minimized; (3) probabilistic prediction and simulation, using expressions that involve random variables, such as expectation, variance and probability of a logical formula; and (4) stochastic or deterministic optimization, where search space is defined as a set of feasible non-deterministic query evaluations.

In theories in which the cosmological constant takes a variety o f v alues in dierent \subuniverses," the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it. This probability is proportional to the fraction of matter which is destined to condense out of the background into mass concentrations large enough to form observers. We calculate this \collapsed fraction" by a simple, pressure-free, spherically symmetric, nonlinear model for the growth of density uctuations in a at universe with arbitrary value of the cosmological constant, applied in a statistical way t o the observed spectrum of density uctuations at recombination. From this, the probability distribution for the vacuum energy density V for Gaussian random density uctuations is derived analytically. (The conventional quantity 0 is the vacuum energy density in units of the critical density at present, 0 = V = crit;0 , where crit;0 = 3 H 2 0 = 8 G.) It is shown that the results depend on only one quantity, 3 , where 2 and are the variance and mean value of the uctuating matter density eld at recombination, respectively. To calculate , w e adopt the at CDM model with nonzero cosmological constant and x the amplitude and shape of the primordial power spectrum in accordance with data on cosmic microwave background anisotropy from the COBE satellite DMR experiment. A comparison of the results of this calculation of the likely values of V with present observational bounds on the cosmological constant indicates that the small, positive v alue of V (up to 3 times greater than the present cosmic mass density)

We present a computationally efficient segmentation-restoration method, based on a probabilistic formulation, for the joint estimation of the label map (segmentation) and the parameters of the feature generator models (restoration). Our algorithm computes an estimation of the posterior marginal probability distributions of the label field based on a Gauss Markov Random Measure Field model. Our proposal introduces an explicit entropy control for the estimated posterior marginals, therefore it improves the parameter estimation step. If the model parameters are given, our algorithm computes the posterior marginals as the global minimizers of a quadratic, linearly constrained energy function; therefore, one can compute very efficiently the optimal (Maximizer of the Posterior Marginals or MPM) estimator for multi-class segmentation problems. Moreover, a good estimation of the posterior marginals allows one to compute estimators different from the MPM for restoration problems, denoising and optical flow computation. Experiments demonstrate better performance over other state of the art segmentation approaches. This work was partially supported by CONACYT, Mexico (grants 40722 and 46270).

This study presents a state-space modelling framework for the purposes of stock assessment. The stochastic population dynamics build on the notion of correlated survival and capture events among individuals. The correlation is thought to arise as a combination of schooling behaviour, a spatially patchy environment, and common but unobserved environmental factors affecting all the individuals. The population dynamics model isolates the key biological processes, so that they are not condensed into one parameter but are kept separate. This approach is chosen to aid the inclusion of biological knowledge from sources other than the assessment data at hand. The model can be tailored to each case by choosing appropriate models for the biological processes. Uncertainty about the model parameters and about the appropriate model structures is then described using prior distributions. Different combinations of, for example, age, size, phenotype, life stage, species, and spatial location can be used to structure the population. To update the prior knowledge, the model can be fitted to data by defining appropriate observation models. Much like the biological parameters, the observation models must also be tailored to fit each individual case.

The first measurements of an exit location distribution are reported for an overdamped nonconservative system perturbed by weak white noise, modeled both numerically and by an analog electronic circuit. In the weak-noise limit the distribution is increasingly concentrated near a saddle point of the dynamics and is increasingly well approximated by a Weibull distribution, in agreement with theoretical predictions. A physical explanation for this behavior is given, which should facilitate the computation of corrections to the limiting form

We study the pattern of activated trajectories in a double well system without detailed balance, in the weak noise limit. The pattern may contain cusps and other singular features, which are similar to the caustics of geometrical optics. Their presence is reflected in the quasipotential of the system, much as phase transitions are reflected in the free energy of a thermodynamic system. By tuning system parameters, a cusp may be made to coincide with the saddle point. Such an anomalous cusp is analogous to a nonclassical critical point. We derive a scaling law, and nonpolynomial 'equations of state', that govern its bifurcation into conventional cusps.

In this paper impact of climate change on precipitation in the arid environment of Iraq is examined. LARS-WG weather generator was applied to 5 representative regions to model current and future precipitation under climate change. Seven Global Climate Models (GCMs) have been employed to account for any uncertainty on future projection for three selected periods

Front detection and declouding algorithms developed at the URI have been applied to the 12-year (1985-1996) Pathfinder SST data set to produce the first comprehensive, objectively derived, year-round climatology of ocean thermal fronts in the eastern China Seas, from 24 • N to 41 • N. Ten fronts have been distinguished, namely Kuroshio,

Front detection and declouding algorithms developed at the URI have been applied to the 12‐year (1985–1996) Pathfinder SST data set to produce the first comprehensive, objectively derived, year‐round climatology of ocean thermal fronts in the eastern China Seas, from 24°N to 41°N. Ten fronts have been distinguished, namely Kuroshio, Zhejiang‐Fujian, Jiangsu, Shandong Peninsula, Bohai Sea, Seohan Bay, Kyunggi Bay, Western and Eastern Chejudo (South Korean Coastal Front), and Yangtze Bank Ring Front. The fronts are seasonally persistent: they emerge and disappear in the same seasons of different years. The frontal pattern remains fairly stable from one year to another, whereas individual fronts display different modes of seasonal variability.

Front detection and declouding algorithms developed at the URI have been applied to the 12-year (1985-1996) Pathfinder SST data set to produce the first comprehensive, objectively derived, year-round climatology of ocean thermal fronts in the eastern China Seas, from 24 • N to 41 • N. Ten fronts have been distinguished, namely Kuroshio,

Combining different prior distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source. The resulting pooled distribution however heavily depends set of weights given to each opinion/prior. In this paper we explore three objective approaches to assigning weights to opinions. Two methods are stated in terms of optimization problems and a third one uses a hierarchical prior that accounts for uncertainty on the weights. We explore an example in which a proportion is estimated using weights assigned to a finite set of opinions and show that, depending on the used method, results vary from discarding some of the expert opinions to the situation in which all opinions are assigned equal weights. Nevertheless, the three methods explored in this paper lead to very similar combined priors, with very similar integrated (margina...

This paper proposes two parallel variants of an Estimation of Distribution Algorithm (EDA) that represents the probability distribution by means of a single connected graphical model based on a polytree structure. The main goal is to design a new and more ef cient EDA. Our algorithm is based on the master/slave model that allows to perform the estimation of the probability distribution (the most time-consuming phase in EDAs) in a parallel way. The aim of our experimental studies is manifold. Firstly, we show that our parallel versions achieve a notable reduction of the total execution time with respect to existing algorithms. Secondly, we study the behavior of the algorithm from the numerical point of view, analyzing the different versions. Finally, our methods are evaluated over three interconnection networks (Fast Ethernet, Gigabit Ethernet, and Myrinet) and a study on the in uence of the parallel platform in the communication is performed.

We introduce the student to the Quantum Mechanic linear potential (constant force) using new variation wave functions for the ground state and the first excited one. This approach use simple wave functions to describe the exact Airy solution.

Climate change has led to non-stationarity in recorded floods all over the world. Although previous studies have widely discussed the design error caused by non-stationarity, most of them explored basins with closed catchment areas. The response of flood level to nonstationary inflow floods and high tidal levels in deltas with a dense river network has hardly been mentioned. Delta areas are extremely vulnerable to floods. To establish reliable standards for flood protection in delta areas, it is crucial to investigate the response of flood level to nonstationary inflow floods and high tidal levels. Pearl River Delta (PRD), the largest delta in South China, was selected as the study area. A theoretical framework was developed to quantify the response of flood level to nonstationary inflow floods and the tidal level. When the non-stationarity was ignored, error up to 18% was found in 100-year design inflow floods and up to 14% in 100-year design tidal level. Meanwhile, flood level in areas that were ≤22 km away from the outlets mainly responded to the nonstationary tidal level, and that ≥45 km to the nonstationary inflow floods. This study will support research on the non-stationarity of floods in delta areas.

Climate change has led to non-stationarity in recorded floods all over the world. Although previous studies have widely discussed the design error caused by non-stationarity, most of them explored basins with closed catchment areas. The response of flood level to nonstationary inflow floods and high tidal levels in deltas with a dense river network has hardly been mentioned. Delta areas are extremely vulnerable to floods. To establish reliable standards for flood protection in delta areas, it is crucial to investigate the response of flood level to nonstationary inflow floods and high tidal levels. Pearl River Delta (PRD), the largest delta in South China, was selected as the study area. A theoretical framework was developed to quantify the response of flood level to nonstationary inflow floods and the tidal level. When the non-stationarity was ignored, error up to 18% was found in 100-year design inflow floods and up to 14% in 100-year design tidal level. Meanwhile, flood level in ...

Context and Motivation. The dark matter problem comprises three independent observational requirements: the seeding of cosmic structure from near-uniform plasma, the gravitational lensing excess at cluster scales, and the persistence of flat rotation curves beyond visible galactic disks. Paper 4 of this series resolved the structure-seeding requirement through the collision cascade angular momentum inheritance relation J = mu_eff (b x v_rel). This paper addresses the lensing excess and, through the validated Milky Way convergence test, provides the strongest current observational anchor for the galacticscale framework.

We numerically simulate the traveling time of a tracer in convective flow between two points ͑injection and extraction͒ separated by a distance r in a model of porous media, dϭ2 percolation. We calculate and analyze the traveling time probability density function for two values of the fraction of connecting bonds p: the homogeneous case pϭ1 and the inhomogeneous critical threshold case pϭp c . We analyze both constant current and constant pressure conditions at pϭp c . The homogeneous pϭ1 case serves as a comparison base for the more complicated pϭp c situation. We find several regions in the probability density of the traveling times for the homogeneous case (pϭ1) and also for the critical case (pϭp c ) for both constant pressure and constant current conditions. For constant pressure, the first region I P corresponds to the short times before the flow breakthrough occurs, when the probability distribution is strictly zero. The second region II P corresponds to numerous fast flow lines reaching the extraction point, with the probability distribution reaching its maximum. The third region III P corresponds to intermediate times and is characterized by a power-law decay. The fourth region IV P corresponds to very long traveling times, and is characterized by a different power-law decaying tail. The power-law characterizing region IV P is related to the multifractal properties of flow in percolation, and an expression for its dependence on the system size L is presented. The constant current behavior is different from the constant pressure behavior, and can be related analytically to the constant pressure case. We present theoretical arguments for the values of the exponents characterizing each region and crossover times. Our results are summarized in two scaling assumptions for the traveling time probability density; one for constant pressure and one for constant current. We also present the production curve associated with the probability of traveling times, which is of interest to oil recovery.

The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet process and all groups share the same base distribution which itself is a drawn from a level one Dirichlet process. It has two concentration parameters with one at each level. The main results of the paper are the law of large numbers and large deviations for the hierarchical Dirichlet process and its mass when both concentration parameters converge to infinity. The large deviation rate functions are identified explicitly. The rate function for the hierarchical Dirichlet process consists of two terms corresponding to the relative entropies at each level. It is less than the rate function for the Dirichlet process, which reflects the fact that the number of clusters under the hierarchical Dirichlet process has a slower growth rate than under the Dirichlet process.

Simultaneous item auctions are simple and practical procedures for allocating items to bidders with potentially complex preferences. In a simultaneous auction, every bidder submits independent bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first-and second-price auctions when bidders have complement-free (a.k.a. subadditive) valuations. While it is known that the social welfare of every pure Nash equilibrium (NE) constitutes a constant fraction of the optimal social welfare, a pure NE rarely exists, and moreover, the full information assumption is often unrealistic. Therefore, quantifying the welfare loss in Bayesian Nash equilibria is of particular interest. Previous work established a logarithmic bound on the ratio between the social welfare of a BNE and the expected optimal social welfare in both first-price auctions (Hassidim et al. [11]) and second-price auctions (Bhawalkar and Roughgarden [2]), leaving a large gap between a constant and a logarithmic ratio. We introduce a new proof technique and use it to resolve both of these gaps in a unified way. Specifically, we show that the expected social welfare of any BNE is at least 1 /2 of the optimal social welfare in the case of first-price auctions, and at least 1 /4 in the case of second-price auctions.

Simultaneous item auctions are simple and practical procedures for allocating items to bidders with potentially complex preferences. In a simultaneous auction, every bidder submits independent bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first-and second-price auctions when bidders have complement-free (a.k.a. subadditive) valuations. While it is known that the social welfare of every pure Nash equilibrium (NE) constitutes a constant fraction of the optimal social welfare, a pure NE rarely exists, and moreover, the full information assumption is often unrealistic. Therefore, quantifying the welfare loss in Bayesian Nash equilibria is of particular interest. Previous work established a logarithmic bound on the ratio between the social welfare of a BNE and the expected optimal social welfare in both first-price auctions (Hassidim et al. [11]) and second-price auctions (Bhawalkar and Roughgarden [2]), leaving a large gap between a constant and a logarithmic ratio. We introduce a new proof technique and use it to resolve both of these gaps in a unified way. Specifically, we show that the expected social welfare of any BNE is at least 1 /2 of the optimal social welfare in the case of first-price auctions, and at least 1 /4 in the case of second-price auctions.

Quantization is performed of a Friedmann-Robertson-Walker universe filled with a conformally invariant scalar field and a perfect fluid with equation of state p = αρ. A continuous set of quantum wormholes is found for cosmic strings (α = −1/3), the latter states having throat radii of any size. Both for radiation (α = 1/3) and cosmic strings (α = −1/3) wave-packet solutions to the Wheeler-DeWitt equation are obtained with all the properties of evolving quantum wormholes. In the case of a radiation fluid, a detailed analysis of the quantum dynamics is made in the context of the Bohm-de Broglie interpretation. It is shown that a repulsive quantum force inversely proportional to the cube of the scale factor prevents singularities in the quantum domain.

This paper — the sixth in a programme of seventeen investigating the hypothesis that quantum vacuum energy gravitates locally — develops the connection between the elastic vacuum framework and inflationary cosmology.

Three results deferred from the companion paper (Paper 5, "The Elastic Vacuum") are delivered. First, the scalar field potential V(ψ) is derived from the elastic properties of spacetime rather than postulated: the Einstein–Hilbert action supplemented by its leading quantum correction (R²) yields, upon conformal transformation, the Starobinsky potential V(ψ) = V₀(1 − exp(−√(2/3) ψ/M_Pl))². This potential — currently the inflationary model most favored by Planck data — is identified as the leading-order nonlinear elastic potential of the vacuum within the R² truncation of the effective action: quadratic near equilibrium (Hooke's law), saturating at large deformation (the yield plateau). Inflation is reinterpreted as the elastic recoil of spacetime geometry from a state of extreme initial deformation.

Second, the flatness feedback parameter β > 0 is derived from the action in the quasi-static limit, completing the proof that spatial flatness is a stable late-time attractor of the elastic vacuum. The sign of β follows from the convexity of V(ψ) at its minimum — a structural result independent of specific parameter values.

Third, the paper argues on quantum-mechanical, thermodynamic, and structural grounds that the initial state of the universe cannot be exactly homogeneous. The Heisenberg uncertainty principle forbids any finite-energy field configuration from having zero spatial variance. Inflation need not create homogeneity from a homogeneous state; it creates approximate homogeneity from an inherently inhomogeneous initial state. A quantitative estimate shows that for total inflation lasting more than approximately 69 e-folds, even Planck-amplitude pre-inflationary perturbations are subdominant on CMB scales.

The paper also introduces a three-dimensional elastic analogy — injection of a substance into a transparent elastic medium — that resolves the principal limitations of the two-dimensional membrane model developed in Paper 5, and identifies the 10⁵⁵ mass hierarchy between the inflationary scalaron and the late-time screening field as the programme's most significant unsolved problem, distinguishing interpretive unification (achieved) from dynamical unification (not yet achieved).

The framework uses only general relativity with standard quantum corrections. The screening scalar field ψ is a new degree of freedom — acknowledged as such — but functions as a collective mode of the elastic vacuum rather than a new matter particle.

Recommended for submission to the Journal of Cosmology and Astroparticle Physics (JCAP).

Files: Connection_of_Vacuum_Energy_with_Inflation.pdf (compiled manuscript, 38 pages) Connection_of_Vacuum_Energy_with_Inflation.tex (LaTeX source) generate_figures.py (Python code for all figures) figures/ (directory containing PDF figures)

Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) General Relativity and Quantum Cosmology (gr-qc) High Energy Physics - Theory (hep-th)



Authors: Boris Kriger Affiliation 1: Information Physics Institute, Gosport, Hampshire, United Kingdom Affiliation 2: Institute of Integrative and Interdisciplinary Research, Toronto, Canada ORCID: 0009-0001-0034-2903

Resource type: Preprint

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Language: English

Keywords: vacuum energy, cosmic inflation, elastic vacuum, Starobinsky potential, primordial fluctuations, flatness problem, initial conditions, cosmological constant problem, R-squared gravity, dark energy, general relativity, quantum corrections to gravity

Related identifiers: Is part of the research programme: "What If the Vacuum Gravitates Locally?" (Paper 6 of 17) Is supplement to: "The Elastic Vacuum: A Sequestering Mechanism for Vacuum Energy and the Complete Dynamical History of Cosmic Expansion" (Paper 5)

We describe a measurement of the top quark mass from events produced in pp collisions at a center-of-mass energy of 1.96 TeV, using the Collider Detector at Fermilab. We identify t t candidates where both W bosons from the top quarks decay into leptons (eν, µν, or τ ν) from a data sample of 360 pb -1 . The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity, t t longitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass. For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parameterized to form continuous probability density functions. A likelihood fit incorporating these parameterized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of 170.1 ± 6.0 (stat.) ± 4.1 (syst.) GeV/c 2 .

We describe a measurement of the top quark mass from events produced in pp collisions at a center-of-mass energy of 1.96 TeV, using the Collider Detector at Fermilab. We identify t t candidates where both W bosons from the top quarks decay into leptons (eν, µν, or τ ν) from a data sample of 360 pb -1 . The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity, t t longitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass. For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parameterized to form continuous probability density functions. A likelihood fit incorporating these parameterized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of 170.1 ± 6.0 (stat.) ± 4.1 (syst.) GeV/c 2 .

The probabilities of finding a certain number of electrons enclosed in a given volume is calculated and discussed for a series of molecules. Two different methodologies to do the partition of the molecular space in separate volumes are investigated: the Atoms in the Molecules, AIM, topologic analysis of the density, and the topologic analysis of the Electron Localization Function (ELF). The formulas to calculate the probability distribution are reviewed and the way to implement them shortly explained. For a series of molecules, we present how the probability distribution complement the chemical information about the localization of the electrons in certain regions of the space. The calculations show that the probability of finding Z electrons in the AIM atomic basin associated to an atom of atomic number Z is, in general, low, even when the average number of electrons is close to Z. The probability distribution on the ELF basins associated to bonds yields new insight about the nature of the respective bond.

Recent studies of heavy ion fragmentation led to the conjecture that the hot and dense compound nuclei formed in the reaction do not decay into just any possible mass partition, but that some decay channels tend to be selected during breakup. We verify this conjecture by means of an extensive analysis of several distributions of decay probabilities. This simplifies the study of nuclear fragmentation tremendously.

We describe a measurement of the top quark mass from events produced in pp collisions at a center-of-mass energy of 1.96 TeV, using the Collider Detector at Fermilab. We identify t t candidates where both W bosons from the top quarks decay into leptons (eν, µν, or τ ν) from a data sample of 360 pb -1 . The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity, t t longitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass. For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parameterized to form continuous probability density functions. A likelihood fit incorporating these parameterized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of 170.1 ± 6.0 (stat.) ± 4.1 (syst.) GeV/c 2 .

The DELPHI experiment at LEP has measured the inclusive c harmless B hadron decay branching ratio, the B branching ratio into two c harmed particles, and the total number of charmed particles per B decay, using the hadronic Z data taken between 1992 and 1995. The results are extracted from a t to the b-tagging probability distribution based on the precise impact parameter measurements made using the microvertex detector. The inclusive c harmless B branching ratio, including B decays into hidden charm (c c), is measured to

A Γ₁-nonderanged permutation group, denoted by
for prime p
5, is defined as
= {
}  where each
is a permutation of the form
= (1) (1+i) mod p (1+2i) mod p ... (1+(p-1)i) mod p. This group has gained increasing attention due to its unique algebraic structure and its connection to non-deranged permutations. In this study, we investigate the undirected inverse graph representation of the Γ₁- nonderanged permutation group, denoted by inv(
). We show that the graph inv(
) is regular only when p = 5, and for every prime p
5, both the diameter and radius of the graph are equal to 2. We further establish that the maximum degree of the graph is p-3 for all primes p
5. Visual illustrations of the inverse graphs for selected prime values are presented, and a Python algorithm for generating inv(
) is provided.

In this paper we address the issue of assessing and communicating the joint probabilities implied by density forecasts from multivariate time series models. We focus our attention in three areas. First, we investigate a new method of producing fan charts that better communicates the uncertainty present in forecasts from multivariate time series models. Second, we suggest a new measure for assessing the plausibility of non-central point forecasts. And third, we describe how to use the density forecasts from a multivariate time series model to assess the probability of a set of future events occurring. An additional novelty of this paper is our use of a regime-switching DSGE model with an occasionally binding zero lower bound constraint, estimated on US data, to produce the density forecasts. The tools we offer will allow practitioners to better assess and communicate joint forecast probabilities, a criticism that has been leveled at central bank communications. JEL-Classification: C6...

In the paper we examine some properties of the generalized coherent states of the Barut-Girardello kind. These states are defined as eigenstates of a generalized lowering operator and they are strongly dependent on the structure constants. Besides the pure coherent states we focused our attention on the mixed states one, which are characterized by different probability distributions. As some examples we consider the thermal canonical distribution and the Poisson distribution functions. We calculate for these cases the Husimi's Q and quasi-probability P -distribution functions.

The present paper is an effort to explore potential utilities and possible physical implications of the mathematical machinery of fractional derivative and fractional integrals in electrical and electronics technologies, Starting with some of the common definitions, properties of fractional differintegrals, various applications of Fractional calculus in electrical and electronics technology are briefly reviewed in this paper. Applications like Fractional cross product and Fractional curl, Fractional calculus in Antenna Radiation Engineering, Electronic Circuit Analysis, Fractional calculus in Control engineering, Fractional Calculus in Electonic System designing are review and presented. 2010 Mathematics Subject Classification. 26A33.

The broad peaks seen in the power spectra of the mean field in a globally coupled map system indicate a subtle coherence between the elements, even in the "turbulent" phase. These peaks are investigated in detail with respect to the number of elements coupled, nonlinearity and global coupling strengths. We find that this roughly periodic behavior also appears in the probability distribution of the mapping, which is therefore not invariant. We also find that these peaks are determined by two distinct components: effective renormalization of the nonlinearity parameter in the local mappings, and the strength of the mean field interaction term. Finally, we demonstrate the influence of background noise on the peaks, which is quite counterintuitive, as they become sharper with increase in strength of the noise, up to a certain critical noise strength.

This study applies a first-order Markov chain modelling approach to Standardised Precipitation Index data derived from 2011 to 2021 annual rainfall data collected across the 37 wards in Mberengwa District, Zimbabwe, to assess its meteorological drought return period patterns. The study aims to estimate the meteorological drought return periods using the steady-state probabilities and calculate multiple-year drought probabilities and the expected duration of drought, providing a probabilistic understanding of drought dynamics to support effective drought risk management and climate adaptation planning in the district and other arid areas. The Standardised Precipitation Index values were classified into drought, normal and wet states based on their magnitudes. The transition probabilities were used to calculate the steady-state probabilities, which were used to estimate the return periods. The Markov Chain Property (Memoryless Property) and stationarity assumptions were validated using the autocorrelation graph and chi-square distribution, respectively. Each validation resulted positively supported the Markov chain assumptions, suggesting that the local authorities could rely on the model's predictions for planning and resource management. The findings indicated that drought conditions occur 23% of the time with a corresponding return period of approximately 4.35 years, normal conditions occur 59% of the time with a corresponding return period of approximately 1.69 years, and wet conditions occur 18% of the time with a corresponding return period of approximately 5.56 years. The probabilities of the multi-year droughts revealed a 24.7% chance of a drought lasting approximately 2 years, diminishing to 0.37% for five consecutive years. The expected length of drought was estimated to be 1.33 years, suggesting that while droughts are a concern, they often resolve relatively quickly. This study emphasises the need for local authorities to develop comprehensive emergency preparedness plans, invest in water conservation infrastructure and foster community engagement to enhance resilience against the impacts of climate variability.

This paper presents an analytical tool to evaluate the probability that a given annual erosion rate occurs during the short period of forest disturbance from fire or harvesting, as common in forest ecosystems. The paper provides an overview of the WEPP model and how it is applied to complex forest conditions. It then gives a review of hydrologic probability analysis methods and builds the case to support a non-parametric method. It describes a new WEPP interface which allows users to easily combine the erosion prediction strength of the WEPP model, the database of forest erodibility properties developed by our research unit, the stochastic features of the CLIGEN climate generator, and a non-parametric probability analysis of the results.

An expert elicitation approach has been developed to estimate probabilities for unsafe human actions (UAs) based on error-forcing contexts (EFCs) identified through the ATHEANA (A Technique for Human Event Analysis) search process. The expert elicitation approach integrates the knowledge of informed analysts to quantify UAs and treat uncertainty ('quantification-including-uncertainty'). The analysis focuses on (a) the probabilistic risk assessment (PRA) sequence EFCs for which the UAs are being assessed, (b) the knowledge and experience of analysts (who should include trainers, operations staff, and PRA/human reliability analysis experts), and (c) facilitated translation of information into probabilities useful for PRA purposes. Rather than simply asking the analysts their opinion about failure probabilities, the approach emphasizes asking the analysts what experience and information they have that is relevant to the probability of failure. The facilitator then leads the group in combining the different kinds of information into a consensus probability distribution. This paper describes the expert elicitation process, presents its technical basis, and discusses the controls that are exercised to use it appropriately. The paper also points out the strengths and weaknesses of the approach and how it can be improved. Specifically, it describes how generalized contextually anchored probabilities (GCAPs) can be developed to serve as reference points for estimates of the likelihood of UAs and their distributions.