Resulting Probability Distribution Research Articles

Cross-platform comparison of arbitrary quantum processes

In this work, we present a protocol for comparing the performance of arbitrary quantum processes executed on spatially or temporally disparate quantum platforms using Local Operations and Classical Communication (LOCC). The protocol involves sampling local unitary operators, which are then communicated to each platform via classical communication to construct quantum state preparation and measurement circuits. Subsequently, the local unitary operators are implemented on each platform, resulting in the generation of probability distributions of measurement outcomes. The max process fidelity is estimated from the probability distributions, which ultimately quantifies the relative performance of the quantum processes. Furthermore, we demonstrate that this protocol can be adapted for quantum process tomography. We apply the protocol to compare the performance of five quantum devices from IBM and the “Qianshi" quantum computer from Baidu via the cloud. The experimental results unveil two notable aspects: Firstly, the protocol adeptly compares the performance of the quantum processes implemented on different quantum computers. Secondly, the protocol scales, although still exponentially, much more favorably with the number of qubits, when compared to the full quantum process tomography. We view our work as a catalyst for collaborative efforts in cross-platform comparison of quantum computers.

High-Similarity-Pass Attention for Single Image Super-Resolution.

Recent developments in the field of non-local attention (NLA) have led to a renewed interest in self-similarity-based single image super-resolution (SISR). Researchers usually use the NLA to explore non-local self-similarity (NSS) in SISR and achieve satisfactory reconstruction results. However, a surprising phenomenon that the reconstruction performance of the standard NLA is similar to that of the NLA with randomly selected regions prompted us to revisit NLA. In this paper, we first analyzed the attention map of the standard NLA from different perspectives and discovered that the resulting probability distribution always has full support for every local feature, which implies a statistical waste of assigning values to irrelevant non-local features, especially for SISR which needs to model long-range dependence with a large number of redundant non-local features. Based on these findings, we introduced a concise yet effective soft thresholding operation to obtain high-similarity-pass attention (HSPA), which is beneficial for generating a more compact and interpretable distribution. Furthermore, we derived some key properties of the soft thresholding operation that enable training our HSPA in an end-to-end manner. The HSPA can be integrated into existing deep SISR models as an efficient general building block. In addition, to demonstrate the effectiveness of the HSPA, we constructed a deep high-similarity-pass attention network (HSPAN) by integrating a few HSPAs in a simple backbone. Extensive experimental results demonstrate that HSPAN outperforms state-of-the-art approaches on both quantitative and qualitative evaluations. Our code and a pre-trained model were uploaded to GitHub (https://github.com/laoyangui/HSPAN) for validation.

Stochastic modeling of porous sound absorbing materials using homogenization method and machine learning

This research introduces a novel approach to investigate porous sound absorbing materials using stochastic modeling techniques. The study employs the homogenization method and machine learning to predict the acoustic properties of porous materials. The homogenization method simplifies the analysis of microstructural properties in porous materials, while machine learning is a data analysis technique that utilizes algorithms to learn from data and make predictions. By integrating these methods, this study quantitatively assesses the impact of microscopic structural randomness on sound absorption properties. The study assumes that microstructural parameters are random variables and calculates the sound absorption coefficient through homogenization method. This dataset serves as input for machine learning. A Gaussian process regression model is developed using the dataset to evaluate the distribution of the sound absorption coefficient via the Gauss-Hermite quadrature method. The study implements Bayesian optimization, utilizing the variance of the resulting probability distribution as the acquisition function, to adaptively update the dataset. By iteratively performing these processes, the probability distribution of the sound absorption coefficient can be predicted efficiently and with high accuracy.

An Uncertainty Model for Strain Gages Using Monte Carlo Methodology.

For the purpose of validation and identification of mechanical systems, measurements are indispensable. However, they require knowledge of the inherent uncertainty to provide valid information. This paper describes a method on how to evaluate uncertainties in strain measurement using electric strain gages for practical engineering applications. Therefore, a basic model of the measurement is deduced that comprises the main influence factors and their uncertainties. This is performed using the example of a project dealing with strain measurement on the concrete surface of a large-span road bridge under static loading. Special attention is given to the statistical modeling of the inputs, the underlying physical relationship, and the incorporation and the impact of nonlinearities for different environmental conditions and strain levels. In this regard, also experiments were conducted to quantify the influence of misalignment of the gages. The methodological approach used is Monte Carlo simulation. A subsequent variance-based sensitivity analysis reveals the degree of nonlinearity in the relationship and the importance of the different factors to the resulting probability distribution. The developed scheme requires a minimum of expert knowledge of the analytical derivation of measurement uncertainties and can easily be modified for differing requirements and purposes.

Latent Growth Models for Count Outcomes: Specification, Evaluation, and Interpretation

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the Poisson or negative binomial distribution and their zero-inflated extensions to account for excess zero counts. This article demonstrates how to specify, evaluate, and interpret LGMs for count outcomes using the Mplus program in the structural equation modeling framework. The foundations of LGMs for count outcomes are discussed and illustrated using empirical count data on self-reported criminal offenses of adolescents (N = 1,664; age 15–18). Annotated syntax and output are presented for all model variants. A negative binomial LGM is shown to best fit the crime growth process, outperforming Poisson, zero-inflated, and hurdle LGMs.

Определение дозы воздействия (пример ионизирующих излучений)

Sanitary and hygienic assessments of working conditions according to the levels of harmful factors in the working environment require the determination of the exposure dose. As a rule, it is determined by indirect measurements - special calculation methods are needed based on the results of a series of successive measurements. The ability to apply regular, rigidly defined techniques is limited to permanent jobs with stably repetitive exposure. In general cases of nonpermanent workplaces with unstable exposure regimes, continuous measurements are required during the working day, which, as a rule, turns out to be unnecessarily difficult for practical reasons. The paper discusses a method for determining exposure doses for real conditions, when workers randomly move between different production sites, and sources of harmful factors turn on at random times and act with random intensity. It is proposed to consider the movements of workers as a sequence of Bernoulli tests with probabilistic exposure. It is found that the resulting probability distribution is given by the binomial law. In addition to average dose values, the probabilistic approach makes it possible to estimate measurement uncertainties of types A and B. The reliability of the results is checked by comparing the difference between the average value of the measurement results and the standard deviation. Measurement results can be trusted if the first is less than the second.

The growth and size of orogenic gold systems: probability and dynamical behaviour

Every nonlinear system grows by increments, and the final probability distributions for components of that system emerge from an amalgamation of these increments. The resulting probability distribution depends on the constraints imposed on each increment by the physical and chemical processes that produce the system. Hence there is the potential that the observed probability distribution can reveal information on these processes. Complex systems that grow by competition between the supply and consumption of energy and mass have growth laws that are cumulative probability distributions for their component parts that reflect such competition. We show that the type of probability distribution is characteristic of the endowment of orogenic gold deposits with the sequence: Weibull → Fréchet → gamma → log normal representative of increasing endowment. Further, the differential entropy of the probability distribution is indicative of the quality of the deposit, with low-quality deposits represented by high entropy and high-quality deposits represented by low or negative entropy. The type of probability distribution gives an indication of the processes that operated to produce the deposit. These conclusions hold for mineralisation as well as for the associated alteration assemblages. We suggest that the probability distribution for the mineralisation or the alteration assemblage gives a good indication of the endowment and quality of a deposit from a single drill hole. KEY POINTS A single drill hole from a deposit can provide information on endowment and organisation. Weibull → Fréchet → gamma → log normal probability distributions are representative of increasing gold endowment. The differential entropies of these distributions characterise the organisation of the system.

Required test durations for converged short-term wave and impact extreme value statistics–Part 2: Deck box dataset

In the assessment of wave-in-deck loads for new and existing maritime structures typically model tests are carried out. To determine the most critical conditions and measure sufficient impact loads, a range of sea states and various seeds (realisations) for each sea state are tested. Based on these measurements, probability distributions can be derived and design loads determined. In air gap model testing usually only few, if any, impact loads occur per 3-hour seed. This can make it challenging to derive reliable probability distributions of the measured loads, especially when only a few seeds are generated. In addition wave impact forces, such as greenwater loading, slamming, or air gap impacts are typically strongly non-linear, resulting in a large variability of the measured loads. This results in the following questions: How many impacts are needed to derive a reliable distribution? How is the repeatability of individual events affecting the overall distribution? To answer these questions wave-in-deck model tests were carried out in 100 x 3-hour realisations of a 10,000 year North Sea sea state. The resulting probability distributions of the undisturbed wave measurements as well as the measured wave-in-deck loads are presented in this paper with focus on deriving the number of seeds and exposure durations required for a reliable estimate of design loads.The presented study is Part 2 of a combined study on guidance for the convergence and variability of wave crests and impact loading extreme values. The data set of Part 1 ([1]) is based on greenwater loads on a sailing ferry and the data set of Part 2 on wave-in-deck loads on a stationary deck box.

Exact and stochastic methods for robustness analysis in the context of Imprecise Data Envelopment Analysis

We consider the problem of measuring the efficiency of decision-making units with a ratio-based model. In this perspective, we introduce a framework for robustness analysis that admits both interval and ordinal performances on inputs and outputs. The proposed methodology exploits the uncertainty related to the imprecise data and all feasible input/output weight vectors delimited through linear constraints. We offer methods for verifying the robustness of three types of outcomes: efficiency scores, efficiency preference relations, and efficiency ranks. On the one hand, we formulate mathematical programming models to compute the extreme, necessary, and possible results. On the other hand, we incorporate the stochastic analysis driven by the Monte Carlo simulations to derive the probability distribution of different outcomes. The framework is implemented in R and made available on open-source software. Its use is illustrated in two case studies concerning Chinese ports or industrial robots.

No need for a gold-standard test: on the mining of diagnostic test performance indices merely based on the distribution of the test value

BackgroundDiagnostic tests are important in clinical medicine. To determine the test performance indices — test sensitivity, specificity, likelihood ratio, predictive values, etc. — the test results should be compared against a gold-standard test. Herein, a technique is presented through which the aforementioned indices can be computed merely based on the shape of the probability distribution of the test results, presuming an educated guess.MethodsWe present the application of the technique to the probability distribution of hepatitis B surface antigen measured in a group of people in Shiraz, southern Iran. We assumed that the distribution had two latent subpopulations — one for those without the disease, and another for those with the disease. We used a nonlinear curve fitting technique to figure out the parameters of these two latent populations based on which we calculated the performance indices.ResultsThe model could explain > 99% of the variance observed. The results were in good agreement with those obtained from other studies.ConclusionWe concluded that if we have an appropriate educated guess about the distributions of test results in the population with and without the disease, we may harvest the test performance indices merely based on the probability distribution of the test value without need for a gold standard. The method is particularly suitable for conditions where there is no gold standard or the gold standard is not readily available.

Guided Colorization Using Mono-Color Image Pairs.

Compared to color images captured by conventional RGB cameras, monochrome (mono) images usually have higher signal-to-noise ratios (SNR) and richer textures due to the lack of color filter arrays in mono cameras. Therefore, using a mono-color stereo dual-camera system, we can integrate the lightness information of target monochrome images with the color information of guidance RGB images to accomplish image enhancement in a colorization manner. In this work, based on two assumptions, we introduce a novel probabilistic-concept guided colorization framework. First, adjacent contents with similar luminance are likely to have similar colors. By lightness matching, we can utilize colors of the matched pixels to estimate the target color value. Second, by matching multiple pixels from the guidance image, if more of these matched pixels have similar luminance values to the target one, we can estimate colors with more confidence. Based on the statistical distribution of multiple matching results, we retain the reliable color estimates as initial dense scribbles and then propagate them to the rest of the mono image. However, for a target pixel, the color information provided by its matching results is quite redundant. Hence, we introduce a patch sampling strategy to accelerate the colorization process. Based on the analysis of the posteriori probability distribution of the sampling results, we can use much fewer matches for color estimation and reliability assessment. To alleviate incorrect color propagation in the sparsely scribbled regions, we generate extra color seeds according to the existed scribbles to guide the propagation process. Experimental results show that, our algorithm can efficiently and effectively restore color images with higher SNR and richer details from the mono-color image pairs, and achieves good performance in solving the color bleeding problem.

Background Independence and Quantum Causal Structure

One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories. Additionally, a combination of the two theories is expected to yield non-classical, or "indefinite", causal structures. In this paper, we present a background-independent formulation of the process matrix formalism – a form of quantum mechanics that allows for indefinite causal structure – while retaining operationally well-defined measurement statistics. We do this by postulating an arbitrary probability distribution of measurement outcomes across discrete "chunks" of spacetime, which we think of as physical laboratories, and then requiring that this distribution be invariant under any permutation of laboratories. We find (a) that one still obtains nontrivial, indefinite causal structures with background independence, (b) that we lose the idea of local operations in distinct laboratories, but can recover it by encoding a reference frame into the physical states of our system, and (c) that permutation invariance imposes surprising symmetry constraints that, although formally similar to a superselection rule, cannot be interpreted as such.

Economic evaluation of digitally enabled aged and neurological rehabilitation care in the Activity and MObility UsiNg Technology (AMOUNT) trial

Objective To investigate the trial-based cost-effectiveness of the addition of a tailored digitally enabled exercise intervention to usual care shown to be clinically effective in improving mobility in the Activity and MObility UsiNg Technology (AMOUNT) rehabilitation trial compared to usual care alone. Design Economic evaluation alongside a pragmatic randomized controlled trial. Participants 300 people receiving inpatient aged and neurological rehabilitation were randomized to the intervention (n = 149) or usual care control group (n = 151). Main measures Incremental cost effectiveness ratios were calculated for the additional costs per additional person demonstrating a meaningful improvement in mobility (3-point in Short Physical Performance Battery) and quality-adjusted life years gained at 6 months (primary analysis). The joint probability distribution of costs and outcomes was examined using bootstrapping. Results The mean cost saving for the intervention group at 6 months was AU$2286 (95% Bootstrapped cost CI: −$11,190 to $6410) per participant; 68% and 67% of bootstraps showed the intervention to be dominant (i.e. more effective and cost saving) for mobility and quality-adjusted life years, respectively. The probability of the intervention being cost-effective considering a willingness to pay threshold of AU$50,000 per additional person with a meaningful improvement in mobility or quality-adjusted life year gained was 93% and 77%, respectively. Conclusions The AMOUNT intervention had a high probability of being cost-effective if decision makers are willing to pay AU$50,000 per meaningful improvement in mobility or per quality-adjusted life year gained, and a moderate probability of being cost-saving and effective considering both outcomes at 6 months post randomization.

A long-term alternative formula for a stochastic stock price model

This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in remote fields, where optimalizty of bet-hedging or diversification strategies is explained based on a measure different from expected value, like geometric mean. When the probability distribution of possible outcomes is significantly skewed, it is generally known that expected value leads to an erroneous picture owing to its sensitivity to outliers, extreme values of rare occurrence. Since geometric mean, or its counterpart median for the log-normal distribution, does not suffer from this drawback, it provides us with a more appropriate measure especially for evaluating long-term outcomes dominated by outliers. Thus, the present formula makes a more realistic prediction for long-term outcomes of a large volatility, for which the probability distribution becomes conspicuously heavy-tailed.

Exact time-dependent dynamics of discrete binary choice models

We provide a generic method to find full dynamical solutions to binary decision models with interactions. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking into account the choices of their peers. We illustrate our method by solving Kirman and Föllmer’s ant recruitment model for any number N of discrete agents and for any choice of parameters, recovering past results found in the limit N → ∞. We then solve extensions of the ant recruitment model for increasing asymmetry between the two choices. Finally, we provide an analytical time-dependent solution to the standard voter model and a semi-analytical solution to the vacillating voter model. Our results show that exact analytical time-dependent solutions can be achieved for discrete choice models without invoking that the number of agents N are continuous or that both choices are symmetric, and additionally show how to practically use the analytics for fast evaluation of the resulting probability distributions.

Derivation of a statistical model for classical systems obeying the fractional exclusion principle.

The violation of the Pauli principle has been surmised in several models of the fractional exclusion statistics and successfully applied to several quantum systems. In this paper, a classical alternative of the exclusion statistics is studied using the maximum entropy methods. The difference between the Bose-Einstein statistics and the Maxwell-Boltzmann statistics is understood in terms of a separable quantity, namely the degree of indistinguishability. Starting from the usual Maxwell-Boltzmann microstate counting formula, a special restriction related to the degree of indistinguishability is incorporated using Lagrange multipliers to derive the probability distribution function at equilibrium under NVE conditions. It is found that the resulting probability distribution function generates real positive values within the permissible range of parameters. For a dilute system, the probability distribution function is intermediate between the Fermi-Dirac and Bose-Einstein statistics and follows the exclusion principle. Properties of various variables of this novel statistical model are studied and possible application to classical thermodynamics is discussed.

Two concepts of noncontextuality in quantum mechanics

There are two different and logically independent concepts of noncontextuality in quantum mechanics. First, an ontological (hidden variable) model for quantum mechanics is called noncontextual if every ontic (hidden) state determines the probability of the outcomes of every measurement independently of what other measurements are simultaneously performed. Second, an ontological model is noncontextual if any two measurements which are represented by the same self-adjoint operator or, equivalently, which have the same probability distribution of outcomes in every quantum state also have the same probability distribution of outcomes in every ontic state. I will call the first concept simultaneous noncontextuality, the second measurement noncontextuality. In the paper I will overview and critically analyze some of the most significant accounts of contextuality in the literature and subsume them under these two categories.

Influence of spatially variable material properties on the resistance of masonry walls under compression

During their assessment, existing masonry structures often reveal a high variability of their material properties. Since this variability is also present within a single wall, the influence of this spatial variability of the material properties on the wall resistance is of major interest. First, experimental investigations on clay brick masonry walls with local weaknesses under compression loading are presented. The results of these experiments serve to validate a finite element model developed to study the influence of spatially variable material properties on the resistance of masonry walls under compression. The model follows the simplified micro-modelling approach and allows for a unit-to-unit variability of the compressive strength and the elastic modulus of masonry. The finite element model is then utilised within Monte Carlo simulations to investigate the resulting probability distribution of the wall resistance for given distributions of the material properties. Finally, parameter studies are conducted to examine the influence of the coefficient of variation of the material properties, the spatial correlation of the material properties, wall length, and wall slenderness on the resulting distribution of the resistance. The studies demonstrate that spatial variability leads to a decrease in the mean value of the wall resistance. However, the resulting variability of the resistance is much smaller than the input variability of the material properties. Considering the spatial nature of the variability can thus lead to higher design/assessment values of the wall resistance and, hence, a positive effect on structural reliability.

Maximum entropy and constraints in composite systems.

The principle of maximum entropy (PME), as expounded by Jaynes, is based on the maximization of the Boltzmann-Gibbs-Shannon (BGS) entropy subject to linear constraints. The resulting probability distributions are of canonical (exponential) form. However, the rationale for linear constraints is nebulous, and probability distributions are not always canonical. Here we show that the correct noncanonical distribution for a system in equilibrium with a finite heat bath is implied by the unconstrained maximization of the total BGS entropy of the system and bath together. This procedure is shown to be equivalent to maximizing the BGS entropy of the system alone subject to a contrived nonlinear constraint which reduces to (a) the usual linear constraint for an infinite heat bath, and (b) a previously enigmatic logarithmic constraint which implies a power-law distribution for a large but finite heat bath. This procedure eliminates the uncertainty as to the proper constraints, and easily generalizes to arbitrary composite systems, for which it provides a simpler alternative to the Jaynes PME.

High frame rate multi-perspective cardiac ultrasound imaging using phased array probes

Ultrasound (US) imaging is used to assess cardiac disease by assessing the geometry and function of the heart utilizing its high spatial and temporal resolution. However, because of physical constraints, drawbacks of US include limited field-of-view, refraction, resolution and contrast anisotropy. These issues cannot be resolved when using a single probe. Here, an interleaved multi-perspective 2-D US imaging system was introduced, aiming at improved imaging of the left ventricle (LV) of the heart by acquiring US data from two separate phased array probes simultaneously at a high frame rate.In an ex-vivo experiment of a beating porcine heart, parasternal long-axis and apical views of the left ventricle were acquired using two phased array probes. Interleaved multi-probe US data were acquired at a frame rate of 170 frames per second (FPS) using diverging wave imaging under 11 angles. Image registration and fusion algorithms were developed to align and fuse the US images from two different probes. First- and second-order speckle statistics were computed to characterize the resulting probability distribution function and point spread function of the multi-probe image data.First-order speckle analysis showed less overlap of the histograms (reduction of 34.4%) and higher contrast-to-noise ratio (CNR, increase of 27.3%) between endocardium and myocardium in the fused images. Autocorrelation results showed an improved and more isotropic resolution for the multi-perspective images (single-perspective: 0.59 mm × 0.21 mm, multi-perspective: 0.35 mm × 0.18 mm). Moreover, mean gradient (MG) (increase of 74.4%) and entropy (increase of 23.1%) results indicated that image details of the myocardial tissue can be better observed after fusion.To conclude, interleaved multi-perspective high frame rate US imaging was developed and demonstrated in an ex-vivo experimental setup, revealing enlarged field-of-view, and improved image contrast and resolution of cardiac images.