South Italy is characterised by a semi-arid climate with scarce rain and high evaporative demand, therefore the need to optimise water resources in this area is crucial, and climate change could worsen this condition. In citrus cultivation, which is one of the most important crops bred in Southern Italy, and more generally in Mediterranean regions, deficit irrigation strategies are im-plemented in order to cope with limited resource availability. On this basis, knowledge on how the territorial distribution of citrus would change in relation to these strategies constitutes valuable information for the stakeholders. Therefore, the objective of this study was to determine the prob-ability of presence of citrus in Sicily at changing of the percentage of water deficit application, in order to analyse change in the surface area and localisation of the crop. The methodology was based on the application of Species Distribution Models and Geographic Information Systems to the case study of the Province of Syracuse in Sicily. Different geostatistical and machine learning models were applied, based on 3-decades bioclimatic variables, DTM and irrigation; assessment of the outcomes was carried by using classification evaluation metrics. The analysis of the outcomes showed that uncorrelated predictor layers mainly included water input that affected most the probability of presence. Moreover, GIS analyses showed that deficit irrigation strategies would generate an overall reduction of cultivation surfaces in the territory and a decrease of citrus pres-ence in southern areas of the considered territory, where climate conditions are less favourable in terms of temperature and precipitations, thus providing useful information for decision support tools in agriculture and land use policy.

Maxwell's electric equation and Schrödinger quantum equation are used to find useful expressions for the probability of electrons existence and the electrons transport. The first expression which uses special relatively also shows that the probability of the electrons existence is higher for lower energy states compared to higher energy states where the probability is low. This means that electrons transport takes place from higher energy states to lower states. This conforms to the laws of chemistry where the atom tends to be stable by forcing electrons to occupy lower energy states. The second expression used the momentum velocity relation instead of special relatively. This expression shows also electrons transport from higher to lower states. It also shows that the probability of the electrons existence is higher for lower electrons density regions and lower for higher electrons density regions. This means that the electrons transport is from higher density regions to lower density regions. This conforms to the diffusion law.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

Finding a good MIMO system model also major issue in Wireless Communication system. It is facing with so many problem, one of the major problem is finding good system model in terms of capacity and transmitting antenna system. In this paper, we analyze the channel capacity of various MIMO system model with some constant SNR level and outage probability. We establish a novel idea for MIMO system models as consider as 2^N- MIMO system model and find-out change in channel capacity when different transmitting antennas with constant SNR and outage probability. The channel capacity ratio CC_R is presented here on the basis of 2^N- MIMO channel capacity model. Number of transmitted antenna presented in MIMO system is increases is well-known however paper shows change in capacity in simple form.

Background and Objectives: Pulmonary Hypertension (PH) is a clinical condition with high mortality rates, particularly in patients over 65. Current guidelines recommend assessing the Probability of Pulmonary Hypertension (PHP) using advanced echocardiography, before pro-ceeding to right heart catheterization. This study proposes using the common femoral vein (CFV), an accessible vein that reflects right atrial pressure, as an alternative method to assess the like-lihood of severe PHP. Materials and Methods: This prospective observational study included 175 emergency patients from three hospitals. Ultrasound assessed the Pulsed Wave Doppler (PW-Doppler) morphology of the CFV. This diagnostic yield for high PHP was evaluated along-side traditional ultrasound parameters (right-to-left ventricular basal diameter ratio greater than 1 (RV>LV), septal flattening, right ventricular outflow acceleration time of less than 105 ms and/or mesosystolic notching, pulmonary artery diameter greater than the aortic root diameter or over 25 mm, early pulmonary regurgitation maximum velocity >2.2 m/s, TAPSE/PASP less than 0.55, in-ferior vena cava (IVC) diameter over 21 mm with decreased inspiratory collapse, and right atrial (RA) area over 18 cm²). Results: The CFV's PW-Doppler cardiac pattern correlated strongly with high PHP, showing a sensitivity (Sn) of 72% and a specificity (Sp) of 96%. RA dilation and TAPSE/PASP < 0.55 also played significant diagnostic roles. Conclusions: The CFV's PW-Doppler cardiac pattern is an effective indicator of high PHP, allowing reliable exclusion of this condition when absent. This approach could simplify initial PHP evaluation in emergency settings or where echocardiographic resources are limited.

Due to the intermittency and fluctuation of photovoltaic (PV) output power, a high proportion of grid-connected PV power generation systems has a significant impact on power systems. Accurate PV power forecasting can alleviate the uncertainty of the PV power and is of great significance for the stable operation and scheduling of the power systems. Therefore, in this study, a feature rise-dimensional (FRD) two-layer ensemble learning (TLEL) model for short-term PV power deterministic forecasting and probability forecasting is proposed. First， based on the eXtreme Gradient Boosting (XGBoost), Random Forest (RF), CatBoost, and Long-short-term memory (LSTM) models, a TLEL model is constructed utilizing the ensemble learning algorithm. Meanwhile, the FRD method is introduced to construct the FRD-XGBoost-LSTM (R-XGBL), FRD-RF-LSTM(R-RFL), and FRD- CatBoost - LSTM (R-CatBL) models. Subsequently, the above models are combined to construct the FRD-TLEL model for deterministic forecasting, and perform probability interval forecasting based on quantile regression(QR). Finally, the performance of the proposed model is demonstrated with a real-world dataset. By comparing with other models, the proposed model displays better forecasting accuracy for deterministic forecasting and reliable forecasting intervals for probability forecasting, and good generalization ability in the datasets of different seasons and weather types.

The probability distribution of the interevent time between two successive earthquakes has been subject of numerous studies due to its key role in seismic hazard assessment. In recent decades, many distributions have been considered and there has been a long debate about the possible universality of the shape of this distribution when the interevent times are suitably rescaled. In this work we aim to find out if there is a link between the different phases of a seismic cycle and the variations in the distribution that best fits the interevent times. To do this, we consider the seismic activity related to the Mw 6.1 L’Aquila earthquake that occurred on April 6, 2009 in central Italy by analyzing the sequence of events recorded from April 2005 to July 2009, and then the seismic activity linked to the sequence of the Amatrice-Norcia earthquakes of Mw 6 and 6.5 respectively and recorded in the period from January 2009 to June 2018. We take into account some of the most studied distributions in the literature: q-exponential, q-generalized gamma, gamma and exponential distributions and, according to the Bayesian paradigm, we compare the value of their posterior marginal likelihood in shifting time windows with a fixed number of data. The results suggest that the distribution providing the best performance changes over time and its variations may be associated with different phases of the seismic crisis.

The entry and exit method is a simple and practical method to determine the critical slip surface of slope. However, it has the drawback of sacrificing computational efficiency to improve search accuracy. To solve this problem, this paper proposes an improved entry and exit method to search for the critical slip surface. Based on the random fields generated by using Karhunen–Loève expansion method, the simplified Bishop’s method combined with the improved entry and exit method is used to determine the critical slip surface and its corresponding minimum factor of safety. Then, the failure probability is calculated by conducting Monte Carlo simulation. Two examples are reanalyzed to verify the accuracy and efficiency of the proposed method. Meaningful comparisons are made to demonstrate the calculating accuracy and calculating efficiency of the improved entry and exit method in searching for the minimum safety factor of slope, based on which the effect of the reduced searching range on slope reliability was explored. The results indicate that the proposed method provides a practical tool for evaluating the reliability of slopes in spatially variable soils. It can greatly improve the computational efficiency in relatively high-computational accuracy of slope reliability analysis.

White noise is fundamentally linked to many processes, it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise.

Estimating the parameters of statistical distributions generally involves solving a system of nonlinear equations or a nonlinear equation, being a technical difficulty in their usual application in hydrology. This article presents improved approximations and, in some cases, new approximations for the estimation with the method of ordinary moments and the method of linear moments, which are useful for the direct calculation of the parameters, because the errors in the approximate estimation are similar to the use of iterative numerical methods. Thirteen statistical distributions of two and three parameters frequently used in hydrology are presented, for which parameter estimation was laborious. Thus, the approximate estimation of the parameters by the two methods is simple but also precise and easily applicable by hydrology researchers. The approximate forms characterized by very small errors are the result of the research conducted within the Faculty of Hydrotechnics to update the romanian normative standards in the hydrotechnical field.

While the foundations of climate science and ethics are well established, fine-grained climate predictions, as well as policy-decisions, are beset with uncertainties. This chapter maps climate uncertainties and classifies them as to their ground, extent and location. A typology of uncertainty is presented, centered along the axes of scientific and moral uncertainty. This typology is illustrated with paradigmatic examples of uncertainty in climate science, climate ethics and climate economics. Subsequently, the chapter discusses the IPCC’s preferred way of representing uncertainties and evaluates its strengths and weaknesses from a risk management perspective. Three general strategies for decision-makers to cope with climate uncertainty are outlined, the usefulness of which largely depends on whether or not decision-makers find themselves in a context of deep uncertainty. The chapter concludes by offering two recommendations to ease the work of policymakers, faced with the various uncertainties engrained in climate discourse.

Identifying the SARS-CoV-2 virus has been a unique challenge for the scientific community. In this paper, we discuss a practical solution to help guide clinicians with interpretation of the probability that a positive, or negative, COVID-19 test result indicates an infected person, based on their clinical estimate of pre-test probability of infection.The authors conducted a small survey on LinkedIn to confirm that hypothesis that that the clinical pre-test probability of COVID-19 increases relative to local prevalence of disease plus patient age, known contact, and severity of symptoms. We examined results of PPA (Positive Percent Agreement, sensitivity) and NPA (Negative Percent Agreement, specificity) from 73 individual laboratory experiments for molecular tests for SARS-CoV-2 as reported to the FIND database ¹, and for selected methods in FDA EUA submissions^2,3. Authors calculated likelihood ratios to convert pre-test to post-test probability of disease and designed an online calculator to create graphics and text to report results. Despite best efforts, false positive and false negative Covid-19 test results are unavoidable^4,5. A positive or negative test result from one laboratory has a different probability for the presence of disease than the same result from another laboratory. Likelihood ratios and confidence intervals can convert the physician or other healthcare professional’s clinical estimate of pre-test probability to post-test probability of disease. Ranges of probabilities differ depending on proven method PPA and NPA in each laboratory. We recommend that laboratories verify PPA and NPA and utilize a the “Clinician’s Probability Calculator” to verify acceptable test performance and create reports to help guide clinicians with estimation of post-test probability of COVID-19.

The novel COVID-19 disease is a contagious acute respiratory infectious disease whose causative agent has been demonstrated to be a new virus of the coronavirus family, SARS- CoV-2. Multiple studies have already reported that risk factors for severe disease include older age and the presence of at least one of several underlying health conditions. However, a recent physiopathological report and the French COVID-19 scientific council have postulated a protective effect of tobacco smoking. Thanks to a meta-analysis, we have been able to demonstrate the statistical significance in this regard of twelve series from China, France and in the US, reporting three different smoking status (current smoker,former smoker, with a smoking history) as well as disease severity (with respectively odds-ratio of 1.78 [1.08-3.10], 4.60 [3.13-7.17], 2.74 [0.63-5.89]). Subsequently and using a Bayesian approach we have established that past, and present smoking is associated with more severe COVID-19 outcomes. Finally, we refute claims linking general population smoking status (N=O(10^8) or O(10^9)) to much smaller disease course series (N=O(10^4)). The latter point in particular is presented to stimulate academic discussion, and must be further investigated by well-designed studies.

Precipitation during a specific return period plays an important role in the design of hydraulic infrastructure. The traditional approach involves collecting annual maximum precipitation data from a station, then subjecting it to statistical probability distributions (PDFs), and finally selecting the one with the lowest value in a goodness-of-fit test (e.g., Kolmogorov-Smirnov). Nevertheless, this methodology assumes current data, leaving uncertainty regarding its suitability for outdated data. The aim of this study is to compare the probability density functions (e.g., Normal, Log Normal, Pearson III) with the machine learning algorithm known as Random Forest (RF) for calculating precipitation at different return periods, using the province of Arequipa in Peru as the study area, through 5 stations located in different parts of the province. This comparison was conducted using the RMSE metric in both methods to evaluate their performance, resulting in RF having a lower RMSE than PDFs in most cases in calculating precipitation for return periods of 2, 5, 10, 20, 50 and 100 years for the studied stations.

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.

In the presented work, on the example of thin-walled specimens made by selective laser melting technology from AlSi10Mg subjected to preliminary heat treatment, it is shown that there is a critical point of transition from the elastic-plastic region of the engineering stress-strain diagram to the yield and fracture stresses. It was found that the critical point has a strong statistically significant correlation (0.83 by Spearman and 0.93 by Pearson) with the strain hardening coeffi-cient calculated in the section from yield strength to fracture strength. A regression equation linking the critical transition point to the strain hardening coefficient was obtained. It is shown that with increasing plasticity of thin-walled samples obtained by selective laser melting of AlSi10Mg leads to a change in the type of stress distribution in the elastic-plastic region (the Weibull distribution changes to a normal distribution) and the contribution of the probability density of stress distribution described by the Cauchy distribution with a mode near the fracture stress to the full probability density of fracture increases.

Maximal quantum correlations of unity do not violate the CSHS-Bell inequalities because the remaining two correlations vanish. The probability of coincident detections should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed. © The Author 2023

By using the Black-Derman-Toy (BDT) model, we predict the future trend of the riskless rate, and then we build an equation that relates the market price of zero-coupon bonds and the theoretical price of zero-coupon bonds calculated using a binomial option pricing model. Based on this, we can find the implied daily return μ, implied natural upturn probability p, and implied daily volatility σ with respect to different time-to-maturity values of zero-coupon bonds. With these results, we can give some suggestions to bond traders.

This paper shows that by applying the Nyquist-Shannon sampling theorem, the spatial and temporal resolution of a simulation can be no more than half the resolution of the simulating reality. This has significant implications for not only the values of the observables in the simulation but also its physical laws. This progressive halving of nested simulations coupled with the minimum resolution compatible with the production of a simulation also sets a limit to the nestedness of a lineage of simulations (it is by no means infinite). The limit of nestedness is then used to calculate the probability that we are living in a simulation assuming a single base reality. This will be shown to be significantly lower than popular expectation. A Kardashev-like scale, with three variants, is also developed to gauge the technological advancement of a civilization in relation to the extent to which it can extract information from space and time.

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. Assuming the queue used in system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in buffer can be preempted by fresher packet with probability η. Instead of considering system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real time changes of the AoI, the age of packet in server, and the age of packet waiting in buffer. We give the explicit expression of system’s average AoI, and show that the average AoI of system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of AoI of system having Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between average discrete AoI with Ber/Geo/1/c queue and the average continuous AoI with M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between average AoI and the packet preemption probability η, as well as AoI’s distribution curves in two extreme cases are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of wireless sensor network, where the packet in buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper we give much more explanations showing that how the results about continuous AoI is derived by analyzing the corresponding discrete time system, and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose our idea to analyze system’s AoI when the service time distribution is relaxed to be arbitrary.

In this article we explore the limiting behavior of the universal prior distribution obtained when applied over multiple meta-level hierarchy of programs and output data of a computational automata model. We were motivated to alleviate the effect of Solomonoff's assumption that all computable functions or hypotheses of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case, the set of all possible program strings of a fixed-length converges to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in digital physics and the constructor theory of life.

The basic principles of geological risk calculation through Probability of Success (PoS) are mostly applied for numerical estimation of additional hydrocarbon existence in proven reservoirs or potential hydrocarbon discoveries in selected geological regional subsurface volume. It can be tailored and validated for a comprehensive input dataset collected in the selected petroleum province, adapted by dividing up geological events into several probability categories and classes. The most applied categories are (existence of) reservoir rocks, traps and isolators, source rocks, migration pathways and preservation conditions for hydrocarbons The methodology results in unique probability values as multiplication of independent statistical events, which can also be applied in the assessment of a potential hydrocarbon discovery of desired minimal volume and its value in any virtual currency like risk-neutral dollars. Such methodology has been extensively developed in the last decades in the Croatian subsurface, mostly in the Croatian part of the Pannonian Basin System (CPBS). Through the adaptation of geological categories, it was also applied in hybrid, i.e., stochastical, models developed in the CPBS (Drava Depression). Stochastically estimation of porosity was already applied. As the robustness of this methodology is very high, it was also modified to estimate the influence of water-flooding in increasing oil recovery in some proven Neogene sandstone reservoirs in the CPBS (Sava Depression). This new modification is being presented to be applied to geological risk calculation, intending to assess the safety of geological environment in deep wells, where depleted radioactive fuel would be disposed, a subject of great importance. The case study encompassed the magmatic and metamorphic rocks in the pre-Neogene basement of the CPBS. For disposal purpose, these are regionally lithologies considered as to be the safest ones considering petrophysical values, water saturation, recent weathering and tectonic activity.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

In the fifth generation communication system, millimeter wave (mmWave) networks will coexist with traditional micro wave (μWave) networks, which allows for higher data transmission rate and better user experience. In this paper, we give a comprehensive framework of mathematical models and analytical methods for multi-tier mmWave and μWave hybrid caching networks based on stochastic geometry. We propose an association strategy by assuming average biased-received power association and Rayleigh fading. Accordingly, by using a D-ball approximating blockage model of mmWave networks, expressions of the cell association probability and the coverage probability of the hybrid networks are derived. Also, we use the average successful delivery probability as the performance metric to analyze the existing caching placement strategies. Simulation results validate the accuracy of our analytical conclusions.

A review of literature, supporting the view on the psychophysical origins of some acceptance effects of cyber-physical systems (CPSs), is presented and discussed in the paper. Psychological effects like the reactance to a robot or the uncanny valley phenomenon suggest that CPSs are perceived as a special type of ‘being’, a phylogenetically emergent category, or a novel ontology in a philosophical sense, culturally developing as a function of the social brain. Justification of this view is provided by the psychophysically-relevant human responses to technologically and socially ambiguous stimuli on the one hand, and the probabilistic independence of the proposed ontology to similar ontologies, subjectively experienced by the human, on the other. The results of the presented in the paper analysis demonstrate the feasibility of the proposed hypothesis of ontological ‘near independence’ of the distribution of the probabilistic psychophysical processes in response to the cyber-physical stimulus as a socially evolving phenomenon.

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

An area has been designated for demonstrating the utility of marine hydrokinetic turbines in Minas Passage, Bay of Fundy. Marine renewable energy may be useful for the transition from carbon-based energy sources but there is concern for the safety of fish that might encounter turbines. Acoustic receivers that detect signals from acoustically tagged fish that pass through the tidal demonstration area and detection efficiency of tag signals might be used to estimate the likelihood of fish encountering marine hydrokinetic turbines. The method requires that tagged fish passing through the development area will be reliably detected by a receiver array. The present research tests the reliability with which passing tags are detected by suspending tags beneath GPS-tracked drifters. Drifters carrying high residency Innovasea tags that transmitted every 2 seconds were usually detected by the receiver array even in fast currents during spring tides but pulse position modulation tags were inadequate. Sometimes very few high residency tag signals were detected when fast tidal currents swept a drifter through the receiver array, so increasing the transmission interval degrades performance at the tidal energy development area. High residency tags suspended close to the sea surface were slightly less likely to be detected if they passed by during calm conditions. Previously measured detection efficiencies were found to slightly overestimate the chances of a high residency tag carried by a drifter being detected as it passed by a receiver. This works elucidates the effectiveness with which acoustically tagged fish are detected in fast, highly turbulent tidal currents and informs the application of detection efficiency measurements to calculate the probability that fish encounter a marine hydrokinetic turbine.

The oil and gas sector has recognised structural integrity assessment of ageing platform for prospective life extension as a rising concern, particularly in encountering the randomness of the harsh ocean environments. This condition leads to uncertainty in wave-in-deck load estimates and a high load level being imposed on offshore structures. This emphasises the necessity of enhanced reliability, as failure might result in inaccessibility because of the uncertainties related to long-distance services, such as accuracy of predictions of loads and responses. Even though the established guidelines present a fundamental assessment, additionally, comprehensive rules are required. This paper performed a reliability analysis incorporating practical approaches that can more accurately represent time-dependent structural deterioration. The following two procedures have been adopted by a majority of significant oil and gas operators to monitor the safety and integrity of these structures: a) Ultimate Strength Assessment (USA) method and b) Reliability Design Assessment (ReDA) method. A comparison of these two reliability approaches was performed on selected ageing jacket structures in the region of the Malaysian sea. The comparative findings, namely, reserve strength ratio (RSR) at various years of the return period (RP) and ratio value for risk of failure regarding the probability of failure (POF), provided a check and balance in strengthening confidence in the results. The findings showed that the structural components might safely survive either using the USA and ReDA method in such conditions, as the reliability indexes were determined to be satisfactory compared to allowable values from ISO 19902 design specifications. Therefore, these evaluations were determined to control the risk level of the structure during the remaining of its lifetime and undertake cost-effective inspections or mitigation strategies when necessary.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of the modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions, but must be computed numerically by means of Monte Carlo. This paper provides the first results about Monte Carlo-based critical value inserted to different scenarios of correlation between the outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, overidentifications and statistical overlap associated with IDS in the presence of a single outlier. Based on such probability levels we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for the case where IDS is in play. MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances that the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection, but the lower the rates of outlier identification. For that case, the larger the Type I Error, the larger the ratio between MIB and MDB. We also highlight that an outlier becomes identifiable when the contribution of the measures to the wrong exclusion rate decline simultaneously. In that case, we verify that the effect of the correlation between the outlier statistics on the wrong exclusion rates becomes insignificant from a certain outlier magnitude, which increases the probability of identification.

A multi-server parallel system dispatches the incoming job, which contains kn tasks into n servers. A job is considered to be computed if all the tasks associated with the job are processed. One job’s tasks can be encoded into at least kn “replicas” such that the job is considered to be served if any kn replicas finishing computation. In this paper, we analyze the random scheduling policy of a multi-server computing system under discrete time model in terms of Quality of Exponent (QoE), which is defined as the probability exponent that a typical job can be computed within a given number of time slots. We let kn/n be a constant. Assuming that any task of any job can be randomly dispatched by a “scheduler” to any server, and computing each task takes exactly one time slot. We divide the calculation of probability exponent into two parts, exponent of numerator and exponent of denominator. For the denominator, we give the almost exact exponent using Lagrange multiplier method, while for the numerator, an upper bound of the numerator’s exponent is provided. In addition, we also express the exponent in terms of information theoretical quantities and reconsider both of exponents in the context of large deviation theory.

Estimates of extreme water level return periods in river systems are crucial for hydraulic engineering design and planning. Recorded historical water level data of Taiwan’s rivers are not long enough for traditional frequency analyses when predicting extreme water levels for different return periods. In this study, the integration of a one-dimensional flash flood routing hydrodynamic model with the Monte Carlo simulation was developed to predict extreme water levels in the Danshuei River system of northern Taiwan. The numerical model was calibrated and verified with observed water levels using four typhoon events. The results indicated a reasonable agreement between the model simulation and observation data. Seven parameters, including the astronomical tide and surge height at the mouth of the Danshuei River and the river discharge at five gauge stations, were adopted to calculate the joint probability and generate stochastic scenarios via the Monte Carlo simulation. The validated hydrodynamic model driven by the stochastic scenarios was then used to simulate extreme water levels for further frequency analysis. The design water level was estimated using different probability distributions in the frequency analysis at five stations. The design high-water levels for a 200-year return period at Guandu Bridge, Taipei Bridge, Hsin-Hai Bridge, Da-Zhi Bridge, and Chung-Cheng Bridge were 2.90 m, 5.13 m, 6.38 m, 6.05 m, and 9.94 m, respectively. The estimated design water levels plus the freeboard are proposed and recommended for further engineering design and planning.

Supervised land-use/land-cover (LULC) classifications are typically conducted using class assignment rules derived from a set of multiclass training samples. Consequently, classification accuracy varies with the training data set and is thus associated with uncertainty. In this study, we propose a bootstrap resampling and reclassification approach that can be applied for assessing not only the uncertainty in classification results of the bootstrap-training data sets, but also the classification uncertainty of individual pixels in the study area. Two measures of pixel-specific classification uncertainty, namely the maximum class probability and Shannon entropy, were derived from the class probability vector of individual pixels and used for the identification of unclassified pixels. Unclassified pixels that are identified using the traditional chi-square threshold technique represent outliers of individual LULC classes, but they are not necessarily associated with higher classification uncertainty. By contrast, unclassified pixels identified using the equal-likelihood technique are associated with higher classification uncertainty and they mostly occur on or near the borders of different land-cover.

A novel approach for designing acceptance sampling plans is presented. It is based on the Bayesian conformity assessment framework from JCGM 106. In particular, the concept of conformance probability plays a central role in the new approach. The new approach takes into account both the producer's and the consumer's perspective by allowing each to have their own prior. In parallel, the JCGM 106 framework allows the definition of Bayesian consumer's and producer's risks which complement the "classical" risks defined in the ISO 2859 and ISO 3951 series. The new approach also casts a new light on the plans from the ISO standards.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U-procedure verses the R-procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of (c+id). All the sample phases forms a group G_R. Taking G_R as the sampling potential, combined with the dynamic phase group G_U，we establish a unified model of U-procedure and R-procedure for the evolution of wavefunction. Based on the Born rule, the probability of a sample is given by the squared magnitude of （c+id）. Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike. The measurement problem widely exists in dynamic analysis, higher cognition, and large data modeling. Thus, the work reported here has a wide range of applications. Keywords: The measurement problem; U-R procedures; the Yes/No type measurement; stochastic sampling; sample phase; Born probability.

Information geometry (IG) is a fascinating combination of differential geometry and statistics where a Riemannian manifold's structure is applied to a statistical model. It may find numerous fascinating uses in the domains of theoretical neurology, machine learning, complexity, and (quantum) information theory, among others. (IG) aims to provide a differential-geometric perspective on statistical geodesic models' structure. In this case, IG, KD, and J-divergence (JD) are used to define the manifold of the Generalised Brownian Motion (GBM). Consequently, the geodesic equations (GEs) are devised, and GB information matrix exponential (IME) is presented. Moreover, for first time ever, the necessary and sufficient mathematical requirement that characterizes the developability of Generalized Brownian Motion(GBM) manifold is devised. Also, a novel sufficient and necessary conditions which characterizes the regions where the surface describing GBM is minimal is determined. Also, it is shown that GBM has a non-zero 0-Gaussian and Ricci curvatures. Consequently, this advances the establishment of a unified GBM- Relativistic Info-Geometric based analysis.

The article continues the author's publications about the matrix-tensor study of universal rules of stochastic (probabilistic) organization of long single-stranded DNA sequences in eukaryotic and prokaryotic genomes. The author reveals that corresponding matrices of probabilities of n-plets in n-textual representations of each genomic DNA are numerically interrelated each with other in such algebraic form, which has analogies with formalisms of the known tensor-matrix theory of digital antenna arrays. These arrays combine many separate antennas into a single coordinated ensemble with unique emergent properties, due to which antenna arrays are widely used in devices of medicine, astrophysics, avionics, etc. The noted analogies allow putting forward the author's hypothesis that the stochastic organization of genomic DNAs is connected with bio-antenna arrays. From the point of view of this hypothesis, many known facts about using principles of antenna arrays in inherited physiological phenomena are collected in a single grouping with genomic DNAs. This new topic about the biological meaning of profitable properties of antenna arrays includes problems of biological evolution, the origin of the genetic code, regenerative medicine, and the development of algebraic biology. These issues are discussed jointly with the author's results of quantum information analysis of stochastic features of genomic DNAs.

This paper proposes a cognitive radio engine platform for making exploitation of available frequency channels usable for a tactical wireless sensor network in presence of incumbent communication devices known as the primary user (PU) required to be protected from undesired harmful interference. In the field of tactical communication networks, it is desperate to find available frequencies for opportunistic and dynamic access to channels in which PU is in active. This paper introduces a cognitive engine plaform for determining available channels on the basis of case-based reasoning technique deployable as core functionality on cognitive radio engine to enable dynamic spectrum access (DSA) with high fidelity. Towards this, this paper introduces a plausible learning engine to characterize channel usage pattern to extract best channel candiates for the tactical cognitive radio node (TCRN). Performance of the proposed cognitive engine is verified by conducting simulation tests which confirm the reliability in functional aspect of the proposed cognitive engine covering the learning engine as well as the case-based reasoning engine with showing how well TCRN can avoid the collision against the PU operation considered as the etiquette secondary user (SU) should have.

In the paper, we prove a joint limit theorem in terms of weak convergence of probability measures on $\mathbb{C}^2$ defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and parameter α are required. The theorem obtained extends and generalizes Bohr-Jessen’s results characterising asymptotic behaviour of the Riemann zeta-function.

Among the possible improvements of Autonomous Emergency Braking (AEB) systems, reducing the intensity of the automatic braking process by studying the kinematics and general behavior of the pedestrian while crossing is crucial to determine the progressiveness of the braking, or replacing part of the braking process by an evasive maneuver when a collision is imminent. This paper proposes the integration of an autonomous avoidance system (Automatic Emergency Steering, AES) that acts directly on the steering system to generate an evasive maneuver and avoid a possible pedestrian collision (OPREVU-AES system), as well as the assessment of its effectiveness compared to a commercial AEB system. OPREVU and VULNEUREA are research projects in which INSIA and CEDINT have cooperated to improve driving assistance systems and the safety of pedestrians and cyclists through Virtual Reality (VR) techniques. The analysis of the kinematic and dynamic response of the OPREVU-AES system is conducted in CarSim© software. The effectiveness evaluation procedure is based on the reconstruction of a sample of road vehicle-to-pedestrian crashes (INSIA-UPM database), using the PCCrash® software, and taking as an indicator the probability of head injury severity (ISP). The results show that the AEB system would have prevented part of the collisions, especially after the incorporation of the OPREVU-AES system. In most of the cases where avoidance is not possible, a significant reduction of the ISP is achieved.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

The demand of high data rate and ubiquitous coverage in heterogeneous cellular (HetNets) is increasing progressively. In order to meet this demand, sophisticated model having applied interference reduction scheme and cell association technique is needed. The small base station (sBS)are deployed inside the broadcasting area of macro base station (mBS), in heterogeneous cellular networks (HetNets). Since mBS has high transmission power therefore a large number of users get connected with mBS. This causes disproportion of load distribution across the HetNets. For load balancing users from high power mBS are migrated to low power sBS to increase network capacity and to decrease the load from mBS. This results in interference in the communication signal because of strong mBS Interference. Hence, we need interference management technique to mitigate interference and user association and to efficiently use sBSs’ resources. Inter-cell interference (ICI) limit the HetNets’ performance. Additionally, there exist deliberate jamming interference which depends on jammers transmission power and its proximity with the target, which notably degrades the network performance. In this paper, we employ reverse frequency allocation scheme (RFA) to reduce inter cell interference, deliberate jamming interference and to accomplish load balancing. The proposed setup is analyzed inquisitively and with the help of simulations. The result shows reduction in interferences as well as balance of load distribution in the network achieved by employing RFA scheme together with cell association.

Thresholding is considered as a statistical-decision making theory which can lessen the average error incurred in allocating pixels to two or more groups. The traditional Bayes decision rule can be applied with the prior knowledge of the Probability Density Function (PDF) of each class. It is surmised that a threshold resulting in the best class separation is the optimal one. In this paper, Otsu’s thresholding for image segmentation has been implemented. The well-known Otsu’s method is to learn a threshold that can maximize the between-class variance or equivalently make light of the within-class variance of the entire image. At first, a color image of a tree is taken. After that, the image is transformed into a grayscale image. Then in the first part, two-level thresholding is conducted, and later on, three-level thresholding is also applied. Again, two-level thresholding, as well as three level thresholding, are also applied to some other images. Finally, the comparison is made between two level thresholding and three level thresholding

This paper proposes a new dynamic analysis of reasoning. It makes the following contributions. First, the current states of the psychology of reasoning are critically reviewed from theoretical and empirical perspectives. The long-standing controversies between logicians and psychologists are clarified by introducing the gauge theoretic structure. The debates between the mental logic theory and the mental models theory are carefully reviewed by identifying the problem types used in the empirical studies. Certain mental fluctuations are found and a quantum theoretic solution is examined. Second, it solves the measurement problem within the Hamiltonian framework. The modeling structure underlying reasoning dynamics is the electrodynamics. They are both the single-charge dynamic systems sharing the U(1) symmetry. The mental logic theory and the mental models theory are now characterized as wavefunctions in a unified account of the dynamic analysis with the yes/no measurements. The stochastic sampling method is introduced to solve the measurement problem, which has a wide range of applications in social sciences. Third, a novel metatheoretic framework of reasoning dynamics within Lagrangian framework is proposed. It solves the “Man vs. Men” problem via gauge theoretic modeling, by making the distinction between the global level and the local level. At each level, the gauge transformations are applied to achieve the global symmetry and the local gauge symmetry. It explains the meanings of the gauge principle and the Nether theorem. Fourth, the special theory of relativity is applied to address the “Man vs. Men” problem. It explains how to draw the global language cone and the individualized local language cones. Finally, it points out that borrowing modeling methods from physics has a long tradition in psychology. The present work utilizes the conceptual and modeling methods found in modern theoretical physics.

The hard open problem of finding the lower bound for the Fokker Planck Kolmogorov’s time-dependent controller parameter probability density function is addressed for the first time in literature in this work. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to multi-interdisciplinary fields of human knowledge, and beyond. So, this by default adds more taste and credibility to this study. Concluding thoughts are included at the end of the work along with a difficult outstanding problem and the direction of future work.

This work is the first in literature to tackle the difficult open problem of determining the upper bound and threshold theorem for the TDCDP (time-dependent controller parameter) of the (Fokker Planck Kolmogorov) probability density function. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to information theory, graph theory, data science, finance, economics, and beyond. So, this by default adds more taste and credibility to this study. This leads by nature to introducing a different flavor to this ground-breaking research by highlighting the impact of Fokker Planck Kolmogorov(FPK) to revolutionize crypocurrency,which have received its name because it uses encryption to verify transactions, a new debatable digital payment system that doesn't rely on banks to verify transactions. It’s a peer-to-peer system that can enable anyone anywhere to send and receive payments. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator.The notion of entangled probability distribution is reviewed. Evolution equations describing the time-dependence of probability distributions identified with quantum system states are discussed.The connection with the Schrödinger equation and the von Neumann equation is clarified.

A method is proposed for describing the dynamics of systems of interacting particles in terms of an auxiliary field, which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic composite field. It is established that for interatomic potentials, the Fourier transform of which is a rational algebraic function of the wave vector, the auxiliary field is a composition of elementary fields that satisfy the Klein-Gordon equation with complex masses. The interaction between particles carried by the auxiliary field is nonlocal both in space variables and in time. The temporal non-locality is due to the dynamic nature of the auxiliary field and can be described in terms of functional-differential equations of retarded type. Due to the finiteness mass of the auxiliary field, the delay in interactions between particles can be arbitrarily large. A qualitative analysis of the dynamics of few-body and many-body systems with retarded interactions has been carried out, and a non-statistical mechanisms for both the thermodynamic behavior of systems and synergistic effects has been established.

With the rapid development of intelligent logistics and network environment, it has become an urgent problem to efficiently and accurately handle and analyse the huge amount of uncertain decision information. Traditional decision making methods often fail to make the best use of complex and incomplete information, especially in the field of cyber defence. To address these problems, this paper introduces a new mathematical tool, discrete multidimensional Z-numbers (MZs), for expressing and dealing with uncertainty and reliability in network defence decisions. In this paper, we first introduce the synthesis method of discrete multidimensional Z-numbers, which allows us to consider the uncertainty and reliability of multi-source information in network defence strategy. Then, the hidden probability of MZs is calculated by using the hidden probability model, and the multidimensional Z+−number is proposed, which improves the expressiveness of the model in dealing with information uncertainty. Based on MZs, we define a variety of utility functions and build a multi-attribute group decision framework for network defence around these functions. The MZs provides a novel perspective for analysing and designing response strategies, especially against highly adaptive and covert attacks. The method in this paper is verified by a case of network security assessment of an intelligent logistics company. The results show that this method can significantly improve the accuracy and efficiency of decision making, demonstrating its unique advantages and wide application potential in network defence. This integrated discrete multidimensional Z-number group decision method is not only suitable for intelligent logistics decision making, but also provides an efficient decision support tool for network defence, which helps to improve the intelligence and adaptability of network security defence.

Here, we propose a prescriptive simulation model of a process operator’s decision-making assisted by artificial intelligence (AI) algorithm in a technical system control loop. We analyze situations fraught with a catastrophic threat that may cause unacceptable damage. Operators’ decision-making is interpreted in terms of a subjectively admissible probability of disaster and subjectively necessary reliability of its assessment. We distinguish four extreme decision-making strategies corresponding to different ratios between the above variables. An experiment simulating a process facility, an AI algorithm and operator's decision-making strategy was held. It showed that depending on the properties of a controlled process (the speed of hazard onset) and the AI algorithm characteristics (Type I and II error rate), each of such strategies or some intermediate strategy may prove to be more beneficial than others. The same approach is applicable to the identification and analysis of sustainability of strategies applied in real-life operating conditions, as well as to the development of a computer simulator to train operators to control hazardous technological processes using AI-generated advice.

Background: Current prostate cancer evaluation can be inaccurate and burdensome. Quantitative evaluation of MRI sequences non-invasively helps prostate tumor assessment. However, including Dynamic Contrast Enhancement in the examined MRI sequence set can add complications, inducing possible side effects from the IV placement or injected contrast material, and prolongs scanning time. Purpose: Predict the risk of developing Clinically Significant (Insignificant) prostate cancer CsPCa (CiPCa) and International Society of Urologic Pathology (ISUP) grade using processed Signal to Clutter Ratio (SCR) derived from spatially registered bi-parametric MRI (SRBP-MRI) and thereby enhance non-invasively management of prostate cancer. Methods: This pilot study retrospectively analyzed 42 consecutive prostate cancer patients from the PI-CAI data collection. BP-MRI (Apparent Diffusion Coefficient, High B-value, T2) were resized, translated, cropped, and stitched to form spatially registered SRBP-MRI. Efficacy of noise reduction was tested by regularizing, eliminating principal components (PC), and minimizing elliptical volume from the covariance matrix to optimize the SCR. MRI guided biopsy (MRBx), Systematic Biopsy (SysBx), combination (MRBx+SysBx), or radical prostatectomy determined the ISUP grade for each patient. ISUP grade >=2 (<2) was judged as CsPCa (CiPCa). Linear and Logistic regression were fitted to ISUP grade and CsPCa/CiPCa SCR. Correlation Coefficients (R) and Area Under the Curves (AUC) for Receiver Operator Curves (ROC) evaluated the performance. Results: High correlation coefficients (R) (>0.55) and high AUC (=1.0) for linear and/or logistic fit from processed SCR and z-score for SRBP-MRI greatly exceed fits using prostate serum antigen, prostate volume, and patient age (R~0.17). Patients assessed with combined MRBx+SysBx and from individual MRI scanners achieved higher R (R=0.207+/-0.118) than using all patients in the fits. Conclusions: In the first study to date to apply and test hyperspectral approaches for assessing tumor aggressiveness on SRBP-MRI, high values of R and exceptional AUC to fit the ISUP grade and CsPCA/CiPCA were comparable or better than those from artificial intelligence in other studies.

We study the short−term memory capacity of ancient readers of the original New Testament written in Greek, of its translations to Latin and modern languages. To model the short–term capacity, we have considered the number of words per interpunctions, the “word interval” , because this parameter can model how the human mind memorizes “chunks” of information. Since can be calculated for any alphabetical text, we can perform experiments − otherwise impossible − with ancient readers by studying the literary works they used to read. The “experiments” compare the of texts of a language/translation to those of another language/translation by measuring the minimum average probability of finding joint readers (those who can read both texts because of their similar short–-term memory capacity) and by defining an “overlap index”. We also define a population of universal readers who can read any the New Testament written in alphabetical language. More than 50% of the readers of specific languages overlap with the universal readers with probability . Future work is vast, with many research tracks, because alphabetical literatures are very large and allow many experiments, such as comparing authors, translations or even texts written by artificial intelligence tools.

Enabling D2D communication in the mm-Wave band has many obstacles which must be mitigated. The primary concern is the introduction of interference from various sources. Thus, we focused our work on the performance of decode and forward (DF) relay assisted D2D communication in the mm-Wave band for increasing the coverage probability and energy efficiency (EE). Three modes are proposed for D2D communication to prevail. Bit-wise binary XOR operation is executed at the relay node which increases the security feature. Radius of coverage expression is derived which indicates the switching of the modes. The diffused incoherent scattering power is also considered as a part of power consumption. Furthermore, a unique relay selection scheme, Dynamic relay selection (DRS) method is proposed to select the optimal relay for information exchange. Comparison of the proposed DF relay scheme with amplify and forward (DF) scheme is also shown. Finally, simulation results prove the efficacy of the proposed work.

Reliability analysis techniques are customary standard tools that are used for evaluating the performance of different equipment and devices in order to minimize their downtime. To predict the reliability, life data from a sample that is satisfactorily representative of the equipment should be fitted to the suitable statistical distribution. The parameterized distribution may be used to estimate essential characteristics such as failure rate; and probability at a precise time, as well as system reliability. In the current study, Weibull++/ALTA software package is used as a novel tool to fit the available data set to estimate the best fitted probability density function (PDF) using Maximum Likelihood (MLE) for parameter estimation. The determined distributions are then assessed using goodness-of-fit test to define how well it fits the available data set. There are multiple methods for determining goodness-of-fit. Weibull distributions and their special cases’ parameters have an effect on life times.

Data collected at the Cascais tide gauge, located on the west coast of Portugal Mainland, have been analyzed and sea level rise rates have been updated. Based on a bootstrapping linear regression model and on polynomial adjustments, time series are used to calculate different empirical projections for the 21^st century sea level rise, by estimating the initial velocity and its corresponding acceleration. The results are consistent to an accelerated sea level rise, showing evidence of a faster rise than previous century estimates. Based on different numerical methods of second order polynomial fitting, it is possible to build a set of projection models of relative sea level rise. Appling the same methods to regional sea level anomaly from satellite altimetry, additional projections are also built with good consistency. Both data sets, tide gauge and satellite altimetry data, enabled the development of an ensemble of projection models. The relative sea level rise projections are crucial for national coastal planning and management since extreme sea level scenarios can potentially cause erosion and flooding. Based on absolute vertical velocities obtained by integrating global sea level models, neo-tectonic studies and permanent Global Positioning System (GPS) station time series, it is possible to transform relative into absolute sea level rise scenarios, and vice-versa, allowing the generation of absolute sea level rise projection curves and its comparison with already established global projections. The sea level rise observed at the Cascais tide gauge has always shown a significant correlation with global sea level rise observations, evidencing relatively low rates of composed vertical land velocity from tectonic and post-glacial isostatic adjustment, and residual synoptic regional dynamic effects rather than a trend. An ensemble of sea level projection models for the 21st century is proposed with its corresponding probability density function, both for relative and absolute sea level rise for the west coast of Portugal Mainland.

A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.

In this paper, we present a rigorous proof demonstrating the stabilization of percolation probability in supercritical regimes for percolation models. We analyze a sequence of expanding compact balls in ℝ௡, incorporating correction terms that vanish asymptotically, and show that the percolation probability within these regions converges to a finite, non‐zero value as the balls expand to cover the entire space. Our approach combines key concepts from percolation theory with measure‐theoretic tools, such as the Monotone Convergence Theorem and Fatouʹs Lemma, to rigorously establish the existence and uniqueness of the limiting percolation probability. The result extends classical results on percolation probability in lattice models and provides a new framework for understanding convergence in infinite systems. The non‐triviality of the limit is demonstrated in the supercritical regime, where percolation occurs with positive probability. The framework introduced here could serve as a bridge between discrete and continuous models in statistical physics

The evidential value of an mtDNA match between biological remains and its potential donor is determined by the random match probability of the haplotype. This probability is based on the haplotype’s population frequency estimate. Consequently, implementing a population study representative of the population relevant to the forensic case is vital to correctly evaluating the evidence. The emerging number of poaching cases and the limited availability of such data emphasizes the need for improved fallow deer mtDNA population databank for forensic purposes, including targeting the entire mitochondrial control region. By sequencing the whole mitochondrial control region in 138 animals from five populations in Hungary we found four different haplotypes, including one which has not yet been described. Our results, supplemented with data already available from previous research do not support the possibility of determining the population of origin, although some patterns of geographical separation can be distinguished. Estimates of molecular diversity indicate approximately similarly low mtDNA diversity (Hd=0.565 and π = 0.002), compared with data from other countries. The calculated random match probability of 0.547 shows a high probability of coincidence and, therefore, a limited capacity for exclusion. Consequently, it may be necessary to search for polymorphic sites on other mitochondrial gene sections or to sequence the entire mitogenome of fallow deer.

The performance in terms of minimal Bayes’ error probability for detection of a high-dimensional random tensor is a fundamental under-studied difficult problem. In this work, we consider two Signal to Noise Ratio (SNR)-based detection problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size Nq  R, i.e, for 1  q  Q, where R, Nq ! ¥ with R1/q/Nq converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear (M1, . . . ,MQ)-rank with large factors of size Nq  Mq, i.e, for 1  q  Q, where Nq,Mq ! ¥ with Mq/Nq converge towards a finite constant. The detection of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the error probability is mathematically intractable. To circumvent this technical difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s?. In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s? = 1/2) can not solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s?. However, thanks to powerful random matrix theory tools, a simple analytical expression of s? is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. A main conclusion of this work is that the BUB is the tightest bound at low SNRs. This property is, however, no longer true for higher SNRs.

When extract building from high resolution remote sensing image with meter/sub-meter accuracy, the shade of trees and interference of roads are the main factors of reducing the extraction accuracy. Proposed a Bayesian Convolutional Neural Networks(BCNET) model base on standard fully convolutional networks(FCN) to solve these problems. First take building with no shade or artificial removal of shade as Sample-A, woodland as Sample-B, road as Sample-C. Set up 3 sample libraries. Learn these sample libraries respectively, get their own set of feature vector; Mixture Gauss model these feature vector set, evaluate the conditional probability density function of mixture of noise object and roofs; Improve the standard FCN from the 2 aspect:(1) Introduce atrous convolution. (2) Take conditional probability density function as the activation function of the last convolution. Carry out experiment using unmanned aerial vehicle(UVA) image, the results show that BCNET model can effectively eliminate the influence of trees and roads, the building extraction accuracy can reach 97%.

This article introduces a novel approach, termed the Asymmetric Probabilistic Tsetlin (APT) Machine, which incorporates the Stochastic Point Location (SPL) algorithm with the Asymmetric Steps technique into the Tsetlin Machine (TM). APT introduces stochasticity into the state transitions of Tsetlin Automata (TA) by leveraging the SPL algorithm, thereby enhancing pattern recognition capabilities. To enhance random search processes, we introduced a decaying normal distribution into the procedure. Meanwhile, the Asymmetric Steps approach biases state transition probabilities towards specific input patterns, further elevating operational efficiency. The efficacy of the proposed approach is assessed across diverse benchmark datasets for classification tasks. The performance of APT is compared with traditional machine learning algorithms and other Tsetlin Machine models, including the Asymmetric Tsetlin (AT) Machine, characterized by deterministic rules for Asymmetric transitions, and the Classical Tsetlin (CT) Machine, employing deterministic rules for symmetric transitions. Strikingly, the introduced APT methodology demonstrates highly competitive outcomes compared to established machine learning methods. Notably, both APT and AT exhibit state-of-the-art performance, surpassing the Classical Tsetlin Machine, emphasizing the efficacy of asymmetric models for achieving superior outcomes. Remarkably, APT exhibits even better performance than AT, particularly in handling complex datasets.

In this article, the multitouch option, also called the n  touch option (or the “baseball” option when n  3 ) is analyzed and valued in closed form. This is a kind of barrier option that sets a gradual knockout / knock-in mechanism based on the number of times the underlying asset has crossed a predefined barrier in various time intervals before expiry. The higher the number of predefined time intervals during which the barrier has been touched, the lower the value of a knock-out contract at expiry, and conversely for a knock-in one. Multitouch options can be viewed as an extension of step barrier options, preserving the ability of the latter to adjust the exposure to risk over time, while eliminating the notorious danger of “sudden death” that holders of step barrier options are faced with. Unlike occupation time derivatives, the payoff at expiry does not depend on the amount of time spent outside the authorized range, but on the number of passages beyond the authorized range.

The usage of Quantum Similarity through the equation Z = {∀θ ∈ Z → ∃s ∈ S ∧ ∃t ∈ T : θ = (s, t)}, represents a way to analyze the way communication works in our DNA. Being able to create the object set reference for z being (s, t) in our DNA strands, we are able to set logical tags and representations of our DNA in a completely computational form. This will allow us to have a better understanding of the sequences that happen in our DNA. With this approach, we can also utilize mathematical formulas such as the Euler–Mascheroni constant, regression analysis, and computational proofs to answer important questions on Quantum biology, Quantum similarity, and Theoretical Physics.

A new attack against the Kirchhoff-Law-Johnson-Noise (KLJN) key distribution system is introduced. The attack is based on 1) Utilizing the dc-voltage-source - which we put at Alice’s end in our mathematical modeling of the attack-that could exist due to errors, imbalances, Electromagnetic interference and etc.2) On studying the number of samples per bit in the security key that the measured Alice/Bob voltages exceeds or falls below a threshold voltage, respectively. The threshold voltage is the average between dc voltages across low and high resistors- generated by a dc-voltage source. We count the number of samples the voltage at Bob’s end (containing both the noise and dc components) exceeds the threshold voltage and how many times it falls below the threshold to judge whether the resistor can be guessed as low or high for every cycle. Also for a pre-specified key-length we count the number of high resistance estimations per bit –at Bob’s end-according to the previous criterion and the non-successful estimations per bit to judge the final guessed resistor value at Alice’s end and Bob’s end, where if we have more bits with most of its measured samples are above the threshold voltage then we will predict Bob’s resistance as high resistance, otherwise we predict Bob’s resistance to be low resistance. The Simulation was conducted and the attack proved that it is successful unless the temperature increased dramatically to ranges more than a threshold temperature ~ Kelvin that increases when the number of samples per bit increases.

An inverse-square probability mass function (PMF) is at Newcomb-Benford Law’s (NBL) root and ultimately at the origin of positional notation and conformality. Under its tail, we find information as harmonic likelihood, leading to the global NBL ruled by the base B. Under its tail, we find information as logarithmic likelihood, leading to the local (fiducial) NBL ruled by the radix R. In the framework of bijective numeration, we prove that the set of Kempner’s series conforms to the global NBL and that the local NBL is length- and position-invariant. The global Bayesian rule multiplies the correlation between numbers, s and t, by a likelihood ratio that is the NBL probability of bucket [s;t) relative to B’s support. To encode the odds of quantum j against i locally, we multiply the prior odds Pr(B;j)/Pr(B;i) by a likelihood ratio that is the NBL probability of bin [i;j) relative to R’s support. This two-factor structure is recurrent under arithmetic operations. A particular case of Bayesian data produces the algebraic field of "referential ratios". The cross-ratio, the central tool in conformal geometry, is a ratio of referential ratios. A one-dimensional coding source reflects the harmonic external world into its logarithmic coding space, the ball {x∈Q| abs(x)< 1-1/B}. The source’s conformal encoding function is y=logR(2x-1), where x is the observed Euclidean distance to an object’s position. The conformal decoding function is x = ½ (1 + ry). Both functions, unique under basic requirements, enable information- and granularity-invariant recursion to model the multiscale reality.

This article provides exact analytical formulae for various kinds of rainbow step barrier options. These are highly flexible and sophisticated multi-asset barrier options based on the following principle : the option life is divided into several time intervals on which different barriers are monitored w.r.t. different underlying assets. From a mathematical point of view, new formulae are provided for the first passage time of a multidimensional geometric Brownian motion to a boundary defined as a step function. The article shows how to implement the obtained valuation formulae in a simple and very efficient manner. Numerical results highlight a strong sensitivity of rainbow step barrier options to the correlations between the underlying assets.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to the stable MG1 queue manifold. More potentially, both service time probability and cumulative functions which make KLDF exact are obtained. The credibility of KLDF is justified through consistency axioms. Some potential applications of Kullback-Leibler divergence to Biometry are presented. The paper concludes with closing remarks combined with some challenging open problems and the next phase of research.

It is claimed that classical mechanics (CM) in terms of its equivalent Koopman-von Neumann formulation (KvN) is indeed a ’real’ quantum theory since the formalism of quantum mechanics (FQM) does not, nor need it, exclude it as a such. This claim is made manifest by suggesting a common structure of which both KvN and ordinary quantum mechanics (OQM) correspond to unitary representations of, although unitarily inequivalent such. It is shown that OQM is obtained by enforcing the extra physical condition of quantized energy levels, which by itself does not constitute the ’quantum mystery’. It is furthermore shown that KvN in a physically realizable sense contain the hallmark quantum behavior of quantum interference. It is hence concluded that both CM and OQM are subjected to the same foundational issues. As the central part of both KvN and OQM is the introduction of probabilities via FQM it is suggested that the foundational issues regarding FQM are less about FQM itself and more about the concept of probability.

Monitoring crown closure evolution using multi-temporal Light Detection and Ranging (LiDAR) surveys is a method that we expect to be increasingly adopted given the availability of LiDAR sensors and the accumulating survey archives. However, little attention was devoted to comparing crown closure estimates from independent surveys. Although survey parameters cannot be modified after the data collection, we speculate that the error associated to crown closure estimates comparison can be reduced by selecting optimal post-survey parameters. In this study, we compared crown closure estimates of three airborne LiDAR surveys from 2018 (40 pt/m²) used as a reference, and two lower-density surveys from 2016 (4.5 pt/m²) and 2018 (2 pt/m²). We studied the effect of the height threshold used to separate canopy points and the grid resolution, using skewness and variance of lagged difference of crown closure. Crown closure estimates using low height thresholds were more different across surveys, resulting in higher root mean squared error (RMSE), bias and more different variograms. Results show that optimal height threshold was 3 m and grid resolution was 25 m, although there was room for decision (RMSE of 7% and 5%, and bias of 4% and 0% for 2016 and 2018 low-density surveys).

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

The recent Google’s claim on breakthrough in quantum computing is a gong signal for further analysis of foundational roots of (possible) superiority of some quantum algorithms over the corresponding classical algorithms. This note is a step in this direction. We start with critical analysis of rather common reference to entanglement and quantum nonlocality as the basic sources of quantum superiority. We elevate the role of the Bohr’s principle of complementarity¹ (PCOM) by interpreting the Bell-experiments as statistical tests of this principle. (Our analysis also includes comparison of classical vs genuine quantum entanglements.) After a brief presentation of PCOM and endowing it with the information interpretation, we analyze its computational counterpart. The main implication of PCOM is that by using the quantum representation of probability, one need not compute the joint probability distribution (jpd) for observables involved in the process of computation. Jpd’s calculation is exponentially time consuming. Consequently, classical probabilistic algorithms involving calculation of jpd for n random variables can be over-performed by quantum algorithms (for big values of n). Quantum algorithms are based on quantum probability calculus. It is crucial that the latter modifies the classical formula of total probability (FTP). Probability inference based on the quantum version of FTP leads to constructive interference of probabilities increasing probabilities of some events. We also stress the role the basic feature of the genuine quantum superposition comparing with the classical wave superposition: generation of discrete events in measurements on superposition states. Finally, the problem of superiority of quantum computations is coupled with the quantum measurement problem and linearity of dynamics of the quantum state update.

The transport and entanglement of photons is becoming prominent in optics applied to information and quantum computing, where the angular momentum of light stands out in the exchange and inversion of quantized states, with prospects for several technological applications, such as the transport and storage of quantum information. In order to contribute to the understanding of quantized states in photon-matter interaction, we describe a quantized state equation in multidimensional Hilbert space for the diagnosis of OAM states, where probabilities arise in a relativistic setting. It was found that the classical-relativistic variability of the probabilities constitutes a resultant capable of describing the quantized states of light, where the state variable is the variation of the angular momentum of the photon, capable of estimating the orbital angular momentum inversion points at angular incidence. It was found that the chances of finding the quantized states of light at angular incidence can be treated by purely relativistic probabilities, explaining that when both states have equal chances of being found and the angular momentum variation is zero, the source-observer synchronizations occur at the step of increasing relativistic regime of the photon dynamics. We found that the relativistic effect from the perspective of the source referential is able to alter the chances of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.

The Estimation of systemic risk in India is still in its infancy stage. There are several methods which are available but none of the methods are fully compatible to forecast the systemic risk since under different circumstances the factors responsible for the risk differs. In this paper the systemic risk estimation in India being carried out based on spread in daily stock market price(Difference between the bid and ask price of a share) of the top 100 firms in India according to market capitalization for the period of July2007 to March 2016. The results were compared with the Financial Stability Report published by Reserve Bank Of India for the period of March 2010 to June 2016.The results clearly indicates that there exits relationship between market illiquidity represented by spread and risks associated with the Financial System. In most of the cases the Z score (deviation from the mean/Standard Deviation) of the spread has become negative which provides the spread which is farther from the mean, also a good indicator of volatility in market and risk to financial system. It is also seen that the Systemic Risk Survey conducted by Reserve Bank of India which started during October 2011 has supported the results.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.