In public health literature the risk of death or disease associated with a dietary, environmental of behavioral factor is most commonly denoted by odds ratio (OR), hazard ratio (HR) or risk ratio (RR). The ratio indices have several desirable statistical properties. However, the most important question is whether there are some evolved innate norms of perception of risk that people use and what they are. We conducted a simple one question survey of 98 individuals with different age, sex, educational and professional backgrounds. The respondents were asked to judge the relative perceived risk of four different hypothetical habits for which data on the percentage of people affected by the disease with and without the habit was given. They were asked to rank the risks for the four habits. Results showed that the habits that had the highest difference between probability of acquiring the disease were ranked high on risk perception. The probability ratios did not affect risk perception significantly. Further age, sex, profession or formal training in statistics did not affect the response significantly. Even individuals that were formally trained to use OR and HR as risk indicators, preferred using probability differences over ratios for judging their own risk in the perceived context. This preliminary inquiry into intuitive statistical perception suggests that designing statistical indices based on people’s innate perception may be a better strategy than trying to train people to understand the indices designed by expert statisticians.

Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

Monitoring is an essential component in ecosystem management and leveraging existing data sources for multiple species of interest can be one effective way to enhance information when making management decisions. Here we analyzed juvenile Chinook Salmon (Oncorhynchus tshawytscha) bycatch data that has been collected by the recently established Enhanced Delta Smelt Monitoring program (EDSM), a survey designed to estimate the abundance and distribution of the San Francisco Estuary’s (estuary) endangered Delta Smelt (Hypomesus transpacificus). Two key aspects of the EDSM program distinguish it from other fish surveys in the estuary: a stratified random sampling design and the spatial scale of its sampling effort. We integrated the EDSM dataset with other existing surveys in the estuary and used an occupancy model to assess detection probability differences across gear types. We saw no large-scale differences in size selectivity, and while detection probability varied among gear types, cumulative detection probability for EDSM was comparable to other surveys due to the program’s use of replicate tows. Based on our occupancy model and sampling effort in the estuary during spring of 2017 and 2018, we highlighted under-sampled regions that saw improvements in monitoring coverage due to EDSM. Our analysis also revealed that each sampling method has its own benefits and constraints. Although the use of random sites with replicates as conducted by EDSM can provide more statistically robust abundance estimates relative to traditional methods, the use of fixed stations and simple methods such as beach seine may provide a more cost-effective way of monitoring salmon occurrence in certain regions of the estuary. Stronger inference on salmon abundance and distribution can be made by leveraging the strengths of each survey’s method. Careful consideration of these trade-offs is crucial as the management agencies of the estuary continue to adapt and improve their monitoring programs.

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.

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.

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.

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' un- certainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.

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.

The question does P = NP has confounded mathematicians and computer scientists alike for over 50 years and although there is an almost unanimous agreement that it in fact does not, there still is no absolute proof. In this paper, I attempt to prove to that P does not equal NP.

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.

Several articles have reported that the low number of COVID-19 cases in Japan is attributed to the small number of diagnostic RT-PCR tests performed. The criticism is based on the low number of the tests performed, and they suspected there would be more potential cases in Japan. The use of pre-test probability among tested subjects is proposed in order to evaluate of the sufficiency of test availability instead of the number of the tests. The pre-test probability means the average probability, i.e., ‘suspicion level’, of having coronavirus among the tested subject in a country. The higher pre-test probability is regarded as less sufficient opportunity of the tests, and the test availability could be evaluated by the pre-test probability. Thus, potential problems of underestimation of COVID-19 cases by insufficient amount of the test would be clear by using pre-test probability. The comparison of the pre-test probability could be replaced with that of the positive rate of the test because of the linear relationship between them under the assumption of common sensitivity and specificity. Japan shows the third lowest rate (8.6%), and is considered that the considerably sufficient number of the tests have been performed. In conclusion, the positive rate of the test as a surrogate index of the pre-test probability is useful to evaluate the sufficiency of test amount instead of the number of the tests performed. In present, the potential problem of underestimation by insufficient test availability would be less serious in Japan.

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.

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.

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 use of large-scale antenna arrays grants considerable benefits in energy and spectral efficiency to wireless systems due to spatial resolution and array gain techniques. By assuming a dominant line-of-sight environment in a massive MIMO scenario with favorable propagation, we derive analytical expressions for the sum-capacity. % Then, we show that convenient simplifications on the sum-capacity expressions are possible when working at low and high SNR regimes. % Furthermore, in the case of a high SNR regime, it is demonstrated that the Gamma PDF can approximate the PDF of the instantaneous channel sum-capacity as the number of BS antennas grows. A second important demonstration presented in this work is that a Gamma PDF can also be used to approximate the PDF of the summation of the channel's singular values as the number of devices increases. Finally, it is important to highlight that the presented framework is useful for LPWAN's as we show that the transmit power of each device can be made inversely proportional to the number of BS antennas.

In the case that ship operators may not be aware of the potential risks of environmental factors in situation of high causation probability during the initial stage of the geometric probability analysis process, it is likely that higher-grade collision accident measures will not be taken. However, if any risks is told to the ship operators, more effective and intentional measures can be taken in time. Moreover, if the causation probability corresponding to environmental factors is no less than the risk early warning critical value calculated based on historical collision accident data, there would be a high-risk level that a collision may occur. A new method is put forward based on quantitative analysis of environmental factors and previous collision statistics to provide early warning of any accident risk, and a risk early-warning critical value (REWCV) can be obtained based on this simple but highly operational and practical method. A case study of Three Gorges Reservoir in China indicates that the range of environmental factors where the probability of collision accident grows rapidly is consistent with environmental limits defined by Chinese maritime standards. In addition, the relationship between the risk early-warning critical value and the number of previous collision accident is also clarified.

Pieron's and Chocholle’s seminal psychophysical work predicts that human response time to information relative to visual contrast and/or sound frequency decreases when contrast intensity or sound frequency increases. The goal of this study is to bring to the fore the ability of individuals to use visual contrast intensity and sound frequency in combination for faster perceptual decisions of relative depth (“nearer”) in planar (2D) object configurations on the basis of physical variations in luminance contrast. Computer controlled images with two abstract patterns of varying contrast intensity, one on the left and one on the right, preceded or not by a pure tone of varying frequency, were shown to healthy young humans in controlled experimental sequences. Their task (two-alternative forced-choice) was to decide as quickly as possible which of two patterns, the left or the right one, in a given image appeared to “stand out as if it were nearer” in terms of apparent (subjective) visual depth. The results show that the combinations of varying relative visual contrast with sounds of varying frequency exploited here produced an additive effect on choice response times in terms of facilitation, where a stronger visual contrast combined with a higher sound frequency produced shorter forced-choice response times. This new effect is predicted by cross-modal audio-visual probability summation.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. The article presents author’s results of studying probabilities of nucleotides on so-called epi-chains of long DNA sequences of various eukaryotic and prokaryotic genomes. DNA epi-chains are algorithmically constructed subsequencies of DNA nucleotide sequences. According to the algorithm of construction of any epi-chain of the order n, the epi-chain is such nucleotide subsequence, in which the numerations of adjacent nucleotides differ by n (n = 2, 3, 4,…). Correspondingly each epi-chain of order n contains n times less nucleotides than the original DNA sequence. The presented results unexpectedly show that nucleotide probabilities on such DNA epi-chains of different orders are practically identical to nucleotide probabilities in the original long DNA sequence. These data allow considering DNA as a regular rich set of epi-chains, which can play a certain role in genetic and epigenetic phenomena as the author belives. Appropriate rules of nucleotide probabilities on epi-chains of long DNA sequences are formulated for further their tests on a wider set of biological genomes. These phenomenological data and their possible biological meaning are discussed.

Steganography is the branch of cryptology that deals with concealing information inside another information. it’s prefer over cryptography as it hides a message inside another innocent looking message, while cryptography shows scrambled message that might arouse attention of an attacker, however the challenges in steganography is the modification of carrier that causes some abnormalities which is detectable and often the methods are not optimize. This paper presents a novel approach in cryptography and steganography, which utilizes mathematical concept of bits combination to optimize time of transmission using sets of multiple transmitter, and receiver’s addresses where each abstractly represents a bits combination without itself modified. In addition, the paper introduces a concept of dynamical clockwise and anti-clockwise rotation of bits combination over addresses after every transmission to reinforce resistivity against steganalysis.

Impressing discoveries in the field of the genetic code have been described by its researchers by means of the terminology borrowed from linguistics and the theory of communications. Leading experts on structural linguistics believe for a long time already that languages of human dialogue were formed not from an empty place, but they are continuation of genetic language or, anyhow, are closely connected with it, confirming the idea of information commonality of organisms. The aticle continues the theme about a connection of linquistic languages with the genetic language. It describes results of comparative study of long Russian literary texts (novels by L.Tolstoy, F.Dostoevsky, A.Pushkin, etc.) and long sequences of hydrogen bonds in double helixes of DNA of different organisms. Formalisms of quantum informatics are used in modeling some of these results taking into account thoughts of many researches about possible using principles of quantum informatics in organisation of living bodies.

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.

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

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.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

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.

This paper introduces an approach that chooses the fault detection by calculating probabilities using probability mass function (pmf) and cumulative distribution function (CDF). This work used a method for multiple stuck-at faults by producing a new test pattern in combinational circuits. We assumed that existence of all multiple faults is only because of one single component that is faulty. A complete test set can be created by all possible single stuck-at faults in a combinational circuit using some combination of gates. The test set generation fault detection method is applied on two different 3-bit input variable and 4-bit input variable circuits. The probability of error occurrence is calculated at both 3-bit and 4-bit input variable circuits. The resulting feature is used to obtain maximum error occurrence probability to detect faults by the logic used that the complexity of the circuit is inversely proportional to the fault occurrence probability. Then again, undetectability is directly proportional to the complexity of the circuit. Therefore, finest feasible circuit should have large input variable components with less complexity to reduce the fault occurrence probability.

This paper investigates the problem of the optimal arrangement for both UAVs’ caching contents and service locations in UAV-assisted networks based on the context awareness, which considers the influence between users and environment. In the existing work, users within the coverage of UAVs are considered to be served perfectly, which ignores the communication probability caused by line-of-sight (LOS) and non- line-of-sight (NLOS) links. However, the links are related to UAV deployment. Moreover, the transmission overhead should be taken into account. To balance the tradeoff between these two factors, we design the ratio of users’ probability and transmission overhead as the performance measure mechanism to evaluate the performance of UAV-assisted networks. Then, we formulate the objective for maximizing the performance of UAV-assisted networks as a UAV-assisted caching game. It is proved that the game is an exact potential game with the performance of UAV-assisted networks serving as the potential function. Next, we propose the log-linear caching algorithm (LCA) to achieve the Nash equilibrium (NE). Finally, related simulation results reflect the great performance of the proposed algorithm.

Technology development changes society and society demands new and innovative technology development. We analyze technology to understand society and technology itself. Many researches have been introduced in various fields. Most of them were about patent analysis. This is because detailed and accurate results of research and development are patented. In this paper, we study on new patent analysis method based on count data model and Bayesian regression analysis. Using count data model, we analyze the technological keywords extracted from the collected patent documents. We use the posterior distribution of Bayesian statistics to reflect the experience and knowledge of the relevant technological experts in the analysis model. Moreover, we apply the proposed model to finding sustainable technologies. Finding and developing sustainable technologies is an important activity for companies and research institutes to maintain their technological competitiveness. To illustrate how our modeling could be applied to real domain, we carry out a case study using the patent documents related to artificial intelligence.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

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 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.

A method for measuring the real part of the weak value of spin for non-zero rest mass atoms is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises helium in the metastable 2³S₁ state. A full simulation for observing the real part of the weak value using the impulsive approximation has been carried out and it predicts a displacement of the beam, Δ_w, that is within the resolution of our detector. It also indicates how this shift might be increased. The full analysis also indicated that there is a limit, L, to the applicability of the weak value approximation and has been evaluated for our apparatus. This experiment has the possibility to be expanded to utilise other nobal gas species such as neon and argon in the ³P₂ metastable state, but we shall restrict this paper to metastable helium only.

This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold $M$. The geometry of family of probability densities on $M$ are inherited from probability densities on Euclidean spaces $\left\{U_\alpha \right\}$ via bundle morphisms, induced by an orientation-preserving diffeomorphisms $\rho_\alpha:U_\alpha \rightarrow M$. Current literature inherits densities on $M$ from tangent spaces via Riemannian exponential map $\exp: T_x M \rightarrow M$; densities on $M$ are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on $U_\alpha$ can be inherited to family of densities on $M$. Furthermore, we provide explicit expressions for parametrized probability densities on $\rho_\alpha(U_\alpha) \subset M$. Finally, using the component densities on $\rho_\alpha(U_\alpha)$, we construct parametrized mixture densities on totally bounded subsets of $M$. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.

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.

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%.

Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

Government support plays an important role in Chinese economy. New energy industries, concerning innovation-driven source and environmental protection, are also supported by government. This paper aims to study the effects of the traditional government support at supply side on firms’ innovation and development. In this paper, we propose enterprise behavior model including characteristics of new energy industries, and study the innovation reaction of firms to government support in different situation. We further use propensity score matching to verify the results in theoretical model, and conduct robustness analysis. Our main conclusions include: (1) In the normal years government support can only promote the innovation output of firms which have innovated, however, can not promote the innovation probability of firms which have not innovated. That is to say, government support can only enhance the intensive margin of innovation, but can not enhance the extensive margin of innovation with less competition. (2) In the situation of bad economic environment and intense competition, firms’ innovation probability rises as the government support increase. Therefore, government should provide more R&D special subsidies and implement strict financial supervision to make the effectiveness of support policies especially in the normal years.

AI is often looked at as a logical rational way to develop a games agent that methodically looks at options and delivers rational solutions. This paper is based on developing an AI agent that plays a game with a similar emotive content like a human. The purpose of the study was to see if the incorporation of this emotive content would influence the outcomes within the game Love Letter. In order to do this an AI agent with an emotive layer was developed to paly the game over a million times. A lower win/loss ratio demonstrates that to some extent this methodology was vindicated and a 100 per cent win for the AI agent did not happen. Machine learning techniques were modelled purposely so as to match extreme models of behavioural change. The results demonstrated a win/loss ration of 0.67 for the AI agent and in many ways reflectd the frustration that a normal player would exhibit during game play. As was hypothesised the final agent investment value was, on average, lower after matchplay than its initial value.

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.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

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.

In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-differential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fixed at zero.

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.

Categorical variables are common in spatial data analysis. Traditional analytical methods for deriving probabilities of class occurrence, such as kriging-family algorithms, have been hindered by the discrete characteristics of categorical fields. This study introduces the theoretical backgrounds of linear Bayesian updating (LBU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to present the solid theoretical foundations of LBU and provide a categorical random field prediction method which yields relatively higher classification accuracy compared with conventional Markov chain random field (MCRF) approach. A real-world case study has also been carried out to demonstrate the superiority of our method. Since the LBU idea is originated from aggregating expert opinions and not restricted to conditional independent assumption (CIA), it may prove to be reasonably adequate for analyzing complex geospatial data sets, like remote sensing images or area-class maps.