Independent Probability Distributions Research Articles

Probabilistic steady-state and short-term voltage stability assessment considering correlated system uncertainties

As correlated uncertainties in power grids become more prevalent, modeling of stochastic dependencies is becoming increasingly necessary. Independent probability distributions disregard these correlated uncertainties, potentially leading to significant errors, underscoring the necessity of dependence structures. This paper presents a probabilistic approach for modeling uncertain system parameters with their inherent correlations. The proposed approach is validated through various aspects of system voltage measures, including voltage profile and static and dynamic voltage stability. In total, nine alternative sampling generation techniques are employed, and their accuracy is measured based on real-world data using root mean square error (RMSE) and coefficient of determination (R2) criteria. The result suggests that multivariate (Gaussian and Student's) copula techniques accurately represent the real system data, consistently achieving high accuracy rates of 98 % for voltage profiles, 97 % for static voltage stability, and 93 % for dynamic voltage stability. In contrast, the independent sampling technique failed to follow the real-world system data for the different aspects of system voltage measures.

Становлення мікро- та макроекономічного аналізу фінансового посередництва. Стаття перша. Теорії посередницьких функцій банків Д. Даймонда і Ф. Дибвіга та становлення мікроекономічного аналізу фінансових інституцій

The first of two articles which reveal the theoretical and practical significance of the researches awarded 2022 Sveriges Riksbank Prize in Economic Sciences. The author shows that the laureates laid the foundations of both the modern microeconomic theory of banks and financial institutions and the analysis of the role of financial intermediation in macroeconomic cycles. It is found that until the 1980s two powerful theoretical traditions dominated in the analysis of financial intermediation. The first tradition was to consider banks primarily as subjects of the money supply. It originates from the controversy between the quantitative theory of money and the real bills doctrine and culminates in the outstanding work by M. Friedman and A. Schwartz. The second tradition was a well-formalized neoclassical approach to the financial system. It was based on the efficient markets hypothesis, the Modigliani-Miller theorem, and the banking theory of E. Fama, where financial institutions are only a veil for real economic activities. It is shown that the growth of interest in the micro- and macroeconomic aspects of the financial sector activities in the late 1970s was due to the growth of its power due to the development of technologies and globalization, and due to the emergence of information economic theory which created a theoretical basis for the endogenous derivation of financial intermediaries that overcome market imperfections in ensuring the flow of funds between savers and borrowers. The article reveals the theoretical and practical importance of D. Diamond and Ph. Dybvig’s works, in which a bank endogenously arises as an optimal contract for solving important socio-economic problems of financing long-term projects with liquid deposits and of delegated monitoring of borrowers. The author emphasizes the importance of the scientists’ analysis and formalization of the incentives that determine the peculiarities of the intermediary role of banks and the nature of their services for financial regulation. It is shown that the model of delegated monitoring by D. Diamond not only demonstrates social benefits of specialization in monitoring, but also solves the problem of depositors' monitoring a bank as a monitor, revealing the incentives for the efficient implementation of borrowers monitoring by the bank: in conditions of diversification of borrowers, when their profits have an independent probability distribution, monitoring helps to avoid liquidation even in the event that part of the borrowers' projects are not successful. It is concluded that the formalization of the banks’ built-in vulnerability in the Diamond-Dybvig model, associated with their function of maturity transformation, and its overcoming by government institutional mechanisms, which, among other things, can distort the banks’ incentives, in effect substantiate the "symbiosis" of a state and banks in ensuring the latter’s stable functioning.

Phases of Small Worlds: A Mean Field Formulation

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, N. In this paper, we present a novel derivation of the small-world property for Gilbert–Erdös–Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime.

Reuse-efficiency model for evaluating circularity of end-of-life products

Reusing end-of-life products is an effective approach to reduce environmental waste. It is crucial to evaluate the number of products that will be reused quantitatively when the durability of circular products and the collection rate of end-of-life products are improved to enhance the circulation of reusable products. Likewise, it is necessary to evaluate how multiple reuse cycles affect the circularity of reusable products in the product design stage. This study develops a reuse-efficiency model to evaluate the extent of reuse of end-of-life products quantitatively. Circular products are characterised by ‘relative deterioration’ and ‘absolute deterioration’, and the time to each type of deterioration follows an independent probability distribution. The reuse-efficiency model is developed based on the harmonic mean of three reuse-efficiency factors generated by the relative and absolute deteriorations. The effects of the product’s durability, collection rate and recycling rate of end-of-life products, and maximum number of reuse cycles on the reuse efficiency are investigated. Furthermore, the optimal durability of a product, optimal collection rate of end-of-life products, and maximum number of reuse cycles are obtained by maximising the reuse efficiency per unit cost, which considers the costs of durability extension and collection of end-of-life products. The insights obtained from this study encourage the redistribution and reuse of products and are expected to establish an improved circular economy.

Stress–Strain Behavior of FRC in Uniaxial Tension Based on Mesoscopic Damage Model

Fiber-reinforced concrete (FRC) is widely used in the field of civil engineering. However, the research on the damage mechanism of FRC under uniaxial tension is still insufficient, and most of the constitutive relations are macroscopic phenomenological. The aim is to provide a new method for the investigation of mesoscopic damage mechanism of FRC under uniaxial tension. Based on statistical damage theory, the damage constitutive model for FRC under uniaxial tension is established. Two kinds of mesoscopic damage mechanisms, fracture and yield, are considered, which ultimately determines the macroscopic nonlinear stress–strain behavior of concrete. The yield damage mode reflects the potential bearing capacity of materials and plays a key role in the whole process. Evolutionary factor is introduced to reflect the degree of optimization and adjustment of the stressed skeleton in microstructure. The whole deformation-to-failure is divided into uniform damage phase and local failure phase. It is assumed that the two kinds of damage evolution follow the independent triangular probability distributions, which could be represented by four characteristic parameters. The validity of the proposed model is verified by two sets of test data of steel fiber-reinforced concrete. Through the analysis of the variation law of the above parameters, the influence of fiber content on the initiation and propagation of micro-cracks and the damage evolution of concrete could be evaluated. The relations among physical mechanism, mesoscopic damage mechanism, and macroscopic nonlinear mechanical behavior of FRC are discussed.

Over-the-Air Computation in Correlated Channels

Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or even constant) scaling of the communication cost as the number of transmitters grows. Among the most common functions computed OTA are linear functions such as weighted sums. In this work, we propose and analyze an analog OTA computation scheme for a class of functions that contains linear functions as well as some nonlinear functions such as $p$-norms of vectors. We prove error bound guarantees that are valid for fast-fading channels and all distributions of fading and noise contained in the class of sub-Gaussian distributions. This class includes Gaussian distributions, but also many other practically relevant cases such as Class A Middleton noise and fading with dominant line-of-sight components. In addition, there can be correlations in the fading and noise so that the presented results also apply to, for example, block fading channels and channels with bursty interference. We do not rely on any stochastic characterization of the distributed arguments of the OTA computed function; in particular, there is no assumption that these arguments are drawn from identical or independent probability distributions. Our analysis is nonasymptotic and therefore provides error bounds that are valid for a finite number of channel uses. OTA computation has a huge potential for reducing communication cost in applications such as Machine Learning (ML)-based distributed anomaly detection in large wireless sensor networks. We illustrate this potential through extensive numerical simulations.

Sensitivity Analysis of Manufacturing Tolerances in Permanent Magnet Synchronous Machines With Stator Segmentation

In this article the sensitivity of manufacturing tolerances on the output of a permanent magnet synchronous machine with stator segmentation is studied. To reduce the simulation effort, a transition of the stator segment air gaps to replacement geometry was applied and the relevant parameters are discussed, whereas the uncertainty of geometric and material parameters is modeled with a normal distribution. Furthermore, tolerance chains are expressed through the convolution of independent probability distributions. For the Design of Experiments Sobol sequences are utilized. To further decrease the number of design parameters an approach is presented to reduce redundant parameters to individual design parameters. For the sensitivity analysis the torque and torque ripple serve as quality objectives. In addition, an approach is revealed to use the variance of the radial forces as quality objective without considering mechanical FE simulations. For manufacturing tolerances a linear regression is satisfying to describe the main effects on the quality objectives. Repetitive machine parameters, e.g. the remanences, have less influence on the machine's output than particular parameters such as the housing radius or static eccentricity. The influences of stator segmentation are negligibly small, whereas the housing radius has the highest sensitivity on the machine's output.

Black Hole Attack Detection in Healthcare Wireless Sensor Networks Using Independent Component Analysis Machine Learning Technique

Background: Wireless Sensor Networks (WSNs) are self-configured infrastructure-less networks are comprising of a number of sensing devices used to monitor physical or environmental quantities such as temperature, sound, vibration, pressure, motion etc. They collectively transmit data through the network to a sink where it is observed and analyzed. Materials and Methods: The major issues in WSN are interference, delay and attacks that degrade their performance due to their distributed nature and operation. Timely detection of attacks is imperative for various real time applications like healthcare, military etc. To improve the Black hole attack detection in WSN, Projected Independent Component Analysis (PICA) technique is proposed herewith, which detects black hole attack by analyzing collected physiological data from biomedical sensors. Results: The PICA technique performs attack detection through Mutual information to measure the dependence in the joint distribution. The dependence among the nodes is identified based on the independent probability distribution functions and mutual probability function. Conclusion: The black hole attack isolation is then performed through the distribution of the attack separation message. This supports to improve Packet Delivery Ratio (PDR) with minimum delay. The simulation is carried out based on parameters such as black hole attack detection rate (BHADR), Black Hole Attack Detection Time (BHADT), False Positive Rate (FPR), PDR and delay.

How fast can we reach a target vertex in stochastic temporal graphs?

Temporal graphs abstractly model real-life inherently dynamic networks. Given a graph G, a temporal graph with G as the underlying graph is a sequence of subgraphs (snapshots) Gt of G, where t≥1. In this paper we study stochastic temporal graphs, i.e. stochastic processes G whose random variables are the snapshots of a temporal graph on G. A natural feature observed in various real-life scenarios is a memory effect in the appearance probabilities of particular edges; i.e. the probability an edge e∈E appears at time step t depends on its appearance (or absence) at the previous k steps. We study the hierarchy of models of memory-k, k≥0, in an edge-centric network evolution setting: every edge of G has its own independent probability distribution for its appearance over time. We thoroughly investigate the complexity of two naturally related, but fundamentally different, temporal path problems, called Minimum Arrival and Best Policy.

Energy‐efficient quantum‐inspired stochastic Q‐HypE algorithm for batch‐of‐stochastic‐tasks on heterogeneous DVFS‐enabled processors

SummaryScheduling on dynamic voltage and frequency scaling enabled processors to determine the Pareto‐optimal solutions with optimized makespan and energy consumption demands faster multi‐objective scheduling algorithms. In general, the problem of multi‐objective optimization, ie, finding the Pareto‐optimal solutions to optimize two or more QoS parameters, has been proven to be an NP‐complete problem. In this work, we propose a novel energy‐efficient quantum‐inspired stochastic Q‐HypE algorithm to schedule the batch‐of‐stochastic‐tasks (BoT) on DVFS‐enabled processors with the aim to optimize the makespan of BoT as well as the energy consumption of processors. The stochastic processing times of tasks are drawn from independent probability distributions. The proposed Q‐HypE algorithm evolves from combined characteristics of quantum computing and a hypervolume based multi‐objective optimization HypE algorithm. The proposed Q‐HypE algorithm simultaneously minimizes the makespan and energy consumption of the Pareto‐optimal solutions whereas the dynamics of quantum computing accelerate the process of HypE to further minimize the overheads of hypervolume estimation. Experimental results reveal the effectiveness of the proposed Q‐HypE algorithm both in terms of the number and quality of solutions offered.

Jensen–Shannon Divergence Based Independent Component Analysis to Detect and Prevent Black Hole Attacks in Healthcare WSN

The black hole attack is an adverse issue in Wireless Sensor Networks (WSNs). Research for detection and circumvention of the black hole attack is underway. However, the false alarm rate, amount of time required to identify the black hole attack nodes in network has not reduced. To overcome such limitations, the Jensen–Shannon Divergence Based Independent Component Analysis (JDICA) technique is proposed in this paper. This technique is introduced with the application of Jensen–Shannon Divergence estimation in Independent Component Analysis model on the contrary to existing works, in order to achieve higher black hole detection accuracy in healthcare WSN. The JDICA technique identifies the black hole attack by analyzing the physiological data gathered from biomedical sensors. The proposed JDICA technique carries out attack detection based on sensor nodes behaviors such as energy, trust and cooperative count. It determines the dependence among the nodes, based on the independent probability distribution functions and mutual probability function by using the Jensen–Shannon Divergence. The divergence result enables JDICA technique to detect black hole attacks with greater accuracy, and helps to quarantine the malicious node from the network by broadcasting the isolation message to all sensor nodes in the network. Hence, JDICA technique enhances the detection of black hole attack nodes as compared to state-of-the-art works, thereby increasing the packet delivery ratio and reducing delay. The JDICA technique simulation is done considering the metrics such as detection rate, detection time, false alarm rate, and packet delivery ratio with respect to a varied number of sensor nodes and data packets. Simulation results makes it apparent that the JDICA technique improves the detection rate and minimizes the detection time of the black hole attack when compared to state-of-the-art works.

A generalized statistical approach for modeling fiber-reinforced materials

We present a generalized statistical approach for the description of fully three-dimensional fiber-reinforced materials, resulting from the composition of two independent probability distribution functions of two spherical angles. We discuss the consequences of the proposed formulation on the constitutive behavior of fibrous materials. Upon suitable assumptions, the generalized formulation recovers existing alternative models, based on averaged structure tensors both at first- and second-order approximations. We demonstrate that the generalized formulation embeds standard behaviors of fiber-reinforced materials such as planar isotropy and transverse isotropy, while any intermediate behavior is easily obtained through the calibration of two material parameters. We illustrate the performance of the model by means of uniaxial and biaxial tests. For uniaxial loading, we introduce a preliminary discussion concerning the generalized tension–compression switch procedure.

Mean-field models for non-Markovian epidemics on networks

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission the message passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length.

Sand particle lift-off velocity measurements and numerical simulation of mass flux distributions in a wind tunnel

Lift-off velocity of saltating sand particles in wind-blown sand located at 1.0 mm above the sand bed surface was measured using a phase Doppler particle analyzer in a wind tunnel. The results show that the probability distribution of lift-off velocity can be expressed as a lognormal function, while that of lift-off angle follows an exponential function. The probability distribution of lift-off angle conditioned for each lift-off velocity also follows an exponential function, with a slope that becomes steeper with increasing lift-off velocity. This implies that the probability distribution of lift-off velocity is strongly dependent on the lift-off angle. However, these lift-off parameters are generally treated as an independent joint probability distribution in the literature. Numerical simulations were carried out to investigate the effects of conditional versus independent joint probability distributions on the vertical sand mass flux distribution. The simulation results derived from the conditional joint probability distribution agree much better with experimental data than those from the independent ones. Thus, it is better to describe the lift-off velocity of saltating sand particles using the conditional joint probability distribution. These results improve our understanding of saltation processes in wind-blown sand.

Energy-aware stochastic scheduler for batch of precedence-constrained jobs on heterogeneous computing system

The problem of optimal scheduling of precedence-constrained jobs as well as finding the Pareto-optimal sets for multi objective scheduling problem have been proven to be nondeterministic polynomial time (NP)-complete. The growing consumption of energy has compelled the researchers to consider energy consumption as an important parameter along with other parameters in multi-objective scheduling problem. Accordingly, many energy-aware precedence-constraints scheduling algorithms have been reported in the literature. Most of the algorithms have a limitation of treating this problem as a single objective optimization problem modelling with deterministic execution times rather than stochastic execution times. This work proposes energy-aware stochastic scheduler to schedule the batch of precedence-constrained jobs on dynamic voltage frequency scaling-enabled processors in order to optimize the energy consumption and the turnaround time. The execution and inter-communication times are stochastic which are drawn from independent probability distributions. A novel encoding for batch of precedence-constrained jobs, stochastic turnaround time and energy models are also proposed. Experimental results show that, compared with other algorithms, the proposed scheduler offers reduced turnaround time and reduced energy consumption.

Analytical equilibrium of bicriterion choices with heterogeneous user preferences: application to the morning commute problem

ABSTRACTThe morning commute problem, introduced in Vickrey [1969. “Congestion Theory and Transport Investment.” American Economic Review 56: 251–260], addresses the equilibrium trip schedule of the users for commuting through a single bottleneck with fixed capacity over the morning peak. In this paper, we adapt the concept of the efficient frontier from Portfolio Theory [Markowitz, H. 1952. “Portfolio Selection.” The Journal of Finance 7 (1): 77–91] to propose an analytical solution to the morning commute problem with a general distribution of the schedule preferences over time and a continuous joint distribution of schedule penalty preferences over the population of the commuters. On this basis, we analytically derive the equilibrium arrivals of the heterogeneous commuters to the bottleneck given the independent probability distributions of earliness and lateness penalty factors. We also propose a method to retrieve independent probability distributions of the schedule penalty factors in the equilibrium condition from a joint distribution. The proposed model can be inversely used to approximate the independent distribution of schedule penalty preferences of the user for the early and late commuters using empirical arrival time data from the network. The result is also used to propose a dynamic pricing strategy to optimize the system by avoiding the formation of a queue, which can also be extended to design a dynamic pricing strategy on the network level using the macroscopic fundamental diagram (MFD). To provide an example, the approach is employed to derive a closed-form solution when the probability distribution of the preferences is uniform. A numerical example is also presented using the proposed model to compare the solutions for different distributions of the schedule deviation penalty preferences.

Manifest and Subtle Cyclic Behavior in Nonequilibrium Steady States

Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the system settles in a stationary state, it will be a nonequilibrium steady state (NESS), with time independent probability distribution as well as persistent probability current loops. The observable consequences of the latter are explored. In particular, cyclic behavior of some form must be present: some are prominent and manifest, while others are more obscure and subtle. We present a theoretical framework to analyze such properties, introducing the notion of “probability angular momentum” and its distribution. Using several examples, we illustrate the manifest and subtle categories and how best to distinguish between them. These techniques can be applied to reveal the NESS nature of a wide range of systems in a large variety of areas. We illustrate with one application: variability of ocean heat content in our climate system.

A surrogate method for density-based global sensitivity analysis

This paper describes an accurate and computationally efficient surrogate method, known as the polynomial dimensional decomposition (PDD) method, for estimating a general class of density-based f-sensitivity indices. Unlike the variance-based Sobol index, the f-sensitivity index is applicable to random input following dependent as well as independent probability distributions. The proposed method involves PDD approximation of a high-dimensional stochastic response of interest, forming a surrogate input–output data set; kernel density estimations of output probability density functions from the surrogate data set; and subsequent Monte Carlo integration for estimating the f-sensitivity index. Developed for an arbitrary convex function f and an arbitrary probability distribution of input variables, the method is capable of calculating a wide variety of sensitivity or importance measures, including the mutual information, squared-loss mutual information, and L1-distance-based importance measure. Three numerical examples illustrate the accuracy, efficiency, and convergence properties of the proposed method in computing sensitivity indices derived from three prominent divergence or distance measures. A finite-element-based global sensitivity analysis of a leverarm was performed, demonstrating the ability of the method in solving industrial-scale engineering problems.

Effect of ignoring input correlation on truck–shovel simulation

This paper presents an approach for handling correlated input variables in discrete event simulation (DES) modelling of truck–shovel systems using commercial DES software and uses a case study to investigate the effect of ignoring correlation between input variables. Multivariate random vectors, instead of independent probability distributions, are used for variables found to be correlated. The authors prove that correlations do exist in truck–shovel haulage systems. The model with multivariate random vectors performs better than the original model. The significance of modelling correlation in input variables depends on the strength of the correlation and the output’s sensitivity to the input variables.

Energy-aware stochastic scheduling model with precedence constraints on DVFS-enabled processors

The stochastic scheduling of precedence-constrained jobs on a heterogeneous processor is a challenging problem that requires solutions with one or more optimized QoS parameters. In this work, an energy-aware stochastic algorithm is proposed to schedule the batch of precedence-constrained jobs on heterogeneous DVFS-enabled processors with the objective of optimizing turnaround time and energy consumption. The processing time of tasks in all jobs and their precedence-constraint times are governed by independent probability distributions. The performance of the proposed stochastic algorithm is compared with SHEFT and ECS based on randomly generated batches of different sizes. The experimental study reveals that the proposed algorithm significantly outperforms the SHEFT and ECS algorithms in terms of turnaround time and energy consumption.