Instantaneous Probability Research Articles

Connectivity of UAV Swarms in 3D Spherical Spaces Under (Un)Intentional Ground Interference

This paper analyzes the wireless connectivity of an Unmanned Aerial Vehicle (UAV) swarm in the presence of (un)intentional external interference from the ground. Different from existing studies, the swarm UAVs fly independently around a given three-dimensional (3D) location and are all within a 3D spherical space. Closed-form bounds are delivered for the average outage probability of a UAV from its nearest neighbor in the swarm, and the density of the swarm, which allows the swarm to operate uninterruptedly in the presence of the interference. Our analysis involves closed-form approximations of the instantaneous outage probability of a UAV from its nearest neighbor by using the first-order Marcum Q-function and the zero-th order modified Bessel function of the first kind. The analysis also involves applying Jensen's inequality to the instantaneous outage probability to bound the average outage probability and the density of the swarm. Corroborated by simulations, our analysis is accurate, and useful to evaluate the impact of external interference on the connectivity of UAV swarms. Interesting insights are shed on the connectivity and coverage of the UAV swarm.

Experimental observations on fine sand winnowing from immobile gravel substrate

Introduction of fine sand into gravel-bed rivers has surged tremendously as a result of human activities. The ecological concerns for river habitats have called for suitable management strategies for cleaning these particles from gravel bed rivers. This paper is concerned with determining movement threshold of fine sand initially entrapped in the spaces between large immobile elements resembling a coarse riverine substrate with flow depths comparable to non-erodible element sizes. Static equilibrium condition was reached during an experimental run by maintaining a zero-supply condition for sand. It was assumed that the flow condition corresponding to this sand level was representative of critical conditions for onset of sand motion. A nonlinear regression curve was fitted between the level of the sand and associated critical shear stress. The flow field measurements using an ultrasonic Doppler rofiler delineate main features of the shallow flow over large roughness elements such as sharp velocity gradients near the crest of the immobile elements, and also a deviation of instantaneous velocity probability density function from normal distribution very close to the sand level.

Patient Age and Survival After Surgery for Esophageal Cancer

BackgroundEsophagectomy for esophageal cancer is associated with a substantial risk of life-threatening complications and a limited long-term survival. This study aimed to clarify the controversial questions of how age influences short-term and long-term survival.MethodsThis population-based cohort study included almost all patients who underwent curatively intended esophagectomy for esophageal cancer in Sweden in 1987–2010, with follow-up through 2016. The exposure was age, analyzed both as a continuous and categorical variable. The probability of mortality was computed using a novel flexible parametric model approach. The reported probabilities are proper measures of the risk of dying, and the related odds ratios (OR) are therefore more suitable measures of association than hazard ratios. The outcomes were 90-day all-cause mortality, 5-year all-cause mortality, and 5-year disease-specific mortality. A novel flexible parametric model was used to derive the instantaneous probability of dying and the related OR along with 95% confidence intervals (CIs), adjusted for sex, education, comorbidity, tumor histology, pathological tumor stage, and resection margin status.ResultsAmong 1737 included patients, the median age was 65.6 years. When analyzed as a continuous variable, older age was associated with slightly higher odds of 90-day all-cause mortality (OR 1.05, 95% CI 1.02–1.07), 5-year all-cause mortality (OR 1.02, 95% CI 1.01–1.03), and 5-year disease-specific mortality (OR 1.01, 95% CI 1.01–1.02). Compared with patients aged < 70 years, those aged 70–74 years had no increased risk of any mortality outcome, while patients aged ≥ 75 years had higher odds of 90-day mortality (OR 2.85, 95% CI 1.68–4.84), 5-year all-cause mortality (OR 1.56, 95% CI 1.27–1.92), and 5-year disease-specific mortality (OR 1.38, 95% CI 1.09–1.76).ConclusionsPatient age 75 years or older at esophagectomy for esophageal cancer appears to be an independent risk factor for higher short-term mortality and lower long-term survival.

How Fast Do Quantum Walks Mix?

The fundamental problem of sampling from the limiting distribution of quantum walks on networks, known as mixing, finds widespread applications in several areas of quantum information and computation. Of particular interest in most of these applications is the minimum time beyond which the instantaneous probability distribution of the quantum walk remains close to this limiting distribution, known as the "quantum mixing time". However, this quantity is only known for a handful of specific networks. In this Letter, we prove an upper bound on the quantum mixing time for almost all networks, i.e., the fraction of networks for which our bound holds, goes to one in the asymptotic limit. To this end, using several results in random matrix theory, we find the quantum mixing time of Erdös-Renyi random networks: networks of n nodes where each edge exists with probability p independently. For example, for dense random networks, where p is a constant, we show that the quantum mixing time is O(n^{3/2+o(1)}). In addition to opening avenues for the analytical study of quantum dynamics on random networks, our work could find applications beyond quantum information processing. Owing to the universality of Wigner random matrices, our results on the spectral properties of random graphs hold for general classes of random matrices that are ubiquitous in several areas of physics. In particular, our results could lead to novel insights into the equilibration times of isolated quantum systems defined by random Hamiltonians, a foundational problem in quantum statistical mechanics.

Improved Availability Index for Repairable Fuzzy Multi-State Systems

Fuzzy multi-state systems (FMSSs) comprise FMS components (FMSCs) aims at analyzing non-probabilistic uncertain circumstances defined by fuzzy state-transition rate and performance numbers. The triangular fuzzy number that features intuitive and algebraic operations is widely used for quantifying fuzziness. This study aims to overcome the drawbacks of the existing FMSS availability index that either does not conform to a normal convex set or is inconsistent with the crisp-circumstance multi-state system (MSS) availability beyond summation over state probabilities that do no equal unity. The proposed method first evaluates the instantaneous state probability (ISP) of FMSCs by establishing the FMSCs Markov model. Subsequently, the FMSSs ISP is evaluated by integrating the FMSCs ISP using the fuzzy universal generating function based on the system-structure function. A “constrained nonlinear parameter programming model” has been developed to evaluate the improved FMSSs availability. The corresponding availability index features the normal convex set whilst fulfilling the MSS theory, which requires state probabilities to equal unity during availability evaluation. The effectiveness of the proposed approach has been verified using an illustrated community-based smart-grid system comprising three FMSCs—solar- and wind-energy systems as well as diesel-generator equipment. Moreover, the results of an independent sensitive analysis provide further insights into the improved FMSSs availability with regard to the time and circumstance fuzziness.

The Study of Dynamic Caching via State Transition Field—the Case of Time-Invariant Popularity

In the second part of this two-part paper, we extend the study of dynamic caching via state transition field (STF) to the case of time-varying content popularity. The objective of this part is to investigate the impact of time-varying content popularity on the STF and how such impact accumulates to affect the performance of a replacement scheme. Unlike the case in the first part, the STF is no longer static over time, and we introduce instantaneous STF to model it. Moreover, we demonstrate that many metrics, such as instantaneous state caching probability and average cache hit probability over an arbitrary sequence of requests, can be found using the instantaneous STF. As a steady state may not exist under time-varying content popularity, we characterize the performance of replacement schemes based on how the instantaneous STF of a replacement scheme after a content request impacts on its cache hit probability at the next request. From this characterization, insights regarding the relations between the pattern of change in the content popularity, the knowledge of content popularity exploited by the replacement schemes, and the effectiveness of these schemes under time-varying popularity are revealed. In the simulations, different patterns of time-varying popularity, including the shot noise model, are experimented. The effectiveness of example replacement schemes under time-varying popularity is demonstrated, and the numerical results support the observations from the analytic results.

The Study of Dynamic Caching via State Transition Field—the Case of Time-Varying Popularity

In the second part of this two-part paper, we extend the study of dynamic caching via state transition field (STF) to the case of time-varying content popularity. The objective of this part is to investigate the impact of time-varying content popularity on the STF and how such impact accumulates to affect the performance of a replacement scheme. Unlike the case in the first part, the STF is no longer static over time, and we introduce instantaneous STF to model it. Moreover, we demonstrate that many metrics, such as instantaneous state caching probability and average cache hit probability over an arbitrary sequence of requests, can be found using the instantaneous STF. As a steady state may not exist under time-varying content popularity, we characterize the performance of replacement schemes based on how the instantaneous STF of a replacement scheme after a content request impacts on its cache hit probability at the next request. From this characterization, insights regarding the relations between the pattern of change in the content popularity, the knowledge of content popularity exploited by the replacement schemes, and the effectiveness of these schemes under time-varying popularity are revealed. In the simulations, different patterns of time-varying popularity, including the shot noise model, are experimented. The effectiveness of example replacement schemes under time-varying popularity is demonstrated, and the numerical results support the observations from the analytic results.

Early warning system for rainfall-triggered landslides based on real-time probabilistic hazard assessment

A methodology to define rainfall-landslide thresholds, using a probabilistic model in which the accumulated rainfall at any time is treated as a random variable, is proposed. The region under study is divided into areas of homogeneous rain hazard. For each homogeneous area, a probability model is fitted using state-of-the-art statistical methods, for each accumulation time considered. Thresholds are obtained by the definition of confidence intervals. Instantaneous accumulated rains, measured in real-time, are used to calculate the instantaneous probabilities of a landslide at each area and accumulation time. The maximum instantaneous probability determines the critical accumulated rain and sets the issued warning level. In addition, the model is tested, retrospectively, with the data for the disaster of April 19, 2017, in Manizales, Colombia, where 38 rainfall-triggered landslides killed 17 people and affected more than 3126 families.

Short-Term Reliability Assessment of UHVdc Systems Based on State Aggregation With SMP

The short-term reliability of the ultra-high-voltage dc (UHVdc) systems has enormous influence on the security of the whole power system. The frequency and duration (F&D) algorithm based on the Markov process (MP) will reduce the accuracy of the short-term reliability indices, due to the exponentially distributed parameters and the strict premises for the state aggregation and combination. In this paper, the short-term aggregation algorithm based on the semi-MP (SMP) is improved. The aggregated transfer rates are obtained by the definition of the semi-Markov kernel elements and the invariability of the transfer probabilities before and after aggregation. The algorithm is applied to the series structure system, which is common in UHVdc. The aggregated kernel matrix and instantaneous transfer probability matrix are derived from those before aggregation directly. A new method is proposed to describe the combined transfer rates by matrices combination and deleting the nonexistent states and transitions, which requires less calculation effort. The Erlang and Weibull distributions are first used to fit the bell-shaped probability density functions (PDFs) of the repair times of the equipments in the UHVdc. The numerical examples show that, compared with the SMP algorithm, the traditional F&D algorithm overestimates the instantaneous equivalent outage hours of the UHVdc. The error is originated from that the F&D algorithm regards the aggregated system as a MP while it is non-Markovian. To show the effectiveness of the bell-shaped repair time, the Erlang and Weibull distributions are compared with the exponential one by the reliability indices. The differences are result from the different PDFs of these distributions.

Analysis of Non-Stationary 3D Air-to-Air Channels Using the Theory of Algebraic Curves

Non-stationary channel models play a crucial role in today’s communication systems. Mobile-to-mobile channels are known to exhibit non-stationary behavior caused by the movement of transmitter and receiver. Non-stationarity can be addressed by introducing time-variant stochastic functions such as the time-variant instantaneous Doppler probability density function or time-variant instantaneous characteristic function. An algebraic analysis of the time-variant Doppler probability density function (pdf) in a classical Cartesian coordinate system is only numerically tractable due to trigonometric functions in the resulting expressions. In contrast, it has been shown that by using prolate spheroidal coordinates for 2D vehicle-to-vehicle channels the algebraic analysis becomes analytically tractable. In this paper, the analysis is extended to air-to-air channels. It is shown that the time-variant Doppler pdf can be represented without trigonometric functions. The description of the Doppler frequency in prolate spheroidal coordinates allows describing it as an algebraic curve. This permits the use of algebraic methods to analyze the Doppler frequency and derive the boundaries of the resulting Doppler pdf. Using the developed tools, we have investigated exemplary air-to-air scenarios. However, the methodology can be extended to any air-to-air configuration.

Stability evaluation of laser-MAG hybrid welding process

This paper describes the laser-MAG hybrid welding of high-strength steel (HSS) formulated with 1.2 mm diameter austenitic stainless steel (ASS) filler wire. A high-speed camera and Hannover analyzers were used to obtain real-time images of droplets and electrical signals during the hybrid welding process. Image processing and mathematical statistics were performed to study how the ratio of laser power to arc power affected the weld morphology, droplet transfer characteristics, instantaneous current probability density. The welding stability was evaluated by using the variation rate of weld width as the main reference. This study provides the fundamentals necessary to select reasonable parameters to obtain better weld stability during the laser-MAG hybrid welding process. The results of this study show that both the laser power and arc power strongly influence both the penetration depth and the width of the weld during the laser-MAG hybrid welding process, respectively. The droplet transfer mode and the ratio of laser energy to arc energy are strongly affected by the distance between the laser and the arc in the laser-MAG hybrid welding process. The droplets have a negligible effect on the keyholes when the distance between the laser and arc is in the range of 2.5–3.5 mm. The welding current is 160 A, which is the critical current of short-circuiting transfer to globular transfer. The critical transition current of globular transfer and projected transfer was shown to occur at a welding current of 180 A. When the welding current is 206 A, the critical transition current of projected transfer and spray transfer is observed. When the welding current is 206–240 A, the fluctuation of the width of weld beam is not significant. When the droplet transfer mode is projected transfer, the welding stability is the best.

Uncertainty-Dependent Warning Threshold for Spacecraft Rendezvous Collision Probability

This paper proposes a warning threshold calculation method for instantaneous collision probability in a spacecraft rendezvous mission. By introducing missing alarm probability, the warning threshold is determined as a function of the propagated trajectory uncertainty and a semianalytical calculation model is presented. The simulation results show that the proposed method makes good use of trajectory uncertainty information and provides a reasonable and accurate method for evaluating the safety of a rendezvous trajectory with uncertainty.

Free-Space Optical Communication Using Coherent Detection and Double Adaptive Detection Thresholds

In this paper, on-off Keying free-space optical (FSO) communication with coherent detection and double adaptive detection thresholds is proposed. The 3-bit encoding and double adaptive detection thresholds presented in the scheme can significantly improve the system performance, and there is no need of acquiring the instantaneous channel state information and probability density function (pdf) of the turbulence model. In order to enhance the accuracy of the threshold even further, the decision-aided method is offered to set the second detection threshold. The pdfs of the detection thresholds and the average bit error rate (BER) of the system are theoretically derived. Numerical studies show that the performance of the system is comparable to the performance of the idealized adaptive detection system and the loss of the signal-to-noise ratio (SNR) performance is only 1 dB at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> over a lognormal turbulence channel with normalized standard deviation of irradiance σ = 0.25 and phase noise with normalized variance $\sigma _{\phi}^2 = 0.07$. Hence, this scheme can contribute to the performance improvement of the FSO system and its practical realization.

Multi-scale Dynamic System Reliability Analysis of Actively-controlled Structures under Random Stationary Ground Motions

This paper proposes a multi-scale dynamic system reliability analysis approach to assess the failure probability of an activelycontrolled structure subject to random stationary ground motions. The proposed approach employs a multi-scale hierarchical framework where a lower-scale system reliability analyses compute the failure probabilities of the structural members during the earthquakes and a higher-scale system reliability analysis computes the failure probability of the structural system based on results of the lower-scale analyses. The multi-scale framework facilitates the system reliability analysis of the large-sized complex system by decomposing the complex system into the manageable-sized subsystems. It also enables us to deal with statistical dependence both in spatial and temporal senses through the decomposition of the reliability analysis in space and time aspects. In these regards, the proposed approach performs a reliability analysis with the dynamic responses in time domain. This dynamic reliability analysis approach can consider uncertainties in system parameters and earthquake excitations simultaneously. In addition, the peak response over a time duration is used to describe the limit state of the structural system, which provides a more realistic measure of the failure probability of a structural system than instantaneous probability. In order to demonstrate the proposed approach, a 3-story shear-type building equipped with an optimal active control device is considered. The control performance under uncertainties is investigated through the reliability assessment by the proposed approach and the Monte Carlo Simulation (MCS) approach, respectively. The numerical study also investigates the influence of the uncertainties in the system parameters and the earthquake excitations on the system failure probability. The results of the numerical examples demonstrate that the proposed approach can efficiently estimate the system reliability and the failure probability of an actively-controlled structure.

A Study of Single Transmit Antenna Selection with Modulation

Multiple-input multiple-output (MIMO) systems have attracted a vast amount of interest, due to improvements offered in capacity and diversity. However, several challenges still remain. Single transmit antenna selection with modulation (STASM) is an important closed-loop variant of MIMO, and addresses several of its challenges, while achieving full-diversity. On this note, the average symbol error probability (ASEP) of STASM with M-ary quadrature amplitude modulation (M-QAM) and M-ary phase shift keying (M-PSK) is formulated and validates the Monte Carlo simulation results. The formulated ASEP expressions are relatively easy to evaluate. Euclidean distance-based antenna selection for spatial modulation (EDAS-SM) is an innovative closed-loop MIMO scheme that provides many advantages. However, since STASM achieves a full-diversity compared to EDAS-SM, there exists a cross-over point after which its error performance is superior to the latter. For multiple receive antennas, the cross-over point only occurs in the moderate-to-high signal-to-noise ratio region, which may be difficult to achieve in practice. Hence, an adaptive transmit mode switching system based on STASM and EDAS-SM as transmission candidates is proposed. A selection criterion for the transmission candidate is based on minimizing the instantaneous symbol error probability in every transmission interval. By switching between STASM and EDAS-SM, the proposed scheme minimizes the ASEP.

Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.

Probabilistic retinal exposure model

Exposure of retinal tissue to a laser source requires two conditions: the person must be exposed to the laser beam and the laser must be in his/her optical field-of-view. The authors have developed a probabilistic model for the second condition. This model is based on random eye movements, known as saccades, about a look direction. This direction is an input to the model and is known either from head orientation or a task. The model calculates the instantaneous probability that the laser is in the optical field-of-view of the retinal tissues of fovea, macula, and retina. Because of saccades, the location of exposure will change several times a second. The duration of laser exposure for the look direction is then used to calculate the probability that the retinal tissue is exposed at least once, based on independent exposures from the saccades. The concepts and equations of the model are presented, along with example calculations from applying the model to a specific exposure scenario. For a given retinal tissue optical field-of-view, the primary contributor to the probability of exposure is the angle between the look direction and the laser.Exposure of retinal tissue to a laser source requires two conditions: the person must be exposed to the laser beam and the laser must be in his/her optical field-of-view. The authors have developed a probabilistic model for the second condition. This model is based on random eye movements, known as saccades, about a look direction. This direction is an input to the model and is known either from head orientation or a task. The model calculates the instantaneous probability that the laser is in the optical field-of-view of the retinal tissues of fovea, macula, and retina. Because of saccades, the location of exposure will change several times a second. The duration of laser exposure for the look direction is then used to calculate the probability that the retinal tissue is exposed at least once, based on independent exposures from the saccades. The concepts and equations of the model are presented, along with example calculations from applying the model to a specific exposure scenario. For a given retinal ...

Power Allocation for Pre-Coding-Aided Spatial Modulation

In this letter, power allocation (PA) algorithms based on the minimization of the upper bound of the instantaneous bit error probability (BEP) are investigated in pre-coding-aided spatial modulation (PSM) systems. First, an upper bound of the instantaneous BEP is derived when PA is taken into account for the antennas in the PSM system. Moreover, the optimal solution of the PA matrix is derived with the aid of convex optimization techniques, in order to minimize the BEP obtained. Furthermore, a low-complexity suboptimal PA algorithm is proposed, where only the dominant part of the BEP upper bound is considered in the optimization process. Simulation results demonstrate that the proposed algorithms improve on the conventional PSM scheme. Furthermore, when the number of receive antennas is large, the performance of the low-complexity suboptimal PA algorithm is close to that of the optimal PA algorithm.

Simulation-based approach for estimation of stochastic performances of deteriorating engineering systems

Engineering systems suffer from deterioration over time due to either aging, regular operation, or extreme loading/environmental conditions. It is critical to model and incorporate deteriorations in the stochastic performance assessment of deteriorating engineering systems. However, deterioration modeling usually entails complex models and large number of uncertainties, where closed-form solutions are not available for estimation of the stochastic performance measures. Some of the traditional approaches face challenges in handling nonlinear models and large number of uncertainties. This paper discusses the use of general simulation-based approach for estimation of the stochastic performance of deteriorating engineering systems. The simulation-based approach allows consideration of various uncertainties associated with the external conditions, deterioration models, performance valuation models, and puts no constraints on the complexity of the adopted models. Simulation-based estimation of performance measures such as instantaneous failure probability, number of shocks to failure, and failure time are established. Also, simulation-based evaluation of various life-cycle performance quantities is discussed with a focus on simulating samples from the probability distributions needed for this evaluation. As key steps in the approach and also the novel contributions, the paper develops explicit simulation steps and equations for the simulation of the stochastic load occurrence, realizations of deterioration processes considering both gradual and shock deteriorations with state-dependent deterioration models, as well as samples for estimating life-cycle performance quantities. Adoption of advanced simulation techniques (e.g., Importance Sampling) is also discussed to further improve the estimation efficiency and reduce the computational effort. The developed simulation-based approach is applied to the stochastic performance evaluation of a reinforced concrete (RC) bridge considering deterioration caused by both earthquakes and chloride-induced corrosion. The computational performance is discussed in detail within the context of the example.

Tracking Temporal Hazard in the Human Electroencephalogram Using a Forward Encoding Model.

Human observers automatically extract temporal contingencies from the environment and predict the onset of future events. Temporal predictions are modeled by the hazard function, which describes the instantaneous probability for an event to occur given it has not occurred yet. Here, we tackle the question of whether and how the human brain tracks continuous temporal hazard on a moment-to-moment basis, and how flexibly it adjusts to strictly implicit variations in the hazard function. We applied an encoding-model approach to human electroencephalographic data recorded during a pitch-discrimination task, in which we implicitly manipulated temporal predictability of the target tones by varying the interval between cue and target tone (i.e. the foreperiod). Critically, temporal predictability either was driven solely by the passage of time (resulting in a monotonic hazard function) or was modulated to increase at intermediate foreperiods (resulting in a modulated hazard function with a peak at the intermediate foreperiod). Forward-encoding models trained to predict the recorded EEG signal from different temporal hazard functions were able to distinguish between experimental conditions, showing that implicit variations of temporal hazard bear tractable signatures in the human electroencephalogram. Notably, this tracking signal was reconstructed best from the supplementary motor area, underlining this area’s link to cognitive processing of time. Our results underline the relevance of temporal hazard to cognitive processing and show that the predictive accuracy of the encoding-model approach can be utilized to track abstract time-resolved stimuli.