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The molecular movement in single particle tracking (SPT) experiments shows a crucial role of diffusion in many biological processes such as signaling, cellular organization, transport mechanisms, and more. The SPT analysis detects not only classical Brownian motion but diffusion with other features. These include directed diffusion and confined motion. The behavior remains a challenging problem for several reasons. Due to the action of many physical processes, random trajectories of cellular molecules are segmented in different diffusive modes. Often their study requires sophisticated algorithms for the analysis of statistical properties. In this paper we consider the segment analysis for trajectories of G proteins and coupled-receptors in living cells. Their movement is often transient and switches among free diffusion, confined diffusion, directed diffusion, and immobility. Moreover, the confined segments can have both Gaussian and non-Gaussian statistics. The types of alternation of diffusive modes along the trajectories of G proteins and coupled-receptors are analyzed. [ABSTRACT FROM AUTHOR]

Renewable integration in utility grid is crucial in the current energy scenario. Optimized utilization of renewable energy can minimize the energy consumption from the grid. This demands accurate forecasting of renewable contribution and planning. Most of the researches aim to find a suitable forecasting model in terms of accuracy and error metrics. However, the uncertainty and variability in these forecasts are also significant. This work combines point forecast with interval forecast to provide comprehensive information about the forecast uncertainty. In this work, solar irradiance forecasting is carried out using artificial intelligence (AI) techniques. Forecasting is done using seasonal auto-regressive moving average with exogenous factors (SARIMAX), support vector regression (SVR), long short term memory (LSTM) techniques and performance is evaluated. SVR model exhibited the best performance with R 2 values of 0.97 and 0.96 for winter and summer respectively and 0.85 for monsoon and post-monsoon seasons. This is followed by forecast error distribution studies and uncertainty analysis. For this, SVR forecast error data is fitted using laplace distribution. Uncertainty study is carried out using confidence intervals and coverage rates. Excellent coverage rates are obtained for various confidence levels for all seasons, indicating the appropriate fitting of error distribution. For the narrow 85% confidence band, coverage rates of 89%, 95%, 90%, and 88% are obtained for winter, summer, monsoon and post-monsoon respectively. The work emphasizes the need for error-distribution studies, modeling of forecast errors and their application in providing reliable forecast intervals with the perspective of enhancing system reliability. [ABSTRACT FROM AUTHOR]

In the area of information retrieval, in order to improve search accuracy and reduce communication overhead, there is an increasing tendency to adopt ranked search in engines. Ranked search allows cloud servers to search for the top k most relevant documents based on the relevance score between the query keywords and the documents. Recently, with the increasing popularity of encrypted search technologies, ranked searchable encryption is proposed accordingly which focuses on solving ranked search problem over encrypted databases. However, recent studies show that some privacy protection methods commonly used in ranked searchable encryption, like order-preserving encryption (OPE), have some security problems. These problems may lead to the leakage of the relevant ranking privacy information. Meanwhile, most of the existing ranked searchable encryption schemes do not consider the problem of payment for outsourced services. In this paper, we propose a scheme called ranked searchable encryption based on differential privacy and blockchain (DPB-RSE). Specifically, we first add noise drawn from a Laplace distribution into the relevance score to disturb its value. Then we design a smart contract to verify the correctness of the results returned by the cloud server and realize payment fairness. The experiment results demonstrate that the accuracy of search results in this scheme can reach 94% in a small privacy budge. [ABSTRACT FROM AUTHOR]

According to the Ray-Knight description, the Brownian local time in some conditional probability space is a diffusion process with respect to spatial variable. This diffusion has a local time. Thus the following definition of local time of the original Brownian local time seems to be natural: such a process is called the second-order Brownian local time. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order. [ABSTRACT FROM AUTHOR]

A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for unsupervised classification of asymmetric clusters in the presence of outliers and noise. A series of constraints are applied to a modified factor analyzer structure of the component scale matrices, yielding a family of twelve models. Application of the modified factor analyzer structure and these parsimonious constraints makes these models effective for the analysis of high-dimensional data by reducing the number of free parameters that need to be estimated. A variant of the expectation-maximization algorithm is developed for parameter estimation with convergence issues being discussed and addressed. Popular model selection criteria like the Bayesian information criterion and the integrated complete likelihood (ICL) are utilized, and a novel modification to the ICL is also considered. Through a series of simulation studies and real data analyses, that includes comparisons to well-established methods, we demonstrate the improvements in classification performance found using the proposed family of models. [ABSTRACT FROM AUTHOR]

We present a novel depth from focus technique. Following prior work, our pipeline starts with a focal stack and an estimation of the amount of defocus as given by, for instance, the ring difference filter. To improve robustness to outliers while avoiding to rely on costly nonlinear optimizations, we propose an original scheme that linearly scans the profile over a fixed size window, searching for the best peak within each window using a linearized least-squares Laplace regression. As a post-process, depth estimates with low confidence are reconstructed though an adaptive moving least squares filter. We show how to objectively evaluate the performance of our approach by generating synthetic focal stacks from which the reconstructed depth maps can be compared to ground truth. Our results show that our method achieves higher accuracy than previous nonlinear Laplace regression technique, while being orders of magnitude faster. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]