Random Process Research Articles

Why Biological Evolution Should Inspire Worship

The theory of biological evolution has often provoked disagreement, which has frequently been divisive and counterproductive. At other times this scientific paradigm has been discussed with an apologetic intent, to explain why the science of biology and the theology of creation cannot be seen to be mutually exclusive. This paper urges Christians to move decisively to a third type of discourse. The new field of comparative genetics has provided conclusive evidence that biological evolution has given rise to the diversity of living forms, including human beings. Consequently, Christians should, with confidence, gladly accept the evolutionary paradigm and look upon evolution as a divinely ordained historical process that develops through random (stochastic, free) process, but that leads to a divinely purposed consummation. As a result, biological history in its freedom but directedness to God’s final purposes should elicit wonder. People who have come to faith in the God revealed redemptively in Jesus should uninhibitedly offer adoration and praise for evolutionary fruitfulness. Worship should characterise the human response to biological history.[1]
 
 [1] In appreciation of Professor Tom McLeish FRS, scientist, teacher, theologian.

Randomized Nonuniform Sampling for Random Signals Bandlimited in the Special Affine Fourier Transform Domain

The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process of uniform sampling after a prefilter in the statistic sense. Then, an approximate reconstruction method based on sinc interpolation is proposed for the randomized nonuniform sampling of SAFT-bandlimited random signals. Finally, we offer the mean square error estimate for the corresponding approximate recovery approach. The results generalize the conclusions of nonuniform sampling of bandlimited random signals in the FrFT and LCT domains to the SAFT domain.

Chemical unclonable functions based on operable random DNA pools

Physical unclonable functions (PUFs) based on unique tokens generated by random manufacturing processes have been proposed as an alternative to mathematical one-way algorithms. However, these tokens are not distributable, which is a disadvantage for decentralized applications. Finding unclonable, yet distributable functions would help bridge this gap and expand the applications of object-bound cryptography. Here we show that large random DNA pools with a segmented structure of alternating constant and randomly generated portions are able to calculate distinct outputs from millions of inputs in a specific and reproducible manner, in analogy to physical unclonable functions. Our experimental data with pools comprising up to >1010 unique sequences and encompassing >750 comparisons of resulting outputs demonstrate that the proposed chemical unclonable function (CUF) system is robust, distributable, and scalable. Based on this proof of concept, CUF-based anti-counterfeiting systems, non-fungible objects and decentralized multi-user authentication are conceivable.

Complex-order scale-invariant operators and self-similar processes

In this paper, we perform the joint study of scale-invariant operators and self-similar processes of complex order. More precisely, we introduce general families of scale-invariant complex-order fractional-derivation and integration operators by constructing them in the Fourier domain. We analyze these operators in detail, with special emphasis on the decay properties of their output. We further use them to introduce a family of complex-valued stable processes that are self-similar with complex-valued Hurst exponents. These random processes are expressed via their characteristic functionals over the Schwartz space of functions. They are therefore defined as generalized random processes in the sense of Gel'fand. Beside their self-similarity and stationarity, we study the Sobolev regularity of the proposed random processes. Our work illustrates the strong connection between scale-invariant operators and self-similar processes, with the construction of adequate complex-order scale-invariant integration operators being preparatory to the construction of the random processes.

Damage Detection in Bridge Structures through Compressed Sensing of Crowdsourced Smartphone Data

Traditional bridge health monitoring methods that necessitate sensor installation are not only costly but also time-consuming. In contrast, utilizing smartphone data collected from vehicles as they traverse bridges offers an efficient and cost-effective alternative. This paper introduces a cutting-edge damage detection framework for indirect monitoring of bridge structures, leveraging a substantial volume of acceleration data collected from smartphones in vehicles passing over the bridge. Our innovative approach addresses the challenge of collecting and transmitting high-frequency data while preserving smartphone battery life and data plans through the integration of compressed sensing (CS) into the crowdsensing-based monitoring framework. CS employs random sampling and signal recovery from a significantly reduced number of samples compared to the requirements of the Nyquist–Shannon sampling theorem. In the proposed framework, acceleration signals from vehicles are initially acquired using smartphone sensors, undergo compression, and are then transmitted for signal reconstruction. Subsequently, feature extraction and dimensionality reduction are performed using Mel-frequency cepstral coefficients and principal component analysis. Damage indexes are computed based on the dissimilarity between probability distribution functions utilizing the Wasserstein distance metric. The efficacy of the proposed methodology in bridge monitoring has been substantiated through the utilization of numerical models and a lab-scale bridge. Furthermore, the feasibility of implementing the framework in a real-world application has been investigated, leveraging the smartphone data from 102 vehicle trips on the Golden Gate Bridge. The results demonstrate that damage detection using the reconstructed signals obtained through compressed sensing achieves comparable performance to that obtained with the original data sampled at the Nyquist measurement sampling rate. However, it is observed that to retain severity information within the signals for accurate damage severity identification, the compression level should be limited to 20%. These findings affirm that compressed sensing significantly reduces the data collection requirements for crowdsensing-based monitoring applications, without compromising the accuracy of damage detection while preserving essential damage-sensitive information within the dataset.

Target-oriented robust satisficing models for the single machine scheduling problems with release time

In this paper, we investigate single machine scheduling problems with release times and random processing times, where the release times can be either deterministic or random. The objective is to determine a scheduling sequence that exhibits strong out-of-sample performance. To achieve this, we employ target-oriented robust satisficing models to obtain the scheduling sequence. For the scheduling problem with deterministic release times, we derive an equivalent mixed-integer linear program and an approximate reformulation to address cases involving a large number of jobs. For the scheduling problem with random release times, we first demonstrate the challenges associated with providing an equivalent reformulation. To overcome this intractability, we propose an approximate reformulation based on the linear decision rule. Numerical experiments are conducted to demonstrate the superiority of our solutions through comparisons with several benchmarks. Furthermore, the numerical results demonstrate that a relatively higher target should be chosen if the worst-case performance is valued, otherwise, the decision-maker should set a relatively lower target to obtain better average performance.

Simplified Formulation for Bush, Gibson, and Thomas Model

Abstract The random process model, also known as the multi-asperity contact model or statistical model, is one of the dominant methodologies for analyzing the contact between nominally flat rough surfaces. In 1975, Bush, Gibson, and Thomas developed a complete random process model (known as the BGT model) assuming that solid–solid contacts occur on the summits of the asperities, which are semi-ellipsoids uniquely described by three random variables (the asperity height and two principal peak curvatures). The Hertzian elliptic contact theory states that the contact area and normal load are implicit functions of the random variables, which results in an original BGT model with a complex formulation. In this study, we used an adapted Hertzian elliptic contact theory to simplify the formulation of the BGT model. The relative contact area to normal load relation predicted by the simplified BGT model perfectly agrees with that of the original formulation. It is anticipated that rough surface contact models with complex asperity interactions can be effectively built under the framework of this simplified BGT model.

Epitaxial Growth of CsPbBr3 Pyramids/CdS Nanobelt Heterostructures for High-Performance Photodetectors.

Perovskites have great potential for optoelectronic applications due to their high photoluminescence quantum yield, large absorption coefficient, great defect tolerance, and adjustable band gap. Perovskite heterostructures may further enhance the performance of optoelectronic devices. So far, however, most of perovskite heterostructures are fabricated by mechanical stacking or spin coating, which could introduce a large number of defects or impurities at the heterointerface owing to the random stacking process. Herein, we report the epitaxial growth of CsPbBr3 pyramids/CdS nanobelt heterostructures via a 2-step vapor deposition route. The CsPbBr3 triangular pyramids are well aligned on the surface of CdS nanobelts with the epitaxial relationships of (0-22)CsPbBr3||(1-20)CdS and (-211)CsPbBr3||(002)CdS. Time-resolved photoluminescence results reveal that effective charge transfer occurred at the heterointerface, which can be attributed to the type-II band arrangement. Theoretical simulations reveal that the unique CsPbBr3 pyramids/CdS nanobelt structure facilitates diminishing the reflection losses and enhancing the light absorption. The photodetector based on these CsPbBr3 pyramids/CdS nanobelt heterostructures exhibited an ultrahigh photoswitching ratio of 2.14 × 105, a high responsivity up to 4.07 × 104 A/W, a high detectivity reaching 1.36 × 1013 Jones, fast photoresponses (τrise = 472 μs and τdecay = 894 μs), low dark current, and suppressed hysteresis.

The Influence of Geological Potential and Investment Climate on Botswana’s Competitiveness

Objective: This article's objective is to evaluate Botswana's attractiveness to investors in mineral exploration. Botswana's competitiveness and ability to attract exploration and mining investment have declined in recent years. Method: Questionnaires were used as part of a mixed methodology to collect data that was subjected to empirical analysis. From a possible 231 respondents including exploration and mining companies, mining consultants, a research firm, and a mining association, a representative sample of 100 were chosen and given the survey through a stratified random sampling process. The data was analyzed using SPSS and both descriptive and inferential analyses were utilized. Result: This study finds that Botswana is only moderately successful in luring exploration investment. Botswana's ability to entice exploration investment is influenced by factors including the country's political stability, mining tax, mineral policy, license approval, quality of geological data, availability of skilled labor, adequate infrastructure, a streamlined licensing process, effective relevant institutions, and clear rules and regulations. Conclusion: The study recommends that Botswana regulators should consider improving mining tax incentives and continue removing bureaucratic requirements that delay the licensing process, as this may result in a more favorable mining environment that encourages both domestic and international mining interests.

Peculiarities of the SCLC Effect in Gate‐All‐Around Silicon Nanowire Field‐Effect Transistor Biosensors

AbstractHigh‐quality liquid gate‐all‐around (LGAA) silicon nanowire (NW) field‐effect transistor (FET) biosensors are fabricated and studied their properties in 1 mm phosphate‐buffered saline solution with pH = 7.4 using transport and noise spectroscopy. At small VDS, the conventional current behavior of FET with a linear dependence on voltage is registered in the output current‐voltage (I‐VM) characteristics with M = 1. At drain‐source voltage VDS > 0.6 V, the I‐V characteristics with stronger power M are revealed. It is shown that the current in LGAA NW FETs follows current proportional to voltage in power M = 4 dependence on small liquid gate voltages. Transport and noise spectroscopy analyses demonstrate that the obtained results are associated with the space‐charge‐limited current (SCLC) effect. Moreover, a strong two‐level random telegraph signal (RTS) is found in the region corresponding to SCLC at VDS values exceeding 0.6 V. The RTS related to single trap phenomena results in a well‐resolved Lorentzian component of noise spectra. The results demonstrate that the SCLC and two‐level RTS phenomenon are correlated effects. They should be taken into account during the development of single‐trap‐based devices, including biosensors.

Experiment on Extraversion Distribution in Groups Through a Group Formation Algorithm

Advances in technology have sparked a surge of interest in systematic group formation in educational contexts. The experimental study investigates group formation by extraversion distributions on group work outcomes, expected to influence group hierarchy. As an initial step in the experimental randomization process, an algorithmic group formation tool ensured an equal partitioning and aligned students into two experimental conditions with either consistent, homogeneous, or varied, heterogeneous, levels of extraversion. Over the course of one semester, a total of 114 students enrolled in several paralleled seminars, were surveyed on both subjective data (satisfaction with group work) and objective data (group performance) to evaluate the effect of the experimental intervention. The formation of extraversion at the group level contributed to the respective outcomes, emphasizing the value of collective social capital for both individuals and groups. Specifically, a homogeneous distribution of extraversion had a positive impact on group performance, as evident in improved grades on course group assignments and increased active participation in group meetings. Findings emphasize considering personality traits at group-level to enhance the success of groups.

Deterioration Models and Service Life Prediction of Vertical Assets of Urban Water Systems

AbstractThis study proposes a methodology for developing deterioration models and predicting the service lives of vertical assets of urban water systems (i.e., water storage tanks and pumping stations) using regression analysis. The main factors contributing to the deterioration of these assets are analyzed. Simple and multiple linear regression models of average and maximum deterioration are calculated for 22 water storage tanks and 17 wastewater pumping stations. Data on a set of four water storage tanks are used to validate the developed deterioration models. Service life prediction is carried out using the developed models and considering two maximum deterioration levels: the maximum recommended and admissible deterioration levels. Two water storage tanks are further studied to illustrate and discuss the effect of maintenance and rehabilitation interventions on asset service life by comparing the asset deterioration before and after the interventions. Results include simple linear regression models of average and maximum deterioration indices as a function of asset age and multiple linear regression models that incorporate other physical, operational and environmental factors. The results show that simple linear regression models of asset deterioration show a better predictive power than multiple regression models. Despite the higher data variability of multiple regression models, these models allow to include the random process of asset deterioration, through the calculation of the standard deviation. This study also shows that periodic interventions are a preferable maintenance and rehabilitation strategy over major sporadic rehabilitation interventions since it allows to maintain assets in good condition and to extend their service life almost indefinitely.

Role of doxycycline in the treatment of dengue infection: An open-label, randomized, controlled, pilot trial

Objective: To measure the effect of doxycycline on inflammatory marker [IL-6, TNF-α, ferritin and C reactive protein (CRP)] levels in patients with dengue infection. Methods: A single-centre, open-label, parallel-group randomized controlled trial was done in PGIMER Chandigarh from June 2021 to October 2022. Patients were randomized using a simple randomization process into two groups: the doxycycline treatment group (n=35) and the control group (n=34). Patients in the treatment group were given oral doxycycline 100 mg twice daily for five days along with standard treatment, whereas patients in the control group received only standard treatment. The objective was to measure the effect of doxycycline on inflammatory markers in dengue infection. Results: On comparative analysis at day 5, there was a statistically significant reduction in the median values of ferritin and CRP in cases compared to the control group (ferritin: P=0.006 and CRP: P=0.006). No significant reduction was noted in the levels of IL-6 and TNF-α. Conclusions: Doxycycline treatment led to a reduction of inflammatory markers in dengue infection.

Isomorphic Multidimensional Structures of the Cyclic Random Process in Problems of Modeling Cyclic Signals with Regular and Irregular Rhythms

This paper is devoted to the research of the isomorphic multidimensional cyclic structure and multidimensional phase structure of the cyclic random process (CRP) and to its formation method, which enables a rigorous formalization of intuitive ideas concerning cyclic stochastic motion. The fundamental properties of the cyclic random process and analytical dependencies between the multidimensional cyclic structure, multidimensional phase structure and rhythm structure of the CRP have been established. This work shows that the CRP is able to take into account the cyclicity of multidimensional distribution functions of cyclic signals as well as the variability in the rhythm of the investigated signals. A subclass of the CRP is the periodic random process, which allows for the use of classical processing methods of cyclic signals with a regular rhythm. Based on a series of experiments, significant advantages of the CRP as a mathematical model of electrocardiographic signals (ECG) compared to the periodic random process are shown.

Universal approximation property of stochastic configuration networks for time series

For the purpose of processing sequential data, such as time series, and addressing the challenge of manually tuning the architecture of traditional recurrent neural networks (RNNs), this paper introduces a novel approach-the Recurrent Stochastic Configuration Network (RSCN). This network is constructed based on the random incremental algorithm of stochastic configuration networks. Leveraging the foundational structure of recurrent neural networks, our learning model commences with a modest-scale recurrent neural network featuring a single hidden layer and a solitary hidden node. Subsequently, the node parameters of the hidden layer undergo incremental augmentation through a random configuration process, with corresponding weights assigned structurally. This iterative expansion continues until the network satisfies predefined termination criteria. Noteworthy is the adaptability of this algorithm to handle time series data, exhibiting superior performance compared to traditional recurrent neural networks with similar architectures. The experimental results presented in this paper underscore the efficacy of the proposed RSCN for sequence data processing, showcasing its advantages over conventional recurrent neural networks in the context of the performed experiments.

Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating.

Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range r ∈ (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.

The hitting time of clique factors

AbstractIn [Trans. Am. Math. Soc. 375 (2022), no. 1, 627–668], Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let and let be divisible by . Then, in the random ‐uniform hypergraph process on vertices, as soon as the last isolated vertex disappears, a perfect matching emerges. In the present work, we prove the analogue of this result for clique factors in the random graph process: at the time that the last vertex joins a copy of the complete graph , the random graph process contains a ‐factor. Our proof draws on a novel sequence of couplings which embeds the random hypergraph process into the cliques of the random graph process. An analogous result is proved for clique factors in the ‐uniform hypergraph process ().

Reporting Quality and Risk of Bias Analysis of Published RCTs Assessing Anti-CGRP Monoclonal Antibodies in Migraine Prophylaxis: A Systematic Review.

Objective: Phase II/III randomized clinical trials (RCTs) are vulnerable to many types of bias beyond randomization. Insights into the reporting quality of RCTs involving migraine patients treated with monoclonal antibodies targeting the calcitonin gene-related peptide system (anti-CGRP MAbs) are currently lacking. Our aim was to analyze the reporting quality of phase II/III RCTs involving migraine patients treated with anti-CGRP MAbs. Methods: A systematic search was performed on the PubMed and EMBASE databases, according to PRISMA guidelines, for relevant RCTs in either episodic or chronic migraine prevention. Additionally, an adapted version of the 2010 CONSORT statement checklist was utilized. The ROBvis online tool was used to document the risk of bias. Results: From the initially identified 179 articles, we finally found 31 RCTs that were eligible for evaluation. The average CONSORT compliance was 88.7% (69.7-100%), while 93.5% (N = 29) of the articles had a compliance greater than 75%. Twenty-eight CONSORT items were reported in more than 75% of the articles. The average compliance of the analyzed RCTs was 93.9% for Galcanezumab, 91.3% for Fremanezumab, followed by 85.4% for Erenumab and Eptinezumab studies. Implementation of the ROB2 tool showed some concerning "missing information" arising from the inadequate reporting. Specifically, 50% of the studies (N = 16) were categorized as having inadequate information regarding the randomization process. Conclusions: Adequate reporting quality was disclosed in the evaluated RCTs with anti-CGRP MAbs in migraine prevention. However, some methodological issues need to be highlighted to be addressed in future studies assessing the efficacy of new molecules targeting CGRP or other candidate pathways implicated in migraine pathophysiology.

Spectral density estimation for random processes with stationary increments

AbstractSpectral density analysis plays an important role in studying a stationary random process on a real line. In this paper, we extend this discussion for the random process with stationary increments. We investigate the properties of the method of moments structure function estimation, and propose a nonparametric spectral density function estimator. Our numerical results show that the proposed spectral density estimator performs comparable with the parametric counterpart when the underlying process is assumed to be band‐limited. Additionally, this method is applied to analyze US Housing Starts Data, where the hidden periodicities are detected, providing consistent conclusions with previous economic studies.

Covariance-analytic performance criteria, Hardy-Schatten norms and Wick-like ordering of cascaded systems

This paper is concerned with robust performance analysis of linear stochastic systems acting as an integral operator on a standard Wiener process at the input and producing a stationary Gaussian random process at the output. We propose a performance criterion which uses the trace of an analytic function of the spectral density of the output process. This class of “covariance-analytic” cost functionals includes the usual mean square and risk-sensitive criteria as particular cases. Due to the “cost-shaping” analytic function, the covariance-analytic performance criterion depends on higher-order Hardy-Schatten norms of the system transfer function. We discuss the links of these norms with the asymptotic behaviour of cumulants of finite-horizon quadratic functionals of the system output and their variational properties pertaining to system robustness to statistically uncertain inputs which differ from the standard Wiener process. In the case of strictly proper finite-dimensional systems, governed in state space by linear stochastic differential equations, we develop a method for recursively computing the Hardy-Schatten norms through a recently proposed technique of rearranging cascaded linear systems, which resembles the Wick ordering of mixed products of noncommuting annihilation and creation operators in quantum mechanics. This computational procedure, which is one of the main results of the paper, involves a recurrence sequence of solutions to algebraic Lyapunov equations and represents the covariance-analytic cost as the squared H2-norm of an auxiliary cascaded system. These results are also compared with an alternative approach, which uses higher-order derivatives of stabilising solutions of parameter-dependent algebraic Riccati equations, and illustrated by a numerical example.