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Focused ultrasound has experimentally been found to enhance the diffusion of nanoparticles; our aim with this work is to study this effect closer using both experiments and non-equilibrium molecular dynamics. Measurements from single particle tracking of 40 nm polystyrene nanoparticles in an agarose hydrogel with and without focused ultrasound are presented and compared with a previous experimental study using 100 nm polystyrene nanoparticles. In both cases, we observed an increase in the mean square displacement during focused ultrasound treatment. We developed a coarse-grained non-equilibrium molecular dynamics model with an implicit solvent to investigate the increase in the mean square displacement and its frequency and amplitude dependencies. This model consists of polymer fibers and two sizes of nanoparticles, and the effect of the focused ultrasound was modeled as an external oscillating force field. A comparison between the simulation and experimental results shows similar mean square displacement trends, suggesting that the particle velocity is a significant contributor to the observed ultrasound-enhanced mean square displacement. The resulting diffusion coefficients from the model are compared to the diffusion equation for a two-time continuous time random walk. The model is found to have the same frequency dependency. At lower particle velocity amplitude values, the model has a quadratic relation with the particle velocity amplitude as described by the two-time continuous time random walk derived diffusion equation, but at higher amplitudes, the model deviates, and its diffusion coefficient reaches the non-hindered diffusion coefficient. This observation suggests that at higher ultrasound intensities in hydrogels, the non-hindered diffusion coefficient can be used. [ABSTRACT FROM AUTHOR]

Ion channels are proteins that play a significant role in physiological processes, including neuronal excitability and signal transduction. However, the precise mechanisms by which these proteins facilitate ion diffusion through cell membranes are not well understood. This is because experimental techniques to characterize ion channel activity operate on a time scale too large to understand the role of the various protein conformations on diffusion. Meanwhile, computational approaches operate on a time scale too short to rationalize the observed behavior at the microscopic scale. In this paper, we present a continuous-time random walk model that aims to bridge the scales between the atomistic models of ion channels and the experimental measurement of their conductance. We show how diffusion slows down in complex systems by using 3D lattices that map out the pore geometry of two channels: Nav1.7 and gramicidin. We also introduce spatial and dynamic site disorder to account for system heterogeneity beyond the mean field approximation. Computed diffusion coefficients show that an increase in spatial disorder slows down diffusion kinetics, while dynamic disorder has the opposite effect. Our results imply that microscopic or phenomenological models based on the potential of mean force data overlook the functional importance of protein dynamics on ion diffusion through channels. [ABSTRACT FROM AUTHOR]

Numerical methods for analyzing diffusion phenomena involving strong discontinuities and complicated interfaces are of great scientific and technical importance. In this paper, we extend the existing step-balanced random walk, which overcomes the problem of detailed balance of a random walker in three-dimensional (3D), diffusion-tensor discontinuous systems, to particle density (ρ) discontinuous systems, and introduce volumetric heat capacity C and temperature T by considering ρ as heat density, i.e., ρ = C T , to apply it to thermal problems. Two types of thermophysical simulations are demonstrated: one is steady-state heat flow due to a temperature difference at the end surfaces on a two-phase slab model unit cell with periodic boundary conditions; the other is the time variation of temperature distribution due to heat diffusion from a point heat source in a repeated two-phase slab model with no periodic boundary conditions. We see the correct behavior of heat and temperature expected in 3D discontinuous systems composed of two phases with anisotropic thermal conductivity. The applicability to problems other than pure diffusion and the limitations of the method are also discussed. [ABSTRACT FROM AUTHOR]

We report simulation studies of 33 single intrinsically disordered proteins (IDPs) using coarse-grained bead-spring models where interactions among different amino acids are introduced through a hydropathy matrix and additional screened Coulomb interaction for the charged amino acid beads. Our simulation studies of two different hydropathy scales (HPS1, HPS2) [Dignon et al., PLoS Comput. Biol. 14, e1005941 (2018); Tesei et al. Proc. Natl. Acad. Sci. U. S. A. 118, e2111696118 (2021)] and the comparison with the existing experimental data indicate an optimal interaction parameter ϵ = 0.1 and 0.2 kcal/mol for the HPS1 and HPS2 hydropathy scales. We use these best-fit parameters to investigate both the universal aspects as well as the fine structures of the individual IDPs by introducing additional characteristics. (i) First, we investigate the polymer-specific scaling relations of the IDPs in comparison to the universal scaling relations [Bair et al., J. Chem. Phys. 158, 204902 (2023)] for the homopolymers. By studying the scaled end-to-end distances ⟨ R N 2 ⟩ / (2 L ℓ p ) and the scaled transverse fluctuations l ̃ ⊥ 2 = ⟨ l ⊥ 2 ⟩ / L , we demonstrate that IDPs are broadly characterized with a Flory exponent of ν ≃ 0.56 with the conclusion that conformations of the IDPs interpolate between Gaussian and self-avoiding random walk chains. Then, we introduce (ii) Wilson charge index (W) that captures the essential features of charge interactions and distribution in the sequence space and (iii) a skewness index (S) that captures the finer shape variation of the gyration radii distributions as a function of the net charge per residue and charge asymmetry parameter. Finally, our study of the (iv) variation of ⟨Rg⟩ as a function of salt concentration provides another important metric to bring out finer characteristics of the IDPs, which may carry relevant information for the origin of life. [ABSTRACT FROM AUTHOR]

Quantum walks are the quantum counterpart of classical random walks and have various applications in quantum information science. Polar molecules have rich internal energy structure and long coherence time and thus are considered as a promising candidate for quantum information processing. In this paper, we propose a theoretical scheme for implementing discrete-time quantum walks on a circle with dipole–dipole coupled SrO molecules. The states of the walker and the coin are encoded in the pendular states of polar molecules induced by an external electric field. We design the optimal microwave pulses for implementing quantum walks on a four-node circle and a three-node circle by multi-target optimal control theory. To reduce the accumulation of decoherence and improve the fidelity, we successfully realize a step of quantum walk with only one optimal pulse. Moreover, we also encode the walker into a three-level molecular qutrit and a four-level molecular ququart and design the corresponding optimal pulses for quantum walks, which can reduce the number of molecules used. It is found that all the quantum walks on a circle in our scheme can be achieved via optimal control fields with high fidelities. Our results could shed some light on the implementation of discrete-time quantum walks and high-dimensional quantum information processing with polar molecules. [ABSTRACT FROM AUTHOR]

Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex-but very common-machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data in general compact metric spaces, for any fixed privacy budget ε bounded away from zero. A key ingredient in our construction is a new superregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmically slowly.

In this study, the quantum random walk is used to generate the initial conditions and control parameters of the chaotic mapping system. The R, G, and B channels of the color image are sorted according to the chaotic sequence generated by the Arcsin–Rrccos–Tent chaotic mapping. At the same time, the chaotic sequence generated by the improved logistic chaotic mapping is used to match it with the rules of DNA encoding and decoding. The chaotic sequence generated by the improved Henon chaotic mapping is used to determine the DNA rules and the number of cycles when the image is encrypted and decrypted. The XOR operation is performed by each pixel of the color image and the DNA complementary rule, and the cyclic iterative processing is performed. Extensive experimental results and analysis show that the scheme performs well in protecting image privacy and resisting attacks. [ABSTRACT FROM AUTHOR]

Summary: The wireless sensor network (WSN) has been assimilated into modern society and is utilized in many crucial application domains, including animal monitoring, border surveillance, asset monitoring, and so forth. These technologies aid in protecting the place of the event's occurrence from the adversary. Maintaining privacy concerning the source location is challenging due to the sensor nodes' limitations and efficient routing strategies. Hence, this research introduces a novel source location privacy preservation using the awareness‐based Gannet with random‐Dijkstra's algorithm (AGO‐RD). The network is initialized by splitting the hotspot and non‐hotspot region optimally using the proposed awareness‐based Gannet (AGO) algorithm. Here, the multi‐objective fitness function is utilized to initialize the network based on factors like throughput, energy consumption, latency, and entropy. Then, the information is forwarded to the phantom node in the non‐hotspot region to preserve the source location's privacy, which is far from the sink node. The proposed random‐Dijkstra algorithm is utilized to route the information from the phantom node to the sink with more security. Analysis of the proposed AGO‐RD‐based source location privacy preservation technique in terms of delay, throughput, network lifetime, and energy consumption accomplished the values of 6.52 ms, 95.68%, 7109.9 rounds, and 0.000125 μJ. [ABSTRACT FROM AUTHOR]

We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero drift. Analogous results in the case of zero drift, where the scaling is different, were obtained by Khoshnevisan [Probab. Theory Related Fields 93 (1992), pp. 377–392]. Our starting point is a version of Strassen's functional law of the iterated logarithm for random walks with drift. For the special case of the area of a planar random walk with drift, we compute explicitly the constant in the iterated-logarithm law by solving an isoperimetric problem reminiscent of the classical Dido problem. For general intrinsic volumes and dimensions, our proof exploits a novel zero–one law for functionals of convex hulls of walks with drift, of some independent interest. As another application of our approach, we obtain iterated-logarithm laws for intrinsic volumes of the convex hull of the centre of mass (running average) process associated to the random walk. [ABSTRACT FROM AUTHOR]

Since 2013, the International GNSS Service (IGS) real-time service (RTS) has been providing precise orbit and clock corrections for ten years, which enables real-time positioning at the decimeter level. High precision positioning relies heavily on accurate orbit and clock. However, constrained by the relatively short observation duration, the accuracy of real-time products are often worse than the final products. Previous studies indicate that compensating for errors in orbit and clock can improve positioning accuracy. Based on this theory, we proposed an improved positioning model, which incorporates the signal-in-space range error (SISRE) into the ionosphere-free combination observation equation and treats it as a parameter in the Kalman filter. Through the analysis of SISRE, we find that the time-varying characteristic of the parameter follows a random walk assumption. To find the optimal parameter settings of the SISRE parameters, a two-dimensional sensitivity analysis is employed, and a set of recommended values are provided. In the simulated kinematic positioning experiments, the proposed method achieves positioning accuracies of 17.3 cm, 19.6 cm, and 18.0 cm for GPS, BDS-3, and Galileo, respectively, representing a 10–20 % improvement over traditional methods. In real-time PPP experiment, the accuracy reaches 21.7 cm, indicating a 12.9 % improvement compared to traditional methods. [ABSTRACT FROM AUTHOR]

We study uniformly random lozenge tilings of general simply connected polygons. Under a technical assumption that is presumably generic with respect to polygon shapes, we show that the local statistics around a cusp point of the arctic curve converge to the Pearcey process. This verifies the widely predicted universality of edge statistics in the cusp case. Together with the smooth and tangent cases proved by Aggarwal‐Huang and Aggarwal‐Gorin, these are believed to be the three types of edge statistics that can arise in a generic polygon. Our proof is via a local coupling of the random tiling with nonintersecting Bernoulli random walks (NBRW). To leverage this coupling, we establish an optimal concentration estimate for the tiling height function around the cusp. As another step and also a result of potential independent interest, we show that the local statistics of NBRW around a cusp converge to the Pearcey process when the initial configuration consists of two parts with proper density growth, via careful asymptotic analysis of the determinantal formulas. [ABSTRACT FROM AUTHOR]

Static node embedding algorithms applied to snapshots of real-world applications graphs are unable to capture their evolving process. As a result, the absence of information about the dynamics in these node representations can harm the accuracy and increase processing time of machine learning tasks related to these applications. Aiming at fill the gap regarding the inability of static methods to capture evolving processes on dynamic networks, we propose a biased random walk method named Evolving Node Embedding (EVNE). EVNE leverages the sequential relationship of graph snapshots by incorporating historic information when generating embeddings for the next snapshot. It learns node representations through a neural network, but differs from existing methods as it: (i) incorporates previously run walks at each step; (ii) starts the optimization of the current embedding from the parameters obtained in the previous iteration; and (iii) uses two time-varying parameters to regulate the behavior of the biased random walks over the process of graph exploration. Through a wide set of experiments we show that our approach generates better embeddings, outperforming baselines by up to 20% in a downstream node classification task. EVNE's embeddings achieve better performance than others, based on experiments with four classifiers and five datasets. In addition, we present seven variations of our model to show the impact of each of EVNE's mechanisms. [ABSTRACT FROM AUTHOR]

Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks \(\mathcal{T}_{t}\) , which turn out to be scale-free, in an iterative manner. As opposed to most of published tree models with scale-free feature, our tree networks have the power-law exponent \(\gamma=1{ + }\ln 5/\ln 2\) that is obviously larger than \(3\). At the same time, "small-world" property can not be found particularly because models \(\mathcal{T}_{t}\) have an ultra-large diameter \(D_{t}\) (i.e., \(D_{t}\sim|\mathcal{T}_{t}|^{\ln 3/\ln 5}\)) and a greater average shortest path length \(\langle\mathcal{W}_{t}\rangle\) (namely, \(\langle\mathcal{W}_{t}\rangle\sim|\mathcal{T}_{t}|^{\ln 3/\ln 5}\)) where \(|\mathcal{T}_{t}|\) represents vertex number. Next, we determine Pearson correlation coefficient and verify that networks \(\mathcal{T}_{t}\) display disassortative mixing structure. In addition, we study random walks on tree networks \(\mathcal{T}_{t}\) and derive exact solution to mean hitting time \(\langle\mathcal{H}_{t}\rangle\). The results suggest that the analytic formula for quantity \(\langle\mathcal{H}_{t}\rangle\) as a function of vertex number \(|\mathcal{T}_{t}|\) shows a power-law form, i.e., \(\langle\mathcal{H}_{t}\rangle\sim|\mathcal{T}_{t}|^{1+\ln 3/\ln 5}\). Accordingly, we execute extensive experimental simulations, and demonstrate that empirical analysis is in strong agreement with theoretical results. Lastly, we provide a guide to extend the proposed iterative manner in order to generate more general scale-free tree networks with large diameter. [ABSTRACT FROM AUTHOR]

In response to the challenging conditions that arise after natural disasters, multi-robot systems are utilized as alternatives to humans for searching and rescuing victims. Exploring unknown environments is crucial in mobile robotics, serving as a foundational stage for applications such as search and rescue, cleaning tasks, and foraging. In our study, we introduced a novel search strategy for multi-robot search and rescue operations. This strategy draws inspiration from the hunting behavior of penguins and combines the Penguin Search Optimization Algorithm with the Random Walk Algorithm to regulate the global and local search behaviors of the robots. To assess the strategy's effectiveness, we implemented it in the ARGoS multi-robot simulator and conducted a series of experiments. The results clearly demonstrate the efficiency and effectiveness of our proposed search strategy. [ABSTRACT FROM AUTHOR]

In this paper, we show that traditional comparisons of mean squared prediction error (MSPE) between two competing forecasts may be highly controversial. This is so because when some specific conditions of efficiency are not met, the forecast displaying the lowest MSPE will also display the lowest correlation with the target variable. Given that violations of efficiency are usual in the forecasting literature, this opposite behavior in terms of accuracy and correlation with the target variable may be a fairly common empirical finding that we label here as "the MSPE paradox." We characterize "paradox zones" in terms of differences in correlation with the target variable and conduct some simple simulations to show that these zones may be non‐empty sets. Finally, we illustrate the relevance of the paradox with a few empirical applications. [ABSTRACT FROM AUTHOR]

Exchange rate modeling has always fascinated researchers because of its complex macroeconomic dynamics. This study documents the exchange rate dynamics of major emerging economies after accounting for their macroeconomic cycles and explores the Bayesian Vector Error Correction Model (VECM) Markov Regime switching model, which uses time‐varying transition probabilities. The main objective is to study the exchange rate dynamics of Brazil, Russia, India, China, and South Africa (BRICS) vis‐à‐vis the US dollar. The Bayesian setup uses two hierarchal shrinkage priors, the normal‐gamma (NG) prior and the Litterman prior, for parameters' estimation. These shrinkage priors allow for a more comprehensive assessment of the regime‐specific coefficients. The model performed well in differentiating between the two regimes for all currencies. The Russian ruble was identified to be the most depreciated currency, whereas the African Rand was the most appreciated. The evaluation of model features revealed that many regime‐specific coefficients differed significantly from their common mean. A forecasting exercise was then performed for the out‐of‐sample period to assess the model's performance. A significant improvement was observed over the basic random walk (RW) model and the linear Bayesian vector autoregression (BVAR) model. [ABSTRACT FROM AUTHOR]

Nonnearest-neighbor hop during random walks is observed in various real situations and their nontrivial roles are also confirmed. On the other hand, the reciprocity also can significantly impact dynamical processes on weighted networks. However, the roles of nonnearest-neighbor hop are less explored in the presence of reciprocity. Here, we quantify the effect of nonnearest-neighbor hop on random walks in the presence of reciprocity. Specifically, a class of directed weighted fractal scale-free networks is proposed to accommodate reciprocity. Subsequently, mixed random walk that includes both nearest-neighbor and next-nearest-neighbor jump is defined on the networks. Finally, a trap is placed at a node of the networks and the average trapping time (ATT) is derived analytically and exactly to determine the effect of next-nearest-neighbor hop on transport efficiency. The obtained closed form solution of ATT shows that (1) Dependent on the combination of values of parameters governing network evolution and reciprocity, ATT can grow linearly, sub-linearly or super-linearly with network size. (2) The parameter manipulating mixed random walk only modifies the prefactor of ATT, so the next-nearest-neighbor hop has no effect on the scaling of transport efficiency in the presence of reciprocity. (3) The weight parameter enters into both the prefactor and leading scaling of ATT, so reciprocity impacts the transport efficiency both qualitatively and quantitatively. [ABSTRACT FROM AUTHOR]

In a previous work, we defined and studied random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that each vertex is labeled upon its first visit. In this work, we calculate the number of random walk labelings of several natural graph families: The wheel, fan, barbell, lollipop, tadpole, friendship, and snake graphs. Additionally, we prove several combinatorial identities that emerged during the calculations. [ABSTRACT FROM AUTHOR]

The spatiotemporal evolution of earthquakes induced by fluid injections into the subsurface can be erratic owing to the complexity of the physical process. To effectively mitigate the associated hazard and to draft appropriate regulatory strategies, a detailed understanding of how induced seismicity may evolve is needed. In this work, we build on the well-established continuous-time random walk (CTRW) theory to develop a purely stochastic framework that can delineate the essential characteristics of this process. We use data from the 2003 and 2012 hydraulic stimulations in the Cooper Basin geothermal field that induced thousands of microearthquakes to test and demonstrate the applicability of the model. Induced seismicity in the Cooper Basin shows all the characteristics of subdiffusion, as indicated by the fractional order power-law growth of the mean square displacement with time and broad waiting-time distributions with algebraic tails. We further use an appropriate master equation and the time-fractional diffusion equation to map the spatiotemporal evolution of seismicity. The results show good agreement between the model and the data regarding the peak earthquake concentration close to the two injection wells and the stretched exponential relaxation of seismicity with distance, suggesting that the CTRW model can be efficiently incorporated into induced seismicity forecasting. [ABSTRACT FROM AUTHOR]

This paper deals with the characterization of mobility models for unmanned aerial vehicles (UAVs) cellular network regarding handovers. The UAVs act as base stations to serve terrestrial users using service models, namely user dependent model and user independent model. The state-of-the-art mobility models, such as straight line, random waypoint (RWP) and modified random direction (M-RD) are employed under two different mobility scenarios for UBSs: same speed model and different speed model. The RWP mobility model achieves lower bound in handover probability followed by M-RD mobility model with an infinitesimal change. The M-RD mobility model exhibiting lowest handover rate has greatly increased its usability in UAVs cellular network. [ABSTRACT FROM AUTHOR]

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Human behaviors have non-negligible impacts on spread of contagious disease. For instance, large-scale gathering and high mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may effectively reduce contacts and suppress the peak of the outbreak. In order to understand how spatial characteristics like population mobility and clustering interplay with epidemic outbreaks, we formulate a stochastic-statistical environment-epidemic dynamic system (SEEDS) via an agent-based biased random walk model on a two-dimensional lattice. The "popularity" and "awareness" variables are taken into consideration to capture human natural and preventive behavioral factors, which are assumed to guide and bias agent movement in a combined way. It is found that the presence of the spatial heterogeneity, like social influence locality and spatial clustering induced by self-aggregation, potentially suppresses the contacts between agents and consequently flats the epidemic curve. Surprisedly, disease responses might not necessarily reduce the susceptibility of informed individuals and even aggravate disease outbreak if each individual responds independently upon their awareness. The disease control is achieved effectively only if there are coordinated public-health interventions and public compliance to these measures. Therefore, our model may be useful for quantitative evaluations of a variety of public-health policies. Author summary: This article investigates at multi-level the roles played by spatial heterogeneities in epidemic dynamics. For this purpose we propose a novel stochastic-statistical particle model implemented on a two-dimensional lattice field, where various individual-varying spatially inhomogeneous human behavioral factors are incorporated into an agent-based epidemic modeling framework. With extensive simulations of our model, we are able to carry out thorough investigations on the impacts of heterogeneities at individual and spatial levels on epidemics trajectories during the early stage of an outbreak. It has been observed that spatial heterogeneity is consistently shown to be connected with suppressed and delayed epidemic peaks. These findings add valuable knowledge on the mechanism of the form and distribution of population clusters affecting an epidemic wave. Moreover, we examine the interplay between spatial/individual heterogeneities and public-health policies in an intensive and systematic way across various parameter regimes, whose conclusions we believe are going to complement beneficially to both the theoretical and practical understanding of epidemic control. [ABSTRACT FROM AUTHOR]

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number R0 of the model and studied the influence of orders a and b on R0. Second, we found that frSIS has a disease-free equilibrium point E0 and an endemic equilibrium point E∗. Moreover, we proved frSIS global stability of the model using R0. If R0<1, the model of E0 is globally asymptotically stable. If R0>1, the model of E∗ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease. [ABSTRACT FROM AUTHOR]

The study of drug–target interaction plays an important role in the process of drug development. The subject of DTI forecasting has advanced significantly in the last several years, yielding numerous significant research findings and methodologies. Heterogeneous data sources provide richer information and comprehensive perspectives for drug–target interaction prediction, so many existing methods rely on heterogeneous networks, and graph embedding technology becomes an important technology to extract information from heterogeneous networks. These approaches, however, are less concerned with potential noisy information in heterogeneous networks and more focused on the extent of information extraction in those networks. Based on this, a potential DTI predictive network model called FBRWPC is proposed in this paper. It uses a fine-grained similarity selection program to first integrate similarity on similar networks and then a bidirectional random walk graph embedding learning method with restart to obtain an updated drug target interaction matrix. Through the use of similarity selection and fine-grained selection similarity integration, the framework can effectively filter out the noise present in heterogeneous networks and enhance the model's prediction performance. The experimental findings demonstrate that, even after being split up into four distinct types of data sets, FBRWPC can still retain great prediction performance, a sign of the model's resilience and good generalization. [ABSTRACT FROM AUTHOR]

Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method. [ABSTRACT FROM AUTHOR]

To predict air traffic flow reasonably, research is conducted in conjunction with complex network link prediction. First, the time series is converted into a visual graph to obtain the topological feature quantity, and then combined with the algorithms based on local information, path, and random walk, the prediction accuracy in different sectors of Sanya is compared. It is found that the RWR0.85 algorithm has the highest prediction accuracy. Due to the fact that link prediction can only predict possible edges and cannot predict nodes, the D-S evidence theory is introduced to predict traffic values, with a maximum prediction accuracy of 99.85%. The results indicate that the combination of complex network link prediction and D-S evidence theory for predicting air traffic flow is feasible and effective, laying a foundation for further in-depth research. [ABSTRACT FROM AUTHOR]

An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of 'hard supersingular curves' that is equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular |$\ell $| -isogeny graph, which does not reveal the endomorphism ring, or a path to a curve of known endomorphism ring. Such a hash function would open up interesting cryptographic applications. In this paper, we document a number of (thus far) failed attempts to solve this problem, in the hope that we may spur further research, and shed light on the challenges and obstacles to this endeavour. The mathematical approaches contained in this article include: (i) iterative root-finding for the supersingular polynomial; (ii) gcd's of specialized modular polynomials; (iii) using division polynomials to create small systems of equations; (iv) taking random walks in the isogeny graph of abelian surfaces, and applying Kummer surfaces and (v) using quantum random walks. [ABSTRACT FROM AUTHOR]

A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric ( M C ) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities. [ABSTRACT FROM AUTHOR]

We consider local probabilities of lower deviations for branching process Zn = Xn,1 + ⋯ + Xn,Zn−1 in random environment η. We assume that η is a sequence of independent identically distributed variables and for fixed η the variables Xi,j are independent and have geometric distributions. We suppose that steps ξi of the associated random walk Sn = ξ1 + ⋯ + ξn has positive mean and satisfies left-side Cramér condition: E exp(hξi) < ∞ if h− < h < 0 for some h− < − 1. Under these assumptions we find the asymptotic of the local probabilities P(Zn = ⌊exp(θn)⌋), n → ∞, for θ ∈ (max(m−, 0); m(− 1)) and for θ in a neighbourhood of m(− 1), where m− and m(− 1) are some constants. [ABSTRACT FROM AUTHOR]

We prove local limit theorems on large deviations for the moment Tn of attaining the level n ∈ ℕ by the random walk in a random environment. Exact asymptotics of probabilities P(Tn = k) are obtained for values of the parameter k corresponding to the large deviations zone. [ABSTRACT FROM AUTHOR]

A sublinear bilipschitz equivalence (SBE) between metric spaces is a map from one space to another that distorts distances with bounded multiplicative constants and sublinear additive error. Given any sublinear function, the associated sublinearly Morse boundaries are defined for all geodesic proper metric spaces as a quasi‐isometrically invariant and metrizable topological space of quasi‐geodesic rays. In this paper, we prove that sublinearly‐Morse boundaries of proper geodesic metric spaces are invariant under suitable SBEs. A tool in the proof is the use of sublinear rays, that is, sublinear bilispchitz embeddings of the half line, generalizing quasi‐geodesic rays. As an application, we distinguish a pair of right‐angled Coxeter groups brought up by Behrstock up to SBE. We also show that under mild assumptions, generic random walks on countable groups are sublinear rays. [ABSTRACT FROM AUTHOR]

We consider a percolation model, the vacant set Vu$\mathcal {V}^u$ of random interlacements on Zd$\mathbb {Z}^d$, d⩾3$d \geqslant 3$, in the regime of parameters u>0$u>0$ in which it is strongly percolative. By definition, such values of u$u$ pinpoint a robust subset of the supercritical phase, with strong quantitative controls on large local clusters. In the present work, we give a new characterization of this regime in terms of a single property, monotone in u$u$, involving a disconnection estimate for Vu$\mathcal {V}^u$. A key aspect is to exhibit a gluing property for large local clusters from this information alone, and a major challenge in this undertaking is the fact that the conditional law of Vu$\mathcal {V}^u$ exhibits degeneracies. As one of the main novelties of this work, the gluing technique we develop to merge large clusters accounts for such effects. In particular, our methods do not rely on the widely assumed finite‐energy property, which the set Vu$\mathcal {V}^u$ does not possess. The characterization we derive plays a decisive role in the proof of a lasting conjecture regarding the coincidence of various critical parameters naturally associated to Vu$\mathcal {V}^u$ in the companion article [Duminil‐Copin, Goswami, Rodriguez, Severo, and Teixeira, Phase transition for the vacant set of random walk and random interlacements, arXiv:2308.07919, 2023]. [ABSTRACT FROM AUTHOR]

Aim: Predicting spatial and temporal changes in species distributions is difficult for highly mobile species, making effective management challenging. We aim to understand the seasonal variability in habitat suitability for Atlantic bluefin tuna (Thunnus thynnus; ABFT) by using tracking data to create species distribution models. Location: North‐east Atlantic Ocean. Methods: Forty‐nine ABFT were tagged with pop‐up archival satellite tags along the west coast of Ireland during successive autumns from 2016 to 2021. Four thousand two hundred and sixteen daily locations were used to build a habitat model to describe ABFT environmental preferences and habitat suitability. For each location, 100 'pseudoabsence' locations were simulated using correlated random walks. Results: Tags had a mean retention rate of 237 ± 107 days, resulting in 11,602 cumulative days at liberty, and a mean daily distance travelled of 51 ± 143 km. ABFT showed two primary migration routes from Ireland, travelling to the Bay of Biscay or across the Mid‐Atlantic ridge in the winter. However, in 2019 six individuals travelled northwards towards Iceland, likely in response to a marine heatwave. Eight ABFT entered the Mediterranean in May/June for putative spawning, with six returning to Irish waters a year later. Five environmental covariates best described ABFT habitat, with habitat suitability highest at sea surface temperatures (SST) of 15–18°C, a mixed layer depth between ~200 and 300 m, high relief bathymetric features (i.e. shelf breaks and seamounts) and frontal regions as revealed by non‐linear preferences of eddy kinetic energy and SST standard deviation. Main Conclusions: In the last decade, ABFT have been re‐establishing historic foraging grounds in higher latitudes, for example, Irish and Nordic waters. Our model shows the extent of suitable habitat in these regions and how recent ocean warming may have contributed to northern expansions. Understanding the drivers behind these reappearances is fundamental to successful future management. Achoimre: Aidhm: Tá sé deacair athraithe i ndáileadh ama agus spásdháileadh speiceas atá an‐soghluaiste a thuar, rud a chiallaíonn go bhfuil sé dúshlánach bainistiú éifeachtach a dhéanamh. Tá muid ag iarraidh inathraitheacht shéasúrach in oiriúnacht ghnáthóg an Tuinnín Gorm Atlantach (Thunnus thynnus; TGA) a thuiscint tríd sonraí rianaithe a úsáid chun samhail dháileadh speiceas a chruthú. Suíomh: Oirthuaisceart an Atlantaigh. Modh: Rinneadh clibeadh ar 49 TGA le clibeanna cartlainne a thagann go barr uisce ar chósta iarthar na hÉireann le linn ceithre fhómhair i ndiaidh a chéile ó 2016–2021. Úsáideadh 4216 suíomhanna laethúil chun samhail ghnáthóg a chruthú a rinne cur síos ar roghanna timpeallachta agus oiriúnacht ghnáthóg an TGA. I gcomhair gach suíomh, ionsamhlaíodh 100 suíomhanna bréag‐neamhláithreacht ag úsáid siúlóidí randamacha comhghaolaithe. Torthaí: Bhí meán ráta coinneála de 237 ± 107 lá ag na clibeanna, rud a thug 11,602 lá taifeadta i ndiaidh a chéile agus meán fhad laethúil taistealta de 51 ± 143 km dá bharr. Léirigh TGA dhá phríomhbhealaí imirce ó hÉirinn, ag taisteal go Bá na Bioscáine nó thar Droim an Atlantaigh Láir i rith an gheimhridh. Ach i 2019 thaisteal sé iasc ó thuaidh i dtreo an Íoslainn, is dócha mar gheall ar thonn teasa mara. Chuaigh ocht TGA isteach sa Mheánmhuir i rith mí Bealtaine/mí an Mheitheamh chun uibheacha a sceitheadh de réir dealraimh. Tháinig sé dóibh ar ais go huiscí na hÉireann an bhliain dar gcionn. Déanann cúig athróg timpeallachta an cur síos is fearr ar ghnáthóg an TGA, tá oiriúnacht ghnáthóg is airde ag teocht barr uisce (TBA) de 15–18°C, nuair atá doimhneacht an chisil mheasctha idir ~200 agus 300 m, ag gnéithe bataiméadrach ard‐rilíf (i.e. scoilteanna scairbhe agus tuláin grinnill), agus ag réigiúin frontacha léirithe ag roghanna neamh‐líneacha fuinneamh cinéatach guairneánach agus diall caighdeánach TBA. Príomhchonclúidí: Le leathscór bliain anuas tá TGA tar éis réigiúin sealgaireachta stairiúil a athbhunú in áiteanna le hard‐domhanleithead, ar nós uiscí na hÉireann agus uiscí Nordacha. Taispeánann ár samhail achar an ghnáthóg oiriúnach sna réigiúin seo agus an bhaint féideartha a bhí ag téámh aigéanach le gairid ar leathadh ó thuaidh. Tá sé buntábhachtach na cúiseanna don athfhilleadh seo a thuiscint i gcomhair bainistiú rathúil amach anseo. [ABSTRACT FROM AUTHOR]

We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate μ between open and closed, following a Glauber dynamics for the random cluster model with parameters p, q. At the same time, the walker jumps at rate 1 as a simple random walk on the torus, but is only allowed to traverse open edges. We show that for small enough p the mixing time of the random walker is of order n 2 / μ . In our proof we construct a non-Markovian coupling through a multi-scale analysis of the environment, which we believe could be more widely applicable. [ABSTRACT FROM AUTHOR]

A celebrated result in probability theory is that a simple symmetric random walk on the d-dimensional lattice \mathbb {Z}^d is recurrent for d=1,2 and transient for d\geq 3. In this note, we derive a closed-form expression, in terms of the Lauricella function F_C, for the return probability for all d\geq 3. Previously, a closed-form formula had only been available for d=3. [ABSTRACT FROM AUTHOR]

Let Q be a probability measure on a finite group G, and let H be a subgroup of G. We show that a necessary and sufficient condition for the random walk driven by Q on G to induce a Markov chain on the double coset space H\backslash G/H is that Q(gH) is constant as g ranges over any double coset of H in G. We obtain this result as a corollary of a more general theorem on the double cosets H \backslash G / K for K an arbitrary subgroup of G. As an application we study a variation on the r-top to random shuffle which we show induces an irreducible, recurrent, reversible and ergodic Markov chain on the double cosets of \mathrm {Sym}_r \times \mathrm {Sym}_{n-r} in \mathrm {Sym}_n. The transition matrix of the induced walk has remarkable spectral properties: we find its invariant distribution and its eigenvalues and hence determine its rate of convergence. [ABSTRACT FROM AUTHOR]

The accurate representation of real floor behavior is crucial for assessing human-induced vibration serviceability. Many researchers focus on developing computational models and field testing to reflect actual serviceability conditions. Although traditional boundary conditions are commonly used, limited attention has been given to optimizing these conditions. To begin with, this paper introduced semirigid boundary conditions into a finite-element model of the floor and optimized physical parameters and boundary constraint stiffness using the simulated annealing-particle swarm optimization (SA-PSO) method, resulting in a more realistic computational model. Subsequently, a random crowd load model was established by combining the social force model (SFM) and the pedestrian load model, and a random crowd-floor mutual coupling calculation model was established based on the improved pedestrian biomechanical model. In addition, the mode shape functions of the floor with semirigid boundary conditions were obtained by extracting the optimized mode shape vector of the floor and using cubic spline interpolation. The dynamic response of the floor was computed using the modal analysis method, and the accuracy of the suggested method and model was verified by experiment. Furthermore, the effect on the vibration serviceability of the floor was analyzed under crowd walks randomly on the floor with different boundary conditions both before and after optimization. This study revealed: (1) achieving a computational model consistent with real floors requires optimization of relevant parameters and boundary conditions, reducing the error in floor frequency from 39.48% to 5.44% compared to measured results. (2) The human-induced vibration serviceability for existing floors may be misjudged by using traditional boundary conditions. The mean value of peak acceleration of floor with semirigid boundary conditions increased by 35.92%, with a 42% increase in the probability of serviceability problems compared to the SSCC boundary. (3) High-frequency floors also experience human-induced vibration serviceability issues. For a floor with a fundamental frequency of 10.3540 Hz, simulation and experimental results during five-person random walks indicate that peak acceleration at the middle position of the floor exceeds serviceability limits. [ABSTRACT FROM AUTHOR]

As the landscape of online social networks continues to evolve, the task of expanding connections and uncovering novel relationships presents a growing complexity. Link prediction emerges as a crucial strategy, harnessing the current network dynamics to forecast future interactions among users. While traditional single-layer network link prediction models boast a storied legacy, recent attention has shifted towards tackling analogous challenges within the realm of multilayer networks. This paradigm shift underscores the critical role of extracting topological and multimodal features to effectively evaluate link weights, thereby enriching link prediction within weighted networks. Furthermore, the establishment of trustworthy pathways between users emerges as a pivotal tactic for translating unweighted similarities into meaningful weighted metrics. Leveraging the foundational principles of local random walk techniques, this paper introduces the trustworthy Lévy-flight semi-local (TLFSL) random walk framework for link prediction in multilayer social networks. By seamlessly integrating intralayer and interlayer information, TLFSL harnesses a dependable Lévy-flight random walk mechanism to anticipate new links within target layers of multilayer networks. Traditional local random walk techniques often overlook global relationships, as they confine path exploration to immediate neighbours. However, the absence of a direct edge between nodes does not necessarily imply a lack of relationship; nodes with semantic affinity may be spatially distant within the network. To overcome this limitation, we introduce the concept of semi-local random walk, which enables walker hopping with a wider global perspective. Meanwhile, TLFSL includes a distributed local community detection strategy to improve the performance of TLFSL in dealing with large-scale networks. Rigorous experimentation across diverse real-world multilayer networks consistently demonstrates TLFSL's superior performance compared to equivalent methods. [ABSTRACT FROM AUTHOR]

Studying the association between microbes and diseases not only aids in the prevention and diagnosis of diseases, but also provides crucial theoretical support for new drug development and personalized treatment. Due to the time‐consuming and costly nature of laboratory‐based biological tests to confirm the relationship between microbes and diseases, there is an urgent need for innovative computational frameworks to anticipate new associations between microbes and diseases. Here, we propose a novel computational approach based on a dual branch graph convolutional network (GCN) module, abbreviated as DBGCNMDA, for identifying microbe–disease associations. First, DBGCNMDA calculates the similarity matrix of diseases and microbes by integrating functional similarity and Gaussian association spectrum kernel (GAPK) similarity. Then, semantic information from different biological networks is extracted by two GCN modules from different perspectives. Finally, the scores of microbe–disease associations are predicted based on the extracted features. The main innovation of this method lies in the use of two types of information for microbe/disease similarity assessment. Additionally, we extend the disease nodes to address the issue of insufficient features due to low data dimensionality. We optimize the connectivity between the homogeneous entities using random walk with restart (RWR), and then use the optimized similarity matrix as the initial feature matrix. In terms of network understanding, we design a dual branch GCN module, namely GlobalGCN and LocalGCN, to fine‐tune node representations by introducing side information, including homologous neighbour nodes. We evaluate the accuracy of the DBGCNMDA model using five‐fold cross‐validation (5‐fold‐CV) technique. The results show that the area under the receiver operating characteristic curve (AUC) and area under the precision versus recall curve (AUPR) of the DBGCNMDA model in the 5‐fold‐CV are 0.9559 and 0.9630, respectively. The results from the case studies using published experimental data confirm a significant number of predicted associations, indicating that DBGCNMDA is an effective tool for predicting potential microbe–disease associations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of reconstructing the past distribution for diffusion equations in multidimensional space with the presence of a poly-fractional operator which takes the following form$ {\mathbb{P}_\alpha }\left({{{\left({ - \Delta } \right)}^\gamma }} \right)u: = \sum\limits_{i = 1}^m {{\alpha _i}} {\left({ - \Delta } \right)^{{\gamma _i}}}u, $for $ m\in {\mathbb N} $, $ 0 < {\gamma _1} \le \cdots \le {\gamma _m} \le 1 $ and $ {\alpha _i} > 0 $ for $ i = \overline{1, m} $. The problem essentially arises from the superposition of multiple stochastic processes with different scales, including classical random walks and Lévy flights. We prove that the investigated problem is extremely ill-posed in the sense of Hadamard. Using an appropriate filtering method, we construct a regularized solution which converges to the original solution in $ L^2 $-sense. If we further impose a Gevrey-type a-priori condition, a Hölder convergence rate can be obtained. Three numerical examples using Matlab are also performed to demonstrate the ill-posedness of the problem and effectiveness of the regularization method. [ABSTRACT FROM AUTHOR]

We investigated the statistical properties of the Moran random walk (Yn)n in one dimension, focusing on short memory. Specifically, employing generating function techniques, we determined the cumulative distribution function and the mean of the height Hn. Furthermore, we derived explicit expressions for the distribution, mean, and variance of Yn, along with its asymptotic distribution. Finally, we provided the distribution of the waiting time τh, which represents the number of steps required to reach a specified level h, as the conclusion of our study. [ABSTRACT FROM AUTHOR]

It is known that many different types of finite random subgraph models undergo quantitatively similar phase transitions around their percolation thresholds, and the proofs of these results rely on isoperimetric properties of the underlying host graph. Recently, the authors showed that such a phase transition occurs in a large class of regular high-dimensional product graphs, generalising a classic result for the hypercube. In this paper we give new isoperimetric inequalities for such regular high-dimensional product graphs, which generalise the well-known isoperimetric inequality of Harper for the hypercube, and are asymptotically sharp for a wide range of set sizes. We then use these isoperimetric properties to investigate the structure of the giant component L 1 in supercritical percolation on these product graphs, that is, when p = 1 + ϵ d , where d is the degree of the product graph and ϵ > 0 is a small enough constant. We show that typically L 1 has edge-expansion Ω 1 d ln d . Furthermore, we show that L 1 likely contains a linear-sized subgraph with vertex-expansion Ω 1 d ln d . These results are best possible up to the logarithmic factor in d. Using these likely expansion properties, we determine, up to small polylogarithmic factors in d, the likely diameter of L 1 as well as the typical mixing time of a lazy random walk on L 1 . Furthermore, we show the likely existence of a cycle of length Ω n d ln d . These results not only generalise, but also improve substantially upon the known bounds in the case of the hypercube, where in particular the likely diameter and typical mixing time of L 1 were previously only known to be polynomial in d. [ABSTRACT FROM AUTHOR]

This research paper presents a methodology for improving wireless sensor network (WSN) performance by leveraging centrality measures, including degree, betweenness, closeness, eigenvector, and Katz centrality. Employing a random walk graph model, this study constructs networks with 30 and 50 nodes to investigate the impact of these centrality metrics on routing decisions to optimize energy efficiency, minimize latency, and enhance overall network reliability. Additionally, the paper provides a comprehensive analysis of the relationships among these centrality measures through various correlation techniques, such as Pearson correlation, Kendall rank correlation, and Spearman correlation, offering insights into how these metrics can effectively improve WSN operations. [ABSTRACT FROM AUTHOR]

Summary: Community detection is a key feature that can be used to extract useful information from networks. In most studies, the same static algorithms are used on real‐time snapshots of the dynamic network. Such an action increases the calculations and the time taken for the clustering operation. The idea of community detection is based on the fact that communities are formed around a node that is more popular and influential. Therefore, in the proposed algorithm, first, several snapshots are received from the network, then for the first snapshot, the influence of each node is calculated using the influence function based on the random walk distance between nodes. Then by selecting k nodes with higher influence, network communities are formed and other nodes belong to the community with the most common edges. In the next step, the next snapshots will be received and then the communities will be updated. Then K nodes with higher influence are selected and their community is created if needed. The proposed method has been compared with state‐of‐the‐art algorithms, and the results show that proposed method has been able to have a suitable performance in the uniformity of communities and also the speed of community formation. [ABSTRACT FROM AUTHOR]

We consider dense graph sequences that converge to a connected graphon and prove that the GHP scaling limit of their uniform spanning trees (USTs) is Aldous' Brownian CRT. Furthermore, we are able to extract the precise scaling constant from the limiting graphon. As an example, we can apply this to the scaling limit of the USTs of the Erdös–Rényi sequence (G(n,p))n≥1$$ {\left(G\left(n,p\right)\right)}_{n\ge 1} $$ for any fixed p∈(0,1]$$ p\in \left(0,1\right] $$, and sequences of dense expanders. A consequence of GHP convergence is that several associated quantities of the spanning trees also converge, such as the height, diameter and law of a simple random walk. [ABSTRACT FROM AUTHOR]

How many edges in an n$$ n $$‐vertex graph will force the existence of a cycle with as many chords as it has vertices? Almost 30 years ago, Chen, Erdős and Staton considered this question and showed that any n$$ n $$‐vertex graph with 2n3/2$$ 2{n}^{3/2} $$ edges contains such a cycle. We significantly improve this old bound by showing that Ω(nlog8n)$$ \Omega \left(n\kern0.2em {\log}^8n\right) $$ edges are enough to guarantee the existence of such a cycle. Our proof exploits a delicate interplay between certain properties of random walks in almost regular expanders. We argue that while the probability that a random walk of certain length in an almost regular expander is self‐avoiding is very small, one can still guarantee that it spans many edges (and that it can be closed into a cycle) with large enough probability to ensure that these two events happen simultaneously. [ABSTRACT FROM AUTHOR]

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems. [ABSTRACT FROM AUTHOR]

Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta‐analysis (NMA) is an active area of research. We extend this work to include the contributions of paths of evidence. We present a general framework, based on the path‐design matrix, that describes the problem of finding path contributions as a linear equation. The resulting solutions may have negative coefficients. We show that two known approaches, called shortestpath and randomwalk, are special solutions of this equation, and both meet an optimization criterion, as they minimize the sum of absolute path contributions. In general, there is an infinite set of solutions, which can be identified using the generalized inverse (Moore‐Penrose pseudoinverse). We consider two further special approaches. For large networks we find that shortestpath is superior with respect to run time and variability, compared to the other approaches, and is thus recommended in practice. The path‐weights framework also has the potential to answer more general research questions in NMA. [ABSTRACT FROM AUTHOR]

Using a two-step approach GMM, this study examines the short- and long-term effects of fiscal deficit on the economic growth of 42 Sub-Saharan African nations between 2011 and 2021. The World Development Index, the most reliable source, is where the panel data is taken from. Using the Levin-Lin-Chu and Hadri LM tests for unit root, it was determined that there is no risk of a random walk in the data. The study's findings indicate that while the fiscal deficit has short-term, positive, and significant benefits on the economic growth of SSA countries, it has long-term, negative repercussions. According to the system GMM's results, an increase in the fiscal deficit of SSA countries is linked to a short-term increase in economic growth of 0.036 percent, while an increase in the fiscal deficit of one percentage point is linked to a long-term decline in economic growth of SSA countries of 0.013 percent, holding all other factors constant. The study's findings also showed that the budget deficit has a larger positive short-run coefficient than a negative long-run coefficient. The study also revealed that while real effective exchange rates and inflation short-term hinder economic growth, gross fixed capital creation and real interest rates are the primary drivers of economic expansion. Long-term economic growth in the SSA countries is also found to be positively and significantly impacted by gross fixed capital formation. According to the study, SSA nations should manage their fiscal deficits and, in the long run, provide more funds for gross fixed capital development. [ABSTRACT FROM AUTHOR]

A geometrically symmetric gear with asymmetric surface wettability exhibits one-way spin on a vibrating water bed. On the side face of the gear, a parafilm was coated to create asymmetry in the surface energy. The gear shows fluctuations in both directions within a shorter timescale; however, for a longer timescale, the gear exhibits a one-way spin. This unique motion is generated by a stochastic process with a biased driving force produced by the interaction between the vibrating water surface and the side face of the gear. This new model resembles an active Brownian ratchet. Until now, most ratchet motors, which obtain regular motion from nonthermal fluctuations, utilize a geometrical ratchet structure. However, in this study, the surface energy forms a ratchet that rectifies the noisy motion. [ABSTRACT FROM AUTHOR]