Search Results (53)

The resistance distance is a squared Euclidean metric on the vertices of a graph derived from the consideration of a graph as an electrical circuit. Its connection with the commute time of a random walker on the graph has made it particularly appealing for the analysis of networks. Here, we prove that the resistance distance is given by a difference of “mass concentrations” obtained at the vertices of a graph by a diffusive process. The nature of this diffusive process is characterized here by means of an operator corresponding to the matrix logarithm of a Perron-like matrix based on the pseudoinverse of the graph Laplacian. We prove also that this operator is indeed the Laplacian matrix of a signed version of the original graph, in which nonnearest neighbors’ “interactions” are also considered. In this way, the resistance distance is part of a family of squared Euclidean distances emerging from diffusive dynamics on graphs. Full article

In this study, we explore the impact of stochastic resetting on the dynamics of random walks on a T-fractal network. By employing the generating function technique, we establish a recursive relation between the generating function of the first passage time (FPT) and derive the relationship between the mean first passage time (MFPT) with resetting and the generating function of the FPT without resetting. Our analysis covers various scenarios for a random walker reaching a target site from the starting position; for each case, we determine the optimal resetting probability ${\gamma }^{*}$ that minimizes the MFPT. We compare the results with the MFPT without resetting and find that the inclusion of resetting significantly enhances the search efficiency, particularly as the size of the network increases. Our findings highlight the potential of stochastic resetting as an effective strategy for the optimization of search processes in complex networks, offering valuable insights for applications in various fields in which efficient search strategies are crucial. Full article

While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter $\rho$ and integrates random coefficients. This approach combines characteristics from both binomial and negative binomial thinning operators, thereby offering a flexible framework capable of generating counting series exhibiting equidispersion, overdispersion, or underdispersion. Notably, our model includes two distinct classes of first-order bivariate geometric integer-valued autoregressive models: one class employs binomial thinning (BVGINAR(1)), and the other adopts negative binomial thinning (BVNGINAR(1)). We establish the stationarity and ergodicity of the model and estimate its parameters using a combination of the Yule–Walker (YW) and conditional maximum likelihood (CML) methods. Furthermore, Monte Carlo simulation experiments are conducted to evaluate the finite sample performances of the proposed estimators across various parameter configurations, and the Anderson-Darling (AD) test is employed to assess the asymptotic normality of the estimators under large sample sizes. Ultimately, we highlight the practical applicability of the examined model by analyzing two real-world datasets on crime counts in New South Wales (NSW) and comparing its performance with other popular overdispersed BINAR(1) models. Full article

Osteoporosis constitutes a significant public health concern necessitating proactive prevention, treatment, and monitoring efforts. Timely identification holds paramount importance in averting fractures and alleviating the overall disease burden. The realm of osteoporosis diagnosis has witnessed a surge in interest in machine learning applications. This burgeoning technology excels at recognizing patterns and forecasting the onset of osteoporosis, paving the way for more efficacious preventive and therapeutic interventions. Smart walkers emerge as valuable tools in this context, serving as data acquisition platforms for datasets tailored to machine learning techniques. These datasets, trained to discern patterns indicative of osteoporosis, play a pivotal role in enhancing diagnostic accuracy. In this study, encompassing 40 participants—20 exhibiting robust health and 20 diagnosed with osteoporosis—data from force sensors embedded in the handlebars of conventional walkers were gathered. A windowing action was used to increase the size of the dataset. The data were normalized, and k-fold cross-validation was applied to assess how well our model performs on untrained data. We used multiple machine learning algorithms to create an accurate model for automatic monitoring of users’ gait, with the Random Forest classifier performing the best with 95.40% accuracy. To achieve the best classification accuracy on the validation dataset, the hyperparameters of the Random Forest classifier were further adjusted on the training data. The results suggest that machine learning-based automatic monitoring of gait parameters could lead to accurate, non-laborious, cost-effective, and efficient diagnostic tools for osteoporosis and other musculoskeletal disorders. Further research is needed to validate these findings. Full article

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási–Albert (BA), Erdös–Rényi (ER), and Watts–Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers $R_M,R_0$ with and without mortality, respectively, and prove that $R_M<R_0$. For $R_M,R_0>1$, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others. Full article

Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are the time-fractional Klein–Gordon equation (KGE), the time-fractional Sharma–Tasso–Olever equation (STOE), and the time-fractional Clannish Random Walker’s Parabolic equation (CRWPE). These models were investigated by using an expansion method for extracting new soliton solutions. Two types of results were found: one was trigonometric and the other one was an exponential form. For a profound explanation of the physical phenomena of the studied fractional models, some results were graphed in 2D, 3D, and contour plots by imposing the distinctive results for some parameters under the oblige conditions. From the numerical investigation, it was noticed that the obtained results referred smooth kink-shaped soliton, ant-kink-shaped soliton, bright kink-shaped soliton, singular periodic solution, and multiple singular periodic solutions. The results also showed that the amplitude of the wave augmented with the pulsation in time, which derived the order of time fractional coefficient, remarkably enhanced the wave propagation, and influenced the nonlinearity impacts. Full article

Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. Different research studies have proposed many node centralities based on the network structure for ranking nodes to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks and is an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node centralities for network dismantling with effective node removal strategies from the literature, namely betweenness, closeness, degree, and k-shell node removal, for synthetic and real-world networks. We evaluate the dismantling of the network by using the size of the largest connected component (LCC). We find that the degree nodes attack is the best strategy overall, and the new node removal strategies based on RW show the highest efficacy in regard to peculiar network topology. Specifically, RW strategy based on covering time emerges as the most effective strategy for a synthetic lattice network and a real-world road network. Our results may help researchers select the best node attack strategies in a specific network class and build more robust network structures. Full article

We study the long-time dynamics of the mean squared displacement of a random walker moving on a comb structure under the effect of stochastic resetting. We consider that the walker’s motion along the backbone is diffusive and it performs short jumps separated by random resting periods along fingers. We take into account two different types of resetting acting separately: global resetting from any point in the comb to the initial position and resetting from a finger to the corresponding backbone. We analyze the interplay between the waiting process and Markovian and non-Markovian resetting processes on the overall mean squared displacement. The Markovian resetting from the fingers is found to induce normal diffusion, thereby minimizing the trapping effect of fingers. In contrast, for non-Markovian local resetting, an interesting crossover with three different regimes emerges, with two of them subdiffusive and one of them diffusive. Thus, an interesting interplay between the exponents characterizing the waiting time distributions of the subdiffusive random walk and resetting takes place. As for global resetting, its effect is even more drastic as it precludes normal diffusion. Specifically, such a resetting can induce a constant asymptotic mean squared displacement in the Markovian case or two distinct regimes of subdiffusive motion in the non-Markovian case. Full article

Random walks (RWs) have been important in statistical physics and can describe the statistical properties of various processes in physical, chemical, and biological systems. In this study, we have proposed a self-interacting random walk model in a continuous three-dimensional space, where the walker and its previous visits interact according to a realistic Lennard-Jones (LJ) potential $u_{LJ}\left(r\right)=\epsilon \left[{\left(r_0/r\right)}^{12}-2{\left(r_0/r\right)}^6\right]$. It is revealed that the model shows a novel globule-to-helix transition in addition to the well-known coil-to-globule collapse in its trajectory when the temperature decreases. The dependence of the structural transitions on the equilibrium distance $r_0$ of the LJ potential and the temperature T were extensively investigated. The system showed many different structural properties, including globule–coil, helix–globule–coil, and line–coil transitions depending on the equilibrium distance $r_0$ when the temperature T increases from low to high. We also obtained a correlation form of k_BT_c = λε for the relationship between the transition temperature T_c and the well depth $\epsilon$, which is consistent with our numerical simulations. The implications of the random walk model on protein folding are also discussed. The present model provides a new way towards understanding the mechanism of helix formation in polymers like proteins. Full article

We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass N sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete model, the limit in which the motion becomes continuous in space and time ($N\to \infty$) is not unique and depends on what physical observables are assumed to be unchanged in the process. In particular, one may (as usually done) choose to keep the speed and diffusion coefficient fixed during this limiting process, in which case, the entropy production is affected. In addition, we also studied processes in which the entropy production is kept constant as $N\to \infty$ at the cost of a modified speed or diffusion coefficient. Furthermore, we also combined this dynamics with work against an opposing force, which made it possible to study the effect of discretization of the process on the thermodynamic efficiency of transferring the power input to the power output. Interestingly, we found that the efficiency was increased in the limit of $N\to \infty$. Finally, we investigated the same process when transitions between sites can only happen at finite time intervals and studied the impact of this time discretization on the thermodynamic variables as the continuous limit is approached. Full article

The composition and seasonal abundance of hymenopteran parasitoids of Liriomyza trifolii (Burgess) was investigated on snap bean (Phaseolus vulgaris L.), tomato (Solanum lycopersicum L.), and squash (Cucurbita pepo L. ‘Enterprise’) from 2010 to 2016 in South Florida in two studies. In the first study (2010–2016), 13 species of parasitoids were collected from the snap bean crop. Opius dissitus Muesebeck (Braconidae) was the most abundant parasitoid throughout the study period from September 2010 to February 2016. Diaulinopsis callichroma Crawford (Eulophidae) was the second most abundant parasitoid on bean in 2010, 2012, 2014, and 2016. Other parasitoids included Euopius sp. (Braconidae)., Diglyphus begini (Ashmead), D. intermedius (Girault), D. isaea (Walker), Neochrysocharis sp., Closterocerus sp., Chrysocharis sp., Zagrammosoma lineaticeps (Girault), Z. muitilineatum (Ashmead), Pnigalio sp. (all Eulophidae), and Halticoptera sp. (Pteromalidae). In the second study on the comparative abundance of parasitoids in three crops conducted in 2014 and 2016 using bean (Phaseolus vulgaris L., tomato (Solanum lycopersicum L.) and squash (Cucurbita pepo L.) arranged in a randomized complete block design, bean attracted more parasitoids than tomato and squash irrespective of parasitoid species and years. This information will help in devising a biocontrol-based integrated program for managing leafminers in beans and other vegetable crops. Full article

Image segmentation is the process of dividing an image into homogeneous regions according to certain features and is widely used in image processing. Complexly structured images usually contain complex and essential objects. These images are non-linear structural images and they contain a large number of elements with required specifications. The main goal of the proposed EPSO (Exponential Particle Swarm Optimization) algorithm is to prevent local solutions and find the exact global optimal solutions for the task of segmenting medical images. The execution time is compared with well-known segmentation algorithms. The EPSO method is superior to the segmentation methods studied, including the graph algorithm. Comparisons were made with existing segmentation algorithms (Grow cut, Random Walker, DPSO, K-means PSO, and hybrid-K-means ant colony optimization algorithm) in tabular form. Full article

Individuals with cerebral palsy functioning at Gross Motor Function Classification System (GMFCS) levels IV and V are unable to use hand-held walkers and require supported-stepping devices with trunk and pelvic support to allow overground stepping in natural environments. This scoping review explored what is known about the use of supported-stepping devices with individuals functioning at GMFCS IV or V. Comprehensive database and hand searches were completed in December 2022. Of 225 unique citations, 68 met the inclusion criteria: 10 syntheses and 58 primary studies including randomized, non-randomized, qualitative, observational and case study designs. Primary studies included 705 unique individuals functioning at GMFCS IV or V, aged 9 months to 47.7 years, while surveys and qualitative studies included 632 therapists. No new experimental studies have been published since previous reviews, however, lived experience and descriptive data suggest that upright positioning and mobility in supported-stepping devices have psycho-social significance with positive impacts on individual self-esteem and autonomy, as well as influencing the perception of others. Improved head and trunk control, use of hands, stepping and independent mobility may promote fitness, functioning, fun, friends, family and future, although environmental and physical challenges may limit use in adolescence and adulthood. Further research on all aspects of supported-stepping device use with individuals at GMFCS IV/V is warranted. Full article

People with diabetic foot ulcers (DFUs) are commonly prescribed offloading walkers, but inadequate adherence to prescribed use can be a barrier to ulcer healing. This study examined user perspectives of offloading walkers to provide insight on ways to help promote adherence. Participants were randomized to wear: (1) irremovable, (2) removable, or (3) smart removable walkers (smart boot) that provided feedback on adherence and daily walking. Participants completed a 15-item questionnaire based on the Technology Acceptance Model (TAM). Spearman correlations assessed associations between TAM ratings with participant characteristics. Chi-squared tests compared TAM ratings between ethnicities, as well as 12-month retrospective fall status. A total of 21 adults with DFU (age 61.5 ± 11.8 years) participated. Smart boot users reported that learning how to use the boot was easy (ρ =−0.82, p$\le$ 0.001). Regardless of group, people who identified as Hispanic or Latino, compared to those who did not, reported they liked using the smart boot (p = 0.05) and would use it in the future (p = 0.04). Non-fallers, compared to fallers, reported the design of the smart boot made them want to wear it longer (p = 0.04) and it was easy to take on and off (p = 0.04). Our findings can help inform considerations for patient education and design of offloading walkers for DFUs. Full article

We introduce a refined way to diffusely explore complex networks with stochastic resetting where the resetting site is derived from node centrality measures. This approach differs from previous ones, since it not only allows the random walker with a certain probability to jump from the current node to a deliberately chosen resetting node, rather it enables the walker to jump to the node that can reach all other nodes faster. Following this strategy, we consider the resetting site to be the geometric center, the node that minimizes the average travel time to all the other nodes. Using the established Markov chain theory, we calculate the Global Mean First Passage Time (GMFPT) to determine the search performance of the random walk with resetting for different resetting node candidates individually. Furthermore, we compare which nodes are better resetting node sites by comparing the GMFPT for each node. We study this approach for different topologies of generic and real-life networks. We show that, for directed networks extracted for real-life relationships, this centrality focused resetting can improve the search to a greater extent than for the generated undirected networks. This resetting to the center advocated here can minimize the average travel time to all other nodes in real networks as well. We also present a relationship between the longest shortest path (the diameter), the average node degree and the GMFPT when the starting node is the center. We show that, for undirected scale-free networks, stochastic resetting is effective only for networks that are extremely sparse with tree-like structures as they have larger diameters and smaller average node degrees. For directed networks, the resetting is beneficial even for networks that have loops. The numerical results are confirmed by analytic solutions. Our study demonstrates that the proposed random walk approach with resetting based on centrality measures reduces the memoryless search time for targets in the examined network topologies. Full article