A mathematical model for data-driven synthesis of neuron morphologies based on random walks

Accurate lung tumor delineation plays an important role in radiotherapy treatment planning. Since the lung tumor has poor boundary in positron emission tomography (PET) images and low contrast in computed tomography (CT) images, segmentation of tumor in the PET and CT images is a challenging task. In this paper, we effectively integrate the two modalities by making fully use of the superior contrast of PET images and superior spatial resolution of CT images. Random walk and graph cut method is integrated to solve the segmentation problem, in which random walk is utilized as an initialization tool to provide object seeds for graph cut segmentation on the PET and CT images. The co-segmentation problem is formulated as an energy minimization problem which is solved by max-flow/min-cut method. A graph, including two sub-graphs and a special link, is constructed, in which one sub-graph is for the PET and another is for CT, and the special link encodes a context term which penalizes the difference of the tumor segmentation on the two modalities. To fully utilize the characteristics of PET and CT images, a novel energy representation is devised. For the PET, a downhill cost and a 3D derivative cost are proposed. For the CT, a shape penalty cost is integrated into the energy function which helps to constrain the tumor region during the segmentation. We validate our algorithm on a data set which consists of 18 PET-CT images. The experimental results indicate that the proposed method is superior to the graph cut method solely using the PET or CT is more accurate compared with the random walk method, random walk co-segmentation method, and non-improved graph cut method.

A number of knowledge graph (KG)-based recommendation algorithms have been introduced; KGs enable users and items and their attributes to be treated in an integrated way and structural information to be captured through graphs. There are many variations of the KG based recommendation algorithms. Among them, KG embedding is often used, but doing this does not take advantage of the meta-path-level proximity between users and items. This paper presents a flexible framework combining random walk and KG embedding methods. The random walk model is formulated on the basis of the similarity between nodes revealed by the KG embedding. This enables the metapath level proximity of users and items to be efficiently utilized. Comparison testing demonstrated that the proposed framework performs better than random- walk-only methods and KG-embedding-only methods, and slightly better than the existing method we have extended.

Study on random walk and its application to solution of heat conduction equation by Monte Carlo method

An important method for testing large and complex protocols repeatedly generates and tests a part of the reachable state space by following a random walk; the main advantage of this method is that it has minimal memory requirements. We use the coupling technique from Markov chain theory to show that short trajectories of the random walk sample accurately the reachable state space of a nontrivial family of protocols, namely, the symmetric dyadic flip-flops. This is the first evidence that the random walk method is amenable to rigorous treatment.Following West's original reasoning, efficient sampling of the reachable state space by random walk suffices to ensure effectiveness of testing. Is, however, efficient sampling of the random walk necessary for the effectiveness of the random walk method? In the context of Markov chain theory, “small cover time” can be thought of as a simpler justification for the effectiveness of testing by random walk; all symmetric (reversible) protocols possess the small cover time property.Thus the conclusions of our work are that (i) the random walk method can be understood in the context of known Markov chain theory, and (ii) symmetry (reversibility) is a general protocol style that supports testing by random simulation.

In this chapter, we present the basics of Monte Carlo method for solving deterministic PDE. We first introduce more theoretic aspects of Monte Carlo method, along with random walk process and method. Then, we introduce the discrete random walk method and floating random walk method, respectively. We try our best to make the presentation not for specific applications, and instead to be of general interest.

With the ever-reducing sizes of electronic devices, the problem of electromigration (EM) has become relevant and requires attention. However, only the EM behavior of Sn–Ag solders within the solder joint structure has been focused on thus far. Therefore, in this study, a thin metallic film composed of Sn–3.5Ag (wt.%) was subjected to a current density of 7.77 × 104 A/cm2 at a temperature of 15 °C to test the ability of existing EM models to predict the nucleation and evolution of voids generated by the resulting atomic migration. A computer simulation was then used to compute the coupled current distribution, thermal distribution, and atomic migration problems. It relied on an original random walk (RW) method, not previously applied to this problem, that is particularly well suited for modelling domains that undergo changes owing to the formation of voids. A comparison of the experimental results and computer simulations proves that the RW method can be applied successfully to this class of problems, but it also shows that imperfections in the film can lead to deviations from predicted patterns.

Random walks are a relatively new component used in several state of the art satisficing planners. Empirical results have been mixed: while the approach clearly outperforms more systematic search methods such as weighted A* on many planning domains, it fails in many others. So far, the explanations for these empirical results have been somewhat ad hoc. This paper proposes a formal framework for comparing the performance of random walk and systematic search methods. Fair homogenous graphs are proposed as a graph class that represents characteristics of the state space of prototypical planning domains, and is simple enough to allow a theoretical analysis of the performance of both random walk and systematic search algorithms. This gives well-founded insights into the relative strength and weaknesses of these approaches. The close relation of the models to some well-known planning domains is shown through simplified but semi-realistic planning domains that fulfill the constraints of the models. One main result is that in contrast to systematic search methods, for which the branching factor plays a decisive role, the performance of random walk methods is determined to a large degree by the Regress Factor, the ratio between the probabilities of progressing towards and regressing away from a goal with an action. The performance of random walk and systematic search methods can be compared by considering both branching and regress factors of a state space.

Random walks are a relatively new component used in several state of the art satisficing planners. Empirical results have been mixed: while the approach clearly outperforms more systematic search methods such as weighted A* on many planning domains, it fails in many others. So far, the explanations for these empirical results have been somewhat ad hoc. This paper proposes a formal framework for comparing the performance of random walk and systematic search methods. Fair homogenous and Infinitely Regressable homogenous graphs are proposed as graph classes that represents characteristics of the state space of prototypical planning domains, and is simple enough to allow a theoretical analysis of the performance of both random walk and systematic search algorithms. This gives well-founded insights into the relative strength and weaknesses of these approaches. The close relation of the models to some well-known planning domains is shown through simplified but semi-realistic planning domains that fulfill the constraints of the models. One main result is that in contrast to systematic search methods, for which the branching factor plays a decisive role, the performance of random walk methods is determined to a large degree by the Regress Factor, the ratio between the probabilities of progressing towards and regressing away from a goal with an action. The performance of random walk and systematic search methods can be compared by considering both branching and regress factors of a state space.

Stochastic sampling is performed to reduce hardware energy consumption and prevent overfitting by reducing parameters, because not all data are required for learning. In this study, a new approach, pseudo‐synaptic sampling (PS2) method, which approximates the conventional synaptic sampling machine (S2M) method through a hardware‐friendly implementation while demonstrating superior efficiency, is introduced. By sampling in front of neurons rather than at each synapse, the PS2 method improves hardware energy efficiency and ensures scalability. Furthermore, it improves energy and area efficiency by eliminating the additional circuit required by other techniques, such as the random walk (RW) method previously used which requires an additional circuit to frequently charge/discharge the membrane potential. Herein, the average firing rate equation for the S2M method is modified to suit the experimental conditions of this study. Through this numerical simulations, it is confirmed that the activation function of the PS2 method aligns with that of the S2M method and verified that the PS2 method can implement stochasticity for restricted Boltzmann machine (RBM) neurons. Experimental validation of the PS2 method, compared to the RW method, for Modified National Institute of Standards and Technology database (MNIST) training and inference on field‐programmable‐gate‐array‐implemented spiking RBM chips reveals promising results. In an MNIST 100‐handwritten digit experiment, the PS2 method exhibits on‐chip training accuracy (92%) comparable to that of the RW method (93%). Furthermore, in the energy consumption analysis, it is shown that the PS2 method reduces power consumption by 94.94% compared to the RW method, highlighting its enhanced power efficiency due to a reduced number of circuit elements. In the investigation into the impact of increasing the frequency at which random bits are generated, it is shown that the RW method experiences accuracy degradation even with slight increases, whereas the PS2 method maintains accuracy over significantly longer periods. This enables further power reduction by allowing for a longer period during random bit generation. In this study, a foundation is laid for maximizing the energy efficiency of spiking neural network processors by optimizing internal noise generation mechanisms.

A new method of generating realistic three dimensional simulated breast lesions known as diffusion limited aggregation (DLA) is presented, and compared with the random walk (RW) method. Both methods of lesion simulation utilize a physics-based method for inserting these simulated lesions into 2D clinical mammogram images that takes into account the polychromatic x-ray spectrum, local glandularity and scatter. DLA and RW masses were assessed for realism via a receiver operating characteristic (ROC) study with nine observers. The study comprised 150 images of which 50 were real pathology proven mammograms, 50 were normal mammograms with RW inserted masses and 50 were normal mammograms with DLA inserted masses. The average area under the ROC curve for the DLA method was 0.55 (95% confidence interval 0.51–0.59) compared to 0.60 (95% confidence interval 0.56–0.63) for the RW method. The observer study results suggest that the DLA method produced more realistic masses with more variability in shape compared to the RW method. DLA generated lesions can overcome the lack of complexity in structure and shape in many current methods of mass simulation.

This study proposes a weighted random walk method on co‐word networks to identify important themes of a field using structural features of the networks. The goal is to test whether the weighted random walk method can be used to produce meaningful results on co‐word networks. In addition, we examined the relationships among the results from the random walk method and other two common metrics for identifying important themes in a field: frequency and point centrality. Using a dataset of 17K bibliographic records for the articles in the LIS field from the Web of Science, our results indicate that all three measures are significantly correlated. A detailed comparison of the top terms ranked by the three metrics from the years of 2002–2006 and 2007–2012 is provided. The results show that the three measures are generally similar in revealing hotspots and development of the field. However, some noticeable differences are also found. The random walk method boosted the rankings of some lower ranked terms in the other two metrics (e.g. “universe”, “servic” and “develop”) due to their cooccurrences with top ranked terms (e.g. “information”). The findings of this study help to understand the use of random walk method on co‐word networks.

The first stage in route choice modeling is the generation of the route choice sets, which directly affects the accuracy of model estimation. The random walk method proposed by Frejinger et al. for this purpose has the advantage of directly calculating the probabilities of paths chosen. However, its application has seldom been seen in a large-scale network of a real large city in the literature. To fill this gap, the performance of the random walk algorithm is examined on a real network in Shanghai, China. It is found that it cannot avoid loops and frequently produces overlong alternative paths. By locating the root cause, an improved random walk algorithm is proposed in this paper. The idea of the new algorithm is to change the value of the shape parameters. Instead of a fixed value in Frejinger et al.’s method, the shape parameter in this approach is dynamically changing, controlled by the allowable probability difference and generalized minimum cost. The algorithm is validated in a large-scale network using real travel survey data. The results of the empirical analysis suggest that the proposed random walk algorithm has a significant improvement with respect to the number and length of generated alternative paths compared to those from the original algorithm. This study's primary contribution is to significantly improve the adaptability of the random walk method in large-scale road networks, which is crucial for improving the accuracy of route choice models and understanding of route choice behaviors.

A new method to simulate solute transport in 1–D heterogeneous media is presented. This time domain random walk method (TDRW), similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location (directly providing the solute breakthrough curve). The main advantage of the method is that the restrictions on the space increments and the time steps which exist with the finite differences and random walk methods are avoided. In a homogeneous zone, the breakthrough curve (BTC) can be calculated directly at a given distance using a few hundred particles or directly at the boundary of the zone. Comparisons with analytical solutions and with the classical random walk method show the reliability of this method. The velocity and dispersivity calculated from the simulated results agree within two percent with the values used as input in the model. For contrasted heterogeneous media, the random walk can generate high numerical dispersion, while the time domain approach does not.

The purpose of area exploration is to cover an area effectively and swarm robots are used widely for this type of area exploration because of their robustness, flexibility, and scalability. Meanwhile, due to the limited individual abilities of swarm robots, the random walk methods have been the generally used area-exploration strategy. Although random walk methods possess better performance in area exploration, there still exist some problems. For one thing, little work has been devoted to the theoretical analysis of the random walk models. For another, no effective measures are used to evaluate the searching efficiency of random walk methods and the searching efficiency is verified mainly by simulation experiments. Therefore, in order to make up for the deficiency, this paper presents the mathematical description of the random walk models by drawing on the experience of related researches in biology. The proposed mathematical theory can not only be used to aid our understanding of random walks but also be easy to analyze and control random motion of the robots. Also, the mean squared displacement (MSD) is introduced as the performance measure to evaluate the effectiveness of the random walk methods. In order to proof the effectiveness of the performance measure of MSD, the area-exploration missions of swarm robots are carried out in the simulation experiments and the the coverage rate is used to evaluate the searching efficiency. The experimental results prove that the MSD is an effective performance measure to evaluate the searching efficiency.

Random walk methods have been successfully applied to prioritizing disease causal genes. In this paper, we propose a bi-random walk algorithm (BiRW) based on a regularization framework for graph matching to globally prioritize disease genes for all phenotypes simultaneously. While previous methods perform random walk either on the protein-protein interaction network or the complete phenome-genome heterogenous network, BiRW performs random walk on the Kronecker product graph between the protein-protein interaction network and the phenotype similarity network. Three variations of BiRW that perform balanced or unbalanced bi-directional random walks are analyzed and compared with other random walk methods. Experiments on analyzing the disease phenotype-gene associations in Online Mendelian Inheritance in Man (OMIM) demonstrate that BiRW effectively improved disease gene prioritization over existing methods by ranking more known associations in the top 100 out of nearly 10,000 candidate genes.