Probability Transition Research Articles

Single-item continuous-review inventory models with random supplies

Abstract This paper analyzes single-item continuous-review inventory models with random supplies in which the inventory dynamic between orders is described by a diffusion process, and a long-term average cost criterion is used to evaluate decisions. The models in this class have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. Random yield is described by a (probability) transition function which depends on the inventory on hand and the nominal amount ordered; it is assumed to be a distribution with support in the interval determined by the order-from and the nominal order-to locations of the stock level. Using weak convergence arguments involving average expected occupation and ordering measures, conditions are given for the optimality of an (s, S) ordering policy in the general class of policies with finite expected cost. The characterization of the cost of an (s, S) policy as a function of two variables naturally leads to a nonlinear optimization problem over the stock levels s and S, and the existence of an optimizing pair $(s^*,S^*)$ is established under weak conditions. Thus, optimal policies of inventory models with random supplies can (easily) be numerically computed. The range of applicability of the optimality result is illustrated on several inventory models with random yields.

Brazilian Road Bridge Management Based On Probabilistic Markov Process Deterioration Models

Objective: The objective of this study is to investigate the feasibility of applying the Markov chain method, with the aim of obtaining deterioration models for road bridges in Brazil. Theoretical Framework: The concept of Condition Index (CI), the determination of the probability transition matrix and deterioration models based on Markov chains are presented. Method: The methodology is based on inspection records of highway bridges inspected by the Agência Nacional de Transporte Terrestre (ANTT) in three sections of different federal highways, based on annual records of condition indexes from 2010 to 2016. Results and Discussion: The deterioration models indicate that in the bridges of the analyzed highway sections, BR-040/MG/RJ, BR-101/RJ and BR-116/BA, the transition from CI=4 to CI=3 is observed in 10 years. The bridges on the BR-040/MG/RJ highway also drop from maximum CI=5 to CI=3 in just 10 years. Research Implications: The results obtained can be applied or influence practices in the field of Transportation Engineering in Brazil. The implications cover the passenger and cargo transportation sectors. Originality/Value: The study uses real data from inspections of highway bridges from a specific period of time. The relevance and value of this research are evidenced by the achievement of bridge deterioration models, which constitute fundamental tools for planning, managing and preparing public works concession notices.

Flexible Local Differential Privacy Mechanism for Collecting Location Data

To address issues in existing location data collection methods, such as poor data utility and large deviations between perturbed and true locations, this paper proposes a personalized local differential privacy (LDP) mechanism for location data collection. Users can select their privacy protection range based on their needs, limiting the perturbed output to this range, thereby improving data utility. To address the issue of large deviations between perturbed and true locations, we introduce a new strategy where the location is perturbed with a probability that is higher the closer it is to the true location. By analyzing the mutual information upper bound of the true and estimated location distributions, the optimal perturbation probability range is determined. Finally, a probability transition matrix is generated from the location transfer probabilities, and the true location distribution is estimated from the perturbed location distribution.

An Earth Mover's Distance-Based Self-Supervised Framework for Cellular Dynamic Grading in Live-Cell Imaging.

Cellular appearance and its dynamics frequently serve as a proxy measurement of live-cell physiological properties. The computational analysis of cell properties is considered to be a significant endeavor in biological and biomedical research. Deep learning has garnered considerable success across various fields. In light of this, various neural networks have been developed to analyze live-cell microscopic videos and capture cellular dynamics with biological significance. Specifically, cellular dynamic grading (CDG) is the task that provides a predefined dynamic grade for a live-cell according to the speed of cellular deformation and intracellular movement. This task involves recording the morphological and cytoplasmic dynamics in live-cell microscopic videos. Similar to other medical image processing tasks, CDG faces challenges in collecting and annotating cellular videos. These deficiencies in medical data limit the performance of deep learning models. In this article, we propose a novel self-supervised framework to overcome these limitations for the CDG task. Our framework relies on the assumption that increasing or decreasing cell dynamic grades is consistent with accelerating or decelerating cell appearance change in videos, respectively. This consistency is subsequently incorporated as a constraint in the loss function for the self-supervised training strategy. Our framework is implemented by formulating a probability transition matrix based on the Earth Mover's Distance and imposing a loss constraint on the elements of this matrix. Experimental results demonstrate that our proposed framework enhances the model's ability to learn spatiotemporal dynamics. Furthermore, our framework outperforms the existing methods on our cell video database.

CC4S: Encouraging Certainty and Consistency in Scribble-Supervised Semantic Segmentation.

Deep learning-based solutions have achieved impressive performance in semantic segmentation but often require large amounts of training data with fine-grained annotations. To alleviate such requisition, a variety of weakly supervised annotation strategies have been proposed, among which scribble supervision is emerging as a popular one due to its user-friendly annotation way. However, the sparsity and diversity of scribble annotations make it nontrivial to train a network to produce deterministic and consistent predictions directly. To address these issues, in this paper we propose holistic solutions involving the design of network structure, loss and training procedure, named CC4S to improve Certainty and Consistency for Scribble-Supervised Semantic Segmentation. Specifically, to reduce uncertainty, CC4S embeds a random walk module into the network structure to make neural representations uniformly distributed within similar semantic regions, which works together with a soft entropy loss function to force the network to produce deterministic predictions. To encourage consistency, CC4S adopts self-supervision training and imposes the consistency loss on the eigenspace of the probability transition matrix in the random walk module (we named neural eigenspace). Such self-supervision inherits the category-level discriminability from the neural eigenspace and meanwhile helps the network focus on producing consistent predictions for the salient parts and neglect semantically heterogeneous backgrounds. Finally, to further improve the performance, CC4S uses the network predictions as pseudo-labels and retrains the network with an extra color constraint regularizer. From comprehensive experiments, CC4S achieves comparable performance to those from fully supervised methods and shows promising robustness under extreme supervision cases.

Sociological education in Russia: content diversity and institutional limitations

Sociological education in Russia continues to develop under the conditions of constant changes occurring both on its external contour and within the sociological educational community. Statistical data allow us to assert that the decline in SCC and the number of students has stopped in the last five years; moreover, there has been an increase in the contingent of sociology students. There has been a sharp decline in sociological education in non-state universities, the share of students studying on a part-time and contractual basis. The ratio of full-time and part-time education in Bachelor’s degree amounted to 86 and 14%, respectively, in Master’s degree 88 and 12%. Special attention is paid to the most acute problem related to the development of draft FSES HE 4 and the probable transition to it in the near future. In the most unfavorable forecasts, sociology education is seriously threatened by the loss of identity. In order to understand the most acute problems that prevent sociological education from being positioned as an integral, established educational process, the curricula of 49 universities that implement sociology training programs were studied. The sample included universities from the RAEX ratings — the subject rating for sociology and the top-100 best universities in Russia, as well as from the Interfax rating of the top-100 universities in Russia. Correlation of the profiles declared by universities with their subject content, as well as blocks of general sociological and special sociological disciplines with blocks of selected instrumental disciplines, practices, socio-humanities and general professional disciplines allowed us to identify a number of features and trends in the implementation of educational programs for training sociologists. As a result, two tendencies were revealed: one is the emergence of signs of the emerging unification of educational programs in sociology, which occurs in the implementation of the profile “Sociology” in classical universities, and the other is the mass implementation of unbalanced educational programs that contain obvious bias towards a certain block of disciplines and do not provide a full-fledged implementation of the declared profile.

Identifying the Most Probable Transition Path with Constant Advance Replicas.

Locating plausible transition paths and enhanced sampling of rare events are fundamental to understanding the functional dynamics of biomolecules. Here, a constraint-based constant advance replicas (CAR) formalism of reaction paths is reported for identifying the most probable transition path (MPTP) between two given states. We derive the temporal-integrated effective dynamics governing the projected subsystem under the holonomic CAR path constraints and show that a dynamical action functional can be defined and used for optimizing the MPTP. We further demonstrate how the CAR MPTP can be located by asymptotically minimizing an upper bound of the CAR action functional using a variational expectation-maximization framework. Essential thermodynamics and kinetic observables are retrieved by integrating the boxed molecular dynamics on the CAR MPTP using a newly proposed adaptive reflecting boundary condition. The efficiency of the proposed method is demonstrated for the Müller potential, the alanine dipeptide isomerization, and the DNA base pairing transition (Watson-Crick to Hoogsteen) in explicit solvent. The CAR representation of transition paths constitutes a robust and extensible platform that can be combined with diverse enhanced sampling methods to aid future flexible and reliable biomolecular simulations.

Attribute enhanced random walk for community detection in attributed networks

Traditional community detection methods often rely solely on network topology, potentially overlooking the influence of attributes. However, community detection in attributed networks presents a unique challenge due to the complex interplay between network topology and node attributes. In this paper, we present AERW, a novel approach that integrates both network topology and node attributes for effective community detection. AERW leverages the principle of homophily by aggregating neighbor attributes within triangles to capture higher-order structural information. Then constructing a bipartite graph to effectively integrate topological and attribute information, ensuring that both aspects are equally represented in the community detection process. Next AERW utilizes hierarchical clustering applied to the probability transition matrix derived from the random walk, enabling the identification of community structures without needing prior knowledge of the number of communities. Extensive experimentation across synthetic and real-world networks underscores AERW’s efficacy, establishing it as a superior approach in community detection within attributed networks.

Dispersive vacuum as a decoherence amplifier of an Unruh–DeWitt detector

Abstract Recently, interest has been growing in studies on discrete or "pixelated'' space-time that, through modifications in the dispersion relation, can treat the vacuum as a dispersive medium. Discrete spacetime considers that spacetime has a cellular structure on the order of the Planck length, and if this is true we should certainly have observable effects. In this paper, we investigated the effects caused by the dispersive vacuum on the decoherence process of an Unruh-DeWitt detector, our setup consists of a uniformly accelerated detector, initially in a qubit state, which interacts with a massless scalar field during a time interval finite. We use dispersion relations drawn from doubly special relativity and Hořava-Lifshitz gravity, with these modifications the vacuum becomes dispersive and has a corresponding refractive index. We calculate the probability transition rates, the probability of finding the detector in the ground state, and the quantum coherence variation. Our results indicate that the decoherence process occurs more quickly in cases with changes in the dispersion relation in the regime of high accelerations and interaction time. Additionally, the decoherence increases as the vacuum becomes more dispersive due to the increase in the order of modification in the dispersion relation, and this happens because the dispersive vacuum amplifies the effects of quantum fluctuations that are captured by the detector when interacting with the field.

Simulation modeling of artillery operations in computer games: approach based on Markov processes

The object of this research is an approach to simulating the combat operation of artillery in computer games based on Markov processes. In modern computer games, an important role is played by the realism and plausibility of combat simulation. One of the most difficult and at the same time most interesting tasks is the modeling of artillery operations, where it is necessary to take into account numerous factors affecting the effectiveness of combat work. The research was aimed at improving the methods and models of controlling the combat work of artillery under the conditions for the firing position change and the presence of external disturbances. The use of stochastic models allows more accurate modeling of the behavior of artillery units, taking into account the random nature of many parameters, such as projectile speed, reload time, and the probability of detection by enemy forces. The proposed approach includes the development of a simulation model that allows determining optimal strategies to achieve maximum effectiveness of combat work. The model is based on Markov processes, which allows taking into account possible system states and probable transitions between them. This allows not only to simulate combat operations, but also to predict the results depending on different scenarios. The results of the study show that the use of Markov processes in the simulation of combat operations can significantly increase the realism and efficiency of artillery operations in computer games. This opens up new opportunities for game developers to create more immersive and authentic gaming experiences. The proposed model can be used as a basis for further research and improvement of combat simulation methods in computer games. It can also be used in military simulators and simulators where realistic combat conditions must be taken into account.

Estimation of probabilities of transitions of markov binary input signal of nonlinear system

The problem of estimating unknown probabilities of transitions of a random Markov binary input signal of a nonlinear one-dimensional discrete system based on estimating the expectation and variance of the output signal is considered. The defined expressions are built on the basis of considering equally probable transitions and the steady-state mode of the algorithm for assessing the state of the system, obtained by approximating the probability density of its output signal by the Pearson type I distribution. An example of comparison of theoretical calculations with the results of imitation mathematical modeling is given.

The Geometry of Dynamic Time-Dependent Best–Worst Choice Pairs

There has been increasing interest in best–worst discrete choice experiments (BWDCEs) in health economics, transportation research, and other fields over the last few years. BWDCEs have distinct advantages compared to other measurement approaches in discrete choice experiments (DCEs). A systematic study of best–worst (BW) choice pairs can be traced back to the 1990s. Recently, new ideas have been introduced to the subject. Calculating utility helps measure the attractiveness of BW choices. The goal of this paper is twofold. First, we extend the idea of the BW choice pair to include dynamic, time-dependent transition probability and capture utility at each time and for each choice pair. Second, we used the geometry of BW choice pairs to capture the correlations among them and to characterize and clarify the BW choice pairs in the network, where properties can be derived within each class. This paper discusses BWDCEs, the probability transition matrix of choices over time, and the utility function. The proposed network classification for BW choice pairs is laid out. A detailed simulated example is presented, and the results are compared with the classical K-means classification.

Random Telegraphic Signals with Fractal-like Probability Transition Rates

Many physical processes feature random telegraph signals, e.g., a time signal c(t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values.

Data or mathematics? Solutions to semantic problems in artificial intelligence

Data support is already driving the development of artificial intelligence. But it cannot solve the semantic problem of artificial intelligence. This requires improving the semantic understanding ability of artificial intelligence. Therefore, a question answering system based on semantic problem processing is proposed in this study. The question answering system utilizes an improved unsupervised method to extract keywords. This technology integrates the semantic feature information of text into traditional word graph model algorithms. On this basis, semantic similarity information is used to calculate and allocate the initial values and edge weights of each node in the PageRank model. And corresponding restart probability matrices and transition probability matrices are constructed for iterative calculation and keyword extraction. Simultaneously, an improved semantic dependency tree was utilized for answer extraction. The improved keyword extraction method shows a decreasing trend in P and R values. The improved answer extraction method has a maximum P-value of 0.876 in the training set and 0.852 in the test set. In a question answering system based on keyword and answer extraction, the improved method has lower loss function values and running time. The improved method has a larger area under ROC. The results of the validation analysis confirm that the improved method in this experiment has high accuracy and robustness when dealing with semantic problems.

Seismic fragility analysis of girder bridges under mainshock‐aftershock sequences based on input‐output hidden Markov model

AbstractCurrent seismic design codes for bridge structures do not account for the influence of aftershock sequences, which, to some extent, overestimate the seismic performance for bridges subjected to mainshock‐aftershock (MS‐AS) scenarios. To address the great need for ground motion sequences tailored to specific research sites for fragility analysis, this study proposes a method for generating artificial MS‐AS ground motion sequences based on the evolutional bimodal Kanai–Tajimi model and the Epidemic–Type Aftershock Sequence model. We establish a framework for MS‐AS fragility analysis using an input–output Hidden Markov Model (IOHMM), where the damage states (DS) of bridge piers are considered unobservable and are inferred statistically through damage indices in an unsupervised manner. Model parameters are trained using intensity measure (IM) sequences and damage index (DI) sequences. Fragility curves for both the mainshock and state‐dependent aftershocks considering multiple aftershocks are formulated based on the initial state probability and state transition probabilities of the proposed IOHMM. The fragility analysis results reveal that as the initial seismic damage level increases, the probability of aftershocks causing higher damage levels in the structure also increases, highlighting the significant impact of aftershocks on structural damage increments. Furthermore, we extend the proposed model to a bivariate seismic intensity measure and develop fragility surfaces. The proposed framework provides a novel approach and insights for tackling seismic fragility under multiple aftershocks.

Convergence analysis for minimum action methods coupled with a finite difference method

Abstract The minimum action method (MAM) is an effective approach to numerically solving minima and minimizers of Freidlin–Wentzell (F-W) action functionals, which is used to study the most probable transition path and probability of the occurrence of transitions for stochastic differential equations (SDEs) with small noise. In this paper, we focus on MAMs based on a finite difference method with nonuniform mesh, and present the convergence analysis of minimums and minimizers of the discrete F-W action functional. The main result shows that the convergence orders of the minimum of the discrete F-W action functional in the cases of multiplicative noises and additive noises are $1/2$ and $1$, respectively. Our main result also reveals the convergence of the stochastic $\theta $-method for SDEs with small noise in terms of large deviations. Numerical experiments are reported to verify the theoretical results.

Research on the Propagation Model of Unsafe Behaviors among Construction Workers Based on a Two-Layer NAN-SIRS Network

Unsafe behaviors among construction workers are a leading cause of safety accidents in the construction industry, and studying the mechanism of unsafe behavior propagation among construction workers is essential for reducing the occurrence of safety accidents. Safety attitude plays a pivotal role in predicting workers’ behavioral intentions. We propose a propagation model of unsafe behaviors based on a two-layer complex network, in which the upper layer depicts the change in construction workers’ safety attitudes, and the lower layer represents the propagation of unsafe behaviors. In this model, we consider the impact of individual heterogeneity and herd mentality on the transmission rate, establishing a partial mapping relationship based on behavioral feedback. After that, by building a probability transition tree, we establish the risk state transition equation in detail using the microscopic Markov chain approach (MMCA) and analyze the established equations to deduce the propagation threshold of unsafe behaviors analytically. The results show that enhancing the influence of individual heterogeneity and behavioral feedback increases the threshold for the spread of unsafe behaviors, thereby reducing its scale, while herd mentality amplifies the spread. Furthermore, the coexistence of safety education and behavioral feedback may lead to one of the mechanisms fails. This research enhances understanding of the propagation mechanism of unsafe behaviors and provides a foundation for managers to implement effective measures to suppress the propagation of unsafe behaviors among construction workers.

The most probable transition pathway of a predator–prey system under noise

Stochastic population dynamics plays a crucial role in biological systems. The number and distribution of biological populations often affect the stability of ecosystems, and even lead to the transition of ecosystems from one steady-state to another. The transition between different states of a population has a significant impact on both population dynamics and biological evolution. In this paper, we examined a stochastic population model and used Onsager–Machlup action functional and neural shooting method to obtain the most probable transition pathway between different states. Moreover, we analyzed the influence of noise intensity, maximum harvest rate [Formula: see text] and time [Formula: see text] on most probable transition pathway in two different parameter scenarios. Our research may provide a better understanding of evolutionary process such as genetic variation in populations and the evolution of species adaptation, meanwhile, may provide a theoretical guidance for species conservation and management in real world.

A review to the Desert Kite: State of the Art!

Although from the beginning of the historical period, known as the emergence of the writing, it has not passed more than several thousand years, but the history of human evolution can be rooted in an era much older than the one seen: in the age of the hunting-gathering culture! Hunter-gatherer culture was the way of life for early humans until around 11,000 to 12,000 years ago. The lifestyle of huntergatherers was based on hunting animals and foraging for food. Desert kites could be mentioned as a probable transition key from the age of hunting-gathering food to pastoralism, which can be dated today with the development of cosmogenesis and luminescence methods. ‘Desert kites’ are stone constructions made of two long low walls called antennae that converge into an enclosure flanked or not by several small cells. Their shape and archeological evidence suggest that these extensive stone structures may have functioned as game traps, designed to capture and kill large numbers of wild animals. The kite is a landmark that reveals a way of occupying territory. It is an architectural feature of social groups, which hence left a reflection of their territory and catchment. However, these people have sometimes left very few traces enabling their identification. Considering the extent and density of these settlements, the kite is a massive phenomenon whose role was probably crucial in the development of societies in arid regions. It has been seen from the eastern Mediterranean to the eastern Caspian, which suggested finding less of the same structure in the Iranian plateau, as the only suitable linkage, when the northern lands were nearly frozen! Thus, the perspective is reversed from traditional archaeological research, where groups are most often identified by their domestic settlements, with their still undefined modes of subsistence. Kites, as a phenomenon, are therefore a challenge for the archaeology that requires creative and novel approaches.

Simulation of electron transport in a catoptric photomultiplier tube concept for large rectangular scintillator crystals

Spectroscopic scintillation detector form factors have been guided primarily by the design of commercially available photonic sensors. These devices, such as photomultiplier tubes, silicon photomultipliers, and hybrid photodetectors have underperformed in one or more areas such as size, power consumption, and resolution. A novel photomultiplier tube having a 50.8×152.4 mm2 rectangular window, utilizing a reflection-mode photocathode, and a low-gain, miniaturized dynode set is considered here to improve photosensor packaging while enabling high-efficiency, low-resolution scintillation spectroscopy with large, planar scintillators. Using a phenomenological multiphysics simulation process informed by empirical data, photoelectron collection efficiency, single-photoelectron response, electron transit time, and transit time spread have been modeled over a range of operating potentials. At 750 V between the photocathode and anode, 72.5% of photoelectrons are collected at the first dynode, and the average gain is estimated to be 805. The most probable transit time is 14.9 ns, with a transit time spread of 2.7 ns full-width at half-maximum.