A toy model for the auditory system that exploits stochastic resonance

The transduction process that occurs in the inner ear of the auditory system is a complex mechanism which requires a non-linear dynamical description. In addition to this, the stochastic phenomena that naturally arise in the inner ear during the transduction of an external sound into an electro-chemical signal must also be taken into account. The presence of noise is usually undesirable, but in non-linear systems a moderate amount of noise can improve the system's performance and increase the signal-to-noise ratio. The phenomenon of stochastic resonance combines randomness with non-linearity and is a natural candidate to explain at least part of the hearing process which is observed in the inner ear. In this work, we present a toy model of the auditory system which shows how stochastic resonance can be instrumental to sound perception, and suggests an explanation of the frequency dependence of the hearing threshold.

Detection of radio signals against the background of strong electromagnetic noise in transport

The problem of detecting a useful signal in the presence of a strong background noise is considered. To solve it, a statistical approach is used, based on a change in the level of chaos in the system when an additional random or deterministic process occurs, which is probabilistically independent from a set of stochastic phenomena that form background noise. It is shown that the occurrence of this process changes the level of entropy of the measured signal; this fact is the basis of the applied mathematical algorithm. It is based on the elements of the Fourier transform apparatus for the probability density with an appropriate choice of a nonlinear function of the random process under study. The proposed approach, based on variations in the randomness in the system in the presence of a useful signal, makes it possible to record its presence against the background of noise components even at low signal-to-noise ratios. The effectiveness of the method is confirmed both by theoretical justification and by the calculations presented in this work. The condition for the implementation of the technique described in the article, which does not impose restrictions on the studied physical fields and frequency ranges, is the comparability of the width of the probabilistic distribution of the desired useful signal with several intervals of discreteness of the measuring equipment. One of the results of this work is a high sensitivity to the emergence of independent random components.

The principles of the theory of fuzzy sets in the formalization of infrastructural and technological interaction of the port railway transport system

Objective: Formulating proposals for improving the indicators of infrastructural and technological interaction when assessing multivariate management decisions in the regional railway system on the example of the “port station – port” system. Methods: Drawing on the analysis of publications in the given research area, a modifi cation of the methods of the theory of fuzzy sets and the theory of probability was applied to select and formalize the most important transport and technological processes of port stations, taking into account possible stochastic phenomena in the management of the interaction between the station and the port. Results: The theoretical substantiation of the degree of belonging of the axiom of station transport and technological processes to certain conditions of interaction between the station and the port, the relationship of their association and inclusion is obtained. A matrix of links between the main technological operations and infrastructural elements for a specifi c port station has been developed. An example is presented and the axioms of transport processes of options for servicing port berths are described. Approaches to the assessment of logical situations and fuzziness of subsets of parameters of transport processes in the control of the interaction between the station and the port are formulated. In the environment of the analytical computing system, the time parameters of the options for organizing transport processes are determined. Practical importance: The visualization of the fuzzy organization of transport sub-processes was performed, the degree of logical correspondence between the axiom of station transport and technological processes and their entropy were assessed, a diagram of the membership of a set of times of transport process variants was constructed, which allows taking into account poorly formalized processes in managing the operation of the “port station – port” system and, in the future, reduce local cars inactivity in the system.

On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

BiPSim: a flexible and generic stochastic simulator for polymerization processes

Detailed whole-cell modeling requires an integration of heterogeneous cell processes having different modeling formalisms, for which whole-cell simulation could remain tractable. Here, we introduce BiPSim, an open-source stochastic simulator of template-based polymerization processes, such as replication, transcription and translation. BiPSim combines an efficient abstract representation of reactions and a constant-time implementation of the Gillespie’s Stochastic Simulation Algorithm (SSA) with respect to reactions, which makes it highly efficient to simulate large-scale polymerization processes stochastically. Moreover, multi-level descriptions of polymerization processes can be handled simultaneously, allowing the user to tune a trade-off between simulation speed and model granularity. We evaluated the performance of BiPSim by simulating genome-wide gene expression in bacteria for multiple levels of granularity. Finally, since no cell-type specific information is hard-coded in the simulator, models can easily be adapted to other organismal species. We expect that BiPSim should open new perspectives for the genome-wide simulation of stochastic phenomena in biology.

The Economic Aspect of Using Different Plug-in Hybrid Driving Techniques in Urban Conditions

Plug-in hybrids (PHEV) have become popular due to zero-emission driving, e.g., in urban areas, and using an internal combustion engine on longer distances. Energy consumption by the PHEV depends on many factors which can be either dependent or independent of the driver. The article examines how the driver can use the vehicle’s capabilities to influence its wear. Determining the optimal driving technique, due to the adopted nature of the timetable, is the basic variable that determines the profitability of using a given drive system. Four driving techniques have been selected to determine which one can offer the largest advantages. A vehicle-dedicated application has recorded the drivetrain performance on a predetermined route through an urban area. The analysis of results has demonstrated which of the driving techniques provides measurable effects in terms of reduced energy consumption and the shortest travelling time. The study shows longitudinal acceleration and torque generated by the electric drive. The information included in the study can help any PHEV user reduce the operating cost by applying an appropriate driving technique. The proposed research introduces the possibilities of assessing the influence of the driving style on energy consumption. The innovative side of this research is the observation of stochastic phenomena that are difficult to detect when using approximation modelling.

Revisiting the Lognormal Modelling of Shadowing Effects during Wireless Communications by Means of the α-μ/α-μ Composite Distribution

Properly modeling the shadowing effects during wireless transmissions is crucial to perform the network quality assessment. From a mathematical point of view, using composite distributions allows one to combine both fast fading and slow fading stochastic phenomena. Numerous statistical distributions have been used to account for the fast fading effects. On the other hand, even though several studies indicate the adequacy of the Lognormal distributon (LNd) as a shadowing model, they also reveal this distribution renders some analytic tractability issues. Past works include the combination of Rayleigh and Weibull distributions with LNd. Due to the difficulty inherent to obtaining closed form expressions for the probability density functions involved, other authors approximated LNd as a Gamma distribution, creating Nakagami-m/Gamma and Rayleigh/Gamma composite distributions. In order to better mimic the LNd, approximations using the inverse Gamma and the inverse Nakagami-m distributions have also been considered. Although all these alternatives were discussed, it is still an open question how to effectively use the LNd in the compound models and still get closed-form results. We present a novel understanding on how the α-μ distribution can be reduced to a LNd by a limiting procedure, overcoming the analytic intractability inherent to Lognormal fading processes. Interestingly, new closed-form and series representations for the PDF and CDF of the composite distributions are derived. We build computational codes to evaluate all the expression hereby derived as well as model real field trial results by the equations developed. The accuracy of the codes and of the model are remarkable.

A Novel Method of Optimization for Stochastic Control System

Stochastic phenomena widely exist in the nature and real dynamic systems. The existence of random phenomena will make the system performance degrade greatly, and even cause instability. For the sake of improving the stability of stochastic control system, this paper proposed a novel method of optimization for stochastic control system by control model and max-plus algebraic algorithm. The simulation results indicate that the optimization method can effectively optimize the stochastic system. The input of the stochastic control system is stable to a certain extent, which weakens the random interference of the input signal in the external environment, thus improving the stability of the stochastic control system.

Deep Learning Without Neural Networks: Fractal-nets for Rare Event Modeling

Complex phenomena of societal interest such as weather, seismic activity and urban crime, are often punctuated by rare and extreme events, which are difficult to model and predict. Evidence of long-range persistence of such events has underscored the need to learn deep stochastic structures in data for effective forecasts. Recently neural networks (NN) have emerged as a defacto standard for deep learning. However, key problems remain with NN inference, including a high sample complexity, a general lack of transparency, and a limited ability to directly model stochastic phenomena. In this study we suggest that deep learning and the NN paradigm are conceptually distinct -- and that it is possible to learn ``deep' associations without invoking the ubiquitous NN strategy of global optimization via back-propagation. We show that deep learning of stochastic phenomena is related to uncovering the emergent self-similarities in data, which avoids the NN pitfalls offering crucial insights into underlying mechanisms. Using the Fractal Net (FN) architecture introduced here, we actionably forecast various categories of rare weather and seismic events, and property and violent crimes in major US cities. Compared to carefully tuned NNs, we boost recall at 90% precision by 161.9% for extreme weather events, 191.3% for light-to-severe seismic events with magnitudes above the local third quartile, and 50.8% - 404.9% for urban crime, demonstrating applicability in diverse systems of societal interest. This study opens the door to precise prediction of rare events in spatio-temporal phenomena, adding a new tool to the data science revolution.