The “friend and foe” of deterministic and stochastic cell-cell variations

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanism is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we mapped the growing population to the Ising model. Model results, confirmed by simulations and experimental data, show that cell-cell variations increase near-linearly with stress. As a consequence, we predict that the entropic gain — the gain in population doubling time compared to an “average” cell — is primarily stochastic at low stress but crosses over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.

Toward a Self-Powered Vibration Sensor: The Signal Processing Strategy

This paper, for the first time, investigates the possibility of exploiting a nonlinear bistable snap-through buckling structure employing piezoelectric transducers, to implement an autonomous sensor of mechanical vibrations, with an embedded energy harvesting functionality. The device is operated in the presence of noisy vibrations superimposed on a subthreshold deterministic (sinusoidal) input signal. While the capability of the device to harvest a significant amount of energy has been demonstrated in previous works, here, we focus on the signal processing methodology aimed to extract from the sensor output the information about the noise level (in terms of the standard deviation) and the root mean square amplitude of the deterministic component. The developed methodology, supported by experimental evidence, removes the contribution to the overall piezoelectric output voltage ascribable to the deterministic component using a thresholding and windowing algorithm. The contribution to the output voltage due to the noise can be used to unambiguously estimate the noise level. Moreover, an analytical model to estimate, from the measurement of the output voltage, the RMS amplitude of the deterministic input and the noise-related component is proposed.

A Safety Factor Method for Reliability-Based Component Design

Reliability-based design (RBD) identifies design variables that maintain reliability at a required level. For many routine component design jobs, RBD may not be practical as it requires nonlinear optimization and specific reliability methods, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a practical approach to reliability-based component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the First Order Reliability Method, which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to several iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so is the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method.

USING THE COMPLEX OF PHOTO AND VIDEO RECORDING OF TRAFFIC VIOLATIONS TO IDENTIFY DETERMINISTIC AND STOCHASTIC COMPONENTS OF THE TRAFFIC FLOW INTENSITY

The relevance of the manuscript is due to the need to process and analyze the information accumulated by the complexes of photo-video recording of traffic violations, which will further develop mathematical, computational and simulation models of road transport, solve problems of optimization and management of traffic flows, make management decisions to reduce the number of congestion and reduce the anthropogenic load on the environment. The object of the study is a part of a three-lane road with heavy one-way traffic, equipped with a software and technical complex that allows measuring the main characteristics of the traffic flow (vehicle speeds, including the average values on the controlled road part, driving time, etc.). The subject of the study is the traffic flow intensity during a 7-day time (from Monday to Sunday). The analysis of the obtained dependences allowed us to formulate a hypothesis about the presence of determin- istic and stochastic components in the traffic flow intensity, which is a random function of time, and the verification of which is the purpose of this study. Statistical processing of the obtained data is used as a theoretical and methodological approach, as well as the assumption that the traffic flow intensity can be represented by the sum of deterministic and stochastic components. The developed approach using the smoothing procedure allowed us to select both components, and this is a scientific novelty of the analysis performed. As a result of the study, it is shown that the deterministic component of the traffic flow intensity for working days is qualitatively different from the deterministic component for weekends. Statistical indicators of probabilistic distributions of traffic flow intensities and random components selected from them are determined. Estimates of the correspondence of the selected curves to the normal law of probability distribution are obtained using the Kolmogorov and Pearson criteria, which contradict each other. Practical significance consists in the use of a deterministic component for predicting traffic flows, controlling the operation of traffic lights, monitoring the operation of equipment, as well as in the reconstruction, design and construction of roads and road objects. The direction of further research is to obtain, statistically process and generalize data on the traffic flows intensity in other parts of the road network.

Revealing the deterministic components in active avalanche-like dynamics

An ensemble of autonomous camphor discs exhibits avalanche-like dynamics with a characteristic/natural frequency. Furthermore, the dynamics show a resonant response to external forcing indicating the presence of a deterministic component in the system.

On the equivalence of the forecast value construction in the “pyramidal” extrapolation method and cubic forecast

The paper is devoted to the new method of short time series extrapolation, which was developed in recent years and was called “pyramidal”. This method can be used for predicting the deterministic component of an arbitrary economic, environmental and geophysical parameters. Numerical results show significant advantages of the proposed method in comparison with approaches to extrapolate, based on the use of polynomials, including Newton’s extrapolation . In this paper we study the procedure for constructing the forecast value in accordance with the pyramidal method and show that it is equivalent to the cubic forecast.

A Practical Safety Factor Method for Reliability-Based Component Design

Reliability-based design (RBD) identifies design variables that maintain reliability at a required level. For many routine component design jobs, RBD may not be practical as it requires nonlinear optimization and specific reliability methods, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a practical approach to reliability-based component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the First Order Reliability Method, which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to a number of iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so it the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method.

Application of parametric modelling methods for estimating the parameters of damped sinusoidal signals

The paper describes the results of analyses aimed at obtaining information on selected parameters of the deterministic component of a signal being the sum of two waveforms, an exponentially damped sinusoidal waveform and a stochastic waveform. Keywords: linear prediction, optimisation, analytical signal