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We carry out a theoretical investigation about quantum noise in coherent mixtures of states with different statistics. On the one hand, we investigate the dependence between the behavior wave-particle and associated noise. On the other hand, we are interested in studying the persistence of chaotic behavior in mixtures of states with quantum and classical behavior. For this, we perform mixtures of single photons with coherent states of different averages. We find that the noise associated with quantum chaos depends on the proportion of the quantum–classical mixture and that quantum wave states are more efficient than classical wave states in terms of their randomness properties. [ABSTRACT FROM AUTHOR]

The Rashba spin–orbit coupling (RSOC) effect on the polarization and shot noise properties in a strained WSe2 multiple barrier structure is studied by transfer-matrix technique. The results indicate that the spin-dependent Fano factor depends on the strain and RSOC strength with oscillatory evolution. Thus, the value of Fano factor with spin rotation can be tuned mechanically and by an external electric field. Also, Fano factor shows high sensitivity to the number of electrostatic barriers in strained WSe2 multiple barrier structure. Meanwhile, in a strained WSe2 multiple barrier structure both sign and value of the valley and spin polarizations could be adjusted by tuning both RSOC and strain strength. These findings show that a WSe2 multiple barrier structure under strain and RSOC can be useful for future spintronics, straintronic and valleytronic devices. [ABSTRACT FROM AUTHOR]

Introduction: Electrical stimulation of the brain has shown promising prospects in treating various brain diseases. Although biphasic pulse stimulation remains the predominant clinical approach, there has been increasing interest in exploring alternative stimulation waveforms, such as sinusoidal stimulation, to improve the effectiveness of brain stimulation and to expand its application to a wider range of brain disorders. Despite this growing attention, the effects of sinusoidal stimulation on neurons, especially on their nonlinear firing characteristics, remains unclear. Methods: To address the question, 50 Hz sinusoidal stimulation was applied on Schaffer collaterals of the rat hippocampal CA1 region in vivo. Single unit activity of both pyramidal cells and interneurons in the downstream CA1 region was recorded and analyzed. Two fractal indexes, namely the Fano factor and Hurst exponent, were used to evaluate changes in the long-range correlations, a manifestation of nonlinear dynamics, in spike sequences of neuronal firing. Results: The results demonstrate that sinusoidal electrical stimulation increased the firing rates of both pyramidal cells and interneurons, as well as altered their firing to stimulation-related patterns. Importantly, the sinusoidal stimulation increased, rather than decreased the scaling exponents of both Fano factor and Hurst exponent, indicating an increase in the long-range correlations of both pyramidal cells and interneurons. Discussion: The results firstly reported that periodic sinusoidal stimulation without long-range correlations can increase the long-range correlations of neurons in the downstream post-synaptic area. These results provide new nonlinear mechanisms of brain sinusoidal stimulation and facilitate the development of new stimulation modes. [ABSTRACT FROM AUTHOR]

The Jensen-variance (JV) distance measure is introduced and some properties are developed. The JV distance measure can be expressed using two interesting representations: the first one is based on mixture covariances, and the second one is in terms of the scaled variance of the absolute difference of two random variables. The connections between the JV distance measure and some well-known informationmeasures, such as Fisher information, Ginimean difference, cumulative residual entropy, Fano factor, varentropy, varextropy, and chi-square distance measures, are examined. Specifically, the JV distance measure possesses metric properties and unifies most of the information measures within a general framework. It also includes variance and conditional variance as special cases. Furthermore, an extension of the JV distance measure in terms of transformed variables is provided. Finally, to demonstrate the usefulness of proposed methods, JV distance is applied to a real-life dataset related to fish condition factor index and some numerical results assuming skew-normal-distributed samples are presented. [ABSTRACT FROM AUTHOR]

We carry out a theoretical investigation about quantum noise in coherent mixtures of states with different statistics. On the one hand, we investigate the dependence between the behavior wave-particle and associated noise. On the other hand, we are interested in studying the persistence of chaotic behavior in mixtures of states with quantum and classical behavior. For this, we perform mixtures of single photons with coherent states of different averages. We find that the noise associated with quantum chaos depends on the proportion of the quantum–classical mixture and that quantum wave states are more efficient than classical wave states in terms of their randomness properties.

Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.

Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution. [ABSTRACT FROM AUTHOR]

A Fano Factor‐based adaptive overcurrent protection scheme, that automatically adjusts the protection settings in response to the prevailing conditions of the power system, is presented. Both phase and ground overcurrent relays are based on the same mathematical algorithm to calculate the operating time using Fano Factors (FFs) estimated for phase and ground current signals, respectively. Effectiveness of the proposed adaptive overcurrent method is validated for various fault types under a plethora of loading current levels, besides a wide range of fault inception angles and fault resistance. Simulation results confirm that the proposed algorithm can detect series and shunt faults, differentiate between grounding and phase faults, and adapt the relay operating time settings using the FF for all conditions examined. The relay algorithm speed and sensitivity are controllable using both the FF setting values and moving data window size. Moreover, it is characterized by being simple, reliable, accurate, and can be implemented practically as a base of digital protective relay for use in substation automation systems and phasor measurement units. [ABSTRACT FROM AUTHOR]

Abstract A Fano Factor‐based adaptive overcurrent protection scheme, that automatically adjusts the protection settings in response to the prevailing conditions of the power system, is presented. Both phase and ground overcurrent relays are based on the same mathematical algorithm to calculate the operating time using Fano Factors (FFs) estimated for phase and ground current signals, respectively. Effectiveness of the proposed adaptive overcurrent method is validated for various fault types under a plethora of loading current levels, besides a wide range of fault inception angles and fault resistance. Simulation results confirm that the proposed algorithm can detect series and shunt faults, differentiate between grounding and phase faults, and adapt the relay operating time settings using the FF for all conditions examined. The relay algorithm speed and sensitivity are controllable using both the FF setting values and moving data window size. Moreover, it is characterized by being simple, reliable, accurate, and can be implemented practically as a base of digital protective relay for use in substation automation systems and phasor measurement units.

Electromagnetically induced slow-light medium is a promising system for quantum memory devices, but controlling its noise level remains a major challenge to overcome. This work considers the simplest model for such medium, comprised of three-level Λ-systems interacting with bosonic bath, and provides a new fundamental trade-off relation in light–matter interaction between the group velocity of light and the Fano factor of photon current due to radiative transitions. Considering the steady state limits of a newly derived Lindblad-type equation, we find that the Fano factor of the photon current maximizes to 3 at the minimal group velocity of light, which holds true universally regardless of detailed values of parameters characterizing the medium. [ABSTRACT FROM AUTHOR]

Nowadays, there are formulas in the literature for determining the Fano factor in a semiconductor material from experimental data. However, the existing formulas do not take into account the contribution of fluctuations of the induced charge on the detector electrodes due to the capture of electrons and holes by traps, as well as the contribution of the induced charge fluctuations due to the distribution function of generation of the electron-hole pairs in the volume of the semiconductor detector. In this work, a formula for the energy resolution of a semiconductor detector was obtained, which allows to determine the contributions of various processes to the energy resolution and their dependence on the properties of the semiconductor material of the detector and the characteristics of the detected particle. The obtained formula for the energy resolution of a semiconductor detector allows to formulate the conditions under which it is possible to obtain information on the Fano factor and fluctuations of the induced charge on the detector electrodes due to the capture of electrons and holes by traps, and the distribution function of generation of electron-hole pairs in its volume from the characteristics of the output signal. As an example, the Fano factor in CdTe semiconductor material has been determined from experimental data. [ABSTRACT FROM AUTHOR]

The effect of the Rashba spin-orbit interaction on the shot noise, spin/valley polarization in 8- Pmmn borophene-based superlattice are studied theoretically, by applying the transfer-matrix approach. The spin-dependent transmission probability can be easily controlled by the number of superlattice barriers, the strength of the Rashba, and the incident electron angle. The Fano factor without spin rotation as well as with spin rotation shows an oscillatory pattern versus the strength of the Rashba, and the oscillatory behavior becomes more pronounced as the number of barriers increases. Also, the Fano factor shows a strong dependence on the superlattice direction and number of barriers. The spin and valley polarizations can be easily controlled by the number of barriers and the direction of superlattice. Our findings in this work could provide useful for valleytronics/spintronics systems based on the 8- Pmmn borophene. [ABSTRACT FROM AUTHOR]

The electronic transport properties of two junctions (BGB, GBG) made of borophene (B) and graphene (G) are investigated. Using the transfer matrix method with Chebyshev polynomials, we have studied single and multiple barriers in a superlattice configuration. We showed that a single barrier exhibits remarkable tilted transport properties, with perfect transmission observed for both junctions under normal incidence. We found that robust superlattice transmission is maintained for multiple barriers, particularly in the BGB junction. It turns out that by varying the incident energy, many gaps appear in the transmission probability. The number, width, and position of these transmission gaps can be manipulated by adjusting the number of cells, incident angle, and barrier characteristics. For diffuse transport, we observed considerable variations in transmission probability, conductance and the Fano factor, highlighting the sensitivity of these junctions to the physical parameters. We showed different behaviors between BGB and GBG junctions, particularly with respect to the response of conductance and Fano factor when barrier height varies. For ballistic transport, we have seen that the minimum scaled conductance is related to the maximum Fano factor, demonstrating their control under specific conditions of the physical parameters. Analysis of the length ratio (geometric factor) revealed some remarkable patterns, where scaled conductance and the Fano factor converged to certain values as the ratio approached infinity. • The electronic transport properties of BGB (borophene–graphene–borophene) and GBG (graphene–borophene–graphene) junctions are investigated. • A single barrier in the junctions exhibits remarkable tilted transport properties, with perfect transmission observed under normal incidence for both BGB and GBG junctions. • Robust superlattice transmission is maintained for multiple barriers, particularly in the BGB junction. • Diffuse transport shows remarkable variations in transmission probability, conductance, and Fano factor, indicating the sensitivity of the junctions to physical parameters. • For ballistic transport, a relationship is found between the minimum conductance and the maximum Fano factor, demonstrating their control under certain conditions of the physical parameters. [ABSTRACT FROM AUTHOR]

Fano factor is a quantity used to measure the departure of the observed variance in the number of charge carriers produced from that predicted using poison statistics. Fano factor varies with the detector type. In case of proportional counters and semiconductor detectors, it is substantially less than unity, whereas, for scintillator detectors, it would be unity. Even in case of semiconductor detectors, it varies with the type and the shape of the detector. Another source of fluctuations that gives the overall resolution of the detector is preamplifier noise. Oversquare coaxial HPGe detectors are a recent development in the field. Literature on the Fano factor of oversquare large volume coaxial detector is not available. In this work, the Fano factor and the electronic noise of an oversquare HPGe coaxial detector are estimated after optimizing the shaping parameters. The Fano factor for the oversquare HPGe detector is estimated as 0.1291 keV, which agrees with the ideal value of 0.13 by 99.98%. The preamplifier noise was found to be 0.048 keV which is 35% lesser than the reported value.

The spin polarization and the valley and spin-dependent shot noise properties in monolayer MoS2-based superlattice in presence of the extrinsic and intrinsic Rashba spin–orbit interaction (ERSOI and IRSOI) are theoretically investigated using the transfer-matrix approach. It is shown that spin-polarization can be adjusted via the electrostatic barrier height, the number of superlattice barriers, and the ERSOI strength. The spin and valley-dependent Fano factor through the monolayer MoS2 superlattice was calculated and analyzed. It was found that the Fano factor depends on the valley and spin degrees of freedom, the electrostatic barrier height, the number of MoS2 superlattice barriers (N), and ERSOI strength. The Fano factor has a Poissonian value for some values of the barrier height. Moreover, it was found that the Fano factor has a gap with respect to the ERSOI strength. Also, when N ≥ 5 , the Fano factor approaches 1 for one of the valleys. [ABSTRACT FROM AUTHOR]

We have investigated the Fano factor and shot noise theoretically in the confined region of the potential well of zigzag graphene nanoribbon (ZGNR). We have found that the Fano factor is approximately 1, corresponding to the minimum conductivity (σ) for both symmetrical and asymmetrical potential wells. The conductivity plot with respect to Fermi energy appears as symmetrical plateaus on both sides of zero Fermi energy. Moreover, a peak observed at zero Fermi energy in the local density of states (LDOS) confirms the edge states in the system. The transmission properties of ZGNR in the confined region of the potential well are examined using the standard tight-binding Green’s function approach. The perfect transmission observed in the confined region of the potential well shows that pnp type transistors can be made with ZGNR. We have discussed the Fano factor, shot noise, conductivity, and nanohub results in the continuation of previous results. Our results show that the presence of van-Hove singularities in the density of states (DOS) matters in the presence of edge states. The existence of these edge states is sensitive to the number of atoms considered and the nature of the potential wells. We have compared our numerical results with the results obtained from the nanohub software (CNTbands) of Purdue University.

Fano factor is a quantity used to measure the departure of the observed variance in the number of charge carriers produced from that predicted using poison statistics. Fano factor varies with the detector type. In case of proportional counters and semiconductor detectors, it is substantially less than unity, whereas, for scintillator detectors, it would be unity. Even in case of semiconductor detectors, it varies with the type and the shape of the detector. Another source of fluctuations that gives the overall resolution of the detector is preamplifier noise. Oversquare coaxial HPGe detectors are a recent development in the field. Literature on the Fano factor of oversquare large volume coaxial detector is not available. In this work, the Fano factor and the electronic noise of an oversquare HPGe coaxial detector are estimated after optimizing the shaping parameters. The Fano factor for the oversquare HPGe detector is estimated as 0.1291 keV, which agrees with the ideal value of 0.13 by 99.98%. The preamplifier noise was found to be 0.048 keV which is 35% lesser than the reported value. [ABSTRACT FROM AUTHOR]

When considering X-ray radiation registration by a scintillation detector, A. Bousselham et al. (Photoelectron Anticorrelations and Sub-Poisson Statistics in Scintillation Detectors), introduced two Fano factors (the Fano factor for scintillation photons and the Fano factor for photoelectrons). They stated their experimental data provided direct evidence for sub-Poissonian statistics for light photons in scintillators. An accurate mathematical description of the processes in the X-rays registration by a scintillation detector allows one to obtain the correct formulas for the mean value, the output signal variance of photodetectors, and the formula for the covariance between the signals of photodetectors. An analysis of these formulas allows one to conclude that a scintillation detector should be characterized by only one Fano factor, which determines the fluctuations of the electron–hole pair generation process in the scintillator. Since the Fano factor for electron–hole pairs in scintillators is on the order of 0.1, this fact explains the results obtained in the article. Thus, the discovery of sub-Poissonian statistics for light photons in scintillators did not take place. [ABSTRACT FROM AUTHOR]

At present, the intrinsic energy resolution of a scintillation detector is understood by many authors in different ways. The existing formulas for energy resolution differ not only in names, but also in the physical meaning of the processes they take into account. The main drawback of all these theories of scintillation spectrometers is the unjustified introduction of different terms into the formula for the energy resolution without considering their connection with the specific characteristics of the scintillation detector. The intrinsic energy resolution of a scintillation detector is most correctly defined as the unavoidable limit that can be reached when all the parameters of the detector reach their limiting values without their fluctuations. On the basis of the microscopic standard theory of scintillation detectors, it is shown that the intrinsic energy resolution is determined by the light yield nonlinearity and fluctuations in the number of electron–hole pairs. [ABSTRACT FROM AUTHOR]

At present, scientists propose different formulas for the energy resolution of scintillation spectrometers, which sometimes contradict each other. The terms included in the formulas for the energy resolution differ not only in their names but also in the physical meaning. The main drawback of all of these theories of scintillation spectrometers is the unjustified introduction of different terms into the formula for the energy resolution without considering their connection with the specific characteristics of the scintillation detector. This approach is not only wrong but also counterproductive, since it does not allow comparison of the results obtained by different scientific groups. In this work, the drawbacks of the theories are analyzed on the basis of the standard theory of scintillation spectrometers with several photodetectors. It is shown that only the formulas of the standard theory for arbitrary moments of the output signal distribution function of the photodetectors of a scintillation spectrometer serve as a reliable basis for linking theoretical and experimental researches in the field of scintillator physics. [ABSTRACT FROM AUTHOR]

The currently existing macroscopic theories of scintillation spectrometers with a single photodetector have a number of fundamental drawbacks. The drawbacks can be overcome by a correct microscopic description of the processes occurring when the energy of the primary particle is converted into an output signal of the scintillation spectrometer. The mathematical model formulated in this work is the basis for the standard theory of scintillation spectrometers with a single photodetector, which allows one to obtain expressions for arbitrary moments of the signal distribution function at the output of the scintillation spectrometer. It is shown that the developed standard theory of scintillation spectrometers with a single photodetector does not have the drawbacks of other theories of scintillation spectrometers. In particular, the contribution to the energy resolution associated with the light yield nonlinearity of the scintillator is considered in the developed standard theory. [ABSTRACT FROM AUTHOR]

Recent studies have shown that neural activity in a well-defined patch in the posterior superior temporal sulcus (the "gaze-following patch," GFP) of the primate brain is strongly modulated when the other's gaze attracts the observer's attention to locations/ objects, the other is looking at. Changes of the mean discharge rate of neurons in the monkey GFP indicate that they are involved in two distinct computations: the allocation of spatial attention guided by the other's gaze vector and the suppression of gaze following if inappropriate in a given situation. Here, we asked if and how the discharge variability of neurons in the GFP is related to the task and if it carries information on behavioral performance. To this end, we calculated the Fano factor as a measure of across-trial discharge variability as a function of time. Our results show that all neurons exhibiting a task-related discharge- rate modulation also exhibit a stimulus onset-dependent drop in the Fano factor. Furthermore, the amplitude of the Fano factor reduction is modulated by task condition and the neuron's selectivity in this regard. We found that these effects are directly related to the monkeys' behavioral performance in that the Fano factor is predictive about upcoming correct or wrong decisions. Our results indicate that neuronal discharge variability as gauged by the Fano factor, hitherto primarily studied in the context of visual perception or motor control, is an informative measure also in studies of the neural underpinnings of complex social behavior. [ABSTRACT FROM AUTHOR]

Introduction: Electrical stimulation of the brain has shown promising prospects in treating various brain diseases. Although biphasic pulse stimulation remains the predominant clinical approach, there has been increasing interest in exploring alternative stimulation waveforms, such as sinusoidal stimulation, to improve the effectiveness of brain stimulation and to expand its application to a wider range of brain disorders. Despite this growing attention, the effects of sinusoidal stimulation on neurons, especially on their nonlinear firing characteristics, remains unclear., Methods: To address the question, 50 Hz sinusoidal stimulation was applied on Schaffer collaterals of the rat hippocampal CA1 region in vivo . Single unit activity of both pyramidal cells and interneurons in the downstream CA1 region was recorded and analyzed. Two fractal indexes, namely the Fano factor and Hurst exponent, were used to evaluate changes in the long-range correlations, a manifestation of nonlinear dynamics, in spike sequences of neuronal firing., Results: The results demonstrate that sinusoidal electrical stimulation increased the firing rates of both pyramidal cells and interneurons, as well as altered their firing to stimulation-related patterns. Importantly, the sinusoidal stimulation increased, rather than decreased the scaling exponents of both Fano factor and Hurst exponent, indicating an increase in the long-range correlations of both pyramidal cells and interneurons., Discussion: The results firstly reported that periodic sinusoidal stimulation without long-range correlations can increase the long-range correlations of neurons in the downstream post-synaptic area. These results provide new nonlinear mechanisms of brain sinusoidal stimulation and facilitate the development of new stimulation modes., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer LZ declared a past collaboration with the authors YY, XY, and ZW to the handling editor., (Copyright © 2024 Yuan, Ye, Cui, Zhang and Wang.)

A hallmark neuronal correlate of working memory (WM) is stimulus-selective spiking activity of neurons in PFC during mnemonic delays. These observations have motivated an influential computational modeling framework in which WM is supported by persistent activity. Recently, this framework has been challenged by arguments that observed persistent activity may be an artifact of trial-averaging, which potentially masks high variability of delay activity at the single-trial level. In an alternative scenario, WM delay activity could be encoded in bursts of selective neuronal firing which occur intermittently across trials. However, this alternative proposal has not been tested on single-neuron spike-train data. Here, we developed a framework for addressing this issue by characterizing the trial-to-trial variability of neuronal spiking quantified by Fano factor (FF). By building a doubly stochastic Poisson spiking model, we first demonstrated that the burst-coding proposal implies a significant increase in FF positively correlated with firing rate, and thus loss of stability across trials during the delay. Simulation of spiking cortical circuit WM models further confirmed that FF is a sensitive measure that can well dissociate distinct WM mechanisms. We then tested these predictions on datasets of single-neuron recordings from macaque PFC during three WM tasks. In sharp contrast to the burst-coding model predictions, we only found a small fraction of neurons showing increased WM-dependent burstiness, and stability across trials during delay was strengthened in empirical data. Therefore, reduced trial-to-trial variability during delay provides strong constraints on the contribution of single-neuron intermittent bursting to WM maintenance. [ABSTRACT FROM AUTHOR]

In this work, the conductance and current correlations properties of a quantum topological interferometer consisting of a quantum dot coupled to two Majorana bound states (MBSs) confined at both ends of a 1D topological superconductor ring nanowire is investigated. The ring in its topological nontrivial and trivial phases is analyzed to show that the tunneling conductance, shot noise, and Fano factor present unique characteristics to distinguish the hallmark of MBSs. The findings are reinforced by taking advantage of the full correspondence between the quantum topological interferometer and a quantum‐dot effectively coupled to a single Majorana state in a straight topological superconductor wire configuration. It is shown that besides the characteristic zero‐bias conductance e2/2h and the already known shot noise features, the Fano factor provides significant information to distinguish the MBSs presence. [ABSTRACT FROM AUTHOR]

Noise can drive the dynamics of stochastic systems to different important states. Delay is another significant parameter that may impart non-Markovian behavior in the system dynamics. The interplay of noise and delay can exhibit interesting, complex behaviors in stochastic systems. In this work, we considered the stochastic gene expression model and studied this interplay of noise and delay in describing the functioning of a gene via transcription and translation processes. The calculated probability distributions of mRNA and protein, both in non-delay and delay, are found to obey certain universal classes, namely Poisson distribution at u , N → l a r g e limit, and Normal distribution at u , ⟨ u ⟩ , N → l a r g e limit. Analytical result of noise, measured by the Fano factor, indicates that, both in delay and non-delay cases, the gene expression system follows sub-Poissonian processes when the values of parameters are far from asymptotic values and that it becomes Poissonian at asymptotic values of the system parameters. We provided a detailed study of the noise using the Fano Factor with respect to different parameters such as mean, initial population, and time delay for the gene expression process. Again, the stochastic simulation results of the model indicate the transition of mRNA states (low and high transcription and translation) driven by the translation rate. [ABSTRACT FROM AUTHOR]

Objective . The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS. Approach . HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes-the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing. Main results . Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences. Conclusion . The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing. Significance . The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS., (Creative Commons Attribution license.)

The Andreev conductance in Δ -shaped quantum dots (QDs) system coupled with Majorana bound states (MBSs) is studied and resulting conductance spectrum displays resonant and non-resonant processes. These fluctuated resonances render features like insulating band, bonding (antibonding) in the low-bias region due to non-trivial role of interdot coupling t c and dots-MBSs coupling λ. On comparing QD levels (𝜀 1 , 𝜀 2 , 𝜀 3) , and the coupling between the MBSs, coherent oscillating dynamics of an electron between the nanowire and the QDs can be portrayed. The insulating band is robust against λ , but highly sensitive to t c , which causes to increase (decrease) the conductance. We can claim that under finite bias voltage, transport can facilitate the researchers to expose the essential features of the Majorana fermion in such closed systems composed of MBSs. [ABSTRACT FROM AUTHOR]

The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently. In this paper we aim to explore this problem in more detail and to study the possible solution, which is to evaluate the Fano factor in the operational time. We use equilibrium renewal and Markov renewal processes as spike train models to describe the method in detail, and we provide an illustration on experimental data.

The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently. In this paper we aim to explore this problem in more detail and to study the possible solution, which is to evaluate the Fano factor in the operational time. We use equilibrium renewal and Markov renewal processes as spike train models to describe the method in detail, and we provide an illustration on experimental data. [ABSTRACT FROM AUTHOR]

Transcription bursting creates variation among the individuals of a given population. Bursting emerges as the consequence of turning on and off the transcription process randomly. There are at least three sub-processes involved in the bursting phenomenon with different timescale regimes viz. flipping across the on–off state channels, microscopic transcription elongation events and the mesoscopic transcription dynamics along with the mRNA recycling. We demonstrate that when the flipping dynamics is coupled with the microscopic elongation events, then the distribution of the resultant transcription rates will be over-dispersed. This in turn reflects as the transcription bursting with over-dispersed non-Poisson type distribution of mRNA numbers. We further show that there exist optimum flipping rates (αC, βC) at which the stationary state Fano factor and variance associated with the mRNA numbers attain maxima. These optimum points are connected via α C = β C β C + γ r . Here α is the rate of flipping from the on-state to the off-state, β is the rate of flipping from the off-state to the on-state and γr is the decay rate of mRNA. When α = β = χ with zero rate in the off-state channel, then there exist optimum flipping rates at which the non-stationary Fano factor and variance attain maxima. Here χ C , v ≃ 3 k r + / 2 1 + k r + t (here k r + is the rate of transcription purely through the on-state elongation channel) is the optimum flipping rate at which the variance of mRNA attains a maximum and χ C , κ ≃ 1.72 / t is the optimum flipping rate at which the Fano factor attains a maximum. Close observation of the transcription mechanism reveals that the RNA polymerase performs several rounds of stall-continue type dynamics before generating a complete mRNA. Based on this observation, we model the transcription event as a stochastic trajectory of the transcription machinery across these on–off state elongation channels. Each mRNA transcript follows different trajectory. The total time taken by a given trajectory is the first passage time (FPT). Inverse of this FPT is the resultant transcription rate associated with the particular mRNA. Therefore, the time required to generate a given mRNA transcript will be a random variable. For a stall-continue type dynamics of RNA polymerase, we show that the overall average transcription rate can be expressed as k r ≃ h ∞ + k r + where k r + ≃ λ r + / L , λr+ is the microscopic transcription elongation rate in the on-state channel and L is the length of a complete mRNA transcript and h∞+ = [β/(α + β)] is the stationary state probability of finding the transcription machinery in the on-state channel. [ABSTRACT FROM AUTHOR]

The effects of carrying capacity of environment K for degradation (the K effect for short) on the constitutive gene expression and a simple genetic regulation system are investigated by employing a stochastic Langevin equation combined with the corresponding Fokker–Planck equation for the two stochastic systems subjected to internal and external noises. This K effect characterizes the limited degradation ability of the environment for RNA or proteins, such as insufficient catabolic enzymes. The K effect could significantly change the distribution of mRNA copy-number in constitutive gene expression, and interestingly, it leads to the Fano factor slightly larger than one if only the internal noise exists. Therefore, that the recent experimental measurements suggest the Fano factor deviates from one slightly [D. L. Jones, R. C. Brewster and R. Phillips, Science346 (2014) 1533], probably originates from the K effect. The K effects on the steady and transient properties of genetic regulation system, have been investigated in detail. It could enhance the mean first passage time significantly especially when the noises are weak and reduce the signal-to-noise ratio in stochastic resonance substantially. [ABSTRACT FROM AUTHOR]

An accurate mathematical description of the processes occurring in a scintillation spectrometer with several photodetectors registering primary particles allows obtaining correct formulas for the mean value and amplitude dispersion at the output of the photodetectors, as well as an expression for the covariance between photodetector signals. In contrast to the formulas available in the literature, the formula obtained in this work for the energy resolution of a scintillation spectrometer with one photodetector contains information on the relation between the corresponding processes occurring in the detector upon the registration of particles with the characteristics of the scintillation crystal and the scintillator-photodetector interface and the characteristics of the photodetector and the electronics of the spectrometer. It is shown that the fluctuations of the light output and the Fano factor for the scintillation crystal material can be determined using the relative covariance between photodetector signals. [ABSTRACT FROM AUTHOR]

Experimental tests on continuous two-stage anaerobic digestion (TSAD) were conducted, to assess its energetic performance, using organic market waste as a substrate. The systems were tested to ascertain the effects of external stressors, which allow the separation into two different microorganism consortia, that is, hydrogen-producing bacteria and hydrogen-consuming bacteria, to be maintained. Two bioreactors were run in series under different operational conditions, including pH, mixing rate, and initial inoculum, and three different decreasing hydraulic retention times were considered, with a fixed ratio of 1:10 in volume between the first bioreactor (hydrogen) and the second one (methane). The performance of the whole system was assessed over > 140 days to monitor the stability of the process, in terms of the reduction of the volatile solids and the energy productivity for each step. Each tested condition was scored using two parameters: efficiency and efficacy. The first corresponds to the fraction of recovered energy of the available (η) and the second (ξ) was used to compare the energy produced by the TSAD with that of one-step anaerobic digestion. The efficiency resulted to be (24–32)%, while the efficacy proved to be around 1.20. The share of energy, under the form of hydrogen, compared to the total energy recovery, was in the (8–12) % range. Finally, the oscillation behaviour of the quasi-steady-state condition was analysed in terms of the Fano factor to establish the most stable conditions. [ABSTRACT FROM AUTHOR]