Shot Noise Model Research Articles

Interpreting the power spectral density of a fluctuating colloidal current.

The transport of molecules through biological and synthetic nanopores is governed by multiple stochastic processes that lead to noisy, fluctuating currents. Disentangling the characteristics of different noise-generating mechanisms is central to better understanding molecular transport at a fundamental level but is extremely challenging in molecular systems due to their complexity and relative experimental inaccessibility. Here, we construct a colloidal model microfluidic system for the experimental measurement of particle currents, where the governing physical properties are directly controllable and particle dynamics directly observable, unlike in the molecular case. Currents of hard spheres fluctuate due to the random arrival times of particles into the channel and the distribution of particle speeds within the channel, which results in characteristic scalings in the power spectral density. We rationalize these scalings by quantitatively comparing to a model for shot noise with a finite transit time, extended to include the distribution of particle speeds. Particle velocity distributions sensitively reflect the confining geometry, and we interpret and model these in terms of the underlying fluid flow profiles. Finally, we explore the extent to which details of these distributions govern the form of the resulting power spectral density, thereby establishing concrete links between the power spectral density and underlying mechanisms for this experimental system. This paves the way for establishing a more systematic understanding of the links between characteristics of transport fluctuations and underlying molecular mechanisms in driven systems such as nanopores.

Tuning Overbias Plasmon Energy and Intensity in Molecular Plasmonic Tunneling Junctions by Atomic Polarizability.

Plasmon excitation in molecular tunnel junctions is interesting because the plasmonic properties of the device can be, in principle, controlled by varying the chemical structure of the molecules. The plasmon energy of the excited plasmons usually follows the quantum cutoff law, but frequently overbias plasmon energy has been observed, which can be explained by quantum shot noise, multielectron processes, or hot carrier models. So far, clear correlations between molecular structure and the plasmon energy have not been reported. Here, we introduce halogenated molecules (HS(CH2)12X, with X = H, F, Cl, Br, or I) with polarizable terminal atoms as the tunnel barriers and demonstrate molecular control over both the excited plasmon intensity and energy for a given applied voltage. As the polarizability of the terminal atom increases, the tunnel barrier height decreases, resulting in an increase in the tunneling current and the plasmon intensity without changing the tunneling barrier width. We also show that the plasmon energy is controlled by the electrostatic potential drop at the molecule-electrode interface, which depends on the polarizability of the terminal atom and the metal electrode material (Ag, Au, or Pt). Our results give new insights in the relation between molecular structure, electronic structure of the molecular junction, and the plasmonic properties which are important for the development of molecular scale plasmonic-electronic devices.

Prediction of the ESD Failure Current Based on a New Method Using the Shot Noise Model

Prediction of the ESD Failure Current Based on a New Method Using the Shot Noise Model

A Poisson Shot Noise Limited MMSE Precoding for Photon-Counting MIMO Systems with Reinforcement Learning

With the development of the Internet of Things (IoT), most communication systems are difficult to implement on a large scale due to their high complexity. Multiple-input multiple-output (MIMO) precoding is a generally used technique for improving the reliability of free-space optical (FSO) communications, which is a key technology in the 6G era. However, traditional MIMO precoding schemes are typically designed based on the assumption of additive white Gaussian noise (AWGN). In this paper, we present a novel MIMO precoding method based on reinforcement learning (RL) that is specifically designed for the Poisson shot noise model. Unlike traditional MIMO precoding schemes, our proposed scheme takes into account the unique statistical characteristics of Poisson shot noise. Our approach achieves significant performance gains compared to existing MIMO precoding schemes. The proposed scheme can achieve the bit error rate (BER) of 10−5 in a strong turbulence channel and exhibits superior robustness against imperfect channel state information (CSI).

Improving the sensitivity of liver tumor classification in ultrasound images via a power-law shot noise model.

Power laws have been observed in various fields and help us understand natural phenomena. Power laws have also been observed in ultrasound images. This study used the power spectrum of the signal identified from the reflected ultrasound signal observed in ultrasonography based on the power-law shot noise (PLSN) model. The power spectrum follows a power law, which has a scaling factor that depends on the characteristics of the tissue in the region where the ultrasound wave propagates. To distinguish between a tumor and blood vessels in the liver, we propose a classification model that includes a scaling factor based on ResNet, a deep learning model for image classification. In a task to classify 6 types of tissue - a tumor, the inferior vena cava, the descending aorta, the Gleason sheath, the hepatic vein, and small blood vessels - tumor sensitivity increased 3.8% and the F-score for a tumor improved 2% while precision was maintained. The scaling factor obtained using the PLSN model was validated for classification of liver tumors.

Multiplicative Shot-Noise: A New Route to Stability of Plastic Networks.

Fluctuations of synaptic weights, among many other physical, biological, and ecological quantities, are driven by coincident events of two "parent" processes. We propose a multiplicative shot-noise model that can capture the behaviors of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. We apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. Using mean-field theory analysis and network simulations, we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. The multiplicative plasticity rule is shown to support efficient learning of input stimuli, and it gives a stable, unimodal synaptic-weight distribution with a large fraction of strong synapses. The strong synapses remain stable over long times but do not "run away." Our results suggest that the multiplicative shot-noise offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks.

Generalized figure of merit for plasmonic dip measurement-based surface plasmon resonance sensors.

We propose a theoretical framework to analyze quantitative sensing performance parameters, including sensitivity, full width at half maximum, plasmonic dip position, and figure of merits for different surface plasmon operating conditions for a Kretschmann configuration. Several definitions and expressions of the figure of merit have been reported in the literature. Moreover, the optimal operating conditions for each figure of merit are, in fact, different. In addition, there is still no direct figure of merit comparison between different expressions and definitions to identify which definition provides a more accurate performance prediction. Here shot-noise model and Monte Carlo simulation mimicking the noise behavior in SPR experiments have been applied to quantify standard deviation in the SPR plasmonic dip measurements to evaluate the performance responses of the figure of merits. Here, we propose and formulate a generalized figure of merit definition providing a good performance estimation to the detection limit. The measurement parameters employed in the figure of merit formulation are identified by principal component analysis and machine learning. We also show that the proposed figure of merit can provide a good estimation for the surface plasmon resonance performance of plasmonic materials, including gold and aluminum, with no need for a resource-demanding computation.

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

ABSTRACT We study the connection of matter density and its tracers from the probability density function (PDF) perspective. One aspect of this connection is the conditional expectation value 〈δtracer|δm〉 when averaging both tracer and matter density over some scale. We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics. Using N-body simulations and mock galaxy catalogues we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization. For haloes hosting typical luminous red galaxies, the Lagrangian model provides a significantly better description of 〈δtracer|δm〉 at second order in perturbations. A second aspect of the matter-tracer connection is shot-noise, i.e. the scatter of tracer density around 〈δtracer|δm〉. It is well known that this noise can be significantly non-Poissonian and we validate the performance of a more general, two-parameter shot-noise model for different tracers and simulations. Both parts of our analysis are meant to pave the way for forthcoming applications to survey data.

Deep learning-based single-shot phase retrieval algorithm for surface plasmon resonance microscope based refractive index sensing application

A deep learning algorithm for single-shot phase retrieval under a conventional microscope is proposed and investigated. The algorithm has been developed using the context aggregation network architecture; it requires a single input grayscale image to predict an output phase profile through deep learning-based pattern recognition. Surface plasmon resonance imaging has been employed as an example to demonstrate the capability of the deep learning-based method. The phase profiles of the surface plasmon resonance phenomena have been very well established and cover ranges of phase transitions from 0 to 2π rad. We demonstrate that deep learning can be developed and trained using simulated data. Experimental validation and a theoretical framework to characterize and quantify the performance of the deep learning-based phase retrieval method are reported. The proposed deep learning-based phase retrieval performance was verified through the shot noise model and Monte Carlo simulations. Refractive index sensing performance comparing the proposed deep learning algorithm and conventional surface plasmon resonance measurements are also discussed. Although the proposed phase retrieval-based algorithm cannot achieve a typical detection limit of 10–7 to 10–8 RIU for phase measurement in surface plasmon interferometer, the proposed artificial-intelligence-based approach can provide at least three times lower detection limit of 4.67 × 10–6 RIU compared to conventional intensity measurement methods of 1.73 × 10–5 RIU for the optical energy of 2500 pJ with no need for sophisticated optical interferometer instrumentation.

Poisson Shot Noise Removal by an Oracular Non-Local Algorithm

In this paper, we address the problem of denoising images obtained under low-light conditions for the Poisson shot noise model. Under such conditions, the variance stabilization transform (VST) is no longer applicable, so that the state-of-the-art algorithms which are proficient for the additive white Gaussian noise cannot be applied. We first introduce an oracular non-local algorithm and prove its convergence with the optimal rate of convergence under a Hölder regularity assumption for the underlying image, when the search window size is suitably chosen. We also prove that the convergence remains valid when the oracle function is estimated within a prescribed error range. We then define a realizable filter by a statistical estimation of the similarity function which determines the oracle weight. The convergence of the realizable filter is justified by proving that the estimator of the similarity function lies in the prescribed error range with high probability. The experiments show that under low-light conditions the proposed filter is competitive compared with the recent state-of-the-art algorithms.

Determinantal Point Processes for Image Processing

Determinantal point processes (DPPs) are probabilistic models of configurations that favor diversity or repulsion. They have recently gained influence in the machine learning community, mainly because of their ability to elegantly and efficiently subsample large sets of data. In this paper, we consider DPPs from an image processing perspective, meaning that the data we want to subsample are pixels or patches of a given image. To this end, our framework is discrete and finite. First, we adapt their basic definition and properties to DPPs defined on the pixels of an image, that we call determinantal pixel processes (DPixPs). We are mainly interested in the repulsion properties of such a process and we apply DPixPs to texture synthesis using shot noise models. Finally, we study DPPs on the set of patches of an image. Because of their repulsive property, DPPs provide a strong tool to subsample discrete distributions such as that of image patches.

Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions.

We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram-Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. This approach extends the results of Brigham and Destexhe (Preprint, 2015a; Phys Rev E 91:062102, 2015b) by the use of exact combinatorial expressions for the moments of multiplicative nonstationary filtered shot noise processes. Our results are confirmed by stochastic simulations and apply to single- and multiple-noise-source models.

The Parameter-free Finger-of-God Model and Its Application to 21 cm Intensity Mapping

Abstract Using the galaxy catalog built from ELUCID N-body simulation and the semianalytical galaxy formation model, we have built a mock H i intensity mapping map. We have implemented the Finger-of-God (FoG) effect in the map by considering the galaxy H i gas velocity dispersion. By comparing the H i power spectrum in redshift space with a measurement from the IllustrisTNG simulation, we have found that the FoG effect can explain the discrepancy between current mock maps built from the N-body simulation and the IllustrisTNG simulation. Then we built a parameter-free FoG model and a shot-noise model to calculate the H i power spectrum. We found that our model can accurately fit both the monopole and quadrupole moments of the H i matter power spectrum. Our approach to building the mock H i intensity map and the parameter-free FoG model will be useful for upcoming 21 cm intensity mapping experiments, such as CHIME, Tianlai, BINGO, FAST, and SKA. It is also vital for studying nonlinear effects in 21 cm intensity mapping.

Shot noise model of the short channel metal-oxide-semiconductor field-effect transistor

<sec>With the development of the semiconductor manufacturing process, the size of the metal-oxide-semiconductor field-effect transistor (MOSFET) device has been on a tens-of-nanometer scale. The shot noise appears in the excess channel noise of the device, and the noise mechanism of the device begins to change gradually. Due to the fact that the electron temperature gradient is neglected in calculation and the significant enhancement of the lateral channel electric field are not taken into consideration, the traditional electron temperature model and the thermal noise model underestimate the effect of hot carrier effects, resulting in the underestimate of the thermal noise. Moreover, the traditional drain-source current model ignores the electron temperature gradient in the calculation and does not include the effect of the electron temperature on the mobility degradation effect either. Therefore, the calculation accuracy of the shot noise and the Fano factor on the basis of the traditional model will be reduced to a certain extent as the size of the device decreases, thus affecting the analysis of the noise mechanism of the device. </sec><sec>In this paper, we establish the channel electron temperature model and the electron velocity model by solving the energy balance equation, and develop the drain source current model based on these two models. Moreover, the shot noise model and the thermal noise model suitable for devices below 40 nm are established based on the drain-source current model. Meanwhile, the Fano factor of the shot noise is calculated. The influence of the MOSFET device size on the noise mechanism and the Fano factor of the shot noise are also investigated when the device is under different bias voltages. The results show that the accuracy of the existing thermal noise model and the shot noise model decline as the device size decreases, which eventually leads the Fano factor of the shot noise to be overestimated. When the size of the NMOSFET device is below 20 nm, the shot noise affects the device noise in the strong inversion region. With the size decreasing, the characteristic of the noise mechanism of the NMOSFET device changes from the characteristic of single thermal noise to the common characteristic of both the thermal noise and the shot noise. When the NMOSFET device size is scaled down to 10 nm, the channel noise of the device can no longer be characterized by the thermal noise alone. Instead, the noise mechanism of the device changes and is characterized by both the channel thermal noise and the suppressed shot noise. The shot noise has become an important factor that contributes to the excessive noise in the device. </sec>

Impact of the Frequency Dependence of the Parasitic Admittance on the Diffusion Noise of a Diode Junction at Low Bias

In this article, we report for the first time that the well-established diffusion noise can be apparently increased in large proportions and that such a situation can be very common at some specific frequencies in the p-n junction structures operating at a very low direct bias current. Noise theories and the associated measurement techniques are a major issue for the emerging semiconductor technologies, the development of accurate computer-aided design (CAD) models, and the designing of low-noise circuits and systems. The conventional shot noise model usually satisfactorily describes the p-n junction noise in solid-state devices, such as diodes and transistors. It has proven to be very efficient for many different conventional and advanced semiconductor technologies. However, alterations may sometimes be needed as previous works indicate scenarios where this so-called shot noise exhibits deviations from the theory, which translates into some noise suppression. In this article, we report on alterations that look like low-frequency diffusion noise enhancement (unexpected noise increase). It occurs at low current levels, for many generic commercially available diodes and the p-n junctions in transistors. Therefore, we propose an appropriate electrical noise model that satisfies both the low-frequency noise experimental data and the electrical behavior of the devices observed from impedance spectroscopy. We also evaluate this model as the ambient temperature is varied. Finally, it is discussed how this model can be connected to the conventional van der Ziel shot noise model and a better insight on the possible origin of such diffusion noise enhancement is provided.

Comparison of the Scaling Properties of EUV Intensity Fluctuations in Coronal Hole and Quiet-Sun Regions

Abstract Using detrended fluctuation analysis and rescaled range analysis, we investigate the scaling properties of extreme ultraviolet (EUV) intensity fluctuations of low-latitude coronal holes (CHs) and neighboring quiet-Sun (QS) regions in signals obtained with the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly instrument. Contemporaneous line-of-sight SDO/Helioseismic and Magnetic Imager magnetic fields provide a context for the physical environment. We find that the intensity fluctuations in the time series of EUV images present at each spatial point a scaling symmetry over the range ∼20 minute to ∼1 hr. Thus we are able to calculate a generalized Hurst exponent and produce image maps, not of physical quantities like intensity or temperature, but of a single dynamical parameter that sums up the statistical nature of the intensity fluctuations at each pixel. In QS regions and in CHs with magnetic bipoles, the scaling exponent (1.0 < α ≤ 1.5) corresponds to anticorrelated turbulent-like processes. In CHs, and in QS regions primarily associated with (open) magnetic field of dominant polarity, the generalized exponent (0.5 < α < 1) corresponds to positively correlated (persistent) processes. We identify a tendency for α ∼ 1 near CH boundaries and in other regions in which open and closed magnetic fields are in proximity. This is a signature of an underlying 1/f type process that is characteristic for self-organized criticality and shot-noise models.

The Study of Dynamic Caching via State Transition Field—the Case of Time-Invariant Popularity

In the second part of this two-part paper, we extend the study of dynamic caching via state transition field (STF) to the case of time-varying content popularity. The objective of this part is to investigate the impact of time-varying content popularity on the STF and how such impact accumulates to affect the performance of a replacement scheme. Unlike the case in the first part, the STF is no longer static over time, and we introduce instantaneous STF to model it. Moreover, we demonstrate that many metrics, such as instantaneous state caching probability and average cache hit probability over an arbitrary sequence of requests, can be found using the instantaneous STF. As a steady state may not exist under time-varying content popularity, we characterize the performance of replacement schemes based on how the instantaneous STF of a replacement scheme after a content request impacts on its cache hit probability at the next request. From this characterization, insights regarding the relations between the pattern of change in the content popularity, the knowledge of content popularity exploited by the replacement schemes, and the effectiveness of these schemes under time-varying popularity are revealed. In the simulations, different patterns of time-varying popularity, including the shot noise model, are experimented. The effectiveness of example replacement schemes under time-varying popularity is demonstrated, and the numerical results support the observations from the analytic results.

The Study of Dynamic Caching via State Transition Field—the Case of Time-Varying Popularity

In the second part of this two-part paper, we extend the study of dynamic caching via state transition field (STF) to the case of time-varying content popularity. The objective of this part is to investigate the impact of time-varying content popularity on the STF and how such impact accumulates to affect the performance of a replacement scheme. Unlike the case in the first part, the STF is no longer static over time, and we introduce instantaneous STF to model it. Moreover, we demonstrate that many metrics, such as instantaneous state caching probability and average cache hit probability over an arbitrary sequence of requests, can be found using the instantaneous STF. As a steady state may not exist under time-varying content popularity, we characterize the performance of replacement schemes based on how the instantaneous STF of a replacement scheme after a content request impacts on its cache hit probability at the next request. From this characterization, insights regarding the relations between the pattern of change in the content popularity, the knowledge of content popularity exploited by the replacement schemes, and the effectiveness of these schemes under time-varying popularity are revealed. In the simulations, different patterns of time-varying popularity, including the shot noise model, are experimented. The effectiveness of example replacement schemes under time-varying popularity is demonstrated, and the numerical results support the observations from the analytic results.

Similar shot profile morphology of fast variability in a cataclysmic variable, X-ray binary, and blazar: The MV Lyrae case

Context. The cataclysmic variable MV Lyr has been found to be present in the Kepler field, yielding a light curve with the duration of almost 1500 days with 60 s cadence. Such high quality data of this nova-like system with obvious fast optical variability reveal multi-component power density spectra, as shown by previous works. Aims. Our goal is to study the light curve from a different point of view and perform a shot profile analysis. We search for characteristics that have not been discovered with standard methods based on power density spectrum. Methods. The shot profile method identifies individual shots in the light curve and averages these shots to reveal all substructures with typical timescales. We also tested the robustness of our analysis using a simple shot noise model. Although the principle of this method is not completely physically correct, we used it as a purely phenomenological approach. Results. We obtain mean profiles with multi-component features. The shot profile method distinguishes substructures with similar timescales which appear as a single degenerate feature in power density spectra. Furthermore, this method yields the identification of another high frequency component in the power density spectra of Kepler and XMM-Newton data that have not been detected so far. Moreover, we found side lobes accompanied with the central spike, making the profile very similar to the Kepler data of blazar W2R 1926+42 and the Ginga data of Cyg X-1. All three objects show similar timescale ratios of the rising versus declining part of the central spikes, while the two binaries also have similar rising profiles of the shots described by a power-law function. Conclusions. The similarity of both binary shot profiles suggests that the shots originate from the same origin, namely, aperiodic mass accretion in the accretion disc. Moreover, the similarity with the blazar may imply that the ejection fluctuations in the blazar jet are connected to accretion fluctuations driving the variability in binaries. This points out the connection between the jet and the accretion disc.

New insights on the behaviour of alternative types of individual-based tree models for natural forests

Agent/individual-based models (A/IBM) help to explain in a mechanistic way how spatial plant patterns evolve through time. In the past, seemingly different and independent types of A/IBMs were developed for modelling the dynamics of tree populations, e.g. growth interaction (GI) and shot noise (SN) models. In this paper, we present a new, advanced methodology of pattern-oriented modelling (POM) for the comparative, synoptic analysis of the behaviour of different types of A/IBMs by using recombinations of model components, validation and sensitivity analysis. We analysed model behaviour for spatio-temporal data from natural forests of interior Douglas fir (Pseudotsuga menziesii var glauca (Mirb.) Franco) and Scots pine (Pinus sylvestris L.) populations from Canada and the UK, respectively. Our detailed analysis clarified that both models, GI and SN along with their recombinations performed similarly and belong to the same group of A/IBMs. From the application of our new methodology we learnt that SN models were able to describe interactions more accurately than GI models and additionally produce interaction fields that can be used for other modelling purposes. On the other hand the GI model was more robust when using observed data that did not include sufficient information on tree interactions. Maximum-likelihood estimations were more reliable in spatial regression analysis than least-squares methods and should be preferred in spatial A/IBM parametrisation.