Single Exponential Distribution Research Articles

MEFDPN: Mixture exponential family distribution posterior networks for evaluating data uncertainty

The computation of uncertainty are crucial for developing a reliable machine learning model. The natural posterior network (NatPN) provides uncertainty estimation for any single exponential family distribution, but real-world data is often complex. Therefore, we introduce a mixture exponential family posterior network (MEFDPN), which extends the prior distribution to a mixture of exponential family distributions, aiming to fit complex distributions that better represent real data. During network training, MEFDPN independently updates the posterior Bayesian estimates for each prior distribution, and the weights of these distributions are updated based on the forward propagation results. Furthermore, MEFDPN calculates two types of uncertainty (aleatoric and epistemic) and combines them using entropy weighting to obtain a comprehensive confidence measure for each data point. Theoretically, MEFDPN achieves higher prediction accuracy, and experimental results demonstrate its capability to compute high-quality data comprehensive confidence. Moreover, it shows encouraging accuracy in Out-of-Distribution(OOD) detection and validation experiments. Finally, we apply MEFDPN to a materials dataset, efficiently filtering out OOD data. This results in a significant enhancement of prediction accuracy for machine learning models. Specifically, removing only 5% of outlier data leads to a 2%–5% improvement in accuracy.

An Asymmetric Galactic Stellar Disk Traced by OB-type Stars from LAMOST DR7

Using 9943 OB-type stars from LAMOST DR7 in the solar neighborhood, we fit the vertical stellar density profile with the model including a single exponential distribution at different positions (R, Φ). The distributions of the scale heights and scale length show that the young disk traced by the OB-type stars is not axisymmetric. The scale length decreases versus the azimuthal angle Φ, i.e., from 1.14−0.19+0.30 kpc with Φ = − 3° to 0.77−0.06+0.08 kpc with Φ = 9°. Meanwhile we find signal of non-symmetry in the distribution of the scale height of the north and south of the disk plane. The scale height in the north side shows signal of flaring of the disk, while that of the south disk stays almost constant around h s = 130 pc. The distribution of the displacement of the disk plane Z 0 also shows variance versus the azimuthal angle Φ, which displays significant differences with the warp model constrained by the Cepheid stars. We also test different values for the position of the Sun, and the distance between the Sun and the Galactic center affects the scale heights and the displacement of the disk significantly, but that does not change our conclusion that the disk is not axisymmetric.

CFD-DEM Simulation of Fast Fluidization of Fine Particles in a Micro Riser

In recent years, the discrete element method (DEM) has gradually been applied to the traditional fluidization simulation of fine particles in a micro fluidized bed (MFB). The application of DEM in the simulating fast fluidization of fine particles in MFB has not yet received attention. This article presents a drag model that relies on the surrounding environment of particles, namely the particle circumstance-dependent drag model or PCDD model. Fast fluidization in an MFB of fine particles is simulated using DEM based on the PCDD model. Simulations indicate that the local structure in an MFB exhibits particle aggregation, which is a natural property of fast fluidization, forming a structure where a continuous dilute phase and dispersed concentrated phase coexist. There exists a strong effect of solid back-mixing in an MFB, leading to relatively low outlet solid flux. The gas back-mixing effect is, however, not so distinct. The axial porosity shows a monotonically increasing distribution with the bed height but does not strictly follow the single exponential distribution. The solid volume fraction at the bottom of the bed is significantly lower than the correlated value in CFB. The axial heterogeneous distribution of the cross-sectional average porosity in the lower half of the bed is also weakened. The radial porosity shows a higher distribution pattern in the central region and a lower one in the sidewall region.

An Experimental Study of Non-Gaussian Properties of Tornado-like Loads on a Low-Rise Building Model

This paper focuses on the non-Gaussian properties of tornado pressure loading on a Texas Tech University (TTU) building model. External pressures of the model were measured at multiple radial positions in a two-celled tornado-like vortex generated by a tornado-like vortex simulator. High-order statistical moments of pressure coefficients were studied. The spatial distributions of non-Gaussian zones were presented and compared with the figure for boundary layer wind. Four exponential models were used to fit the probability density of tornado pressures. The peak factors obtained by five methods were also investigated. Results indicate that non-Gaussian regions of a low-rise building in a tornado-like vortex significantly differ from that in boundary layer wind. The peak pressure coefficients exhibit a maximum value near the end of windward eaves when the model is located at a tornadic core radius. The probability density of tornado pressure time series cannot be fitted by a single exponential distribution. The gamma distribution and generalized extreme value (GEV) distribution can describe the probabilistic behavior of pressure coefficients at the most unfavorable load position. Compared with other methods, the skewness-dependent peak factor method exhibits the advantages of reliable results, easy calculation, and wide applicability.

Video imaging of structural dynamics of amyloid β protofibrils.

Soluble aggregates including oligomers and protofibrils (PFs) of amyloid β (Aβ) have been reported to be more toxic than mature fibrils (MFs). Recently, clinical trials of antibodies targeting these aggregates are also in progress. Their structure is dynamic, which makes it difficult to extract and analyze them in a stable state. Therefore, the molecular process among the soluble Aβ aggregates has been unclear. Development of high-speed atomic force microscopy (HS-AFM) allows video-imaging of structural dynamics of individual amyloid aggregates in liquid. Here, we investigated structural dynamics and mechanical property of Aβ protofibrils and anti-Aβ antibody binding to PFs, using HS-AFM. Aβ1-42 PF and MF were prepared in vitro, which was deposited on the HS-AFM stage. Structural dynamics of the aggregates were observed by HS-AFM in phosphate buffered saline (PBS). Young's moduli of the individual aggregates were measured by force spectrometry mode of HS-AFM in PBS. The anti-Aβ antibody was added in the chamber, followed by HS-AFM observation of the antibody binding to PFs. Aβ1-42 PF showed diffusive 2D motion on bare mica and its typical structure was composed of several globular parts in a polygonal line. The angle between each segment of a PF was maintained during the diffusive motion. The length of PFs showed a single exponential distribution. Its mean length depended on PF concentration. The Young's modulus of PFs was higher than that of MFs in liquid. Lecanemab (BAN2401) bounded to PFs both most rapidly and abundantly, while 4G8 showed the weakest and least binding to PFs. Assembly and disassembly of the globular parts in PFs are dynamic, while their segment structure is stiffer than MFs and the bonds between the globular parts are rigid. These characteristics indicated the difference in internal structure between PFs and MFs, which supports that PFs may not be a direct precursor of MFs. Lecanemab binds to all various parts and length of PFs.

Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise.

We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ=0 and κ=∞ correspond to fully nonreactive and fully reactive sinks, respectively. We explore the effect of two competitive mechanisms: the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes.

The Flow of Axonal Information Among Hippocampal Subregions: 1. Feed-Forward and Feedback Network Spatial Dynamics Underpinning Emergent Information Processing.

The tri-synaptic pathway in the mammalian hippocampus enables cognitive learning and memory. Despite decades of reports on anatomy and physiology, the functional architecture of the hippocampal network remains poorly understood in terms of the dynamics of axonal information transfer between subregions. Information inputs largely flow from the entorhinal cortex (EC) to the dentate gyrus (DG), and then are processed further in the CA3 and CA1 before returning to the EC. Here, we reconstructed elements of the rat hippocampus in a novel device over an electrode array that allowed for monitoring the directionality of individual axons between the subregions. The direction of spike propagation was determined by the transmission delay of the axons recorded between two electrodes in microfluidic tunnels. The majority of axons from the EC to the DG operated in the feed-forward direction, with other regions developing unexpectedly large proportions of feedback axons to balance excitation. Spike timing in axons between each region followed single exponential log-log distributions over two orders of magnitude from 0.01 to 1 s, indicating that conventional descriptors of mean firing rates are misleading assumptions. Most of the spiking occurred in bursts that required two exponentials to fit the distribution of inter-burst intervals. This suggested the presence of up-states and down-states in every region, with the least up-states in the DG to CA3 feed-forward axons and the CA3 subregion. The peaks of the log-normal distributions of intra-burst spike rates were similar in axons between regions with modes around 95 Hz distributed over an order of magnitude. Burst durations were also log-normally distributed around a peak of 88 ms over two orders of magnitude. Despite the diversity of these spike distributions, spike rates from individual axons were often linearly correlated to subregions. These linear relationships enabled the generation of structural connectivity graphs, not possible previously without the directional flow of axonal information. The rich axonal spike dynamics between subregions of the hippocampus reveal both constraints and broad emergent dynamics of hippocampal architecture. Knowledge of this network architecture may enable more efficient computational artificial intelligence (AI) networks, neuromorphic hardware, and stimulation and decoding from cognitive implants.

Distribution Pattern of Anchorage Stress and Water Sensitivity Analysis of Red Clay

Red clay is a special soil layer with complex engineering properties distributed in tropical and subtropical regions. An anchor cable support is a common form of red clay slope support. The effectiveness of the anchor cable support is mainly determined by the anchoring force provided by the red clay stratum. Increase of the water content will lead to the rapid deterioration of the mechanical properties of red clay, which will lead to the reduction of the anchoring force of the slope anchor cable and lead to the failure of the support. Based on the classical Phillips and uniform anchorage shear stress distribution theory, this paper puts forward a uniform-exponential distribution pattern of anchorage shear stress according to the specific characteristics of red clay by using the characteristics of the peak shear strength and residual shear strength of the rock and soil mass. With increasing anchorage force, the dynamic evolution (single exponential distribution ⟶ double single exponential distribution ⟶ uniform index exponential complex distribution ⟶ uniform distribution) of the anchorage shear stress is analysed. Based on the peak and residual test of the cohesive force and internal friction angle, the relationship between the anchoring force and buried depth and water content is established by analysing the factors influencing the anchoring force. It can be found from the field test that, according to the relationship established, the limit anchorage force of the anchor cable in the red clay stratum can be calculated and the water sensitivity of the anchor cable’s limit anchorage force can be quantitatively analysed.

Size Distribution of Emission Vortex Rings in Turbulence Induced by Vibrating Wire in Superfluid $$^4$$He

We report the spontaneous emission of vortex rings from turbulence induced by a vibrating wire in superfluid $$^4$$ He, and investigate the statistical behavior of quantum turbulence. Using a set of vibrating wires as a turbulence generator and vortex detectors, we measured the distribution of times of flights between the generator and the detectors for emission directions parallel and perpendicular to the vibration direction of the generator wire. We find that the times exhibit a single exponential distribution for emissions in both directions, indicating temporally random emission of vortex rings with a single mean emission rate. When a limit is set on the detection diameter of the vortex rings, the detection times exhibit a double exponential distribution for the perpendicular direction for ring diameters above 10 $$\upmu \hbox {m}$$ , suggesting that large vortex rings reach the detector with a high rate emission at later times. In the parallel emission direction, the emission rate during an equilibrium state exhibits a power law behavior with a minimum diameter of detected vortex rings, implying that a vortex tangle generated by an oscillating object has a self-similar structure of vortex lines.

Run length distribution of dimerized kinesin-3 molecular motors: comparison with dimeric kinesin-1

Kinesin-3 and kinesin-1 molecular motors are two families of the kinesin superfamily. It has been experimentally revealed that in monomeric state kinesin-3 is inactive in motility and cargo-mediated dimerization results in superprocessive motion, with an average run length being more than 10-fold longer than that of kinesin-1. In contrast to kinesin-1 showing normally single-exponential distribution of run lengths, dimerized kinesin-3 shows puzzlingly Gaussian distribution of run lengths. Here, based on our proposed model, we studied computationally the dynamics of kinesin-3 and compared with that of kinesin-1, explaining quantitatively the available experimental data and revealing the origin of superprocessivity and Gaussian run length distribution of kinesin-3. Moreover, predicted results are provided on ATP-concentration dependence of run length distribution and force dependence of mean run length and dissociation rate of kinesin-3.

Vortex Emission from Quantum Turbulence Generated by Vibrating Wire in Superfluid $$^4\hbox {He}$$

To investigate the formation of quantum turbulence in superfluid $$^4\hbox {He}$$ , we have studied the vortex emission from a turbulence region generated by a vibrating wire. The time of flight of vortex rings emitted from a generator to a detector exhibits a single exponential distribution, suggesting that vortex detection is a Poisson process. This means that the detector observes vortex rings at irregular intervals with a mean interval time. Therefore, the single exponential distribution suggests a constant emission rate of vortex rings during turbulence generation, which is proportional to the mean detection rate. By setting a limit on the diameter of detected vortex rings, we find that the emission rate exhibits a power law relationship with the ring diameter. Since the diameter of a vortex ring is related to the vortex line spacing within turbulence when reconnection occurs, the distribution of vortex line spacings is considered to be reflected in the size distribution of the emission rate. Therefore, the power law dependence of the emission rate suggests that the vortex lines within turbulence have a self-similar fractal structure.

Generalization of electron avalanche statistics based on negative binomial distribution—multielectron initiation and Gaussian approximation

The electron avalanche statistics was mainly developed in the approximation of a single electron initiation, following Furry and exponential distributions. The electron avalanche statistics is now generalized relying on the multielectron initiation and the negative binomial distribution (NBD). In an extreme case, for the probability of finding n electrons in an avalanche, the following approximations are applied: a) a Furry/exponential distribution for a single initiating electron (k=1); b) a Gaussian distribution for the multielectron initiation (k ≫ 1). The multielectron initiation leads to a deviation of electron number distributions from exponential ones (i.e. an underpopulation at low electron numbers). In this case, the avalanche statistics is successfully described by NBDs. Statistical models based on NBDs are supported by a Monte Carlo simulation of the avalanche size distributions.

Reliability estimation of stress–strength model using finite mixture distributions under progressively interval censoring

This paper considers the reliability estimation of the stress–strength model based on progressively Type-I interval censored data, where the random stress variable follows a Lindley distribution and the random strength variable follows a finite mixture of exponential distributions. The maximum likelihood estimation and 95% confidence interval estimation of the stress–strength reliability are deduced by using EM algorithm and Bootstrap sampling, respectively. The Bayesian estimation and 95% highest posterior density credible interval of the stress–strength reliability under squared error loss function are obtained by using the Metropolis–Hastings within Gibbs algorithm. To test the homogeneity of the finite mixture distributions, the D -test statistic is introduced. Then, we use the D -test statistic to test the homogeneity of a real data, compare the finite mixture exponential distributions with a single exponential distribution by using the Akaike information criterion (AIC) values, and analyze this data using the proposed methodology. Finally, Monte Carlo simulations are performed for illustrative purpose. • The stress–strength model applied to the progressively Type-I interval censoring. • The finite mixture distributions are applied to describe the strength variables. • The reliability is estimated by EM algorithm and MH within Gibbs algorithm. • The homogeneity of the mixture distribution is tested by the D-test statistic.

Derivation of persistent time for anisotropic migration of cells**Project supported by the National Natural Science Foundation of China (Grant Nos. 31370830, 11675134, 11474345, and 11604030), the State Key Development Program for Basic Research of China (Grant No. 2013CB837200), the 111 Project, China (Grant No. B16029), and the China Postdoctoral Science Foundation (Grant No. 2016M602071).

Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in which two different and independent persistent times are assumed for cell migrations in the x- and y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function (VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.

Response-bout analysis of interresponse times in variable-ratio and variable-interval schedules

The purpose of this study was to analyze the response pattern difference between variable-ratio (VR) and variable-interval (VI) schedules of reinforcement by modeling interresponse time distributions of rats’ lever presses. All eight rats showed higher response rates under VR 30 than under inter-reinforcement intervals yoked VI. The 30 models consisting of single Exponential (with and without the lower limit on interresponse times), Weibull, Normal, Log-Normal or Gamma distributions, all possible two component combinations of those, and 3 and 4 component models consisting of Weibull, Normal, Log-Normal, or Gamma distribution combinations were compared. The 4 component Log-Normal model was the best in terms of the Akaike information criterion and visual inspection of fitting outcome. Parameter estimates for the L4 model showed that the VR-VI response rate difference is due to a difference in short interresponse times or within bout responses. This results suggests that the VR-VI response rate difference is not an indication of a difference in the overall tendency to respond but it is rather a difference in terms of what types of response patterns are engendered between the two schedules.

Effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure.

Using 3D Langevin dynamics simulations, we investigate the effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure. We show that the chain closure in good solvents is a purely diffusive process. By extrapolation to zero solvent viscosity, we find that the internal friction of a chain plays a non-ignorable role in the dynamics of the chain closure. When the solvent quality changes from good to poor, the mean closure time τc decreases by about 1 order of magnitude for the chain length 20 ≤ N ≤ 100. Furthermore, τc has a minimum as a function of the solvent quality. With increasing the chain length N, the minimum of τc occurs at a better solvent. Finally, the single exponential distributions of the closure time in poor solvents suggest that the negative excluded volume of segments does not alter the nearly Poisson statistical characteristics of the process of the chain closure.

THE SINS/zC-SINF SURVEY OFz∼ 2 GALAXY KINEMATICS: EVIDENCE FOR GRAVITATIONAL QUENCHING

As part of the SINS/zC-SINF surveys of high-z galaxy kinematics, we derive the radial distributions of H-alpha surface brightness, stellar mass surface density, and dynamical mass at ~2 kpc resolution in 19 z~2 star-forming disks with deep SINFONI AO spectroscopy at the ESO VLT. From these data we infer the radial distribution of the Toomre Q-parameter for these main-sequence star forming galaxies (SFGs), covering almost two decades of stellar mass (10^9.6 to 10^11.5 solar masses). In more than half of our SFGs, the H-alpha distributions cannot be fit by a centrally peaked distribution, such as an exponential, but are better described by a ring, or the combination of a ring and an exponential. At the same time the kinematic data indicate the presence of a mass distribution more centrally concentrated than a single exponential distribution for 5 of the 19 galaxies. The resulting Q-distributions are centrally peaked for all, and significantly exceed unity there for three quarters of the SFGs. The occurrence of H-alpha rings and of large nuclear Q-values is strongly correlated, and is more common for the more massive SFGs. While our sample is small and there remain substantial uncertainties and caveats, our observations are consistent with a scenario in which cloud fragmentation and global star formation are secularly suppressed in gas rich high-z disks from the inside out, as the central stellar mass density of the disks grows.

Charge dynamics and its energetic features in polymeric materials

Modeling charge transport and linking charge dynamics with dissipative processes responsible for electrical ageing are a challenging objective for developing a mature approach in insulation design. Such an approach is exemplified here for polyethylene-based materials by introducing two models describing bipolar Space Charge Limited Current in transient and steady states. They rely on two classical descriptions of the distribution function of the energy levels of trap states -single trapping level or exponential distribution. Their predictions are discussed as regards the experimental behavior. They notably highlight the importance of recombination processes in explaining the sigmoidal shape of the steady-state current-voltage characteristic. Also, bipolar charge transport seems to be a necessary factor for the observed features of oscillatory charge packets. The energetic features of charge dynamics is reviewed with particular emphasis on recombination phenomena because the latter promote electronically excited states that are chemically reactive and could be involved in ageing reaction. The relationship between charge recombination and electroluminescence is highlighted through experiments and simulation. The spectral analysis of the emitted light advocates the existence of massive chemical/physical degradation in the electrical regime where recombination is a major factor of the Space Charge Limited Current (SCLC).

Generation and detection of vortex rings in superfluid 4He at very low temperature

Motions of vortices are fundamental characteristics of quantum turbulence. These motions are expected to be governed only by quantized circulations in superfluids at the zero temperature limit. In the present paper, we report the motions of vortex rings emitted from a quantum turbulence in superfluid 4He, by detecting vortex rings using a vortex-free vibrating wire as a detector. The time of flights of vortex rings are distributed, because vortex rings are emitted in any direction from a turbulent region and the detector can respond only to a reachable vortex ring. By measuring time-of-flights many times, we find an exponential distribution of time-of-flights with a non-detection period, which corresponds to the fastest time of flights of vortex rings. For a larger generation power of vortex rings, a distribution of time-of-flights still shows a single exponential distribution, but a non-detection period becomes shorter. This result implies that sizes of emitted vortex rings are distributed dependently on the generation power of turbulence. The observed exponential distributions are confirmed by numerical simulations of the dynamics of vortex rings.

Turbulent particle transport in streams: Can exponential settling be reconciled with fluid mechanics?

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection–diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances.