Bernoulli Parameter Research Articles

Isolated Random Forest Assisted Spatio-Temporal Ant Colony Evolutionary Algorithm for Cell Tracking in Time-Lapse Sequences.

Multi-Object tracking in real world environments is a tough problem, especially for cell morphogenesis with division. Most cell tracking methods are hard to achieve reliable mitosis detection, efficient inter-frame matching, and accurate state estimation simultaneously within a unified tracking framework. In this paper, we propose a novel unified framework that leverages a spatio-temporal ant colony evolutionary algorithm to track cells amidst mitosis under measurement uncertainty. Each Bernoulli ant colony representing a migrating cell is able to capture the occurrence of mitosis through the proposed Isolation Random Forest (IRF)-assisted temporal mitosis detection algorithm with the assumption that mitotic cells exhibit unique spatio-temporal features different from non-mitotic ones. Guided by prediction of a division event, multiple ant colonies evolve between consecutive frames according to an augmented assignment matrix solved by the extended Hungarian method. To handle dense cell populations, an efficient group partition between cells and measurements is exploited, which enables multiple assignment tasks to be executed in parallel with a reduction in matrix dimension. After inter-frame traversing, the ant colony transitions to a foraging stage in which it begins approximating the Bernoulli parameter to estimate cell state by iteratively updating its pheromone field. Experiments on multi-cell tracking in the presence of cell mitosis and morphological changes are conducted, and the results demonstrate that the proposed method outperforms state-of-the-art approaches, striking a balance between accuracy and computational efficiency.

Comparison of magnetized thick disks around black holes and boson stars

Boson stars are considered as promising candidates for black hole mimickers. Similar to other compact objects they can form accretion disks around them. The properties of these disks could possibly distinguish them from other compact objects like black holes in future observations. Retrograde thick disks around boson stars and the influence of strong magnetic fields on them were already studied and it was shown that they can harbor very distinct features compared to black hole disks. However, the case of prograde thick disks is mostly unexplored, since they may appear much more similar to black hole disks. In this work we will investigate similarities and differences regarding prograde thick disks around non-selfinteracting rotating boson stars and rotating black holes. We assume thereby a polytropic equation of state and a constant specific angular momentum distribution of the disks. We classify the various conceivable boson star and black hole solutions by a dimensionless spin parameter a and compare their corresponding disk solutions. The influence of toroidal magnetic fields on the disks is analyzed by selected disk properties, as the rest-mass density distribution and the Bernoulli parameter. Disk solutions are characterized by their degree of magnetization represented by the magnetization parameter βmc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{mc}$$\\end{document}. We found that strong magnetic fields can strengthen the differences of disk solutions or oppositely even lead to a correlation in disk properties, depending on the spin parameter of the boson star and black hole solutions. We identify the vertical thickness of the boson star disks as the main differentiating factor, since for most solutions the vertical density distribution is far more outreaching for boson star disks compared to black hole disks.

Global transonic solution of hot accretion flow with thermal conduction

ABSTRACT We examine the effect of thermal conduction on the low-angular momentum hot accretion flow (HAF) around non-rotating black holes accreting mass at very low rate. While doing so, we adopt the conductive heat flux in the saturated form, and solve the set of dynamical equations corresponding to a steady, axisymmetric, viscous, advective accretion flow using numerical methods. We study the dynamical and thermodynamical properties of accreting matter in terms of the input parameters, namely energy (ε0), angular momentum (ℓ0), viscosity parameter (α), and saturation constant (Φs) regulating the effect of thermal conduction. We find that Φs plays a pivotal role in deciding the transonic properties of the global accretion solutions. In general, when Φs is increased, the critical point (rc) is receded away from the black hole, and flow variables are altered particularly in the outer part of the disc. To quantify the physically acceptable range of Φs, we compare the global transonic solutions with the self-similar solutions, and observe that the maximum saturation constant ($\Phi ^{\rm max}_{\rm s}$) estimated from the global solutions exceeds the saturated thermal conduction limit (Φsc) derived from the self-similar formalism. Moreover, we calculate the correlation between α and $\Phi ^{\rm max}_{\rm s}$ and find ample disagreement between global solutions and self-similar solutions. Further, using the global flow variables, we compute the Bernoulli parameter (Be) which remains positive all throughout the disc, although flow becomes loosely unbound for higher Φs. Finally, we indicate the relevance of this work in the astrophysical context in explaining the possibility of mass-loss/outflows from the unbound disc.

ALPHA: Audit that learns from previously hand-audited ballots

A risk-limiting election audit (RLA) offers a statistical guarantee: if the reported electoral outcome is incorrect, the audit has a known maximum chance (the risk limit) of not correcting it before it becomes final. BRAVO (Lindeman, Stark and Yates (In Proceedings of the 2011 Electronic Voting Technology Workshop/Workshop on Trustworthy Elections (EVT/WOTE’11) (2012) USENIX)), based on Wald’s sequential probability ratio test for the Bernoulli parameter, is the simplest and most widely tried method for RLAs, but it has limitations. It cannot accommodate sampling without replacement or stratified sampling which can improve efficiency and are sometimes required by law. It applies only to ballot-polling audits which are less efficient than comparison audits. It applies to plurality, majority, supermajority, proportional representation, and instant-runoff voting (IRV, using RAIRE (Blom, Stuckey and Teague (In Electronic Voting (2018) 17–34 Springer))) but not to other social choice functions for which there are RLA methods. And while BRAVO has the smallest expected sample size among sequentially valid ballot-polling-with-replacement methods when the reported vote shares are exactly correct, it can require arbitrarily large samples when the reported reported winner(s) really won but the reported vote shares are incorrect. ALPHA is a simple generalization of BRAVO that: (i) works for sampling with and without replacement, with and without weights, with and without stratification, and for Bernoulli sampling; (ii) works not only for ballot polling but also for ballot-level comparison, batch polling, and batch-level comparison audits; (iii) works for all social choice functions covered by SHANGRLA (Stark (In Financial Cryptography and Data Security (2020) Springer)), including approval voting, STAR-Voting, proportional representation schemes, such as D’Hondt and Hamilton, IRV, Borda count, and all scoring rules, and (iv) in situations where both ALPHA and BRAVO apply, requires smaller samples than BRAVO when the reported vote shares are wrong but the outcome is correct—five orders of magnitude in some examples. ALPHA includes the family of betting martingale tests in RiLACS (Waudby-Smith, Stark and Ramdas (In Electronic Voting. E-Vote-ID 2021 (2021) Springer)) with a different betting strategy parametrized as an estimator of the population mean and explicit flexibility to accommodate sampling weights and population bounds that change with each draw. A Python implementation is provided.

A new grey intelligent prediction algorithm with multiobjective correction strategy

As a combination of the differential equation prediction model and intelligent optimization algorithm, the grey intelligent prediction algorithm has attracted increasing attention due to its outstanding performance in small-sample environments. However, most studies focus only on the improvement of algorithm performance, with little regard to the uniformity, ill-condition and overfitting of the algorithm. To promote the development of this field, we develop a new grey intelligent prediction algorithm with multiobjective correction strategy based on the new weakened accumulation grey optimization model and the multiobjective grey wolf optimizer. In this new prediction algorithm, the new weakened accumulation operation is utilized to enhance the predictive ability of the algorithm and mitigate the ill-condition of the system, the Bernoulli parameter and a discretization technique are used to activate the uniformity and unbiasedness of the algorithm, respectively, and the multiobjective grey wolf optimizer is employed to alleviate the overfitting of the system. Compared with the previous grey intelligent prediction models, the new prediction algorithm is more perfect and reasonable. Taking two energy datasets as research cases, the evaluation results of a system consisting of six evaluation metrics and the Diebold-Mariano test show that the proposed model outperforms the other six comparative models in terms of prediction performance and stability, which confirms the feasibility and validity of the algorithm.

A New Conformable Fractional-Order Time-Delay Grey Bernoulli Model with the Arithmetic Optimization Algorithm and Its Application in Rural Regional Economy

To further promote the development of the grey system theory, this paper develops a novel conformable fractional-order grey Bernoulli model with a time-delay effect, namely, the CFTDNGBM (1, 1) model. In addition, the arithmetic optimization algorithm (AOA) is incorporated into the system of the model to solve the hyperparameters existing in the model. Compared with the previous grey prediction models, the CFTDNGBM (1, 1) model with a conformable fractional-order accumulation operation (CFAO), time-delay factor, and Bernoulli parameter has stronger compatibility in structure. The proposed model and its nine competitive models with excellent performance are used to predict and analyze the consumption level and per capita consumption expenditure of rural residents in China to verify the feasibility of the proposed method. The case results show that in both cases, the seven descriptive indicators of the CFTDNGBM (1, 1) model are higher than those of its competing models. Therefore, the CFTDNGBM (1, 1) model has a certain application value.

Exact Inference in a Tetranomial Distribution

Sequential sampling plans for unbiased estimation of the Bernoulli parameter ‘p’ and its functions have been studied almost 70 years back. An extension of the idea to parametric function estimation in a tetranomial distribution has been considered in this paper. The cell probabilities are taken to be p 2, q 2, r 2 and 2(pq+pr+qr), satisfying p, q, r > 0, p +q +r = 1. Some illustrative examples have been studied to demonstrate the underlying concepts and the computational procedure. The emphasis is on unbiased estimation in the exact sense which makes it difficult and challenging.

Large-scale outflow structure and radiation properties of super-Eddington flow: Dependence on the accretion rates

Abstract In order to evaluate the impacts made by super-Eddington accretors on their environments precisely, it is essential to guarantee a large enough simulation box and long computational time to avoid any artefacts from numerical settings as much as possible. In this paper, we carry out axisymmetric two-dimensional radiation hydrodynamic simulations around a 10 M⊙ black hole in large simulation boxes and study the large-scale outflow structure and radiation properties of super-Eddington accretion flow for a variety of black hole accretion rates, ${\dot{M}}_{\,\,\rm BH} = (110\!-\!380)L_{\rm Edd}/c^{\,\,2}$ (with LEdd being the Eddington luminosity and c being the speed of light). The Keplerian radius of the inflow material, at which centrifugal force balances with gravitational force, is fixed to 2430 Schwarzschild radii. We find that the mechanical luminosity grows more rapidly than the radiation luminosity with an increase of ${\dot{M}}_{\,\,\rm BH}$. When seen from a nearly face-on direction, especially, the isotropic mechanical luminosity grows in proportion to ${\dot{M}}_{\,\,\rm BH}^{\,\,2.7}$, while the total mechanical luminosity is proportional to ${\dot{M}}_{\,\,\rm BH}^{\,\,1.7}$. The reason for the former is that the higher ${\dot{M}}_{\,\,\rm BH}$ is, the more vertically inflated the disk surface becomes, which makes radiation fields more confined in the region around the rotation axis, thereby strongly accelerating outflowing gas. The outflow is classified into pure outflow and failed outflow, depending on whether the outflowing gas can reach the outer boundary of the simulation box or not. The fraction of the failed outflow decreases with a decrease of ${\dot{M}}_{\,\,\rm BH}$. We analyze physical quantities along each outflow trajectory, finding that the Bernoulli parameter (Be) is not a good indicator to discriminate between pure and failed outflows, since it is never constant because of continuous acceleration by radiation-pressure force. Pure outflow can arise, even if Be < 0 at the launching point.

A Majorization-Minimization Algorithm for Nonnegative Binary Matrix Factorization

This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model's expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability.

On the Consistency of Maximum Likelihood Estimators for Causal Network Identification

We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph indicate that the state of the node at a particular time instant is influenced by the states of the corresponding parental nodes in the previous time instant. The associated edge weights determine the corresponding level of influence from each parental node. In the simplest setup, the Bernoulli parameter of a particular node's state variable is a convex combination of the parental node states in the previous time instant and an additional Bernoulli noise random variable. This letter focuses on the problem of edge weight identification using Maximum Likelihood (ML) estimation and proves that the ML estimator is strongly consistent for two variants of the BAR model. We additionally derive closed-form estimators for the aforementioned two variants and prove their strong consistency.

Large-scale Dynamics of Winds Originating from Black Hole Accretion Flows. I. Hydrodynamics

Abstract Winds from black hole accretion flows are ubiquitous. Previous works mainly focus on the launching of wind on the accretion flow scale. It still remains unclear how far the winds can propagate outward and what their large-scale dynamics is. As the first paper of this series, we study the large-scale dynamics of thermal wind beyond accretion scales via analytical and numerical methods. Boundary conditions, which are crucial to our problem, are analyzed and presented based on small-scale simulations combined with observations of winds. Both black hole and galaxy potential are taken into account. For winds originating from hot accretion flows, we find that the wind can reach large scales. The radial profiles of velocity, density, and temperature can be approximated by and , where v r0, ρ 0, and T 0 are the velocity, density, and temperature of winds at the boundary , and γ is the polytropic index. During the outward propagation, the enthalpy and rotational energy compensate for the increase of gravitational potential. For thin disks, we find that because the Bernoulli parameter is smaller, winds cannot propagate as far as the hot winds, but stop at a certain radius where the Bernoulli parameter is equal to the potential energy. Before the winds stop, the profiles of dynamical quantities can also be approximated by the above relations. In this case, the rotational energy alone compensates for the increase in potential energy.

Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, in this paper, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of $p$ and up to 1.86 dB for the estimation of $\log p$ .

An Automated Cell Tracking Approach With Multi-Bernoulli Filtering and Ant Colony Labor Division.

In this article, we take as inspiration the labor division into scouts and workers in an ant colony and propose a novel approach for automated cell tracking in the framework of multi-Bernoulli random finite sets. To approximate the Bernoulli parameter sets, we first define an existence probability of an ant colony as well as its discrete density distribution. During foraging, the behavior of scouts is modeled as a chaotic movement to produce a set of potential candidates. Afterwards, a group of workers, i.e., a worker ant colony, is recruited for each candidate, which then embark on gathering heuristic information in a self-organized way. Finally, the pheromone field is formed by the corresponding worker ant colony, from which the Bernoulli parameter is derived and the state of the cell is estimated accordingly to be associated with the existing tracks. Performance comparisons with other previous approaches are conducted on both simulated and real cell image sequences and show the superiority of this algorithm.

Effective aspects of Bernoulli randomness

AbstractIn this paper, we study Bernoulli random sequences, i.e. sequences that are Martin-Löf random with respect to a Bernoulli measure $\mu _p$ for some $p\in [0,1]$, where we allow for the possibility that $p$ is noncomputable. We focus in particular on the case in which the underlying Bernoulli parameter $p$ is proper (i.e. Martin-Löf random with respect to some computable measure). We show for every Bernoulli parameter $p$, if there is a sequence that is both proper and Martin-Löf random with respect to $\mu _p$, then $p$ itself must be proper, and explore further consequences of this result. We also study the Turing degrees of Bernoulli random sequences, showing, for instance, that the Turing degrees containing a Bernoulli random sequence do not coincide with the Turing degrees containing a Martin-Löf random sequence. Lastly, we consider several possible approaches to characterizing blind Bernoulli randomness, where the corresponding Martin-Löf tests do not have access to the Bernoulli parameter $p$, and show that these fail to characterize blind Bernoulli randomness.

Hot Accretion Flow in Two-Dimensional Spherical Coordinates: Considering Pressure Anisotropy and Magnetic Field

For systems with extremely low accretion rate, such as Galactic Center Sgr A* and M87 galaxy, the ion collisional mean free path can be considerably larger than its Larmor radius. In this case, the gas pressure is anisotropic to magnetic field lines. In this paper, we pay attention to how the properties of outflow change with the strength of anisotropic pressure and the magnetic field. We use an anisotropic viscosity to model the anisotropic pressure. We solve the two-dimensional magnetohydrodynamic (MHD) equations in spherical coordinates and assume that the accretion flow is radially self-similar. We find that the work done by anisotropic pressure can heat the accretion flow. The gas temperature is heightened when anisotropic stress is included. The outflow velocity increases with the enhancement of strength of the anisotropic force. The Bernoulli parameter does not change much when anisotropic pressure is involved. However, we find that the energy flux of outflow can be increased by a factor of 20 in the presence of anisotropic stress. We find strong wind (the mass outflow is about 70% of the mass inflow rate) is formed when a relatively strong magnetic field is present. Outflows from an active galactic nucleus can interact with gas in its host galaxies. Our result predicts that outflow feedback effects can be enhanced significantly when anisotropic pressure and a relatively powerful magnetic field is considered.

Effect of plasma composition on magnetized outflows

In this paper, we study magnetized winds described by variable adiabatic index equation of state in Paczyński & Wiita pseudo-Newtonian potential. We identify the flow solutions with the parameter space of the flow. We also confirm that the physical wind solution is the one which passes through the slow, Alfvén, and fast critical points. We study the dependence of the wind solution on the Bernoulli parameter E and the total angular momentum L. The adiabatic index, which is a function of temperature and composition, was found to be variable in all the outflow solutions. For the same values of the Bernoulli parameter and the total angular momentum, a wind in strong gravity is more accelerated, compared to a wind in Newtonian gravity. We show that flow variables such as the radial and azimuthal velocity components and temperature all depend on the composition of the flow. Unlike the outflow solutions in hydrodynamic regime, the terminal speed of a magnetically driven wind also depends on the composition parameter.

Self-Similar Solution of Hot Accretion Flow with Anisotropic Pressure

For the accretion flow in extremely low-luminosity active galactic nuclei, such as our Galactic center (Sgr A*) and M 87, the collisional mean-free path of ions may be much larger than its gyroradius. In this case, the pressure parallel to the magnetic field is different from that perpendicular to the field; therefore, the pressure is anisotropic. We study the effects of anisotropic pressure on the dynamics of accretion flow by assuming the flow is radially self-similar. We find that in the case where the outflow is present, the radial and rotational velocities, the sound speed, and the Bernoulli parameter of the accretion flow are all increased when the anisotropic pressure is taken into account. This result suggests that it becomes easier for the accretion flow to generate outflow in the presence of anisotropic pressure.

Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model.

Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of situations routinely encountered in applications. More recently, there has been growing interest in using group testing to simultaneously estimate the joint probabilities of two correlated traits using a multinomial model. Unfortunately, basic estimation results, such as the maximum likelihood estimator (MLE), have not been adequately addressed in the literature for such cases. In this paper, we show that finding the MLE for this problem is equivalent to maximizing a multinomial likelihood with a restricted parameter space. A solution using the EM algorithm is presented which is guaranteed to converge to the global maximizer, even on the boundary of the parameter space. Two additional closed form estimators are presented with the goal of minimizing the bias and/or mean square error. The methods are illustrated by considering an application to the joint estimation of transmission prevalence for two strains of the Potato virus Y by the aphid Myzus persicae.

Quantized Output Feedback Control for Stochastic Semi-Markov Jump Systems With Unreliable Links

This brief is concerned with the problem of quantized output feedback (OF) control for semi-Markov jump systems subject to unreliable links. The jump among the operation modes is subject to the semi-Markov process, where the transition probabilities depend not only on the next system mode but the sojourn time at current mode as well. The communication link is considered to be unreliable, in which the packet dropouts described by a stochastic Bernoulli parameter and signal quantization are taken into account simultaneously. The purpose is to synthesize an OF controller, which ensures that the closed-loop system is mean-square $\sigma $ -error stable. Some sojourn time-dependent criteria are established for the realizability of admissible OF controller. With the help of those criteria, the controller gains could be obtained by finding a solution to a convex optimization problem. Finally, both a numerical example and a PWM-driven boost converter are presented to confirm the availability and feasibility of the proposed approach.

Supernova-driven winds in simulated dwarf galaxies

We investigate galactic winds driven by supernova (SN) explosions in an isolated dwarf galaxy using high-resolution (particle mass |$m_{\rm gas} = 1\, {\rm M_\odot}$|⁠, number of neighbour Nngb = 100) smoothed-particle hydrodynamics simulations that include non-equilibrium cooling and chemistry, individual star formation, stellar feedback, and metal enrichment. Clustered SNe lead to the formation of superbubbles which break out of the disc and vent out hot gas, launching the winds. We find much weaker winds than what cosmological simulations typically adopt at this mass scale. At the virial radius, the time-averaged loading factors of mass, momentum, and energy are 3, 1, and 0.05, respectively, and the metal enrichment factor is 1.5. Winds that escape the halo consist of two populations that differ in their launching temperatures. Hot gas acquires enough kinetic energy to escape when launched while warm gas does not. However, warm gas can be further accelerated by the ram pressure of the subsequently launched hot gas and eventually escape. The strong interactions between different temperature phases highlight the caveat of extrapolating properties of warm gas to large distances based on its local conditions (e.g. the Bernoulli parameter). Our convergence study finds that wind properties converge when the cooling masses of individual SNe are resolved, which corresponds to |$m_{\rm gas}=5 \, {\rm M_\odot}$| with an injection mass of |$500 \, {\rm M_\odot}$|⁠. The winds weaken dramatically once the SNe become unresolved. We demonstrate that injecting the terminal momentum of SNe, a popular sub-grid model in the literature fails to capture SN winds irrespective of the inclusion of residual thermal energy.