approximate probability
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Author(s):  
O. Kazemi ◽  
A. Pourdarvish ◽  
J. Sadeghi

We study the connected components of the stochastic geometry model on Poisson points which is obtained by connecting points with a probability that depends on their relative position. Equivalently, we investigate the random clusters of the ran- dom connection model defined on the points of a Poisson process in d-dimensional space where the links are added with a particular probability function. We use the thermodynamicrelationsbetweenfreeenergy,entropyandinternalenergytofindthe functions of the cluster size distribution in the statistical mechanics of extensive and non-extensive. By comparing these obtained functions with the probability function predicted by Penrose, we provide a suitable approximate probability function. More- over, we relate this stochastic geometry model to the physics literature by showing how the fluctuations of the thermodynamic quantities of this model correspond to other models when a phase transition (10.1002/mma.6965, 2020) occurs. Also, we obtain the critical point using a new analytical method.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Maoke Miao ◽  
Weiwei Cai ◽  
Xiaofeng Li

In this paper, the challenges of parameter estimation for the Gamma-Gamma turbulence channels with generalized pointing errors are addressed. The Kolmogorov-Smirnov goodness-of-fit statistical test results indicate that the approximate probability density function obtained by the saddlepoint approximation (SAP) method provides a better approximation for a larger value w z , and this means that the proposed method is more efficient for the FSO links over long distances when the transmit divergence angle at the transmitter side is fixed. Also, an additional parameter k needs to be estimated in addition to the shaping parameters α and β under the SAP method. An estimation scheme for the shaping parameters is proposed based on the SAP method. The performance of the proposed estimation is investigated by using the mean square error (MSE) and normalized mean square error (NMSE). The results indicate the proposed estimator exhibits satisfactory performance in both noiseless and noisy environments. The effects of the receiver aperture on the estimation performance are also discussed.


2021 ◽  
Author(s):  
Zachary Smith ◽  
Pratyush Tiwary

Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain all thermodynamic information, but they prove increasingly difficult to compute and interpret as the dimensionality increases. Here, inspired by tools in probabilistic graphical modeling, we develop a factor graph trained through belief propagation that helps factorize the joint probability into an approximate tractable form that can be easily visualized and used. We validate the study through the analysis of the conformational dynamics of two small peptides with 5 and 9 residues. Our validations include testing the conditional dependency predictions through an intervention scheme inspired by Judea Pearl. Secondly we directly use the belief propagation based approximate probability distribution as a high-dimensional static bias for enhanced sampling, where we achieve spontaneous back-and-forth motion between metastable states that is up to 350 times faster than unbiased MD. We believe this work opens up useful ways to thinking about and dealing with high-dimensional molecular simulations.


Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 573
Author(s):  
Siniša Tomović ◽  
Milica Knežević ◽  
Miodrag J. Mihaljević

This paper reconsiders a powerful man-in-the-middle attack against Random-HB# and HB# authentication protocols, two prominent representatives of the HB family of protocols, which are built based on the Learning Parity in Noise (LPN) problem. A recent empirical report pointed out that the attack does not meet the claimed precision and complexity. Performing a thorough theoretical and numerical re-evaluation of the attack, in this paper we identify the root cause of the detected problem, which lies in reasoning based on approximate probability distributions of the central attack events, that can not provide the required precision due to the inherent limitations in the use of the Central Limit Theorem for this particular application. We rectify the attack by employing adequate Bayesian reasoning, after establishing the exact distributions of these events, and overcome the mentioned limitations. We further experimentally confirm the correctness of the rectified attack and show that it satisfies the required, targeted accuracy and efficiency, unlike the original attack.


Author(s):  
Shirin Nezampour ◽  
G. G. Hamedani

The problem of characterizing a probability distribution is an important problem which has attracted the attention of many researchers in the recent years. To understand the behavior of the data obtained through a given process, we need to be able to describe this behavior via its approximate probability law. This, however, requires to establish conditions which govern the required probability law. In other words we need to have certain conditions under which we may be able to recover the probability law of the data. So, characterization of a distribution plays an important role in applied sciences, where an investigator is vitally interested to find out if their model follows the selected distribution. In this short note, certain characterizations of three recently introduced discrete distributions are presented to complete, in some way, the works ofHussain(2020), Eliwa et al.(2020) and Hassan et al.(2020).


2020 ◽  
Vol 12 (1) ◽  
pp. 14-29
Author(s):  
László Bognár ◽  
Antal Joós ◽  
Bálint Nagy

AbstractIn this paper the conditions and the findings of a simulation study is presented for assessing the effect size of users’ consciousness to the computer network vulnerability in risky cyber attack situations at a certain business. First a simple model is set up to classify the groups of users according to their skills and awareness then probabilities are assigned to each class describing the likelihood of committing dangerous reactions in case of a cyber attack. To quantify the level of network vulnerability a metric developed in a former work is used. This metric shows the approximate probability of an infection at a given business with well specified parameters according to its location, the type of the attack, the protections used at the business etc. The findings mirror back the expected tendencies namely if the number of conscious user is on the


2020 ◽  
Author(s):  
Philipp Baumeister ◽  
Sebastiano Padovan ◽  
Nicola Tosi ◽  
Grégoire Montavon ◽  
Nadine Nettelmann ◽  
...  

<p>We explore the application of machine-learning, based on mixture density neural networks (MDNs), to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number k<sub>2</sub>. MDNs are a special subset of neural networks, able to predict the parameters of a Gaussian mixture distribution instead of single output values, which enables them to learn and approximate probability distributions. With a dataset of 900,000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, we train an MDN using planetary mass and radius as inputs to the network. We show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet.</p><p>The fluid Love number k<sub>2</sub> bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding k<sub>2</sub> as an input to the MDN significantly decreases the degeneracy of possible interior structures.</p>


Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 480
Author(s):  
Zhi Wang ◽  
Xiao Hu ◽  
Jian Zhang ◽  
Zhao Lv ◽  
Yang Guo

As the Moore’s law era will draw to a close, some domain-specific architectures even non-Von Neumann systems have been presented to keep the progress. This paper proposes novel annealing in memory (AIM) architecture to implement Ising calculation, which is based on Ising model and expected to accelerate solving combinatorial optimization problem. The Ising model has a symmetrical structure and realizes phase transition by symmetry breaking. AIM draws annealing calculation into memory to reduce the cost of information transfer between calculation unit and the memory, improves the ability of parallel processing by enabling each Static Random-Access Memory (SRAM) array to perform calculations. An approximate probability flipping circuit is proposed to avoid the system getting trapped in local optimum. Bit-serial design incurs only an estimated 4.24% area above the SRAM and allows the accuracy to be easily adjusted. Two vision applications are mapped for acceleration and results show that it can speed up Multi-Object Tracking (MOT) by 780× and Multiple People Head Detection (MPHD) by 161× with only 0.0064% and 0.031% energy consumption respectively over approximate algorithms.


Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 43 ◽  
Author(s):  
Alice Le Brigant ◽  
Stéphane Puechmorel

Finding an approximate probability distribution best representing a sample on a measure space is one of the most basic operations in statistics. Many procedures were designed for that purpose when the underlying space is a finite dimensional Euclidean space. In applications, however, such a simple setting may not be adapted and one has to consider data living on a Riemannian manifold. The lack of unique generalizations of the classical distributions, along with theoretical and numerical obstructions require several options to be considered. The present work surveys some possible extensions of well known families of densities to the Riemannian setting, both for parametric and non-parametric estimation.


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