scholarly journals Derivation of Gaussian Probability Distribution: A New Approach

2020 ◽  
Vol 11 (06) ◽  
pp. 436-446
Author(s):  
A. T. Adeniran ◽  
O. Faweya ◽  
T. O. Ogunlade ◽  
K. O. Balogun
2004 ◽  
Vol 18 (06) ◽  
pp. 827-840
Author(s):  
CHIH-CHUN CHIEN ◽  
NING-NING PANG ◽  
WEN-JER TZENG

We study the restricted solid-on-solid (RSOS) model by grouping consecutive sites into local configurations and obtain the master equations of the probability distribution of these local configurations in closed forms. The obtained solutions to these equations fit very well with those from direct computer simulation of the RSOS model. To demonstrate the effectiveness of this new approach for studying interfacial phenomena, we then calculate the correlation functions and even scaling exponents based on this obtained probability distribution of local configurations. The results are also consistent very well with those obtained from the KPZ equation or direct simulation of the RSOS model.


2020 ◽  
Vol 36 (15) ◽  
pp. 4323-4330 ◽  
Author(s):  
Cong Sun ◽  
Zhihao Yang ◽  
Leilei Su ◽  
Lei Wang ◽  
Yin Zhang ◽  
...  

Abstract Motivation The biomedical literature contains a wealth of chemical–protein interactions (CPIs). Automatically extracting CPIs described in biomedical literature is essential for drug discovery, precision medicine, as well as basic biomedical research. Most existing methods focus only on the sentence sequence to identify these CPIs. However, the local structure of sentences and external biomedical knowledge also contain valuable information. Effective use of such information may improve the performance of CPI extraction. Results In this article, we propose a novel neural network-based approach to improve CPI extraction. Specifically, the approach first employs BERT to generate high-quality contextual representations of the title sequence, instance sequence and knowledge sequence. Then, the Gaussian probability distribution is introduced to capture the local structure of the instance. Meanwhile, the attention mechanism is applied to fuse the title information and biomedical knowledge, respectively. Finally, the related representations are concatenated and fed into the softmax function to extract CPIs. We evaluate our proposed model on the CHEMPROT corpus. Our proposed model is superior in performance as compared with other state-of-the-art models. The experimental results show that the Gaussian probability distribution and external knowledge are complementary to each other. Integrating them can effectively improve the CPI extraction performance. Furthermore, the Gaussian probability distribution can effectively improve the extraction performance of sentences with overlapping relations in biomedical relation extraction tasks. Availability and implementation Data and code are available at https://github.com/CongSun-dlut/CPI_extraction. Supplementary information Supplementary data are available at Bioinformatics online.


2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xingwang Huang ◽  
Chaopeng Li ◽  
Yunming Pu ◽  
Bingyan He

Quantum-behaved bat algorithm with mean best position directed (QMBA) is a novel variant of bat algorithm (BA) with good performance. However, the QMBA algorithm generates all stochastic coefficients with uniform probability distribution, which can only provide a relatively small search range, so it still faces a certain degree of premature convergence. In order to help bats escape from the local optimum, this article proposes a novel Gaussian quantum bat algorithm with mean best position directed (GQMBA), which applies Gaussian probability distribution to generate random number sequences. Applying Gaussian distribution instead of uniform distribution to generate random coefficients in GQMBA is an effective technique to promote the performance in avoiding premature convergence. In this article, the combination of QMBA and Gaussian probability distribution is applied to solve the numerical function optimization problem. Nineteen benchmark functions are employed and compared with other algorithms to evaluate the accuracy and performance of GQMBA. The experimental results show that, in most cases, the proposed GQMBA algorithm can provide better search performance.


1984 ◽  
Vol 1 (19) ◽  
pp. 35 ◽  
Author(s):  
Michel K. Ochi ◽  
Wei-Chi Wang

This paper presents the results of a study on non-Gaussian characteristic of coastal waves. From the results of the statistical analysis of more than 500 records obtained in the growing stage of the storm, the parameters involved in the non-Gaussian probability distribution which are significant for predicting wave characteristics are clarified, and these parameters are expressed as a function of water depth and sea severity. The limiting sea severity below which the wind-generated coastal waves are considered to be Gaussian is obtained for a given water depth.


2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Kamal Barghout

A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by 2 that follows a recurrent pattern of the form x,1,x,1…, where x represents divisions by 2 more than once. The sequence presents a probability of 50:50 of division by 2 more than once as opposed to division by 2 once over the even natural numbers. The sequence also gives the same 50:50 probability of consecutive Collatz even elements when counted for division by 2 more than once as opposed to division by 2 once and a ratio of 3:1. Considering Collatz function producing random numbers and over sufficient number of iterations, this probability distribution produces numbers in descending order that lead to the convergence of the Collatz function to 1, assuming that the only cycle of the function is 1-4-2-1.


2000 ◽  
Vol 661 ◽  
Author(s):  
D. E. Hanson

ABSTRACTWe present a mesoscale model that describes the tensile stress of silica-filled polydimethylsiloxane (PDMS) under elongation. Atomistic simulations of a single chain of PDMS, interacting with itself and/or a hydroxylated silica surface provide estimates of the microscopic forces required to stretch or uncoil a chain of PDMS, or detach it from a silica surface Using these results, we develop a mesoscale, inter-particle strength model for uncrosslinked, silica-filled PDMS. The strength model includes these atomistic forces, as determined from the simulations, a small entropic component, and a Gaussian probability distribution to describe the distribution of chain lengths of PDMS strands connecting two silica particles and the chain lengths in the free ends. We obtain an analytic stress/strain expression whose predictions agree with experiment.


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