scholarly journals A Stochastic Graphs Semantics for Conditionals

Erkenntnis ◽  
2019 ◽  
Author(s):  
Krzysztof Wójtowicz ◽  
Anna Wójtowicz
Keyword(s):  
Conditional Probability ◽  
General Problem ◽  
Powerful Method ◽  
Mathematical Methods ◽  
Simple Method ◽  
Stochastic Graphs ◽  
Standard Notion ◽  
Stochastic Graph ◽  
Satisfactory Answer

AbstractWe define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional (the global and the local interpretation, and generalizations of them) and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under these two interpretations. It also yields a powerful method of handling more complex issues (such as nested conditionals). The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the (standard) notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.

scholarly journals Finding Maximum Clique in Stochastic Graphs Using Distributed Learning Automata

2015 ◽  
Vol 23 (01) ◽  
pp. 1-31 ◽  
Author(s):  
Alireza Rezvanian ◽  
Mohammad Reza Meybodi
Keyword(s):  
Community Structure ◽  
Dominating Set ◽  
Learning Automata ◽  
Random Variables ◽  
Graph Model ◽  
Maximum Clique ◽  
Distribution Functions ◽  
Maximum Clique Problem ◽  
Stochastic Graphs ◽  
Stochastic Graph

Because of unpredictable, uncertain and time-varying nature of real networks it seems that stochastic graphs, in which weights associated to the edges are random variables, may be a better candidate as a graph model for real world networks. Once the graph model is chosen to be a stochastic graph, every feature of the graph such as path, clique, spanning tree and dominating set, to mention a few, should be treated as a stochastic feature. For example, choosing stochastic graph as the graph model of an online social network and defining community structure in terms of clique, and the associations among the individuals within the community as random variables, the concept of stochastic clique may be used to study community structure properties. In this paper maximum clique in stochastic graph is first defined and then several learning automata-based algorithms are proposed for solving maximum clique problem in stochastic graph where the probability distribution functions of the weights associated with the edges of the graph are unknown. It is shown that by a proper choice of the parameters of the proposed algorithms, one can make the probability of finding maximum clique in stochastic graph as close to unity as possible. Experimental results show that the proposed algorithms significantly reduce the number of samples needed to be taken from the edges of the stochastic graph as compared to the number of samples needed by standard sampling method at a given confidence level.

scholarly journals Sterility of gamma-irradiated pathogens: a new mathematical formula to calculate sterilizing doses

2020 ◽  
Vol 61 (6) ◽  
pp. 886-894
Author(s):  
Eve V Singleton ◽  
Shannon C David ◽  
Justin B Davies ◽  
Timothy R Hirst ◽  
James C Paton ◽  
...  
Keyword(s):  
Gamma Irradiation ◽  
Influenza A ◽  
Irradiation Dose ◽  
Semliki Forest Virus ◽  
High Titre ◽  
Mathematical Methods ◽  
Simple Method ◽  
Sterility Testing ◽  
Gamma Irradiated ◽  
Multiple Hit

Abstract In recent years there has been increasing advocacy for highly immunogenic gamma-irradiated vaccines, several of which are currently in clinical or pre-clinical trials. Importantly, various methods of mathematical modelling and sterility testing are employed to ensure sterility. However, these methods are designed for materials with a low bioburden, such as food and pharmaceuticals. Consequently, current methods may not be reliable or applicable to estimate the irradiation dose required to sterilize microbiological preparations for vaccine purposes, where bioburden is deliberately high. In this study we investigated the applicability of current methods to calculate the sterilizing doses for different microbes. We generated inactivation curves that demonstrate single-hit and multiple-hit kinetics under different irradiation temperatures for high-titre preparations of pathogens with different genomic structures. Our data demonstrate that inactivation of viruses such as Influenza A virus, Zika virus, Semliki Forest virus and Newcastle Disease virus show single-hit kinetics following exposure to gamma-irradiation. In contrast, rotavirus inactivation shows multiple-hit kinetics and the sterilizing dose could not be calculated using current mathematical methods. Similarly, Streptococcus pneumoniae demonstrates multiple-hit kinetics. These variations in killing curves reveal an important gap in current mathematical formulae to determine sterility assurance levels. Here we propose a simple method to calculate the irradiation dose required for a single log10 reduction in bioburden (D10) value and sterilizing doses, incorporating both single- and multiple-hit kinetics, and taking into account the possible existence of a resistance shoulder for some pathogens following exposure to gamma-irradiation.

A Simple Approach to an Approximate Two-Dimensional Cascade Theory

1958 ◽  
Vol 25 (4) ◽  
pp. 607-612
Author(s):  
Max J. Schilhansl
Keyword(s):  
Simple Approach ◽  
Geometrical Shape ◽  
Approximate Theory ◽  
Two Dimensional ◽  
Mathematical Methods ◽  
Simple Method ◽  
Sources And Sinks ◽  
Singularity Method ◽  
Two Dimensional Flow ◽  
Stagger Angle

Abstract The following simple approach to an approximate theory of incompressible two-dimensional flow past cascades, Fig. 1, is based on the so-called singularity method, in which the blade sections are replaced by sheets of vortexes, sources and sinks, and the flow induced by these singularities is calculated. The condition that the flow must be tangential to the blade surface, sometimes termed as the tangency condition, leads to a relation between the geometrical shape of the blade sections (camber and thickness), the cascade parameters (solidity and stagger angle), and the singularity distributions along the mean camber lines. As soon as these distributions are known, the pressure distribution and the lift may be determined. The calculation of the velocities at the blades is the most laborious portion of the whole problem. It has been carried out by various authors [1–4], with different mathematical methods. In this paper, a short, simple method of calculating the velocities induced by the singularities will be described. This approach has already been applied by others [5, 6], in less elaborate form.

scholarly journals Solving Nonlinear Wave Equation Based on Topology

2021 ◽  
Vol 15 ◽  
pp. 1232-1241
Author(s):  
Liang Song ◽  
Guihua Li ◽  
Shaodong Chen
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Node Degree ◽  
Solution Flow ◽  
First Order ◽  
Division Theorem ◽  
Stochastic Graphs ◽  
Stochastic Graph ◽  
Threshold Range

A method of solving nonlinear wave equation based on topology is proposed. Firstly, the characteristics of stochastic graph and Scaleless network are compared, and their topological characteristics are analyzed. Because of the existence of a few axis nodes, Scaleless networks have higher average aggregation than those with the same number of airport nodes and connected stochastic graphs. According to the topological structure of nonlinear wave equation, the first-order integral method is used to solve the nonlinear wave equation. According to the first integration, the threshold range is set, and the solution flow is designed in line with the division theorem. The topology of the network is analyzed according to the node degree, aggregation coefficient and reciprocity of the network, so as to verify and analyze. The experimental results show that the application of this method is 98%, which is still effective for the hyperbolic development equation of the same type.

scholarly journals A graph model for probabilities of nested conditionals

2021 ◽  
Author(s):  
Anna Wójtowicz ◽  
Krzysztof Wójtowicz
Keyword(s):  
Markov Chains ◽  
General Problem ◽  
Possible Worlds ◽  
Graph Model ◽  
Inference Rules ◽  
Mathematical Methods ◽  
Simple Description ◽  
Link Type ◽  
The Status ◽  
Bernoulli Models

AbstractWe define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz (Erkenntnis, 1–35. 10.1007/s10670-019-00144-z, 2019). The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning logical and metalogical issues such as setting up an axiomatic framework, inference rules, defining semantics, proving completeness, soundness etc. Our theory is motivated by the possible-worlds approach (the direct formal inspiration is the Stalnaker Bernoulli models); however, our model is generally more flexible. In the paper we focus on right-nested conditionals, discussing them in detail. The graph model makes it possible to account in a unified way for both shallow and deep interpretations of right-nested conditionals (the former being typical of Stalnaker Bernoulli spaces, the latter of McGee’s and Kaufmann’s causal Stalnaker Bernoulli models). In particular, we discuss the status of the Import-Export Principle and PCCP. We briefly discuss some methodological constraints on admissible models and analyze our model with respect to them. The study also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.

scholarly journals A CRISPR-based method for testing the essentiality of a gene

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yan You ◽  
Sharmila G. Ramachandra ◽  
Tian Jin
Keyword(s):  
Dictyostelium Discoideum ◽  
Essential Gene ◽  
Model Organism ◽  
Open Reading Frame ◽  
Proof Of Concept ◽  
Powerful Method ◽  
Simple Method ◽  
Reading Frame ◽  
Target Sites ◽  
Selective Elimination

Abstract The CRISPR/Cas9 system is a powerful method of editing genes by randomly introducing errors into the target sites. Here, we describe a CRISPR-based test for gene essentiality (CRISPR-E test) that allows the identification of essential genes. Specifically, we use sgRNA-mediated CRISPR/Cas9 to target the open reading frame of a gene in the genome and analyze the in-frame (3n) and frameshift (3n + 1 and 3n + 2) mutations in the targeted region of the gene in surviving cells. If the gene is non-essential, the cells would carry both in-frame (3n) and frameshift (3n + 1 and 3n + 2) mutations. In contrast, the cells would carry only in-frame (3n) mutations if the targeted gene is essential, and this selective elimination of frameshift (3n + 1 and 3n + 2) mutations of the gene indicate its essentiality. As a proof of concept, we have used this CRISPR-E test in the model organism Dictyostelium discoideum to demonstrate that Dync1li1 is an essential gene while KIF1A and fAR1 are not. We further propose a simple method for quantifying the essentiality of a gene using the CRISPR-E test.

BASIC PROBABILISTIC METHODS IN GEOLOGICAL SEARCH

Geophysics ◽  
1964 ◽  
Vol 29 (1) ◽  
pp. 105-108 ◽  
Author(s):  
A. Kyrala
Keyword(s):  
Poisson Distribution ◽  
Conditional Probability ◽  
Optimal Allocation ◽  
Probabilistic Methods ◽  
A Posteriori ◽  
Mathematical Methods ◽  
Geological Structures ◽  
Restrictive Assumption ◽  
Specific Distribution ◽  
Successful Search

An exposition of the basic mathematical methods used in calculating the probability of successful search for geological structures in a discrete set of regions is given. The argument is framed without the restrictive assumption of a specific distribution for the conditional probability of discovery but is subsequently illustrated by the specific case of a Poisson distribution. The optimal allocation of search effort to the various regions is determined. The important question of how the probabilities of occurrence of deposits should be adjusted after unsuccessful search is specifically answered by calculation of the a posteriori probabilities.

ANALYSIS OF CONTEXT-DEPENDENT ERRORS FOR ILLUMINA SEQUENCING

2012 ◽  
Vol 10 (02) ◽  
pp. 1241005 ◽  
Author(s):  
IRINA ABNIZOVA ◽  
STEVEN LEONARD ◽  
TOM SKELLY ◽  
ANDY BROWN ◽  
DAVID JACKSON ◽  
...  
Keyword(s):  
Conditional Probability ◽  
Variant Calling ◽  
Candidate Snps ◽  
Simple Method ◽  
Second Best ◽  
Sequencing Errors ◽  
Sequencing Technologies ◽  
Nucleotide Context ◽  
Quality Value ◽  
New Generation

The new generation of short-read sequencing technologies requires reliable measures of data quality. Such measures are especially important for variant calling. However, in the particular case of SNP calling, a great number of false-positive SNPs may be obtained. One needs to distinguish putative SNPs from sequencing or other errors. We found that not only the probability of sequencing errors (i.e. the quality value) is important to distinguish an FP-SNP but also the conditional probability of "correcting" this error (the "second best call" probability, conditional on that of the first call). Surprisingly, around 80% of mismatches can be "corrected" with this second call. Another way to reduce the rate of FP-SNPs is to retrieve DNA motifs that seem to be prone to sequencing errors, and to attach a corresponding conditional quality value to these motifs. We have developed several measures to distinguish between sequence errors and candidate SNPs, based on a base call's nucleotide context and its mismatch type. In addition, we suggested a simple method to correct the majority of mismatches, based on conditional probability of their "second" best intensity call. We attach a corresponding second call confidence (quality value) of being corrected to each mismatch.

scholarly journals LEARNING AUTOMATA-BASED ALGORITHMS FOR FINDING MINIMUM WEAKLY CONNECTED DOMINATING SET IN STOCHASTIC GRAPHS

2010 ◽  
Vol 18 (06) ◽  
pp. 721-758 ◽  
Author(s):  
JAVAD AKBARI TORKESTANI ◽  
MOHAMMAD REZA MEYBODI
Keyword(s):  
Dominating Set ◽  
Learning Automata ◽  
Sampling Rate ◽  
Connected Dominating Set ◽  
Stochastic Graphs ◽  
Vertex Set ◽  
Stochastic Graph ◽  
Standard Sampling ◽  
Definition Of ◽  
Weakly Connected Dominating Set

A weakly connected dominating set (WCDS) of graph G is a subset of G so that the vertex set of the given subset and all vertices with at least one endpoint in the subset induce a connected sub-graph of G. The minimum WCDS (MWCDS) problem is known to be NP-hard, and several approximation algorithms have been proposed for solving MWCDS in deterministic graphs. However, to the best of our knowledge no work has been done on finding the WCDS in stochastic graphs. In this paper, a definition of the MWCDS problem in a stochastic graph is first presented and then several learning automata-based algorithms are proposed for solving the stochastic MWCDS problem where the probability distribution function of the weight associated with the graph vertices is unknown. The proposed algorithms significantly reduce the number of samples needs to be taken from the vertices of the stochastic graph. It is shown that by a proper choice of the parameters of the proposed algorithms, the probability of finding the MWCDS is as close to unity as possible. Experimental results show the major superiority of the proposed algorithms over the standard sampling method in terms of the sampling rate.

scholarly journals An application of Sturm-Liouville theory to a class of two-part boundary-value problems

1957 ◽  
Vol 53 (2) ◽  
pp. 368-381 ◽  
Author(s):  
Samuel N. Karp
Keyword(s):  
Boundary Value Problems ◽  
General Problem ◽  
Boundary Value ◽  
Simple Solution ◽  
Wave Guide ◽  
Liouville Theory ◽  
Simple Method ◽  
Sturm Liouville

ABSTRACTA simple solution of a general problem involving a bifurcated wave guide is presented. The purpose of the work is to explain a new and simple method of solving such problems and to exhibit an organic connexion between Sturm–Liouville theory and the theory of two-part boundary-value problems.

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