The Statistical Mechanics of Dynamical Social Networks |Chapter 3 | Science and Technology: Recent Updates and Future Prospects Vol. 11

We propose an information-theoretic model for sociological networks. Usually, networks are considered as the array of links connecting the net nodes. Here we analyze a dynamical net in which every node is connected to all other nodes and links that randomly move between the pairs of nodes. These nets are similar to i.e. the internet where the sites are the nodes and the transferred bits are the links. The analysis of this net is analogous to a microcanonical ensemble of states and particles. The states are all the possible pairs of nodes (i.e. people, sites, and alike) that exchange particles which in the case of the internet are the information bits. In analogy to boson gas, we define these networks: entropy, volume, pressure, and temperature. We show that these definitions are consistent with Carnot efficiency (the second law) and ideal gas law. Therefore, if we have two large networks: hot and cold having temperatures TH and TC and we remove Q energetic bits from the hot network to the cold network we can save W profit bits that are calculated from the Carnot efficiency. In addition, it is shown that when two dynamical networks are merged the entropy increases. This explains the tendency of economic and social networks to merge. Equilibrium thermodynamics proved to be an important tool in engineering, chemistry, and physics. Applying these tools to sociological network dynamics may prove to be of some use.

 

 

Author(s) Details

Oded Kafr
Kafri Nihul Ltd., Tel Aviv 68165, Israel.

 

Please see the link:- https://doi.org/10.9734/bpi/strufp/v11/1781

Improved Hoeffding’s Lemma and Hoeffding’s Tail Bounds: A Recent Study | Chapter 08 | Novel Research Aspects in Mathematical and Computer Science Vol. 3

 This chapter aims to enhance Hoeffding's lemma and, as a result, Hoeffding's tail limits. To begin, we'll offer Hoeffding's lemma with a proof that differs from the original, and then show and prove the better Hoeffding's lemma. The enhancement is for left skewed zero mean random variables X[a,b], with a0 and -a>b. The proof of Hoeffding's improved lemma employs Taylor's expansion, the convexity of exp(sx),sR, and an unnoticed observation made since Hoeffding's publication in 1963 that the maximum of the intermediate function (1-) appearing in Hoeffding's proof is attained at an endpoint rather than at =0.5 as in the case b>-a. We get one-sided and two-sided tail limits for P(Snt) and P(Snt) using Hoeffding's improved lemma. P(Snt) and P(|S n |t), where S n= (i=1)n X i and X i[a i,b i],i=1,...,n are independent zero mean random variables, respectively (not necessarily identically distributed). For any X i:-a ib i,i=1,...,n, we might additionally enhance Hoeffding's two-sided bound. This is because P(-Snt) should raise the one-sided bound, forcing left-skewed intervals to become right-skewed and vice versa.

Author(S) Details

David Hertz
Akko, Israel.

View Book:- https://stm.bookpi.org/NRAMCS-V3/article/view/6815

Channel Capacity Enhancement on Maximization of Modified Verma and Bose-Einstein Entropies by Gaussian Distribution | Chapter 8 | Recent Advances in Mathematical Research and Computer Science Vol. 4

 This chapter examined how to improve channel capacity by using a Gaussian distribution [5] and Kullback-[3] Leibler's information measure of directed divergence to maximise modified Verma and Bose-Einstein entropies.

Author(S) Details

Rohit Kumar Verma
Department of Mathematics, Bhilai Institute of Technology, Durg (C.G.), India.

View Book:- https://stm.bookpi.org/RAMRCS-V4/article/view/4874