Related papers: Jumping champions and prime gaps using information…
In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of…
A quantum system subjected to a strong continuous monitoring undergoes quantum jumps. This very well known fact hides a neglected subtlety: sharp scale-invariant fluctuations invariably decorate the jump process even in the limit where the…
We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are…
This paper introduces a new method to find the next prime number after a given prime ${P}$. The proposed method is used to derive a system of inequalities, that serve as constraints which should be satisfied by all primes whose successor is…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
Neural networks are able to extract information from the timing of spikes. Here we provide new results on the behavior of the simplest neuronal model which is able to decode information embedded in temporal spike patterns, the so called…
Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…
Most existing Spiking Neural Network (SNN) works state that SNNs may utilize temporal information dynamics of spikes. However, an explicit analysis of temporal information dynamics is still missing. In this paper, we ask several important…
A measurement performed on a quantum system is an act of gaining information about its state, a view that is widespread in practical and foundational work in quantum theory. However, the concept of information in quantum theory…
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). It is shown that multiplicative nature of the noise is the main reason for the…
In recent work, we considered the frequencies of patterns of consecutive primes $\pmod{q}$ and numerically found biases toward certain patterns and against others. We made a conjecture explaining these biases, the dominant factor in which…
It is well known that networks generated by common mechanisms such as preferential attachment and homophily can disadvantage the minority group by limiting their ability to establish links with the majority group. This has the effect of…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
The Shannon information-entropy uncertainty (in brief as "information uncertainty") is used to analyze the fragments in the measured 140$A$ MeV $^{40, 48}$Ca + $^{9}$Be and $^{58, 64}$Ni + $^{9}$Be reactions. A scaling phenomenon is found…
How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is…
We present the results of detailed numerical study of a model for the sharing and sorting of informations in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite…
In this paper, we show some results about the gap between a prime number and its consecutive prime number for large enough prime numbers. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than…
The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and…