Related papers: Notes on properties of binary strings which encode…
Big data is becoming ever more ubiquitous, ranging over massive video repositories, document corpuses, image sets and Internet routing history. Proximity search and clustering are two algorithmic primitives fundamental to data analysis, but…
This article introduces a novel binary representation of the canonical genetic code based on both the structural similarities of the nucleotides, as well as the physicochemical properties of the encoded amino acids. Each of the four mRNA…
This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for…
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…
Comparative prime number theory is the study of the {\em{discrepancies}} of distributions when we compare the number of primes in different residue classes. This work presents a list of the problems being investigated in comparative prime…
The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and…
Seth (Mathematics Stack Exchange, http://math.stackexchange.com/q/1812699) posed a problem that is equivalent to the following: how many binary strings of length n have exactly k pairs of consecutive 0s and exactly m pairs of consecutive…
Assuming the Riemann Hypothesis we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Omega-term, we prove that our result is essentially the best…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
In this note we describe a method for finding prime numbers as fixed points of particularly simple sequences. Some basic calculations show that success rates for identifying primes this way are over 99.9%. In particular, it seems that the…
The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use…
This article is meant to provide an additional point of view, applying known knowledge, to supply keys that have a series of non-repeating digits, in a manner that is not usually thought of. Traditionally, prime numbers are used in…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…
We investigate the most general phase space of configurations, consisting of all possible ways of assigning elementary attributes, ``energies'', to elementary positions, ``cells''. We discuss how this space possesses structures that can be…
We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…
This paper is the continuation of \cite{htl}, where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In case of non-degenerate sequences we give bounds for the…
We develop efficient binary (i.e., 1-bit) and multi-bit coding schemes for estimating the scale parameter of $\alpha$-stable distributions. The work is motivated by the recent work on one scan 1-bit compressed sensing (sparse signal…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…