Related papers: The Khipu-Based Numeration System
The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…
Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top"…
This an article about some elementary geometric and combinatorial natures of various knot energies. A related "new" knot invariant -- the X-crossing number -- is introduced.
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…
We show one possible dynamical approach to the study of the distribution of prime numbers. Our approach is based on two complexity methods, the Computable Information Content and the Entropy Information Gain, looking for analogies between…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result…
Chirp signals have established diverse applications caused by the capable of producing time-dependent linear frequencies. Most feature extraction transformation methods for chirp signals focus on enhancing the performance of transform…
In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a…
In the paper we present a description of complex systems in terms of self-organization processes of prime integer relations. A prime integer relation is an indivisible element made up of integers as the basic constituents following a single…
Studies investigating neural information processing often implicitly ask both, which processing strategy out of several alternatives is used and how this strategy is implemented in neural dynamics. A prime example are studies on predictive…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
A primitive $k$-batch code encodes a string $x$ of length $n$ into string $y$ of length $N$, such that each multiset of $k$ symbols from $x$ has $k$ mutually disjoint recovering sets from $y$. We develop new explicit and random coding…
In this paper we are interested in BB knots, namely knots and links where the bridge index equals the braid index. Supported by observations from experiments, it is conjectured that BB knots possess a special geometric/physical property…
Recent advances in Quantum Topology assign $q$-series to knots in at least three different ways. The $q$-series are given by generalized Nahm sums (i.e., special $q$-hypergeometric sums) and have unknown modular and asymptotic properties.…
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long awaited) simple bijection which explains…
This paper presents the InScript corpus (Narrative Texts Instantiating Script structure). InScript is a corpus of 1,000 stories centered around 10 different scenarios. Verbs and noun phrases are annotated with event and participant types,…
In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some of their generalizations. The aim of this work is to…