Related papers: The Khipu-Based Numeration System
The application of phylogenetic techniques to the documentation of cultural history can present a distorted picture due to horizontal transmission and blending. Moreover, the units of cultural transmission must be communicable concepts,…
Simultaneously recorded neurons exhibit correlations whose underlying causes are not known. Here, we use a population of threshold neurons receiving correlated inputs to model neural population recordings. We show analytically that small…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures. More generally, we show that the chain complexes…
We provide a combinatorial approach to counting the number of spanning trees at the $n$-th layer of a branched $\mathbb{Z}_p$-cover of a finite connected graph $\mathsf{X}$. Our method achieves in explaining how the position of the ramified…
This paper presents a method of universal coding based on the Narayana series. The rules necessary to make such coding possible have been found and the length of the resulting code has been determined to follow the Narayana count.
Nunchaku is a new higher-order counterexample generator based on a sequence of transformations from polymorphic higher-order logic to first-order logic. Unlike its predecessor Nitpick for Isabelle, it is designed as a stand-alone tool, with…
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, characterizing spike patterns in the resulting data, and linking…
It is known that the arc index of alternating knots is the minimal crossing number plus two and the arc index of prime nonalternating knots is less than or equal to the minimal crossing number. We study some cases when the arc index is…
Celtic knots are an ancient art form often attributed to Celtic cultures, used to decorate monuments and manuscripts, and to symbolise eternity and interconnectedness. This paper describes the framework CelticGraph to draw graphs as Celtic…
This paper presents a simple extension of the binary heap, the List Heap. We use List Heaps to demonstrate the idea of adaptive heaps: heaps whose performance is a function of both the size of the problem instance and the disorder of the…
We introduce a new combinatorial method to encode knots and links with applications to knot invariants. Clasp diagrams defined in this paper are combinatorial blueprints for building knot diagrams out of full twists on two strings rather…
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…
Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the…
Pre-trained Transformer models have achieved successes in a wide range of NLP tasks, but are inefficient when dealing with long input sequences. Existing studies try to overcome this challenge via segmenting the long sequence followed by…
This paper is brief review of three aspects of the isotope - based quantum information: computation, teleportation and cryptography. Our results demonstrate not only that entanglement exists in elementary excitation of isotope - mixed…
In this paper we present a new method of coding/decoding algorithms using Fibonacci $Q$-matrices. This method is based on the blocked message matrices. The main advantage of our model is the encryption of each message matrix with different…
We introduce a new method for estimating the parameter of the bivariate Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard boot-strapping procedure for inferring random…
In this work, we leverage the intrinsic segmentation of language sequences and design a new positional encoding method called Bilevel Positional Encoding (BiPE). For each position, our BiPE blends an intra-segment encoding and an…
A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the…