Related papers: Necklaces and bracelets in R
Neural networks are increasingly used to support decision-making. To verify their reliability and adaptability, researchers and practitioners have proposed a variety of tools and methods for tasks such as NN code verification, refactoring,…
An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$,…
M. B. Levin used Sobol-Faure low discrepancy sequences with Pascal matrices modulo $2$ to construct, for each integer $b$, a real number $x$ such that the first $N$ terms of the sequence $(b^n x \mod 1)_{n\geq 1}$ have discrepancy $O((\log…
Blockchain also known as a distributed ledger technology stores different transactions/operations in a chain of blocks in a distributed manner without needing a trusted third-party. Blockchain is proven to be immutable which helps for…
Le diagrams and Grassmann necklaces both index the collection of positroids in the nonnegative Grassmannian $Gr_{\geq 0}(k,n)$, but they excel at very different tasks: for example, the dimension of a positroid is easily extracted from its…
Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the…
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.
Pearltrees is a social service, using which people can organise Web contents, photos and notes. These contents are the "pearls" on some trees. Besides the social opportunities, the trees can be used as a tool to organise references and for…
Knowledge tracing---where a machine models the knowledge of a student as they interact with coursework---is a well established problem in computer supported education. Though effectively modeling student knowledge would have high…
While many production-ready and robust algorithms are available for the task of recommendation systems, many of these systems do not take the order of user's consumption into account. The order of consumption can be very useful and matters…
The necklace polynomials \[ M_n(x)=\frac1n\sum_{d\mid n}\mu(d)x^{n/d} \] play a central role in discrete mathematics: they count aperiodic necklaces, enumerate monic irreducible polynomials over finite fields, and give the dimensions of…
Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…
Networks are useful for representing phenomena in a broad range of domains. Although their ability to represent complexity can be a virtue, it is sometimes useful to focus on a simplified network that contains only the most important edges:…
A first order inference system, called R-calculus, is defined to develop the specifications. It is used to eliminate the laws which is not consistent with the user's requirements. The R-calculus consists of the structural rules, an axiom, a…
NeXML is a powerful and extensible exchange standard recently proposed to better meet the expanding needs for phylogenetic data and metadata sharing. Here we present the RNeXML package, which provides users of the R programming language…
An extension to a recently introduced architecture of clique-based neural networks is presented. This extension makes it possible to store sequences with high efficiency. To obtain this property, network connections are provided with…
Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…
In constraint languages for RDF graphs, such as ShEx and SHACL, constraints on nodes and their properties in RDF graphs are known as "shapes". Schemas in these languages list the various shapes that certain targeted nodes must satisfy for…
Over the long history of machine learning, which dates back several decades, recurrent neural networks (RNNs) have been used mainly for sequential data and time series and generally with 1D information. Even in some rare studies on 2D…
Machine learning relies on randomness as a fundamental component in various steps such as data sampling, data augmentation, weight initialization, and optimization. Most machine learning frameworks use pseudorandom number generators as the…