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Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…
A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
Gated networks are networks that contain gating connections, in which the outputs of at least two neurons are multiplied. Initially, gated networks were used to learn relationships between two input sources, such as pixels from two images.…
We introduce an algebra of data linkages. Data linkages are intended for modelling the states of computations in which dynamic data structures are involved. We present a simple model of computation in which states of computations are…
For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.
We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.
The main definitions and properties of Lie superalgebras are proposed a la facon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure of simple Lie superalgebras and their…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
It is argued that string theory may pose new conceptual issues for the history and philosophy of science.
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Data Science is a complex and evolving field, but most agree that it can be defined as a combination of expertise drawn from three broad areascomputer science and technology, math and statistics, and domain knowledge -- with the purpose of…
Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\; (x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras over…