Related papers: The Spaces of Data, Information, and Knowledge
Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction,…
In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and…
Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…
Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…
Knowledge is the most precious asset of humankind. People extract the experience from the data that provide for us the reality through the feelings. Generally speaking, it is possible to see the analogy of knowledge elaboration between…
Object reconstruction is an important task in many fields of application as it allows to generate digital representations of our physical world used as base for analysis, planning, construction, visualization or other aims. A reconstruction…
The trends of open science have enabled several open scholarly datasets which include millions of papers and authors. Managing, exploring, and utilizing such large and complicated datasets effectively are challenging. In recent years, the…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
Deep neural models in recent years have been successful in almost every field, including extremely complex problem statements. However, these models are huge in size, with millions (and even billions) of parameters, thus demanding more…
The methodological foundations of the construction of information technology, formalized models and tools for the implementation of the research-related design of smart systems based on the use of the concepts of transdisciplinarity and…
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…
The success of neural networks builds to a large extent on their ability to create internal knowledge representations from real-world high-dimensional data, such as images, sound, or text. Approaches to extract and present these…
We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These…
In a previous work, "pure data" is proposed as an axiomatic foundation for mathematics and computing, based on "finite sequence" as the foundational concept rather than based on logic or type. Within this framework, objects with…
Joint representation learning of text and knowledge within a unified semantic space enables us to perform knowledge graph completion more accurately. In this work, we propose a novel framework to embed words, entities and relations into the…
A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g.,…
We observe that some natural mathematical definitions are lifting properties relative to simplest counterexamples, namely the definitions of surjectivity and injectivity of maps, as well as of being connected, separation axioms $T_0$ and…
Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…