Papers by Danny Gómez-Ramírez
arXiv (Cornell University), Nov 12, 2012
We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. I... more We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra. This criterion allows further simplifications when the base ring is local, or onedimensional, or factorial. Besides, we discuss whether the connectedness is a local property. Finally, we present a characterization of the integral closure of an ideal by means of the universal connectedness of the forcing algebra.
arXiv (Cornell University), Oct 11, 2017
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in t... more We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism together with its relation to classic notions like primitive positive definability and Diophantiveness. Additionally, we analyze the semantic variability of functional conceptual substratum when small syntactic modifications are done. Finally, we describe mathematically natural inference rules for definitions inspired by functional conceptual substratum and show that they are sound and complete w.r.t. standard calculi.
arXiv (Cornell University), Apr 6, 2018
We show that the (typical) quantitative considerations about proper (as too big) and small classe... more We show that the (typical) quantitative considerations about proper (as too big) and small classes are just tangential facts regarding the consistency of Zermelo-Fraenkel Set Theory with Choice. Effectively, we will construct a first-order logic theory D-ZFC (Dual theory of ZFC) strictly based on (a particular sub-collection of) proper classes with a corresponding special membership relation, such that ZFC and D-ZFC are meta-isomorphic frameworks (together with a more general dualization theorem). More specifically, for any standard formal definition, axiom and theorem that can be described and deduced in ZFC, there exists a corresponding 'dual' version in D-ZFC and vice versa. Finally, we prove the meta-fact that (classic) mathematics (i.e. theories grounded on ZFC) and dathematics (i.e. dual theories grounded on D-ZFC) are meta-isomorphic. This shows that proper classes are as suitable (primitive notions) as sets for building a foundational framework for mathematics.
Technology and economics of smart grids and sustainable energy, Aug 13, 2022
The use of shared electric vehicles has spread widely in response to the global need of reducing ... more The use of shared electric vehicles has spread widely in response to the global need of reducing CO2 emissions. Hence, in the literature, authors have proposed strategies to minimize the operative costs of shared EVs, such as the provision of electrical ancillary services. However, to provide these kinds of services jointly with transportation, charging/discharging and fleet management strategies are required. And, the currently available strategies from the literature do not consider shared EVs. Therefore, to fill this gap, this paper presents an optimization-based management strategy for shared EVs that provide ancillary services and sell energy, which is applied to a study case located in Colombia. Additionally, it includes the analysis of the economic contracts that should be established between the EVs operator and the energy retailer; in which, it was found that the best option for EVs operator is to purchase the energy at the stock electricity price and establish a bilateral contract for energy sales. Moreover, it suggests that EVs be charged at the early morning hours when the stock price is lowest, that the ancillary services be provided at hours with the highest stock price, and that the energy be sold at the hours in which the provision of ancillary services is not suitable. Finally, the paper suggests, from the application of a Lagrangian parametric technique, an incentive of at least $ 115 [COP/kWh], to make the electrical services competitive with the car-sharing transportation service, which is paid at a price 23 times higher, within the Colombian context.
arXiv (Cornell University), Oct 11, 2017
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in t... more We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism together with its relation to classic notions like primitive positive definability and Diophantiveness. Additionally, we analyze the semantic variability of functional conceptual substratum when small syntactic modifications are done. Finally, we describe mathematically natural inference rules for definitions inspired by functional conceptual substratum and show that they are sound and complete w.r.t. standard calculi.
Technology and Economics of Smart Grids and Sustainable Energy
The use of shared electric vehicles has spread widely in response to the global need of reducing ... more The use of shared electric vehicles has spread widely in response to the global need of reducing CO2 emissions. Hence, in the literature, authors have proposed strategies to minimize the operative costs of shared EVs, such as the provision of electrical ancillary services. However, to provide these kinds of services jointly with transportation, charging/discharging and fleet management strategies are required. And, the currently available strategies from the literature do not consider shared EVs. Therefore, to fill this gap, this paper presents an optimization-based management strategy for shared EVs that provide ancillary services and sell energy, which is applied to a study case located in Colombia. Additionally, it includes the analysis of the economic contracts that should be established between the EVs operator and the energy retailer; in which, it was found that the best option for EVs operator is to purchase the energy at the stock electricity price and establish a bilateral contract for energy sales. Moreover, it suggests that EVs be charged at the early morning hours when the stock price is lowest, that the ancillary services be provided at hours with the highest stock price, and that the energy be sold at the hours in which the provision of ancillary services is not suitable. Finally, the paper suggests, from the application of a Lagrangian parametric technique, an incentive of at least $ 115 [COP/kWh], to make the electrical services competitive with the car-sharing transportation service, which is paid at a price 23 times higher, within the Colombian context.
arXiv (Cornell University), Mar 16, 2022
Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is ... more Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when W R := {p ∈ Spec(R) : F Ep is finitely generated as a ring over its degree zero piece} is an open set in the Zariski topology, where F Ep denotes the Frobenius algebra attached to the injective hull of the residue field of Rp. We show that this is true when R is a Stanley-Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.
arXiv (Cornell University), Dec 4, 2021
The new computational paradigm of conceptual computation has been introduced in the research prog... more The new computational paradigm of conceptual computation has been introduced in the research program of Artificial Mathematical Intelligence. We provide the explicit artificial generation (or conceptual computation) for the fundamental mathematical notion of topological groups. Specifically, we start with two basic notions belonging to topology and abstract algebra, and we describe recursively formal specifications in the Common Algebraic Specification Language (CASL). The notion of conceptual blending between such conceptual spaces can be materialized computationally in the Heterogeneous Tool Set (HETS). The fundamental notion of topological groups is explicitly generated through three different artificial specifications based on conceptual blending and conceptual identification, starting with the concepts of continuous functions and mathematical groups (described with minimal set-theoretical conditions). This constitutes in additional heuristic evidence for the third pillar of Artificial Mathematical Intelligence.
arXiv (Cornell University), May 29, 2021
Examining a 20 th -century Scandinavian legal theoretical tradition, we can extract an ontologica... more Examining a 20 th -century Scandinavian legal theoretical tradition, we can extract an ontological naturalistic, a logical empiristic, and a modern idealistic rationale. We introduce the mathematical syntactic figure present in the "logical empiricism" in a contemporary mathematical logic. A new formal framework for describing explicit purchase statutes (Sweden) is gradually developed and subsequently proposed. This new framework is based on a many-sorted first-order logic (MFOL) approach, where the semantics are grounded in concrete "physical" objects and situations with a legal relevance. Specifically, we present a concrete formal syntactic translation of one of the central statutes of Swedish legislation for the purchase of immovable property. Additionally, we discuss the potential implications that a subsequent development of such formalisations would have for constructing artificial agents (e.g., software) that can be used as "co-creative" legal assistance for solving highly complex legal issues concerning the transfer of property, among others. The 19 th and 20 th centuries in the European continental and Anglo-American philosophical traditions feature shifts in the paradigmatic descriptions of knowledge production. These shifts range from given categories of perception of an empiric subject with the ability to synthesise
Artificial Mathematical Intelligence, 2020
We show that the (typical) quantitative considerations about proper (as too big) and small classe... more We show that the (typical) quantitative considerations about proper (as too big) and small classes are just tangential facts regarding the consistency of Zermelo-Fraenkel Set Theory with Choice. Effectively, we will construct a first-order logic theory D-ZFC (Dual theory of ZFC) strictly based on (a particular sub-collection of) proper classes with a corresponding special membership relation, such that ZFC and D-ZFC are meta-isomorphic frameworks (together with a more general dualization theorem). More specifically, for any standard formal definition, axiom and theorem that can be described and deduced in ZFC, there exists a corresponding 'dual' version in D-ZFC and vice versa. Finally, we prove the meta-fact that (classic) mathematics (i.e. theories grounded on ZFC) and dathematics (i.e. dual theories grounded on D-ZFC) are meta-isomorphic. This shows that proper classes are as suitable (primitive notions) as sets for building a foundational framework for mathematics.
Semantic and Morpho-Syntactic Prevention’s Guidelines for COVID-19 Based on Cognitively Inspired Artificial Intelligence and Data Mining. Case Study: Europe, North America, and South America
Artificial Intelligence for COVID-19, 2021
Based on a combination of cognitively inspired methods in artificial intelligence such as artific... more Based on a combination of cognitively inspired methods in artificial intelligence such as artificial mathematical intelligence and data mining, we study the correlation between the COVID-19 pandemic and the sentiment analysis (qualitative ontological nature) of tweets and their linguistic patterns from the presidents and the populations of five countries from Europe (Spain and the United Kingdom), North America (The United States of America), and South America (Chile and Colombia). The results show that tweets classified as negative are the most common in all presidential tweeter accounts, except in one country, Colombia. However, tweets classified as neutral are dominant in the population tweets in each country examined. Based on the results obtained and on some of the foundational cognitive techniques of artificial mathematical intelligence, we conclude by providing COVID-19 prevention guidelines at the linguistic and cognitive levels.
International Conference on Computational Creativity, 2015
We model the mathematical process whereby new mathematical theories are invented. Here we explain... more We model the mathematical process whereby new mathematical theories are invented. Here we explain the use of conceptual blending for this purpose, and show examples to illustrate the process in action. Our longerterm goal is to support machine and human mathematical creativity. Thus we have a blend as in the earlier examples: Colimit
Chapter 3 Conceptual Blending in DOL: Evaluating Consistency and Conflict Resolution
Concept Invention, 2018
In cognitive science the theory of conceptual blending provides an explanation of the human abili... more In cognitive science the theory of conceptual blending provides an explanation of the human ability to invent concepts. This cognitive theory provides an inspiration for computational concept invention theory, which has the goal of building creative systems that generate new concepts automatically. In Chapter 3 we discuss a workflow for a system that (a) creatively blends two concepts into a new concept, (b) identifies conflicts, (c) resolves conflicts by generalising the input spaces, and (d) evaluates the new concept against requirements.
Artificial Intelligence for COVID-19, 2021
We describe in a contextualized manner the indirect and evident correlation that the strong quara... more We describe in a contextualized manner the indirect and evident correlation that the strong quarantine's conditions, originated by the global spread of COVID-19, possess with respect to mental health of people. In particular, we analyse this correlation with mental deceases like depression, stress, anxiety and bipolar and mood disorders. Specifically, we focus on the relation between the former phenomena and the modified workflow and structure of verbal communication among the quarantine. Moreover, we describe the most fundamental features and abilities that chatbots can simulate and stimulate in communication with people. Based on the former results we proposed hybrid therapeutic directions combining chatbots and human therapists for improving the mental health of people cognitively affected by the pandemic and with pronounced shy behaviour. Although there are news of the COVID-19 virus since the first reported case in December 2019 in Asia, it was in February 2020 that the need to implement health measures in countries like Colombia began to be considered. Even more, such a measures were explicitly applied concretely since March where a national quarantine began to be carried out in order to control the outbreak of the pandemic, while the country's medical service was strengthened. Preventive isolation in Colombia were initially shown to be a temporary situation, something that would only last 14 days, with a maximum of two months of duration. However, the months passed and the pandemic began to be noticed as an unprecedented event, which is not known when or how it is going to finish. Preventive isolation measures forced the country's population
The construction of a universal natural scientific truth-criteria inspired by the refined develop... more The construction of a universal natural scientific truth-criteria inspired by the refined developed mathematical and empirical tools applied for the validation, mapping and prediction of natural phenomena (naturalism) [15, p. 62]; and a theory of concepts based on the dynamically evolving expressive power of mathematics capable of projecting empirically verifiable relations and identities to an obtuse materia (philosophy of symbolic forms) [13, p. 45-85]. Mathematical logic [22] and [45]. Logic positivism, analytical philosophy, linguistic phenomonology, structural linguistics, transformal generative grammatics [23, p. 14-15]. The use of methods from different mathematical disciplines such as topology and transcendental algebra to construct logical theorems in theory of models. 9 Epistemological models based on an intuitive empirism: naturalism [59, p. 83] and phenomenology -also referred to as representationalistic or correlationalistic constructions [52, p. 324]. Non-empirically founded epistemological models: modern philosophical idealism, minimal phenomenology, liberal naturalism [61, p. 402 f.], naturalistic monism -as a consequence non-representationalistic or non-correlationalistic constructions. The distinction between a contemporary Anglo-American tradition and a contintental European tradition: naturalism vs. naturalistic monism [81].
Towards the (Cognitive) Reality of Mathematics and the Mathematics of (Cognitive) Reality
The Most Outstanding (Future) Challenges Towards Global AMI and Its Plausible Extensions
Meta-Modeling of Classic and Modern Mathematical Proofs and Concepts
Chapter 8 Formal Conceptual Blending in the (Co-)Invention of (Pure) Mathematics
Concept Invention, 2018
We claim that conceptual blending plays a key role in mathematical discovery and invention. We us... more We claim that conceptual blending plays a key role in mathematical discovery and invention. We use a formalisation of blending in terms of colimits of many-sorted first-order logical specifications to illustrate the processes involved. In particular we present a development structured around notions from abstract areas of pure mathematics such as Commutative Algebra, Number Theory, Fields and Galois Theory. This development shows a new formal route which builds up the classical theory in the area, and also gives rise to new equivalences that characterise the notion of Dedekind Domain. We comment on the significance of this work for the computer support of abstract mathematical theory construction, as well as for (co-)inventing classic and new mathematical notions (i.e., inventing with the help of a computer program), and on the cognitive aspects involved.
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Papers by Danny Gómez-Ramírez