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We present a new word embedding technique in a (non-linear) metric space based on the shared membership of terms in a corpus of textual documents, where the metric is naturally defined by the Boolean algebra of all subsets of the corpus and a measure μ defined on it. Once the metric space is constructed, a new term (a noun, an adjective, a classification term) can be introduced into the model and analyzed by means of semantic projections, which in turn are defined as indexes using the measure μ and the word embedding tools. We formally define all necessary elements and prove the main results about the model, including a compatibility theorem for estimating the representability of semantically meaningful external terms in the model (which are written as real Lipschitz functions in the metric space), proving the relation between the semantic index and the metric of the space (Theorem 1). Our main result proves the universality of our word-set embedding, proving mathematically that every word embedding based on linear space can be written as a word-set embedding (Theorem 2). Since we adopt an empirical point of view for the semantic issues, we also provide the keys for the interpretation of the results using probabilistic arguments (to facilitate the subsequent integration of the model into Bayesian frameworks for the construction of inductive tools), as well as in fuzzy set-theoretic terms. We also show some illustrative examples, including a complete computational case using big-data-based computations. Thus, the main advantages of the proposed model are that the results on distances between terms are interpretable in semantic terms once the semantic index used is fixed and, although the calculations could be costly, it is possible to calculate the value of the distance between two terms without the need to calculate the whole distance matrix. "Wovon man nicht sprechen kann, darüber muss man schweigen". Tractatus Logico-Philosophicus. L. Wittgenstein. [ABSTRACT FROM AUTHOR]

Predicting the survival of startups is a complex challenge due to the multifaceted nature of entrepreneurial ecosystems and the dynamic interplay of internal and external factors. Despite advances in empirical research, existing models often lack integration with robust conceptual frameworks. This study addresses these gaps by developing a multivariate AI-driven model for predicting startup survival, leveraging Lipschitz extensions, neural networks, and linear regression. Using a dataset of 20 startups, selected across diverse industries and evaluated on attributes such as team dynamics, market conditions, and financial metrics, the model demonstrated high accuracy and clustering capabilities. Key findings highlight the pivotal role of team dynamics and product differentiation in determining survival probabilities. By integrating conceptual insights with empirical data, the study bridges gaps in existing literature and offers a practical decision-making tool for entrepreneurs, investors, and policymakers. These findings underscore the importance of fostering collaborative, innovative ecosystems to enhance entrepreneurial success and societal well-being. [ABSTRACT FROM AUTHOR]

Performance analysis, utilizing video technology and recent technological advancements in soccer stadiums, provides a wealth of data, including player trajectories and real-time game statistics, which are crucial for tactical evaluation and decision-making by coaches and players. These data allow for the definition of metrics that not only enrich the experience for soccer fans through enhanced visual displays but also empower coaching staff and managers to make informed, real-time decisions that directly impact match outcomes. Ultimately, these data serve as a pivotal tool for improving team strategy based on comprehensive post-match data analysis. In this article, we present a mathematical model to study the concept of pressure between players and, subsequently, between teams. We first explore the concept in a fixed frame of a match, determining what we call influence areas between players. We introduce the unit pressure function and analyze the total number of pressure interactions. Then, we apply these concepts to football matches, considering various factors such as players and the radius of the area of influence and examining pressure efficiency through mean unitary pressure. Lastly, a real case study is presented, showcasing visualizations like a heatmap matrix displaying individual and collective pressure, as well as the team pressure balance. [ABSTRACT FROM AUTHOR]

The extension of the concept of p-summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space M afforded by the associated Arens–Eells space, along with the duality between M and the metric dual space M # defined by the real-valued Lipschitz functions on M. However, alternative approaches to measuring distances between sequences of elements of metric spaces (essentially involved in the definition of p-summability) exist. One approach involves considering specific subsets of the unit ball of M # for computing the distances between sequences, such as the real Lipschitz functions derived from evaluating the difference in the values of the metric from two points to a fixed point. We introduce new notions of summability for Lipschitz operators involving such functions, which are characterized by integral dominations for those operators. To show the applicability of our results, in the last part of this paper, we use the theoretical tools obtained in the first part to analyze metric graphs. In particular, we show new results on the behavior of numerical indices defined on these graphs satisfying certain conditions of summability and symmetry. [ABSTRACT FROM AUTHOR]

Introduction. Open Government is a form of public policy based on the pillars of collaboration and citizen participation, transparency and the right of access to public information. With the help of information and communication technologies, governments and administrations carry out open data initiatives, making reusable datasets available to all citizens. The academic community, highly qualified personnel, can become potential reusers of this data, which would lead to its use for scientific research, generating knowledge, and for teaching, improving the training of university students and promoting the reuse of open data in the future. Method. This study was developed using a quantitative research methodology (survey), which was distributed by email in one context block and six technical blocks, with a total of 30 questions. The data collection period was between 15 March and 10 May 2021. Analysis. The data obtained through this quantitative methodology were processed, normalised, and analysed. Results. A total of 783 responses were obtained, from 34 Spanish provinces. The researchers come from 47 Spanish universities and 21 research centres, and 19 research areas of the State Research Agency are represented. In addition, a platform was developed with the data for the purpose of visualising the results of the survey. Conclusions. The sample thus obtained is representative and the conclusions can be extrapolated to the rest of the Spanish university teaching staff. In terms of gender, the study is balanced between men and women (41.76% W vs. 56.58% M). In general, researchers responding to the survey know what open data is (79.31%) but only 50.57% reuse open data. The main conclusion is that open government data prove to be useful sources of information for science, especially in areas such as Social Sciences, Industrial Production, Engineering and Engineering for Society, Information and Communication Technologies, Economics and Environmental Sciences. [ABSTRACT FROM AUTHOR]

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. It has the distinct characteristic that, when calculated along the same path, it may result in a shorter distance between far-apart vertices than between adjacent ones. This property can be particularly useful for modeling scenarios where the connections between vertices are obscured by numerous intermediate vertices, such as in cases of financial fraud. For example, to hide dirty money from financial authorities, fraudsters often use multiple institutions, banks, and intermediaries between the source of the money and its final recipient. Our distance would serve to make such situations explicit. Thus, although our algorithm is based on arguments similar to those at work for the Bellman–Ford and Dijkstra methods, it is in fact essentially different, since the calculation formula contains a weight that explicitly depends on the number of intermediate vertices. This fact totally conditions the algorithm, because longer paths could provide shorter distances—contrary to the classical algorithms mentioned above. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples. [ABSTRACT FROM AUTHOR]

L'objectiu de la investigació és presentar un procediment que permeti conèixer el desenvolupament econòmic i social d'una entitat local a partir d'iniciatives de govern obert i obertura de la informació. Es proposa una metodologia que faciliti aquesta acció mitjançant la incorporació de plataformes analítiques a disposició del ciutadà. Per mostrar l'aplicació d'aquesta metodologia, s'explica la creació de la plataforma COMUNDA, que utilitza dades disponibles de l'Ajuntament de la Pobla de Vallbona (València) sobre les despeses municipals per analitzar aspectes de la contractació pública. Aquests instruments de segon nivell, creats a partir de dades publicades pels ajuntaments, poden constituir eines analítiques per detectar irregularitats i per publicitar el teixit empresarial del municipi que poden permetre als ajuntaments articular polítiques adequades, i a les empreses i als particulars conèixer millor les característiques socioeconòmiques de la població. S'ha comprovat la utilitat del protocol d'actuació i anàlisi proposat, extrapolable a altres casos, sobre el cas concret de la plataforma citada. En aquest cas, la mètrica MELODA dona una qualificació de 48,3% de qualitat en la reutilització i s'ha pogut comprovar que la utilització del nostre procediment constata un increment de la contractació pública al municipi l'any 2011, un dels pitjors anys de la crisi econòmica, i que la contractació a empreses externes al municipi és de dos a tres milions d'euros superior a la contractació local. This study describes a procedure that can trackthe economic and social development of a local government body, based on open government initiatives and openness of information. A methodology is proposed that incorporates analytical platforms available to the general public. To illustrateits application, the creation of the COMUNDA platform is described. The COMUNDA platform uses data provided from the Town Council of La Pobla de Vallbona (Valencia) on municipal spending in order to analyse aspects of public procurement. These second-level instruments, created from data published by the councils, can be useful analytical tools for detecting irregularities and for focusing attention on the business fabric of the municipality. The information obtained can help councils to design appropriate policies and help companies and individuals to understand the socioeconomic characteristics of the population. The article confirms the usefulness of the action and analysis protocolproposed for the platform mentioned, and the results suggest that it can be extrapolated to other scenarios. In this case, the MELODA metric gives a data reusabilityrating of 48.3%. Our procedure shows an increase in public procurement in the municipality in 2011, one of the worst years of the economic crisis, and also finds that outsourcing to external companies in the municipality accounts for 2 to 3 million € more than local contracting.

El objetivo de la investigación es presentar un procedimiento que permita conocer el desarrollo económico y social de una entidad local a partir de iniciativas de gobierno abierto y apertura de la información. Se propone una metodología que facilite esta acción mediante la incorporación de plataformas analíticas a disposición del ciudadano. Para mostrar la aplicación de esta metodología, se explica la creación de la plataforma COMUNDA, que utiliza datos disponibles del Ayuntamiento de la Pobla de Vallbona (Valencia) sobre los gastos municipales para analizar aspectos de la contratación pública. Estos instrumentos de segundo nivel, creados a partir de datos publicados por los ayuntamientos, pueden constituir herramientas analíticas para detectar irregularidades y para publicitar el tejido empresarial del municipio que pueden permitir a los ayuntamientos articular políticas adecuadas, ya las empresas y los particulares conocer mejor las características socioeconómicas de la población. Se ha comprobado la utilidad del protocolo de actuación y análisis propuesto, extrapolable a otros casos, sobre el caso concreto de la plataforma citada. En este caso, la métrica MELODA da una calificación de 48,3% de calidad en la reutilización y se ha podido comprobar que la utilización de nuestro procedimiento constata un incremento de la contratación pública en el municipio en el año 2011, uno de los peores años de la crisis económica, y que la contratación a empresas externas al municipio es de dos a tres millones de euros superior a la contratación local. This study describes a procedure that can trackthe economic and social development of a local government body, based on open government initiatives and openness of information. A methodology is proposed that incorporates analytical platforms available to the general public. To illustrateits application, the creation of the COMUNDA platform is described. The COMUNDA platform uses data provided from the Town Council of La Pobla de Vallbona (Valencia) on municipal spending in order to analyse aspects of public procurement. These second-level instruments, created from data published by the councils, can be useful analytical tools for detecting irregularities and for focusing attention on the business fabric of the municipality. The information obtained can help councils to design appropriate policies and help companies and individuals to understand the socioeconomic characteristics of the population. The article confirms the usefulness of the action and analysis protocolproposed for the platform mentioned, and the results suggest that it can be extrapolated to other scenarios. In this case, the MELODA metric gives a data reusabilityrating of 48.3%. Our procedure shows an increase in public procurement in the municipality in 2011, one of the worst years of the economic crisis, and also finds that outsourcing to external companies in the municipality accounts for 2 to 3 million € more than local contracting.

The axioms of symmetry and indiscernibility of a metric function can be eliminated and still define a topological space with good enough properties. However, among all the axioms that constitute the notion of a metric, the subadditivity or triangular inequality is the one that has been more difficult to relax. Even so, and due to the potential applications in other fields such as Artificial Intelligence, several efforts have been made in this direction. The notion of quasi-Banach space or the notion of b-metric space, are examples of structures where the subadditivity has been replaced by a weaker inequality. Following this line, in this paper we consider the non-symmetric version of the so called strong b-metric spaces. We focus our attention on the possibility of extending semi-Lipschitz maps, and still preserve (a uniform multiple of) the Lipschitz constant. As our main result, we prove that the possibility of obtaining such extensions characterizes the spaces satisfying the proposed weak versions of the triangular inequality. We also show how our results can be applied in Machine Learning to solve some technical issues, in particular, some problems related to the extension of Lipschitz functions with respect to the cosine distance. [ABSTRACT FROM AUTHOR]