Quantum álgorithms for the combinatorial invariants of numerical semigroups

It was back in spring 2014 when the author of this doctoral dissertation was finishing its master thesis, whose main objective was the understanding of Peter W. Shor’s most praised result, a quantum algorithm capable of factoring integers in polynomial time. During the development of this master thesis, me and my yet-tobe doctoral advisor studied the main aspects of quantum computing from a purely algebraic perspective. This research eventually evolved into a sufficiently thorough canvas capable of explaining the main aspects and features of the mentioned algorithm from within an undergraduate context. Just after its conclusion, we seated down and elaborated a research plan for a future Ph.D. thesis, which would expectantly involve quantum computing but also a branch of algebra whose apparently innocent definitions hide some really hard problems from a computational perspective: the theory of numerical semigroups. As will be seen later, the definition of numerical semigroup does not involve sophisticated knowledge from any somewhat obscure and distant branch of the tree of mathematics. Nonetheless, a number of combinatorial problems associated with these numerical semigroups are extremely hard to solve, even when the size of the input is relatively small. Some examples of these problems are the calculations of the Frobenius number, the Apéry set, and the Sylvester denumerant, all of them bearing the name of legendary mathematicians. This thesis is the result of our multiple attempts to tackle those combinatorial problems with the help of a hypothetical quantum computer. First, Chapter 2 is devoted to numerical semigroups and computational complexity theory, and is divided into three sections. In Section 2.1, we give the formal definition of a numerical semigroup, along with a description of the main problems involved with them. In Section 2.2, we sketch the fundamental concepts of complexity theory, in order to understand the true significance within the inherent hardness concealed in the resolution of those problems. Finally, in Section 2.3 we prove the computational complexity of the problems we aim to solve. Chapter 3 is the result of our outline of the theory of quantum computing. We give the basic definitions and concepts needed for understanding the particular place that quantum computers occupy in the world of Turing machines, and also the main elements that compose this particular model of computation: quantum bits and quantum entanglement. We also explain the two most common models of quantum computation, namely quantum circuits and adiabatic quantum computers. For all of them we give mathematical definitions, but always having in mind the physical experiments from which they stemmed. Chapter 4 is also about quantum computing, but from an algorithmical perspective. We present the most important quantum algorithms to date in a standardized way, explaining their context, their impact and consequences, while giving a mathematical proof of their correctness and worked-out examples. We begin with the early algorithms of Deutsch, Deutsch-Jozsa, and Simon, and then proceed to explain their importance in the dawn of quantum computation. Then, we describe the major landmarks: Shor’s factoring, Grover’s search, and quantum counting. Chapter 5 is the culmination of all previously explained concepts, as it includes the description of various quantum algorithms capable of solving the main problems inside the branch of numerical semigrops. We present quantum circuit algorithms for the Sylvester denumerant and the numerical semigroup membership, and adiabatic quantum algorithms for the Ap´ery Set and the Frobenius problem. We also describe a C++ library called numsem, specially developed within the context of this doctoral thesis and which helps us to study the computational hardness of all previously explained problems from a classical perspective. This thesis is intended to be autoconclusive at least in the main branches of mathematics in which it is supported; that is to say numerical semigroups, computational complexity theory, and quantum computation. Nevertheless, for the majority of concepts explained here we give references for the interested reader that wants to delve more into them

The Relationship between Social Responsibility and Business Performance: An Analysis of the Agri-Food Sector of Southeast Spain

This study aims to contribute to the existing debate on the impact of corporate social responsibility (CSR) orientation on different measures of business performance through the proposal of a conceptual model. Drawing on stakeholder theory, we conceptualize CSR as a broad and multidimensional construct with seven dimensions: employees, partners, customers, farmers, environment, community, and competition. We also extend the concept of business performance, which includes tangible variables, namely financial performance (FP) and export performance (EXP), as well as intangible variables, namely image and reputation (IR) and the satisfaction of relevant stakeholders (SS). The research context of this study is the agri-food sector in southeastern Spain. This sector has been the focus of attention of numerous researchers due to the relevance that social and environmental aspects have had in its development. To test the proposed model, the partial least-squares technique (PLS-SEM) was applied to data collected by means of a survey from a sample of 107 companies, which represent 81.4% of the turnover of the sector analyzed. The results show that CSR has a positive effect on financial performance, improves the volume and performance of exports, positively affects the corporate image and reputation, and increases the level of satisfaction of relevant stakeholders. Further research should examine the model from the perceptions of other stakeholders (e.g., customers, employees, and suppliers), using a longitudinal research design and exploring other contexts

Ruminal Fistulation and Cannulation: A Necessary Procedure for the Advancement of Biotechnological Research in Ruminants

Rumen content is a complex mixture of feed, water, fermentation products, and living organisms such as bacteria, fungi, and protozoa, which vary over time and with different feeds. As it is impossible to reproduce this complex system in the laboratory, surgical fistulation and cannulation of the rumen is a powerful tool for the study (in vivo and in situ) of the physiology and biochemistry of the ruminant digestive system. Rumen fistulation in cattle, sheep, and goats has been performed extensively to advance our understanding of digestive physiology and development, nutrient degradability, and rumen microbial populations. The literature reports several fistulation and cannulation procedures in ruminants, which is not the focus of this paper. However, this method questions the ethical principles that alter the opinions of certain animal groups or those opposed to animal experimentation. In this article, we analyze the objectives of fistulation and cannulation of ruminants and the care needed to ensure that the welfare of the animal is maintained at all times. Due to the ethical issues raised by this technique, several in vitro digestion methods for simulating ruminal fermentation have been developed. The most relevant ones are described in this article. Independently of the procedure, we want to point out that research carried out with animals is obliged by legislation to follow strict ethical protocols, following the well-being and health status of the animal at all timesS

Insects in ruminant nutrition as an urgent measure in the light of the scarcity of raw feedstock

Global population growth will lead to an increase in demand for animal-based foods, such as meat and milk from ruminants, which will require restructuring some of the components of the ration (Castillo et al., 2017; Van Huis, 2020). This need is controversial for several reasons: 1) contribution to the depletion of environmental resources; 2) competition of protein sources with human food or fuel increasing prices for farmers, minimising farm profitabilityS

Distributed cognition applied to the empirical analysis of computer supported collaborative kowledge management interactions

In the field of Human Computer Interaction, and more specifically in the field of Computer Supported Collaborative Work and Knowledge Management, cognitive and sociological dimensions cannot be neglected in the design of value analysis. The material and social environment models almost all cognitive processes because the vast majority of them are mediated by the interaction with other agents and other artifacts. Computers connected to the Internet, are becoming fundamental elements of these interactions. Following these premises, in this paper, a methodological framework is applied, called MAIA (Methodology for the analysis of the interaction between agents of a socio-technical system), structured and based on distributed cognition in order to facilitate the analysis of a collaborative Web system oriented to knowledge management in an academic context, at high university level. Specifically, the analysis focuses on the interactions of cognitive agents that occur during the cycle of knowledge management (activities to use, create, distribute and share knowledge), and on how they affect coordination, communication and collaboration, key aspects of group work.XI Workshop de Ingeniería de SoftwareRed de Universidades con Carreras de Informática (RedUNCI

Certifying entanglement of spins on surfaces using ESR-STM

We propose a protocol to certify the presence of entanglement in artificial on-surface atomic and molecular spin arrays using electron spin resonance carried by scanning tunnel microscopy (ESR-STM). We first generalize the theorem that relates global spin susceptibility as an entanglement witness to the case of anisotropic Zeeman interactions, relevant for surfaces. We then propose a method to measure the spin susceptibilities of surface-spin arrays combining ESR-STM with atomic manipulation. Our calculations show that entanglement can be certified in antiferromagnetically coupled spin dimers and trimers with state-of-the-art ESR-STM magnetometry.J.F.R. acknowledges financial support from FCT (Grant No. PTDC/FIS-MAC/2045/2021), SNF Sinergia (Grant Pimag), FEDER/Junta de Andalucía, (Grant No. P18-FR-4834), Generalitat Valenciana funding Prometeo2021/017 and MFA/2022/045, and funding from MICINN-Spain (Grant No. PID2019-109539GB-C41). Y.D.C. acknowledges funding from FCT and QPI, (Grant No. SFRH/BD/151311/2021) and acknowledges the hospitality of the Departamento de Física Aplicada at the Universidad de Alicante

Distributed cognition applied to the empirical analysis of computer supported collaborative kowledge management interactions

In the field of Human Computer Interaction, and more specifically in the field of Computer Supported Collaborative Work and Knowledge Management, cognitive and sociological dimensions cannot be neglected in the design of value analysis. The material and social environment models almost all cognitive processes because the vast majority of them are mediated by the interaction with other agents and other artifacts. Computers connected to the Internet, are becoming fundamental elements of these interactions. Following these premises, in this paper, a methodological framework is applied, called MAIA (Methodology for the analysis of the interaction between agents of a socio-technical system), structured and based on distributed cognition in order to facilitate the analysis of a collaborative Web system oriented to knowledge management in an academic context, at high university level. Specifically, the analysis focuses on the interactions of cognitive agents that occur during the cycle of knowledge management (activities to use, create, distribute and share knowledge), and on how they affect coordination, communication and collaboration, key aspects of group work.XI Workshop de Ingeniería de SoftwareRed de Universidades con Carreras de Informática (RedUNCI

Optimization of a refinery scheduling process with column generation and a quantum annealer

This study focuses on the optimization of a refinery scheduling process with the help of an adiabatic quantum computer, and more concretely one of the quantum annealers developed by D-Wave Systems. We present an algorithm for finding a global optimal solution of a MILP that leans on a solver for QUBO problems, and apply it to various possible cases of refinery scheduling optimization. We analyze the inconveniences found during the whole process, whether due to the heuristic nature of D-Wave or the implications of reducing a MILP to QUBO, and present some experimental resultsS