Divisibility networks of the rational numbers in the unit interval

[EN] Divisibility networks of natural numbers present a scale-free distribution as many other process in real life due to human interventions. This was quite unexpected since it is hard to find patterns concerning anything related with prime numbers. However, it is by now unclear if this behavior can also be found in other networks of mathematical nature. Even more, it was yet unknown if such patterns are present in other divisibility networks. We study networks of rational numbers in the unit interval where the edges are defined via the divisibility relation. Since we are dealing with infinite sets, we need to define an increasing covering of subnetworks. This requires an order of the numbers different from the canonical one. Therefore, we propose the construction of four different orders of the rational numbers in the unit interval inspired in Cantor's diagonal argument. We motivate why these orders are chosen and we compare the topologies of the corresponding divisibility networks showing that all of them have a free-scale distribution. We also discuss which of the four networks should be more suitable for these analysesJAC was funded by MEC grant number MTM2016-75963-P. PASH acknowledges the support of MESCyT-RD, Casa Brugal, and Fundacion Proyecto Escuela Hoy Inc. for his PhD grants. MAGM acknowledges funding from the Spanish Ministry of Education and Vocational Training (MEFP) through the Beatriz Galindo program 2018 (BEAGAL18/00203) and Spanish Ministry MINECO FIDEUA PID2019-106901GB-I00/10.13039/501100011033.Solares-Hernández, PA.; Garcia March, MA.; Conejero, JA. (2020). Divisibility networks of the rational numbers in the unit interval. Symmetry (Basel). 12(11):1-12. https://doi.org/10.3390/sym12111879S112121

Multiple-Locus Variable Number Tandem Repeat Analysis for Streptococcus pneumoniae: Comparison with PFGE and MLST

In the era of pneumococcal conjugate vaccines, surveillance of pneumococcal disease and carriage remains of utmost importance as important changes may occur in the population. To monitor these alterations reliable genotyping methods are required for large-scale applications. We introduced a high throughput multiple-locus variable number tandem repeat analysis (MLVA) and compared this method with pulsed-field gel electrophoresis (PFGE) and multilocus sequence typing (MLST). The MLVA described here is based on 8 BOX loci that are amplified in two multiplex PCRs. The labeled PCR products are sized on an automated DNA sequencer to accurately determine the number of tandem repeats. The composite of the number of repeats of the BOX loci makes up a numerical profile that is used for identification and clustering. In this study, MLVA was performed on 263 carriage isolates that were previously characterized by MLST and PFGE. MLVA, MLST and PFGE (cut-off of 80%) yielded 164, 120, and 87 types, respectively. The three typing methods had Simpson's diversity indices of 98.5% or higher. Congruence between MLST and MLVA was high. The Wallace of MLVA to MLST was 0.874, meaning that if two strains had the same MLVA type they had an 88% chance of having the same MLST type. Furthermore, the Wallace of MLVA to clonal complex of MLST was even higher: 99.5%. For some isolates belonging to a single MLST clonal complex although displaying different serotypes, MLVA was more discriminatory, generating groups according to serotype or serogroup. Overall, MLVA is a promising genotyping method that is easy to perform and a relatively cheap alternative to PFGE and MLST. In the companion paper published simultaneously in this issue we applied the MLVA to assess the pneumococcal population structure of isolates causing invasive disease in the Netherlands before the introduction of the 7-valent conjugate vaccine

Population dynamics of rhesus macaques and associated foamy virus in Bangladesh.

Foamy viruses are complex retroviruses that have been shown to be transmitted from nonhuman primates to humans. In Bangladesh, infection with simian foamy virus (SFV) is ubiquitous among rhesus macaques, which come into contact with humans in diverse locations and contexts throughout the country. We analyzed microsatellite DNA from 126 macaques at six sites in Bangladesh in order to characterize geographic patterns of macaque population structure. We also included in this study 38 macaques owned by nomadic people who train them to perform for audiences. PCR was used to analyze a portion of the proviral gag gene from all SFV-positive macaques, and multiple clones were sequenced. Phylogenetic analysis was used to infer long-term patterns of viral transmission. Analyses of SFV gag gene sequences indicated that macaque populations from different areas harbor genetically distinct strains of SFV, suggesting that geographic features such as forest cover play a role in determining the dispersal of macaques and SFV. We also found evidence suggesting that humans traveling the region with performing macaques likely play a role in the translocation of macaques and SFV. Our studies found that individual animals can harbor more than one strain of SFV and that presence of more than one SFV strain is more common among older animals. Some macaques are infected with SFV that appears to be recombinant. These findings paint a more detailed picture of how geographic and sociocultural factors influence the spectrum of simian-borne retroviruses

Contextual factors multiplex to control multisensory processes.

This study analyzed high-density event-related potentials (ERPs) within an electrical neuroimaging framework to provide insights regarding the interaction between multisensory processes and stimulus probabilities. Specifically, we identified the spatiotemporal brain mechanisms by which the proportion of temporally congruent and task-irrelevant auditory information influences stimulus processing during a visual duration discrimination task. The spatial position (top/bottom) of the visual stimulus was indicative of how frequently the visual and auditory stimuli would be congruent in their duration (i.e., context of congruence). Stronger influences of irrelevant sound were observed when contexts associated with a high proportion of auditory-visual congruence repeated and also when contexts associated with a low proportion of congruence switched. Context of congruence and context transition resulted in weaker brain responses at 228 to 257 ms poststimulus to conditions giving rise to larger behavioral cross-modal interactions. Importantly, a control oddball task revealed that both congruent and incongruent audiovisual stimuli triggered equivalent non-linear multisensory interactions when congruence was not a relevant dimension. Collectively, these results are well explained by statistical learning, which links a particular context (here: a spatial location) with a certain level of top-down attentional control that further modulates cross-modal interactions based on whether a particular context repeated or changed. The current findings shed new light on the importance of context-based control over multisensory processing, whose influences multiplex across finer and broader time scales

Sets of numbers from complex networks perspective

Tesis por compendio[EN] The study of Complex Systems is one of the scientific fields that has had the highest productivity in recent decades and has not ceased to fascinate the community dedicated to studying its properties. In particular, Network Science has proven to be one of the most prolific areas within Complex Systems. In recent years, his methods have been applied to model multiple phenomena in real life, both naturally generated, such as in biology, and due to the actions and interactions of man, such as social networks or communication networks. Recently, it has been seen how the methods of Network Science can be applied in the context of mathematics, as is the case of Number Theory. One of the most studied cases is networks whose elements are numbers and which are related through the divisibility relation. The main objective of this thesis is to extend these studies to other sets of numbers. On the one hand, we study the divisibility in natural numbers when we obtain these from Pascal matrices of increasing size, which allows us to extract non-sequential sets of numbers with non-constant increments between them. On the other hand, we study the case of the divisibility relation of rational numbers. Cantor's diagonal argument provides a way to order all rational numbers, which allows us to check to what extent some of the properties observed for the divisibility of natural numbers are extensible to a more general context. The thesis is divided into 4 Chapters. Chapter 1 contains a general introduction to the thesis and it is structured into 6 sections. In Sections 1.1 and 1.2, we briefly introduce Network Science, show some application examples, and motivate the study of networks of numbers generated from the divisibility property. In Section 1.3, we define the objectives of this PhD thesis and its scope. In Section 1.4, we present the notion of network, its representations, and some measures that can be calculated on them, such as nodes degrees, their distribution, the assortativity and the clustering coefficients. In another hand, in Section 1.5, we review the best-known network models such as Erdo¿s and Re'nyi random networks, Watts and Strogatz small-world networks, Baraba'si and Albert scale-free networks, and hierarchical networks. Finally, at the end of this Chapter 1, we show in Section 1.6 a review of various studies carried out in order to apply Network Science methods to problems and properties that arise in Number Theory, such as divisibility networks or networks generated from Collatz's Conjecture. or Goldbach's Strong Conjecture. In Chapters 2 and 3, we show the results obtained and that have been published to date. Finally, in Chapter 4, we summarize the conclusions obtained and indicate some related problems that we consider of interest to address in the future.[ES] El estudio de los Sistemas Complejos es uno de los campos científicos que ha tenido mayor productividad en las últimas décadas y no ha dejado de fascinar a la comunidad que se dedica al estudio de sus propiedades. En particular, la Ciencia de Redes se ha mostrado como una de las áreas más prolíficas dentro de los Sistemas Complejos. En los últimos años, sus métodos han sido aplicados para modelar múltiples fenómenos de la vida real tanto generados de manera natural, como puede ser en el caso de la biología, como debidos a las acciones e interacciones del hombre, como puede ser el caso de las redes sociales o las redes de comunicaciones. Recientemente, se ha visto cómo los métodos de la Ciencia de Redes pueden ser aplicados en el contexto de las matemáticas, como es el caso de la Teoría de Números. Uno de los casos que más se han estudiado es el de las redes cuyos elementos son números y que se relacionan mediante la relación de la divisibilidad. El objetivo principal de esta tesis es extender estos estudios a otros conjuntos de números. Por una parte, estudiamos la divisibilidad en los números naturales cuando obtenemos estos a partir de subconjuntos de números naturales extraídos de matrices de Pascal de orden creciente, lo que nos permite extraer conjuntos de números de manera no secuencial y con incrementos no constantes entre ellos. Por otra parte, estudiamos el caso de la relación de divisibilidad de los números racionales, dado que a partir del argumento diagonal de Cantor se pueden ordenar, lo que nos permite comprobar hasta qué punto algunas de las propiedades observadas para la divisibilidad de los números naturales son extensibles a un contexto más general. La tesis se divide en 4 capítulos. El capítulo 1 contiene una introducción general a la tesis y está estructurado en 6 secciones. En las secciones 1.1 y 1.2, presentamos brevemente la Ciencia de Redes, mostrando algunos ejemplos de aplicación y motivamos el estudio de redes de números generadas a partir de la propiedad de divisibilidad. En la Section 1.3, definimos los objetivos de esta tesis doctoral y su alcance. En la sección 1.4, presentamos la noción de red, sus formas de representación y algunas medidas que se pueden calcular sobre ellas, como son los grados de los nodos, la distribución de estos grados, la asortatividad y los coeficientes de clustering. Por otro lado, en la Sección 1.5, revisamos los modelos de redes más conocidos como son las redes aleatorias de Erdös y Rényi, las redes de pequeño mundo de Watts y Strogatz, las redes libres de escala de Barabási y Albert y las redes jerárquicas. Mostramos en la Sección 1.6, una revisión de diversos estudios realizados con el fin de aplicar métodos de la Ciencia de Redes a problemas y propiedades que surgen en la Teoría de Números, como son las redes de divisibilidad o redes generadas a partir de la Conjetura de Collatz o la Conjetura Fuerte de Goldbach. En los Capítulos 2 y 3, mostramos los resultados obtenidos y que han sido publicados hasta la fecha y, finalmente, en el Capítulo 4, resumimos las conclusiones obtenidas e indicamos algunos problemas relacionados que consideramos de interés abordar en un futuro.[CAT] L'estudi dels Sistemes Complexos és un dels camps científiques que ha tingut major productivitat en les últimes dècades i no ha deixat de fascinar a la comunitat que es dedica a l'estudi de les seues propietats. En particular, la Ciència de Xarxes s'ha mostrat com una de les àrees més prolífica dins dels Sistemes Complexos. En els últims anys, els seus mètodes han sigut aplicats per a modelar múltiples fenòmens de la vida real tant generats de manera natural, com pot ser en el cas de la biologia, com deguts a les accions i interaccions de l'home, com pot ser el cas de les xarxes socials o les xarxes de comunicacions. Recentment, s'ha vist com els mètodes de la Ciència de Xarxes poden ser aplicats en el context de les matemàtiques, com és el cas de la Teoria de Números. Un dels casos que més s'han estudiat és el de les xarxes els elements de les quals són números i que es relacionen mitjançant la relació de la divisibilitat. L'objectiu principal d'aquesta tesi és estendre aquests estudis a altres conjunts de números. D'una banda, estudiem la divisibilitat en els nombres naturals quan obtenim aquests a partir de matrius de Pascal de grandària creixent, la qual cosa ens permet extraure conjunts de números de manera no sequëncial i amb increments no constants entre ells. D'altra banda, estudiem el cas de la relació de divisibilitat dels nombres racionals, atés que a partir de l'argument diagonal de Cantor es poden ordenar, la qual cosa ens permet comprovar fins a quin punt algunes de les propietats observades per a la divisibilitat dels nombres naturals són extensibles a un context més general. La tesi es troba dividida en 4 Capítols. El capítol 1, conté una introducció general a la tesi i está estructurat en 6 seccions. En les seccions 1.1 i 1.2, presentem breument la Ciència de Xarxes, mostrant alguns exemples d'aplicació i motivem l'estudi de xarxes de números generades a partir de la propietat de divisibilitat. En la Section 1.3, definim els objectius d'aquesta tesi doctoral y el seu abast. En la Secció 1.4, presentem la noció de xarxa, les seves formes de representació i algunes mesures que es poden calcular sobre elles, com són els graus dels nodes, la distribució d'aquests graus, la asortatividad i els coeficients de clustering. En la Sección 1.5, revisem els models de xarxes més coneguts com són les xarxes aleatòries de Erdös i Renyi, les xarxes de xicotet món de Watts i Strogatz, les xarxes lliures d'escala de Barabási i Albert i les xarxes jeràrquiques. Mostrem en la Sección 1.6 una revisió de diversos estudis realitzats amb la finalitat d'aplicar mètodes de la Ciència de Xarxes a problemes i propietats que sorgeixen en la Teoria de Números, com són les xarxes de divisibilitat o xarxes generades a partir de la Conjectura de Collatz o la Conjectura Forta de Goldbach. En els Capítols 2 i 3, vam mostrar els resultats obtinguts i que han sigut publicats fins hui i, finalment, en el Capítol 4, resumim les conclusions obtingudes i indiquem alguns problemes relacionats que considerem d'interés abordar en un futur.Solares Hernández, PA. (2021). Sets of numbers from complex networks perspective [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176015TESISCompendi

Criminal justice and global public goods: The Prüm Forensic Biometric Cooperation

This article places sharing forensic biometric data for international criminal justice cooperation purposes within the domain of global public goods. Such cooperation is a rational response to globalization, but faces several obstacles. These range from socio-cultural and political concerns about national legal and criminal justice autonomy to the potential impact of market fundamentalism on scientific standardization and cooperation mechanism delivery. The significance of such inhibitors will vary as societal and personal perceptions of stability change. These issues are examined by analysing the progress achieved with the EU Prüm forensic biometric data exchange model. Shocks to European stability, such as the increased scale of terrorist crimes and the UK EU referendum result will inevitably test the resilience of Prüm. Combining insights from global public goods and criminal law scholarship, however, may help to identify how reactions to such shocks, including questions about future UK participation in Prüm, might be managed

Quantum communication networks with optical vortices

Quantum communications bring a paradigm change in internet security by using quantum resources to establish secure keys between parties. Present-day quantum communications networks are mainly point-to-point and use trusted nodes and key management systems to relay the keys. Future quantum networks, including the quantum internet, will have complex topologies in which groups of users are connected and communicate with each-other. Here we investigate several architectures for quantum communication networks. We show that photonic orbital angular momentum (OAM) can be used to route quantum information between different nodes. Starting from a simple, point-to-point network, we will gradually develop more complex architectures: point-to-multipoint, fully-connected and entanglement-distribution networks. As a particularly important result, we show that an $n$-node, fully-connected network can be constructed with a single OAM sorter and $n-1$ OAM values. Our results pave the way to construct complex quantum communication networks with minimal resources.Comment: 10 pages, 9 figure

Epidemiological studies of Streptococcus pneumoniae carriage in the post-vaccination era among two risk groups: children and the elderly

Dissertation presented to obtain the Ph.D. degree in Biology/ Molecular BiologyStreptococcus pneumoniae is a global cause of disease including pneumonia, otitis media, conjunctivitis, sepsis, and bacterial meningitis. These infections are not essential to the transmission or long-term survival of the bacterium; indeed, S. pneumoniae depends on asymptomatic colonization of the human nasopharynx for its dissemination to additional hosts. Considering this, colonization studies are a good way to monitor changes in the pneumococcal epidemiology that may result from the use of antibiotics and vaccines. The molecular characterization of pneumococci is crucial to assess these changes which highlight the need for the development and validation of easier and faster methods of molecular typing. Since 1996 our group has been monitoring the pneumococcal population colonizing children attending day care centers. However, for several years these studies have been confined to the Lisbon area. In this PhD we have addressed this situation by including other regions of Portugal in our study. In addition, we have started to study pneumococcal colonization in the elderly, the other age group where the incidence of pneumococcal infections is high. This thesis summarizes five studies conducted during this PhD. The first four studies were focused on the pneumococcal epidemiology among the two age groups where the rates of pneumococcal disease are highest: children up to six years old and adults older than 60 years. The fifth and last study describes the evaluation and validation of a new genotyping strategy for pneumococci.(...)Financial support from Fundação para a Ciência e a Tecnologia, Portugal through grant SFRH/BD/40706/2007 awarded to Sónia Nunes