Nine Chapters of Analytic Number Theory in Isabelle/HOL

In this paper, I present a formalisation of a large portion of Apostol\u27s Introduction to Analytic Number Theory in Isabelle/HOL. Of the 14 chapters in the book, the content of 9 has been mostly formalised, while the content of 3 others was already mostly available in Isabelle before. The most interesting results that were formalised are: - The Riemann and Hurwitz zeta functions and the Dirichlet L functions - Dirichlet\u27s theorem on primes in arithmetic progressions - An analytic proof of the Prime Number Theorem - The asymptotics of arithmetical functions such as the prime omega function, the divisor count sigma_0(n), and Euler\u27s totient function phi(n

Strategyproofness and Proportionality in Party-Approval Multiwinner Elections

In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each party can be assigned multiple seats. Two central requirements in this setting are proportional representation and strategyproofness. Intuitively, proportional representation requires that every sufficiently large group of voters with similar preferences is represented in the committee. Strategyproofness demands that no voter can benefit by misreporting her true preferences. We show that these two axioms are incompatible for anonymous party-approval multiwinner voting rules, thus proving a far-reaching impossibility theorem. The proof of this result is obtained by formulating the problem in propositional logic and then letting a SAT solver show that the formula is unsatisfiable. Additionally, we demonstrate how to circumvent this impossibility by considering a weakening of strategy\-proofness which requires that only voters who do not approve any elected party cannot manipulate. While most common voting rules fail even this weak notion of strategyproofness, we characterize Chamberlin--Courant approval voting within the class of Thiele rules based on this strategyproofness notion.Comment: Appears in the 37th AAAI Conference on Artificial Intelligence (AAAI), 202

Estudio de la biopelícula formada por dos especies de pseudomonas asociadas a plantas

Las bacterias pertenecientes al género Pseudomonas constituyen un modelo de estudio de la interacción microorganismo-planta. Pseudomonas syringae es una especie que produce enfermedades en la parte aérea de algunas plantas. Por otro lado, Pseudomonas chlororaphis interacciona con la raíz y ha demostrado ser un agente de control biológico. Ambas especies forman biopelículas y, a pesar de su diferente estilo de vida, análisis in silico han puesto de manifiesto la existencia de regiones genómicas tanto comunes como diferenciales que parecen estar implicadas en la biosíntesis de matriz extracelular. En este trabajo se han construido mutantes de estas regiones y analizado su implicación en la formación de biopelícula y aspectos relacionados.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Este trabajo ha sido financiado por el Proyecto de Excelencia de la CICE, Junta de Andalucía (P12-AGR-1473) y el Proyecto del Plan Nacional I+D+I MINECO (AGL2017-83368-C2-l-R), cofinanciados ambos con fondos FEDER. Zaira María Heredia está financiada por un contrato del programa FPU del Ministerio de Educación (referencia FPU15/03644)

A Psl-like polysaccharide has a key role in the biofilm architecture of two plant-associated Pseudomonas

Comunicación congresoThe Psl polysaccharide has only been studied in Pseudomonas aeruginosa, and its role in bacteria that interact with plants is still unknown. On the one hand, P. syringae is a model of study of plant-pathogen interactions. On the other hand, P. chlororaphis is a biocontrol agent of plant-fungal diseases, as the white root rot caused by Rosellinia necatrix. In silico analysis have let us identify in both species a genomic region which is ortholog to the Psl-encoding region of P. aeruginosa PAO1. We constructed mutants of this region in both strains and analysed its phenotype in biofilm formation, both in static microwell plates and dynamic flow-cell chamber experiments. The results revealed a different and an important role of this polysaccharide in the biofilm architecture of both strains. Furthermore, in P. syringae this Psl-like polysaccharide has a very important role in swarming motility. All these striking phenotypes led us further study the implication of this polysaccharide in the lifestyles of both models of plant-bacteria interaction.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. AGL2017-83368-C2-1-

Notch regulates Th17 differentiation and controls trafficking of IL-17 and metabolic regulators within Th17 cells in a context-dependent manner

Th17 cells play critical roles in host defense and autoimmunity. Emerging data support a role for Notch signaling in Th17 cell differentiation but whether it is a positive or negative regulator remains unclear. We report here that T cell-specific deletion of Notch receptors enhances Th17 cell differentiation in the gut, with a corresponding increase in IL-17 secretion. An increase in Th17 cell frequency was similarly observed following immunization of T cell specific Notch mutant mice with OVA/CFA. However, in this setting, Th17 cytokine secretion was impaired, and increased intracellular retention of IL-17 was observed. Intracellular IL-17 co-localized with the CD71 iron transporter in the draining lymph node of both control and Notch-deficient Th17 cells. Immunization induced CD71 surface expression in control, but not in Notch-deficient Th17 cells, revealing defective CD71 intracellular transport in absence of Notch signaling. Moreover, Notch receptor deficient Th17 cells had impaired mTORC2 activity. These data reveal a context-dependent impact of Notch on vesicular transport during high metabolic demand suggesting a role for Notch signaling in the bridging of T cell metabolic demands and effector functions. Collectively, our findings indicate a prominent regulatory role for Notch signaling in the fine-tuning of Th17 cell differentiation and effector function

A Supersymmetric Explanation of the Excess of Higgs-Like Events at LEP

Searches for the Standard Model Higgs boson by the four LEP experiments found excess events in two mass ranges: a 2.3 sigma excess around 98 GeV, and an 1.7 sigma excess around 115 GeV. The latter has been discussed widely in the literature, but the former has attracted little attention so far. In this paper I explore the possibility of explaining the excess near 98 GeV through production of the lighter CP--even Higgs boson in the Minimal Supersymmetric Standard Model (MSSM). It is shown that this allows to simultaneously explain the excess near 115 GeV through the production of the heavier CP--even MSSM Higgs boson. The resulting light Higgs sector offers opportunities for charged Higgs boson searches at the Tevatron and LHC. Neutral Higgs boson searches at the LHC in the di--muon channel are also promising. However, conclusive tests of this scenario may have to wait for the construction of a linear e+ e- collider.Comment: LaTeX, 14 pages, 7 .eps-files (included). Added references and a couple of footnotes; results unchanged. Version to appear in PR

A 3D individual-based model to investigate the spatially heterogeneous response of bacterial biofilms to antimicrobial agents

The response of bacterial biofilms to treatment with antimicrobial agents is often characterized by the emergence of recalcitrant cellular microcolonies. We present an individual-based model to investigate the biophysical mechanisms of the selective resistance that arises within the biofilm and leads to a spatially heterogeneous response upon treatment with antibiotics. The response occurs in 3 distinct phases. In the first phase, the subpopulation of metabolically active cells diminishes due to antibiotic-induced cell death. Subsequently, in the second phase, increased nutrient availability allows dormant cells in the lower layers of the biofilm to transform into metabolically active cells. In the third phase, survival of the biofilm is governed by the interplay between 2 contrasting factors: (1) rate of antibiotic-induced cell death and (2) rate of transformation of dormant cells into active ones. Metabolically active cells at the distal edge of the biofilm sacrifice themselves to protect the dormant cells in the interior by (1) reducing local antibiotic concentrations and (2) increasing nutrient availability. In the presence of quorum sensing, biofilms exhibit increased tolerance compared with the quorum sensing-negative strains. Extracellular polymeric substance (EPS) forms a protective layer at the top of the biofilm, thereby limiting antibiotic penetration. The surviving cells, in turn, produce EPS resulting in a feedback-like mechanism of resistance. Whereas resistance in QS- biofilms occurs because of transformation of dormant cells into metabolically active cells, this transformation is less pronounced in QS+ biofilms, and resistance is a consequence of the sequestration of the antibiotic by EPS

A Fistful of Dollars: Formalizing Asymptotic Complexity Claims via Deductive Program Verification

Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018International audienceWe present a framework for simultaneously verifying the functional correctness and the worst-case asymptotic time complexity of higher-order imperative programs. We build on top of Separation Logic with Time Credits, embedded in an interactive proof assistant. We formalize the O notation, which is key to enabling modular specifications and proofs. We cover the subtleties of the multivariate case, where the complexity of a program fragment depends on multiple parameters. We propose a way of integrating complexity bounds into specifications, present lemmas and tactics that support a natural reasoning style, and illustrate their use with a collection of examples