La funció Z de Riemann

El novembre de 1859 Riemann envià un manuscrit de sis fulls a l’Acadèmia de Berlín titulat Sobre el nombre de primers menors que una quantitat donada, el qual seria l’única publicació dedicada a la teoria de nombres de tota la seva producció científica. Aquest treball, sens dubte una de les peces mestres de les matemàtiques de tots els temps, és pioner en l’aplicació de tècniques analítiques per a l’estudi de problemes aritmètics. En ell Riemann introdueix la funció Z i en dóna diverses propietats, de les quals en treu conseqüències sobre l’acumulació dels nombres primers. També hi enuncia la famosa conjectura sobre els seus zeros que ha passat a la història amb el nom d’hipòtesi de Riemann, i que, havent resistit els esforços de molts dels millors matemàtics del segle xx, és considerada avui dia el problema obert més important de les matemàtiques. L’objectiu d’aquestes notes és explicar el contingut del treball de Riemann i el paper fonamental que ha jugat en l’estudi de la distribució dels nombres primers.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

L'esquema universal de clústers de 2-seccions d'una família de superfícies

Generalitzem el concepte de clúster de punts d'una superfície a clúster de seccions d'una família de superfícies per passar al cas relatiu, és a dir, a clústers de B-punts d'una B-superfície. Llavors definim, amb una propietat universal, la família universal de clusters de 2-seccions d'una família de superfícies, que, en cas que existir, és un esquema que parametritza tots els clústers de 2-seccions d'una famíla de superfícies. Demostrem la seva existencia sota certes hipotesis i trobem que es pot construir en termes de blowups a partir del producte de la família universal de seccions de la fmília de superficies per si mateixa. Al final del treball hi ha tres exemples que mostren part de la teoria estudiada.

Id Gene regulation and function in the prosensory domains of the chicken inner ear: a link between Bmp Signaling and Atoh1

Bone morphogenetic proteins (Bmps) regulate the expression of the proneural gene Atoh1 and the generation of hair cells in the developing inner ear. The present work explored the role of Inhibitor of Differentiation genes (Id1-3) in this process. The results show that Id genes are expressed in the prosensory domains of the otic vesicle, along with Bmp4 and Bmp7. Those domains exhibit high levels of the phosphorylated form of Bmp-responding R-Smads (P-Smad1,5,8), and of Bmp-dependent Smad transcriptional activity as shown by the BRE-tk-EGFP reporter. Increased Bmp signaling induces the expression of Id1-3 along with the inhibition of Atoh1. Conversely, the Bmp antagonist Noggin or the Bmp-receptor inhibitor Dorsomorphin elicit opposite effects, indicating that Bmp signaling is necessary for Id expression and Atoh1 regulation in the otocyst. The forced expression of Id3 is sufficient to reduce Atoh1 expression and to prevent the expression of hair cell differentiation markers. Together, these results suggest that Ids are part of the machinery that mediates the regulation of hair cell differentiation exerted by Bmps. In agreement with that, during hair cell differentiation Bmp4 expression, P-Smad1,5,8 levels and Id expression are downregulated from hair cells. However, Ids are also downregulated from the supporting cells which contrarily to hair cells exhibit high levels of Bmp4 expression, P-Smad1,5,8, and BRE-tk-EGFP activity, suggesting that in these cells Ids escape from Bmp/Smad signaling. The differential regulation of Ids in time and space may underlie the multiple functions of Bmp signaling during sensory organ development.

Intrinsic subspace convergence in TDD MIMO communication

In numerical linear algebra, students encounter earlythe iterative power method, which finds eigenvectors of a matrixfrom an arbitrary starting point through repeated normalizationand multiplications by the matrix itself. In practice, more sophisticatedmethods are used nowadays, threatening to make the powermethod a historical and pedagogic footnote. However, in the contextof communication over a time-division duplex (TDD) multipleinputmultiple-output (MIMO) channel, the power method takes aspecial position. It can be viewed as an intrinsic part of the uplinkand downlink communication switching, enabling estimationof the eigenmodes of the channel without extra overhead. Generalizingthe method to vector subspaces, communication in thesubspaces with the best receive and transmit signal-to-noise ratio(SNR) is made possible. In exploring this intrinsic subspace convergence(ISC), we show that several published and new schemes canbe cast into a common framework where all members benefit fromthe ISC.

Kumar's algorithm for solving Toeplitz systems of equations over finite fields

Adaptació de l'algorisme de Kumar per resoldre sistemes d'equacions amb matrius de Toeplitz sobre els reals a cossos finits en un temps 0 (n log n).

An update of the mechanisms of resistance to EGFR-tyrosine kinase inhibitors in breast cancer: gefitinib (Iressatrade mark)-induced changes in the expression and nucleo-cytoplasmic trafficking of HER-ligands (Review)

Intrinsic resistance to the epidermal growth factor receptor (EGFR; HER1) tyrosine kinase inhibitor (TKI) gefitinib, and more generally to EGFR TKIs, is a common phenomenon in breast cancer. The availability of molecular criteria for predicting sensitivity to EGFR-TKIs is, therefore, the most relevant issue for their correct use and for planning future research. Though it appears that in non-small-cell lung cancer (NSCLC) response to gefitinib is directly related to the occurrence of specific mutations in the EGFR TK domain, breast cancer patients cannot be selected for treatment with gefitinib on the same basis as such EGFR mutations have beenreported neither in primary breast carcinomas nor in several breast cancer cell lines. Alternatively, there is a generalagreement on the hypothesis that the occurrence of molecular alterations that activate transduction pathways downstreamof EGFR (i.e., MEK1/MEK2 - ERK1/2 MAPK and PI-3'K - AKT growth/survival signaling cascades) significantly affect the response to EGFR TKIs in breast carcinomas. However,there are no studies so far addressing a role of EGF-related ligands as intrinsic breast cancer cell modulators of EGFR TKIefficacy. We recently monitored gene expression profiles andsub-cellular localization of HER-1/-2/-3/-4 related ligands (i.e., EGF, amphiregulin, transforming growth factor-α, ß-cellulin,epiregulin and neuregulins) prior to and after gefitinib treatment in a panel of human breast cancer cell lines. First, gefitinibinduced changes in the endogenous levels of EGF-related ligands correlated with the natural degree of breast cancer cellsensitivity to gefitinib. While breast cancer cells intrinsically resistant to gefitinib (IC50 ≥15 μM) markedly up-regulated(up to 600 times) the expression of genes codifying for HERspecific ligands, a significant down-regulation (up to 106 times)of HER ligand gene transcription was found in breast cancer cells intrinsically sensitive to gefitinib (IC50 ≤1 μM). Second,loss of HER1 function differentially regulated the nuclear trafficking of HER-related ligands. While gefitinib treatment induced an active import and nuclear accumulation of the HER ligand NRG in intrinsically gefitinib-resistant breastcancer cells, an active export and nuclear loss of NRG was observed in intrinsically gefitinib-sensitive breast cancer cells.In summary, through in vitro and pharmacodynamic studies we have learned that, besides mutations in the HER1 gene,oncogenic changes downstream of HER1 are the key players regulating gefitinib efficacy in breast cancer cells. It now appears that pharmacological inhibition of HER1 functionalso leads to striking changes in both the gene expression and the nucleo-cytoplasmic trafficking of HER-specific ligands,and that this response correlates with the intrinsic degree of breast cancer sensitivity to the EGFR TKI gefitinib. Therelevance of this previously unrecognized intracrine feedback to gefitinib warrants further studies as cancer cells could bypassthe antiproliferative effects of HER1-targeted therapeutics without a need for the overexpression and/or activation of other HER family members and/or the activation of HER-driven downstream signaling cascades

Elements crisipians en àlgebres d-completes i àlgebres de Sales

El autor estudia los elementos de comportamiento clásico, o crisipianos, en álgebras d-completas (introducidas por él mismo como el sustrato algebraico de las lógicas completas) y en álgebras de Sales (sustrato algebraico de las lógicas multivaloradas). Da caracterizaciones de estos elementos en ambos casos. Estudia la relación de dichos elementos con los espectros irreducible, primo y completamente irreducible. Además obtiene que el conjunto de elementos crisipianos de un álgebra de Sales es una subálgebra y es un álgebra de Abbott (o de implicación).

The differentiable chain functor is not homotopy equivalent to the continuous chain functor

Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

Monoidal functors, acyclic models and chain operads

We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.

Dels jeroglífics egipcis a la compartició de secrets

En aquest article parlarem d'un jeroglífic inscrit als laterals de la llinda de Sant Andreu de la Barroca, una petita església perduda en un indret recòndit de la Vall del Llémena, a la Garrotxa. A propòsit d'aquest petit enigma ludolingüístic, plantejarem(i finalment resoldrem) un problema de naturalesa combinatòria que el lector interessat pot provar de resoldre com a exercici. També fem un breu repàs de la història del desxiframent '’escriptures de civilitzacions antigues. Aprofitem l'avinentesa per introduir els conceptes d'entropia i redundància del llenguatge, que ens ajudaran a entendre per què, tard o d'hora, qualsevolescriptura antiga finalment acaba essent desxifrada quan es té una conjectura raonable sobre quina és la llengua que transcriu. Finalment, definim el concepte d'esquema de compartició de secrets, un problema de criptografia moderna en el qual un conjunt de persones gestiona petits fragments d'informació compartida, i que es resol aplicant de manera brillant una idea que prové del món de l'àlgebra lineal més elemental

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem.