Zeta functions and Eisenstein series on classical groups

We construct an Euler product from the Hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a CM field and the eigenform is holomorphic. We also prove analytic continuation of an Eisenstein series on another unitary group, containing the group just mentioned defined with such an eigenform. As an application of our methods, we prove an explicit class number formula for a totally definite hermitian form over a CM field.

Congruences between modular forms: Raising the level and dropping Euler factors

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida’s result accounts for congruences in terms of the value of an L-function, and Ribet’s result is related to the behavior of the period that appears there. Wiles’ theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at “nonminimal level” is obtained from one at “minimal level” by dropping Euler factors from the L-function.

Prime Minister Fico’s Russian card. OSW COMMENTARY NUMBER NUMBER 175/01.07.2015

Since the beginning of the Ukrainian-Russian conflict, the position of Slovakia’s left-wing government towards Russia has been ambiguous. Bratislava has accepted the EU sanctions targeting Russia and the plan for strengthening NATO’s eastern flank. At the same time, however, Prime Minister Robert Fico’s government has maintained close political relations with the Kremlin. It has called for the intensification of Slovak-Russian economic relations and has repeatedly criticised the sanctions, speaking in tandem with Russian propaganda in so doing. Slovakia’s Prime Minister is hoping that by playing the role of one of the leaders in the EU and NATO who are most willing to cooperate with Russia, he will gain economic benefits and win votes in next spring’s upcoming parliamentary elections. Despite numerous pro-Russian gestures, Slovakia has been limiting the number of areas in which Moscow could exert pressure on Bratislava. As it strives to become independent of Russia, Slovakia has ensured possible alternative fuel supplies for itself. Moreover, it has been gradually replacing Russian-made military equipment with equipment made in the West. The Slovak government does intend to develop the country’s cooperation with Russia, including in strategic areas involving supplies and transit of oil and gas, as well as supplies of nuclear fuel. Nevertheless, it has been making efforts to gain easy access to an alternative source of supplies in each of these areas. Beset by crises, Russia has ever fewer economic cooperation opportunities to offer Slovakia, and Slovak businesses operating on the Russian market have to take into account the growing risk of insolvency of local contractors. To a great extent, therefore, Slovak-Russian relations have been reduced to rhetorical statements confirming the desire for closer cooperation, and to visions of joint projects accompanied by an ever shorter list of feasible cooperation initiatives.

China’s foreign direct investments within the ‘16+1’ cooperation formula: strategy, institutions, results. OSW Commentary Number 191|27.11.2015

The ‘16+1’ formula of cooperation between the countries of Central and Eastern Europe (CEE) and China was launched in 2012. One of its priorities involved increasing the inflow of China’s foreign direct investments (FDI) to the region. China has been interested in carrying out investments which are likely to help Chinese companies gain competitive advantage in areas such as advanced technologies, recognizable brands and distribution channels. The following sectors were identified as areas of priority importance in CEE: construction and modernisation of transport infrastructure, including motorways; development of the network of railways, airports and sea ports; energy, in particular renewable sources of energy and nuclear energy; companies trading in commodities; the food production sector. China’s strategy mainly involves purchasing existing companies, preceded by cherry picking the most favourable candidates for investment, rather than making large greenfield investments.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Projecto suspensão formula student

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Number of X-ray examinations performed on paediatric and geriatric patients compared with adult patients.

The age of the patient is of prime importance when assessing the radiological risk to patients due to medical X-ray exposures and the total detriment to the population due to radiodiagnostics. In order to take into account the age-specific radiosensitivity, three age groups are considered: children, adults and the elderly. In this work, the relative number of examinations carried out on paediatric and geriatric patients is established, compared with adult patients, for radiodiagnostics as a whole, for dental and medical radiology, for 8 radiological modalities as well as for 40 types of X-ray examinations. The relative numbers of X-ray examinations are determined based on the corresponding age distributions of patients and that of the general population. Two broad groups of X-ray examinations may be defined. Group A comprises conventional radiography, fluoroscopy and computed tomography; for this group a paediatric patient undergoes half the number of examinations as that of an adult, and a geriatric patient undergoes 2.5 times more. Group B comprises angiography and interventional procedures; for this group a paediatric patient undergoes a one-fourth of the number of examinations carried out on an adult, and a geriatric patient undergoes five times more.

An HIV-1 clade C DNA prime, NYVAC boost vaccine regimen induces reliable, polyfunctional, and long-lasting T cell responses

The EuroVacc 02 phase I trial has evaluated the safety and immunogenicity of a prime-boost regimen comprising recombinant DNA and the poxvirus vector NYVAC, both expressing a common immunogen consisting of Env, Gag, Pol, and Nef polypeptide domain from human immunodeficiency virus (HIV)-1 clade C isolate, CN54. 40 volunteers were randomized to receive DNA C or nothing on day 0 and at week 4, followed by NYVAC C at weeks 20 and 24. The primary immunogenicity endpoints were measured at weeks 26 and 28 by the quantification of T cell responses using the interferon gamma enzyme-linked immunospot assay. Our results indicate that the DNA C plus NYVAC C vaccine regimen was highly immunogenic, as indicated by the detection of T cell responses in 90% of vaccinees and was superior to responses induced by NYVAC C alone (33% of responders). The vaccine-induced T cell responses were (a) vigorous in the case of the env response (mean 480 spot-forming units/10(6) mononuclear cells at weeks 26/28), (b) polyfunctional for both CD4 and CD8 T cell responses, (c) broad (the average number of epitopes was 4.2 per responder), and (d) durable (T cell responses were present in 70% of vaccinees at week 72). The vaccine-induced T cell responses were strongest and most frequently directed against Env (91% of vaccines), but smaller responses against Gag-Pol-Nef were also observed in 48% of vaccinees. These results support the development of the poxvirus platform in the HIV vaccine field and the further clinical development of the DNA C plus NYVAC C vaccine regimen

Development of Railroad Highway Grade Crossing Consolidation Rating Formula, 2015

The goal of this project was to provide an objective methodology to support public agencies and railroads in making decisions related to consolidation of at-grade rail-highway crossings. The project team developed a weighted-index method and accompanying Microsoft Excel spreadsheet based tool to help evaluate and prioritize all public highway-rail grade crossings systematically from a possible consolidation impact perspective. Factors identified by stakeholders as critical were traffic volume, heavy-truck traffic volume, proximity to emergency medical services, proximity to schools, road system, and out-of-distance travel. Given the inherent differences between urban and rural locations, factors were considered, and weighted, differently, based on crossing location. Application of a weighted-index method allowed for all factors of interest to be included and for these factors to be ranked independently, as well as weighted according to stakeholder priorities, to create a single index. If priorities change, this approach also allows for factors and weights to be adjusted. The prioritization generated by this approach may be used to convey the need and opportunity for crossing consolidation to decision makers and stakeholders. It may also be used to quickly investigate the feasibility of a possible consolidation. Independently computed crossing risk and relative impact of consolidation may be integrated and compared to develop the most appropriate treatment strategies or alternatives for a highway-rail grade crossing. A crossing with limited- or low-consolidation impact but a high safety risk may be a prime candidate for consolidation. Similarly, a crossing with potentially high-consolidation impact as well as high risk may be an excellent candidate for crossing improvements or grade separation. The results of the highway-rail grade crossing prioritization represent a consistent and quantitative, yet preliminary, assessment. The results may serve as the foundation for more rigorous or detailed analysis and feasibility studies. Other pertinent site-specific factors, such as safety, maintenance costs, economic impacts, and location-specific access and characteristics should be considered.

Comparison of Immunogenicity in Rhesus Macaques of Transmitted-Founder, HIV-1 Group M Consensus, and Trivalent Mosaic Envelope Vaccines Formulated as a DNA Prime, NYVAC, and Envelope Protein Boost.

An effective human immunodeficiency virus type 1 (HIV-1) vaccine must induce protective antibody responses, as well as CD4(+) and CD8(+) T cell responses, that can be effective despite extraordinary diversity of HIV-1. The consensus and mosaic immunogens are complete but artificial proteins, computationally designed to elicit immune responses with improved cross-reactive breadth, to attempt to overcome the challenge of global HIV diversity. In this study, we have compared the immunogenicity of a transmitted-founder (T/F) B clade Env (B.1059), a global group M consensus Env (Con-S), and a global trivalent mosaic Env protein in rhesus macaques. These antigens were delivered using a DNA prime-recombinant NYVAC (rNYVAC) vector and Env protein boost vaccination strategy. While Con-S Env was a single sequence, mosaic immunogens were a set of three Envs optimized to include the most common forms of potential T cell epitopes. Both Con-S and mosaic sequences retained common amino acids encompassed by both antibody and T cell epitopes and were central to globally circulating strains. Mosaics and Con-S Envs expressed as full-length proteins bound well to a number of neutralizing antibodies with discontinuous epitopes. Also, both consensus and mosaic immunogens induced significantly higher gamma interferon (IFN-γ) enzyme-linked immunosorbent spot assay (ELISpot) responses than B.1059 immunogen. Immunization with these proteins, particularly Con-S, also induced significantly higher neutralizing antibodies to viruses than B.1059 Env, primarily to tier 1 viruses. Both Con-S and mosaics stimulated more potent CD8-T cell responses against heterologous Envs than did B.1059. Both antibody and cellular data from this study strengthen the concept of using in silico-designed centralized immunogens for global HIV-1 vaccine development strategies. IMPORTANCE: There is an increasing appreciation for the importance of vaccine-induced anti-Env antibody responses for preventing HIV-1 acquisition. This nonhuman primate study demonstrates that in silico-designed global HIV-1 immunogens, designed for a human clinical trial, are capable of eliciting not only T lymphocyte responses but also potent anti-Env antibody responses.

On some Density Theorems in Number Theory and Group Theory

Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.

Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

Exam 2000

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