Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

Skew-symmetric identities of octonions

Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skew-symmetric identities and central polynomials of octonions are classified. (C) 2008 Elsevier B.V. All rights reserved.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

The Borsuk-Ulam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

The 3-colored Ramsey number of even cycles

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdos conjectured that when L is the cycle C(n) on n vertices, R(C(n), C(n), C(n)) = 4n - 3 for every odd n > 3. Luczak proved that if n is odd, then R(C(n), C(n), C(n)) = 4n + o(n), as n -> infinity, and Kohayakawa, Simonovits and Skokan confirmed the Bondy-Erdos conjecture for all sufficiently large values of n. Figaj and Luczak determined an asymptotic result for the `complementary` case where the cycles are even: they showed that for even n, we have R(C(n), C(n), C(n)) = 2n + o(n), as n -> infinity. In this paper, we prove that there exists n I such that for every even n >= n(1), R(C(n), C(n), C(n)) = 2n. (C) 2009 Elsevier Inc. All rights reserved.

Vinylens två världar : Unga människors relation till vinylen i den digitala eran

Vinylen har lyckats överleva trots att både CD:n och det digitala formatet gett oss nya och lättare sätt att lyssna på musiken. Vinylen tilltalar personer i yngre åldrar som inte växte upp med vinylen som det vardagliga formatet. Det tydligaste resultat som kommit att visa sig i undersökning för denna uppsats är att vinyler fortfarande upplevs tilltalande av intervjupersonerna, även om det digitala formatet fortfarande används dagligen. Intervjupersonerna tilltalas av olika aspekter av vinylen som gör det värt att gå och köpa en skiva, även om vi lever i en tid där vi näst intill har obegränsad tillgång till musik digitalt. Vinylen lockar personer på olika sätt när det kommer till användningen av skivorna och på samma sätt när det kommer till det materiella och det estetiska. Detta är dock inte tillräckligt för att personerna ska ändra sina lyssningsvanor och byta format från det digitala till analogt. För det är fortfarande det digitala formatet som används mest av intervjupersonerna.

Association of soluble tumor necrosis factor receptors 1 and 2 with nephropathy, cardiovascular events, and total mortality in type 2 diabetes

AIMS/HYPOTHESIS: Soluble tumor necrosis factor receptors 1 and 2 (sTNFR1 and sTNFR2) contribute to experimental diabetic kidney disease, a condition with substantially increased cardiovascular risk when present in patients. Therefore, we aimed to explore the levels of sTNFRs, and their association with prevalent kidney disease, incident cardiovascular disease, and risk of mortality independently of baseline kidney function and microalbuminuria in a cohort of patients with type 2 diabetes. In pre-defined secondary analyses we also investigated whether the sTNFRs predict adverse outcome in the absence of diabetic kidney disease. METHODS: The CARDIPP study, a cohort study of 607 diabetes patients [mean age 61 years, 44 % women, 45 cardiovascular events (fatal/non-fatal myocardial infarction or stroke) and 44 deaths during follow-up (mean 7.6 years)] was used. RESULTS: Higher sTNFR1 and sTNFR2 were associated with higher odds of prevalent kidney disease [odd ratio (OR) per standard deviation (SD) increase 1.60, 95 % confidence interval (CI) 1.32-1.93, p < 0.001 and OR 1.54, 95 % CI 1.21-1.97, p = 0.001, respectively]. In Cox regression models adjusting for age, sex, glomerular filtration rate and urinary albumin/creatinine ratio, higher sTNFR1 and sTNFR2 predicted incident cardiovascular events [hazard ratio (HR) per SD increase, 1.66, 95 % CI 1.29-2.174, p < 0.001 and HR 1.47, 95 % CI 1.13-1.91, p = 0.004, respectively]. Results were similar in separate models with adjustments for inflammatory markers, HbA1c, or established cardiovascular risk factors, or when participants with diabetic kidney disease at baseline were excluded (p < 0.01 for all). Both sTNFRs were associated with mortality. CONCLUSIONS/INTERPRETATIONS: Higher circulating sTNFR1 and sTNFR2 are associated with diabetic kidney disease, and predicts incident cardiovascular disease and mortality independently of microalbuminuria and kidney function, even in those without kidney disease. Our findings support the clinical utility of sTNFRs as prognostic markers in type 2 diabetes.

On certain geometric aspects of portfolio optimisation with higher moments

We discuss geometric properties related to the minimisation of a portfolio kurtosis given its first two odd moments, considering a risk-less asset and allowing for short sales. The findings are generalised for the minimisation of any given even portfolio moment with fixed excess return and skewness, and then for the case in which only excess return is constrained. An example with two risky assets provides a better insight on the problems related to the solutions. The importance of the geometric properties and their use in the higher moments portfolio choice context is highlighted.

Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice

Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.

Entrevista com Arne Westad (LSE)

Odd Arne Westad é professor do Departamento de História International da London School of Economics and Political Science. Desde 2004, é chefe de departamento e co-diretor da LSE Cold War Studies Centre. Entrevista realizada em 28 de setembro de 2010.

Leituras brasileiras sobre a nova ordem internacional (1989-1994)

O presente trabalho é resultado de pesquisa realizada a respeito das leituras brasileiras sobre a Nova Ordem Internacional. A partir da investigação em fontes históricas depositadas no Centro de Pesquisa e Documentação em História Contemporânea do Brasil (CPDOC/FGV), como os documentos textuais do Arquivo Marcílio Marques Moreira e as entrevistas de Celso Amorim, Celso Lafer, Gelson Fonseca e Luiz Felipe Lampreia, procurouse analisar as principais ideias de três personagens históricos diretamente envolvidos com a formulação da política externa brasileira no período da Nova República, mais especificamente entre 1989 e 1994: Celso Lafer, Gelson Fonseca e Rubens Ricupero. Para tanto, buscou-se destacar as principais formas de interpretação do sistema internacional alterado pelo fim do conflito bipolar com o apoio da literatura mais recente produzida na área, como os trabalhos de Odd Westad (2005), Andrew Hurrell (2001, 2007) e John Ikenberry (2005). Os dados coletados durante o processo de feitura da pesquisa permitem-nos afirmar que, no Brasil, os temas da autonomia e do desenvolvimento são resilientes. Os debates sobre autonomia e desenvolvimento, tão caros ao discurso acadêmico e político nacionalista desenvolvido nos anos 50, além de terem permanecido como preocupação de fundo nas análises dos formuladores de política externa, demonstra que, no Brasil, o discurso modernizante retomou as ideias básicas do pensamento político nativo.

On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

Limiting glutamate transmission in a Vglut2-expressing subpopulation of the subthalamic nucleus is sufficient to cause hyperlocomotion

The subthalamic nucleus (STN) is a key area of the basal ganglia circuitry regulating movement. We identified a subpopulation of neurons within this structure that coexpresses Vglut2 and Pitx2, and by conditional targeting of this subpopulation we reduced Vglut2 expression levels in the STN by 40%, leaving Pitx2 expression intact. This reduction diminished, yet did not eliminate, glutamatergic transmission in the substantia nigra pars reticulata and entopeduncular nucleus, two major targets of the STN. The knock-out mice displayed hyperlocomotion and decreased latency in the initiation of movement while preserving normal gait and balance. Spatial cognition, social function, and level of impulsive choice also remained undisturbed. Furthermore, these mice showed reduced dopamine transporter binding and slower dopamine clearance in vivo, suggesting that Vglut2-expressing cells in the STN regulate dopaminergic transmission. Our results demonstrate that altering the contribution of a limited population within the STN is sufficient to achieve results similar to STN lesions and high-frequency stimulation, but with fewer side effects.