Uniqueness of low genus optimal curves over F_2

A projective, smooth, absolutely irreducible algebraic curve X of genus g defined over a finite field F_q is called optimal if for every other such genus g curve Y over F_q one has $\#Y(F_q)\le \#X(F_q)$. In this paper we show that for $g\le 5$ there is a unique optimal genus g curve over F_2. For g=6 there are precisely two and for g=7 there are at least two.Comment: 21 page

Dirac spinors for Doubly Special Relativity and κ\kappa-Minkowski noncommutative spacetime

We construct a Dirac equation that is consistent with one of the recently-proposed schemes for a "doubly-special relativity", a relativity with both an observer-independent velocity scale (still naturally identified with the speed-of-light constant) and an observer-independent length/momentum scale (possibly given by the Planck length/momentum). We find that the introduction of the second observer-independent scale only induces a mild deformation of the structure of Dirac spinors. We also show that our modified Dirac equation naturally arises in constructing a Dirac equation in the kappa-Minkowski noncommutative spacetime. Previous, more heuristic, studies had already argued for a possible role of doubly-special relativity in kappa-Minkowski, but remained vague on the nature of the consistency requirements that should be implemented in order to assure the observer-independence of the two scales. We find that a key role is played by the choice of a differential calculus in kappa-Minkowski. A much-studied choice of the differential calculus does lead to our doubly-special relativity Dirac equation, but a different scenario is encountered for another popular choice of differential calculus.Comment: 26 pages, LaTex. v2: Alessandra Agostini (contributing some results from her PhD thesis) is added to the list of authors. The results presented in v1 remain unchanged and are contained in Section 2. Sections 3,4,5 add results not present in v1, concerning the realization of the DSR-deformed Dirac equation in kappa-Minkowski noncommutative spacetime. Title changed accordingl

The Sodium Channel B4-Subunits are Dysregulated in Temporal Lobe Epilepsy Drug-Resistant Patients

Temporal lobe epilepsy (TLE) is the most common type of partial epilepsy referred for surgery due to antiepileptic drug (AED) resistance. A common molecular target for many of these drugs is the voltage-gated sodium channel (VGSC). The VGSC consists of four domains of pore-forming α-subunits and two auxiliary β-subunits, several of which have been well studied in epileptic conditions. However, despite the β4-subunits’ role having been reported in some neurological conditions, there is little research investigating its potential significance in epilepsy. Therefore, the purpose of this work was to assess the role of SCN4β in epilepsy by using a combination of molecular and bioinformatics approaches. We first demonstrated that there was a reduction in the relative expression of SCN4B in the drug-resistant TLE patients compared to non-epileptic control specimens, both at the mRNA and protein levels. By analyzing a co-expression network in the neighborhood of SCN4B we then discovered a linkage between the expression of this gene and K+ channels activated by Ca2+, or K+ two-pore domain channels. Our approach also inferred several potential effector functions linked to variation in the expression of SCN4B. These observations support the hypothesis that SCN4B is a key factor in AED-resistant TLE, which could help direct both the drug selection of TLE treatments and the development of future AED

Household's vulnerability to shocks in Zambia

Zambia is a county characterized by a high incidence of poverty and exposure to several types of shocks like HIV/AIDS, macroeconomic instability and periodic droughts. In this paper the authors conduct an in depth analysis of the incidence and impact of those shocks on poverty. The analysis of the HIV/AIDS epidemic, carried out using the data on the occurrence of the death of an adult in the previous 12 months and the existence of foster children, shows the existence of a generaldecrease in consumption with the exception of non poor rural families. The deterioration of the economic situation and the related high level of unemployment resulted in a lower level of economic wellbeing. Finally, the analysis of the impact of the drought shows that while a significant percentage (17 percent) of the poorest households in rural areas would experience significant losses in maize production (covering 8 percent of all the households), they are concentrated in a few communities in Southern, Central and Western provinces. In order to identify those households that might suffer more from the negative impact of the shocks and/or have a low level of human capital the authors defined"vulnerable households", those that are likely to be poor and exposed to shocks, and"chronically poor households", those that are likely to be poor and have low levels of human capital outcomes. According to this definition, about 20 percent of the households are vulnerable whilst almost 40 percent are chronically poor and 10 percent are at the same time both vulnerable and chronically poor and therefore at most risk. Private coping mechanisms and private transfers are very common, but they do not seem to be effective in helping households to deal with the adverse impact of shocks. On the other hand, household participation in food for work programs increase after the death of a household member. Therefore there is a need for long term household human capital investments, programs to alleviate the burden of HIV/AIDS, and targeted programs for the alleviating weather related shocks like the drought.Rural Poverty Reduction,Services&Transfers to Poor,Poverty Assessment,Small Area Estimation Poverty Mapping,Housing&Human Habitats

Exact supersymmetry on the lattice: the Wess-Zumino model

It is shown that the lattice Wess-Zumino model written in terms of Ginsparg-Wilson fermions is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. This transformation is non-linear in the scalar fields and depends on the superpotential parameters. The implications of this lattice invariance are discussed.Comment: 3 pages, Lattice2004(theory), Fermilab, June 21-26, 200