Separating invariants for the basic G_a-actions

We explicitly construct a finite set of separating invariants for the basic \Ga-actions. These are the finite dimensional indecomposable rational linear representations of the additive group \Ga of a field of characteristic zero, and their invariants are the kernel of the Weitzenb\"ock derivation $D_{n}=x_{0}\frac{\partial}{\partial{x_{1}}}+...+ x_{n-1}\frac{\partial}{\partial{x_{n}}}$.Comment: 10 page

Bose Einstein condensation of the classical axion field in cosmology?

The axion is a motivated cold dark matter candidate, which it would be interesting to distinguish from weakly interacting massive particles. Sikivie has suggested that axions could behave differently during non-linear galaxy evolution, if they form a Bose-Einstein condensate, and argues that ``gravitational thermalisation'' drives them to a Bose-Einstein condensate during the radiation dominated era. Using classical equations of motion during linear structure formation, we explore whether the gravitational interactions of axions can generate entropy. At linear order in Newton's constant, we interpret that the principle activities of gravity are to expand the Universe and grow density fluctuations. To quantify the rate of entropy creation we use the anisotropic stress to estimate a short dissipation scale for axions, which does not confirm previous estimates of their gravitational thermalisation rate.Comment: version accepted for publication, modified intro to Bose Einstein condensatio

Heavy Z': resonant versus non-resonant searches

Collider searches for new vector-like particles such as Z' have mostly been pursued by looking for a peak in the invariant mass spectrum of the decay products. However off-shell Z' exchange may leave an imprint on other kinematic distributions, leading thus to non-resonant searches. The aim of this paper is to assess, in the context of the LHC, the interplay between resonant (s-channel) and non-resonant (t-channel) searches for a generic leptophobic Z' model. We show in particular that while non-resonant searches are less sensitive to small couplings, they tend to be more adapted at high masses and large couplings. We discuss our findings both at the level of the current limits and the expectations at higher luminosities

Zero-separating invariants for linear algebraic groups

Let G be linear algebraic group over an algebraically closed field k acting rationally on a G-module V , and N(G,V) its nullcone. Let δ(G, V ) and σ(G, V ) denote the minimal number d, such that for any v ∈ V^G \ N(G,V) and v ∈ V \ N(G,V) respectively, there exists a homogeneous invariant f of positive degree at most d such that f (v) = 0. Then δ(G) and σ(G) denote the supremum of these numbers taken over all G-modules V . For positive characteristics, we show that δ(G) = ∞ for any subgroup G of GL 2 (k) which contains an infinite unipotent group, and σ(G) is finite if and only if G is finite. In characteristic zero, δ(G) = 1 for any group G, and we show that if σ(G) is finite, then G 0 is unipotent. Our results also lead to a more elementary proof that β_sep(G) is finite if and only if G is finite

On separating a fixed point from zero by invariants

Assume a fixed point v in V^G can be separated from zero by a homogeneous invariant f ∈ k[V]^G of degree p^r d where p > 0 is the characteristic of the ground field k and p, d are coprime. We show that then v can also be separated from zero by an invariant of degree p^r , which we obtain explicitly from f . It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power

The genetic architecture underlying the evolution of a rare piscivorous life history form in brown trout after secondary contact and strong introgression

Identifying the genetic basis underlying phenotypic divergence and reproductive isolation is a longstanding problem in evolutionary biology. Genetic signals of adaptation and reproductive isolation are often confounded by a wide range of factors, such as variation in demographic history or genomic features. Brown trout ( ) in the Loch Maree catchment, Scotland, exhibit reproductively isolated divergent life history morphs, including a rare piscivorous (ferox) life history form displaying larger body size, greater longevity and delayed maturation compared to sympatric benthivorous brown trout. Using a dataset of 16,066 SNPs, we analyzed the evolutionary history and genetic architecture underlying this divergence. We found that ferox trout and benthivorous brown trout most likely evolved after recent secondary contact of two distinct glacial lineages, and identified 33 genomic outlier windows across the genome, of which several have most likely formed through selection. We further identified twelve candidate genes and biological pathways related to growth, development and immune response potentially underpinning the observed phenotypic differences. The identification of clear genomic signals divergent between life history phenotypes and potentially linked to reproductive isolation, through size assortative mating, as well as the identification of the underlying demographic history, highlights the power of genomic studies of young species pairs for understanding the factors shaping genetic differentiation

Neurofunctional and Behavioral Correlates of Phonetic and Temporal Categorization in Musically Trained and Untrained Subjects

The perception of rapidly changing verbal and nonverbal auditory patterns is a fundamental prerequisite for speech and music processing. Previously, the left planum temporale (PT) has been consistently shown to support the discrimination of fast changing verbal and nonverbal sounds. Furthermore, it has been repeatedly shown that the functional and structural architecture of this supratemporal brain region differs as a function of musical training. In the present study, we used the functional magnetic resonance imaging technique, in a sample of professional musicians and nonmusicians, in order to examine the functional contribution of the left PT to the categorization of consonant-vowel syllables and their reduced-spectrum analogues. In line with our hypothesis, the musicians showed enhanced brain responses in the left PT and superior discrimination abilities in the reduced-spectrum condition. Moreover, we found a positive correlation between the responsiveness of the left PT and the performance in the reduced-spectrum condition across all subjects irrespective of musical expertise. These results have implications for our understanding of musical expertise in relation to segmental speech processin