On the closure in M̄g of smooth curves having a special Weierstrass point

Let wt(2) be the closure in M̄g, the coarse moduli space of stable complex curves of genus g ≥ 3, of the locus in M̄g of curves possessing a Weierstrass point of weight at least 2. The class of wt(2) in the group Pic(M̄g) ⊗ Q is computed. The computation heavily relies on the notion of "derivative" of a relative Wronskian, introduced in [15] for families of smooth curves and here extended to suitable families of Deligne-Mumford stable curves. Such a computation provides, as a byproduct, a simpler proof of the main result proven in [6]

Critical Endpoint and Inverse Magnetic Catalysis for Finite Temperature and Density Quark Matter in a Magnetic Background

In this article we study chiral symmetry breaking for quark matter in a magnetic background, $\bm B$, at finite temperature and quark chemical potential, $\mu$, making use of the Ginzburg-Landau effective action formalism. As a microscopic model to compute the effective action we use the renormalized quark-meson model. Our main goal is to study the evolution of the critical endpoint, ${\cal CP}$, as a function of the magnetic field strength, and investigate on the realization of inverse magnetic catalysis at finite chemical potential. We find that the phase transition at zero chemical potential is always of the second order; for small and intermediate values of $\bm B$, ${\cal CP}$ moves towards small $\mu$, while for larger $\bm B$ it moves towards moderately larger values of $\mu$. Our results are in agreement with the inverse magnetic catalysis scenario at finite chemical potential and not too large values of the magnetic field, while at larger $\bm B$ direct magnetic catalysis sets in.Comment: 6 pages, 2 figure

Jet bundles on Gorenstein curves and applications

In the last twenty years a number of papers appeared aiming to construct locally free replacements of the sheaf of principal parts for families of Gorenstein curves. The main goal of this survey is to present to the widest possible audience of mathematical readers a catalogue of such constructions, discussing the related literature and reporting on a few applications to classical problems in Enumerative Algebraic Geometry

The cohomology of the Grassmannian is a glngl_n-module

The integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra gl n ðZÞ of all the n n matrices with integral entries. The simplest case, r 1⁄4 1, recovers the well known fact that any vector space is a module over the Lie algebra of its own endomorphisms. The other extremal case, r 1⁄4 ∞; corresponds to the bosonic vertex representation of the Lie algebra gl ∞ ðZÞ on the polynomial ring in infinitely many indeterminates, due to Date, Jimbo, Kashiwara and Miwa. In the present article we provide the structure of this irreducible representation explicitly, by means of a distinguished Hasse-Schmidt derivation ation on an exterior algebra, borrowed from Schubert Calculus

Baseline data on the oceanography of Cook Inlet, Alaska

Regional relationships between river hydrology, sediment transport, circulation and coastal processes were analyzed utilizing aircraft, ERTS-1 and N.O.A.A. -2 and -3 imagery and corroborative ground truth data. The use of satellite and aircraft imagery provides a means of acquiring synoptic information for analyzing the dynamic processes of Cook Inlet in a fashion not previously possible

Land use/vegetation mapping in reservoir management. Merrimack River basin

This report consists of an analysis of: ERTS-1 Multispectral Scanner imagery obtained 10 August 1973; Skylab 3 S190A and S190B photography, track 29, taken 21 September 1973; and RB-57 high-altitude aircraft photography acquired 26 September 1973. These data products were acquired on three cloud-free days within a 47-day period. The objectives of this study were: (1) to make quantitative comparisons between high-altitude aircraft photography and satellite imagery, and (2) to demonstrate the extent to which high resolution (S190A and B) space-acquired data can be used for land use/vegetation mapping and management of drainage basins

Temporal Requirements of the Fragile X Mental Retardation Protein in Modulating Circadian Clock Circuit Synaptic Architecture

Loss of fragile X mental retardation 1 (FMR1) gene function is the most common cause of inherited mental retardation and autism spectrum disorders, characterized by attention disorder, hyperactivity and disruption of circadian activity cycles. Pursuit of effective intervention strategies requires determining when the FMR1 product (FMRP) is required in the regulation of neuronal circuitry controlling these behaviors. In the well-characterized Drosophila disease model, loss of the highly conserved dFMRP causes circadian arrhythmicity and conspicuous abnormalities in the circadian clock circuitry. Here, a novel Sholl Analysis was used to quantify over-elaborated synaptic architecture in dfmr1-null small ventrolateral neurons (sLNvs), a key subset of clock neurons. The transgenic Gene-Switch system was employed to drive conditional neuronal dFMRP expression in the dfmr1-null mutant background in order to dissect temporal requirements within the clock circuit. Introduction of dFMRP during early brain development, including the stages of neurogenesis, neuronal fate specification and early pathfinding, provided no rescue of dfmr1 mutant phenotypes. Similarly, restoring normal dFMRP expression in the adult failed to restore circadian circuit architecture. In sharp contrast, supplying dFMRP during a transient window of very late brain development, wherein synaptogenesis and substantial subsequent synaptic reorganization (e.g. use-dependent pruning) occur, provided strong morphological rescue to reestablish normal sLNvs synaptic arbors. We conclude that dFMRP plays a developmentally restricted role in sculpting synaptic architecture in these neurons that cannot be compensated for by later reintroduction of the protein at maturity

Genetic Controls Balancing Excitatory and Inhibitory Synaptogenesis in Neurodevelopmental Disorder Models

Proper brain function requires stringent balance of excitatory and inhibitory synapse formation during neural circuit assembly. Mutation of genes that normally sculpt and maintain this balance results in severe dysfunction, causing neurodevelopmental disorders including autism, epilepsy and Rett syndrome. Such mutations may result in defective architectural structuring of synaptic connections, molecular assembly of synapses and/or functional synaptogenesis. The affected genes often encode synaptic components directly, but also include regulators that secondarily mediate the synthesis or assembly of synaptic proteins. The prime example is Fragile X syndrome (FXS), the leading heritable cause of both intellectual disability and autism spectrum disorders. FXS results from loss of mRNA-binding FMRP, which regulates synaptic transcript trafficking, stability and translation in activity-dependent synaptogenesis and plasticity mechanisms. Genetic models of FXS exhibit striking excitatory and inhibitory synapse imbalance, associated with impaired cognitive and social interaction behaviors. Downstream of translation control, a number of specific synaptic proteins regulate excitatory versus inhibitory synaptogenesis, independently or combinatorially, and loss of these proteins is also linked to disrupted neurodevelopment. The current effort is to define the cascade of events linking transcription, translation and the role of specific synaptic proteins in the maintenance of excitatory versus inhibitory synapses during neural circuit formation. This focus includes mechanisms that fine-tune excitation and inhibition during the refinement of functional synaptic circuits, and later modulate this balance throughout life. The use of powerful new genetic models has begun to shed light on the mechanistic bases of excitation/inhibition imbalance for a range of neurodevelopmental disease states