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Introduction: Conditionally immortalised human neural progenitor cells (hNPCs) represent a robust source of native neural cells to investigate physiological mechanisms in both health and disease. However, in order to recognise the utility of such cells, it is critical to determine whether they retain characteristics of their tissue of origin and generate appropriate neural cell types upon differentiation. To this end, we have characterised the conditionally immortalised, cortically-derived, human NPC line, CTX0E16, investigating the molecular and cellular phenotype of differentiated neurons to determine whether they possess characteristics of cortical glutamatergic neurons. Methods: Differentiated CTX0E16 cells were characterised by assessing expression of several neural fates markers, and examination of developing neuronal morphology. Expression of neurotransmitter receptors, signalling proteins and related proteins were assessed by q- and RT-PCR and complemented by Ca2+ imaging, electrophysiology and assessment of ERK signalling in response to neurotransmitter ligand application. Finally, differentiated neurons were assessed for their ability to form putative synapses and to respond to activity-dependent stimulation. Results: Differentiation of CTX0E16 hNPCs predominately resulted in the generation of neurons expressing markers of cortical and glutamatergic (excitatory) fate, and with a typical polarized neuronal morphology. Gene expression analysis confirmed an upregulation in the expression of cortical, glutamatergic and signalling proteins following differentiation. CTX0E16 neurons demonstrated Ca2+ and ERK1/2 responses following exogenous neurotransmitter application, and after 6 weeks displayed spontaneous Ca2+ transients and electrophysiological properties consistent with that of immature neurons. Differentiated CTX0E16 neurons also expressed a range of pre- and post-synaptic proteins that co-localized along distal dendrites, and moreover, displayed structural plasticity in response to modulation of neuronal activity. Conclusions: Taken together, these findings demonstrate that the CTX0E16 hNPC line is a robust source of cortical neurons, which display functional properties consistent with a glutamatergic phenotype. Thus CTX0E16 neurons can be used to study cortical cell function, and furthermore, as these neurons express a range of disease-associated genes, they represent an ideal platform with which to investigate neurodevelopmental mechanisms in native human cells in health and disease. [ABSTRACT FROM AUTHOR]

Our main result is a local limit law tor the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach is to adapt some techniques from recent papers of Erdös-Yau-Yin. We also use an algebraic description of the law of the anlicommutator of free semicircular variables due to Nica-Speicher, the lineatization trick due to Haagerup-Schultz-Thorbjørnsen in a self-adjointness-preserving variant and the Schwinger-Dyson equation. A by-product ot our work is a relatively simple deterministic version of the local semicircle law. [ABSTRACT FROM AUTHOR]

Introduction: Conditionally immortalised human neural progenitor cells (hNPCs) represent a robust source of native neural cells to investigate physiological mechanisms in both health and disease. However, in order to recognise the utility of such cells, it is critical to determine whether they retain characteristics of their tissue of origin and generate appropriate neural cell types upon differentiation. To this end, we have characterised the conditionally immortalised, cortically-derived, human NPC line, CTX0E16, investigating the molecular and cellular phenotype of differentiated neurons to determine whether they possess characteristics of cortical glutamatergic neurons. Methods: Differentiated CTX0E16 cells were characterised by assessing expression of several neural fates markers, and examination of developing neuronal morphology. Expression of neurotransmitter receptors, signalling proteins and related proteins were assessed by q- and RT-PCR and complemented by Ca2+ imaging, electrophysiology and assessment of ERK signalling in response to neurotransmitter ligand application. Finally, differentiated neurons were assessed for their ability to form putative synapses and to respond to activity-dependent stimulation. Results: Differentiation of CTX0E16 hNPCs predominately resulted in the generation of neurons expressing markers of cortical and glutamatergic (excitatory) fate, and with a typical polarized neuronal morphology. Gene expression analysis confirmed an upregulation in the expression of cortical, glutamatergic and signalling proteins following differentiation. CTX0E16 neurons demonstrated Ca2+ and ERK1/2 responses following exogenous neurotransmitter application, and after 6 weeks displayed spontaneous Ca2+ transients and electrophysiological properties consistent with that of immature neurons. Differentiated CTX0E16 neurons also expressed a range of pre- and post-synaptic proteins that co-localized along distal dendrites, and moreover, displayed structural plasticity in response to modulation of neuronal activity. Conclusions: Taken together, these findings demonstrate that the CTX0E16 hNPC line is a robust source of cortical neurons, which display functional properties consistent with a glutamatergic phenotype. Thus CTX0E16 neurons can be used to study cortical cell function, and furthermore, as these neurons express a range of disease-associated genes, they represent an ideal platform with which to investigate neurodevelopmental mechanisms in native human cells in health and disease. [ABSTRACT FROM AUTHOR]

Abstract: A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú. [Copyright &y& Elsevier]

We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz–Tate t-motives). We give examples of combinatorially involved relations that these multizeta values satisfy. [ABSTRACT FROM PUBLISHER]

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poincaré type. Special cases treated, with an explicit evaluation of limiting variances, are generalized Wigner and Wishart matrices. [ABSTRACT FROM AUTHOR]

Abstract: Let X be a nonsingular projective curve of genus one defined over an algebraically closed field of characteristic 0. Let D be a divisor of X of degree and let O be a (closed) point of X. As is well known, there exists a unique morphism such that if and only if the divisor is principal. Our main result is a simple explicit description of the map in terms of Wronskians and certain Wronskian-like determinants lacunary in the sense that derivatives of some orders are skipped. Further, for we interpret our main result as a syzygy from classical invariant theory, thus reconciling our work with a circle of ideas treated in two papers by Weil and a recent paper by An, Kim, Marshall, Marshall, McCallum and Perlis. [Copyright &y& Elsevier]

The expansion in Schur functions of the product ∏i is well known. It is more or less equivalent to Weyl''s identity for root-systems of type Dn. In this paper we obtain the expansion in Schur functions of the product ∏i0aℓxixj(xiℓ-xjℓ)/(xi-xj)), thus generalizing Weyl''s identity. We obtain this result by systematic calculation in fermionic Fock space. But familiarity with the latter is not a prerequisite for reading this paper. We develop from scratch the modest amount of theory that we need in elementary and purely algebraic fashion, taking pains to integrate the theory with classical symmetric function theory. The tools developed in this paper ought to have many further applications, e.g., to random matrix theory and to computational abelian function theory. [Copyright &y& Elsevier]

The notion of determinant groupoid is a natural outgrowth of the theory of the Sato Grassmannian and thus well-known in mathematical physics. We briefly sketch here a version of the theory of determinant groupoids over an artinian local ring, taking pains to put the theory in a simple concrete form suited to number-theoretical applications. We then use the theory to give a simple proof of a reciprocity law for the Contou-Carrère symbol. Finally, we explain how from the latter to recover various classical explicit reciprocity laws on nonsingular complete curves over an algebraically closed field, namely sum-of-residues-equals-zero, Weil reciprocity, and an explicit reciprocity law due to Witt. Needless to say, we have been much influenced by the work of Tate on sum-of-residues-equals-zero and the work of Arbarello-De Concini-Kac on Weil reciprocity. We also build in an essential way on a previous work of the second-named author. [ABSTRACT FROM AUTHOR]

The abeliant is a polynomial rule which to each n×n by n+2 array with entries in a commutative ring with unit associates an n×n matrix with entries in the same ring. The theory of abeliants, first introduced in an earlier paper of the author, is simplified and extended here. Now let J be the Jacobian of a nonsingular projective algebraic curve defined over an algebraically closed field. With the aid of the theory of abeliants we obtain explicit defining equations for J and its group law. [Copyright &y& Elsevier]

The article discusses a study on an explicit algebraic representation of the Abel map as defined in Theorem 2.5.1. It provides a brief review of the elements of the theory of algebraic functions of one variable dealing with algebraic curves. It notes that a simple and explicit collection of equations are used as a nonsingular projective curve of genus g and an effective divisor G of positive even degree not less than 4g.

The neuronal ceroid lipofuscinoses (NCLs or Batten disease) are a group of inherited, fatal neurodegenerative disorders of childhood. In these disorders, glial (microglial and astrocyte) activation typically occurs early in disease progression and predicts where neuron loss subsequently occurs. We have found that in themost common juvenile form of NCL (CLN3 disease or JNCL) this glial response is less pronounced in both mouse models and human autopsy material, with the morphological transformation of both astrocytes and microglia severely attenuated or delayed. To investigate their properties, we isolated glia and neurons from Cln3-deficient mice and studied their basic biology in culture. Upon stimulation, both Cln3-deficient astrocytes and microglia also showed an attenuated ability to transform morphologically, and an altered protein secretion profile. These defects were more pronounced in astrocytes, including the reduced secretion of a range of neuroprotective factors, mitogens, chemokines and cytokines, in addition to impaired calcium signalling and glutamate clearance. Cln3-deficient neurons also displayed an abnormal organization of their neurites. Most importantly, using a co-culture system, Cln3-deficient astrocytes and microglia had a negative impact on the survival and morphology of both Cln3-deficient and wildtype neurons, but these effects were largely reversed by growing mutant neurons with healthy glia. These data provide evidence that CLN3 disease astrocytes are functionally compromised. Together with microglia, they may play an active role in neuron loss in this disorder and can be considered as potential targets for therapeutic interventions. [ABSTRACT FROM AUTHOR]