Mesio-temporal lobe epilepsy (MTLE) is often accompanied by granule cell dispersion (GCD), a widening of the granule cell layer. The molecular determinants of GCD are poorly understood. Here, we used an animal model to study whether GCD results from an increased dentate neurogenesis associated with an abnormal migration of the newly generated granule cells. Adult mice were given intrahippocampa...

An embedding (called a GCD theory) of partly ordered abelian group G into abelian l-group Γ is investigated such that any element of Γ is an infimum of a subset (possible non-finite) from G. It is proved that a GCD theory need not be unique. A complete GCD theory is introduced and it is proved that G admits a complete GCD theory if and only if it admits a GCD theory G Γ such that Γ is an Archim...

We undertake a thorough complexity study of the following fundamental optimization problem, known as the `p-norm shortest extended GCD multiplier problem: given a1, . . . , an ∈ Z, find an `p-norm shortest gcd multiplier for a1, . . . , an, i.e., a vector x ∈ Z with minimum ( ∑n i=1 |xi|) satisfying ∑n i=1 xiai = gcd(a1, . . . , an). First, we prove that the shortest GCD multiplier problem (in ...

Let C be a smooth irreducible complex projective curve of genus $$g \ge 2$$ and M the moduli space stable vector bundles on rank n degree d with $$\gcd (n,d)=1$$ . A generalised Picard sheaf is direct image tensor product universal bundle $$M\times C$$ by pullback $$E_0$$ C. In this paper, we investigate stability sheaves and, in case where these are locally free, their deformations. When $$g\g...

The computation of the Greatest Common Divisor (GCD) of many polynomials is a nongeneric problem. Techniques defining “approximate GCD” solutions have been defined, but the proper definition of the “approximate” GCD, and the way we can measure the strength of the approximation has remained open. This paper uses recent results on the representation of the GCD of many polynomials, in terms of fac...

We generalize a formula of B. Litow [7] and propose several new formula linked with the parallel Integer Coprimality, Integer GCD and Modular Inverse problems as well. Particularly, we find a new trigonometrical definition of the GCD of two integers a, b ≥ 1 : gcd(a, b) = 1 π ∫ π 0 cos[ (b− a)x ] sin (abx) sin(ax) sin(bx) dx. We also suggest a generalization of the GCD function to real numbers.

We describe a new subquadratic left-to-right gcd algorithm, inspired by Schönhage’s algorithm for reduction of binary quadratic forms, and compare it to the first subquadratic gcd algorithm discovered by Knuth and Schönhage, and to the binary recursive gcd algorithm of Stehlé and Zimmermann. The new gcd algorithm runs slightly faster than earlier algorithms, and it is much simpler to implement....

Let m, k be positive integers such that m gcd(m,k) ≥ 3, p be an odd prime and π be a primitive element of Fpm. Let h1(x) and h2(x) be the minimal polynomials of −π−1 and π pk+1 2 over Fp, respectively. In the case of odd m gcd(m,k) , when k is even, gcd(m,k) is odd or when k gcd(m,k) is odd, Zhou et al. in [25] obtained the weight distribution of a class of cyclic codes C over Fp with parity-ch...

We compute the first André-Quillen homology modules for the simple over-rings of integrally closed domains and study an ideal theoretic condition arising from the vanishing of H1. André-Quillen (co)homology is known to be a powerful tool in characterizing various classes of rings or morphisms between noetherian rings. Regular and complete intersection local rings, regular, (formally) smooth or ...

In a quadratic number field Q(V~D), D a squarefree integer, with class number 1, any algebraic integer can be decomposed uniquely into primes, but for only 21 domains Euclidean algorithms are known. It was shown by Cohn [5] that for D < —19 even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs. We extend this result by showing that there does no...