What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

Antidiarrhoeal Activity of Leaf Extract of Moringa Oleifera In Experimentally Induced Diarrhoea In Rats

To evalauate the antidiarrhoeal activity of the hydroalcoholic extract of moringa oleifera leaves. The hydroalchoholic extract was evaluated using rodent animal models of diarrhoea like the castor oil and magnesium sulfate induced gastrointestinal motility, in a model of enteropooling induced by the administration of castor oil and PGE2, Charcoal meal test. Acute toxicity and phytochemical constituents were also been evaluated using standardized methods. The results of the present study indicates that the hydroalcoholic extract of moringa oleifera leaves was effective in inducing a significant protection against experimentally induced diarrhoea by castor oil and magnesium sulfate, as evidenced by a decrease in the number of frequency, weight of stools after 4 hours with respect to control. The extract also prevented the enteropooling induced by castor oil and PGE2 at all the doses tested. Acute toxicity studies indicated that the extract is safe till 2500 mg/kg. The antidiarrhoeal activity though, not ascribed to any particular phytochemical present, general tests performed indicated the presence of flavonoids, tannis which were reported to produce antidiarrhoeal activity. These results showed that Moringa oleifera leaves possess anti-diarrheal properties mediated through inhibition of hyper secretion and gastrointestinal motility that substantiate its use in the treatment of diarrhea in traditional medicines or folklore use. Keywords: enteropooling, hyper secretion, Moringa oleifer

Arithmetical Congruence Preservation: from Finite to Infinite

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational polynomials (taking only integral values) and the function giving the least common multiple of $1,2,\ldots,k$. The tool used to obtain these characterizations is "lifting": if $\pi\colon X\to Y$ is a surjective morphism, and $f$ a function on $Y$ a lifting of $f$ is a function $F$ on $X$ such that $\pi\circ F=f\circ\pi$. In this paper we relate the finite and infinite notions by proving that the finite case can be lifted to the infinite one. For $p$-adic and profinite integers we get similar characterizations via lifting. We also prove that lattices of recognizable subsets of $Z$ are stable under inverse image by congruence preserving functions

Correlating the Energetics and Atomic Motions of the Metal-Insulator Transition of M1 Vanadium Dioxide

Materials that undergo reversible metal-insulator transitions are obvious candidates for new generations of devices. For such potential to be realised, the underlying microscopic mechanisms of such transitions must be fully determined. In this work we probe the correlation between the energy landscape and electronic structure of the metal-insulator transition of vanadium dioxide and the atomic motions occurring using first principles calculations and high resolution X-ray diffraction. Calculations find an energy barrier between the high and low temperature phases corresponding to contraction followed by expansion of the distances between vanadium atoms on neighbouring sub-lattices. X-ray diffraction reveals anisotropic strain broadening in the low temperature structure's crystal planes, however only for those with spacings affected by this compression/expansion. GW calculations reveal that traversing this barrier destabilises the bonding/anti-bonding splitting of the low temperature phase. This precise atomic description of the origin of the energy barrier separating the two structures will facilitate more precise control over the transition characteristics for new applications and devices.Comment: 11 Pages, 8 Figure

Analysis of rolling contact spall life in 440 C steel bearing rims

The results of a two year study of the mechanisms of spall failure in the HPOTP bearings are described. The objective was to build a foundation for detailed analyses of the contact life in terms of: cyclic plasticity, contact mechanics, spall nucleation, and spall growth. Since the laboratory rolling contact testing is carried out in the 3 ball/rod contact fatigue testing machine, the analysis of the contacts and contact lives produced in this machine received attention. The results from the experimentally observed growth lives are compared with calculated predictions derived from the fracture mechanics calculations

Dual-acting stapled peptides target both HIV-1 entry and assembly

Background: Previously, we reported the conversion of the 12-mer linear and cell-impermeable peptide CAI to a cell-penetrating peptide NYAD-1 by using an i,i + 4 hydrocarbon stapling technique and confirmed its binding to the C-terminal domain (CTD) of the HIV-1 capsid (CA) protein with an improved affinity (Kd ~ 1 μM) compared to CAI (Kd ~ 15 μM). NYAD-1 disrupts the formation of both immature- and mature-like virus particles in in vitro and cell-based assembly assays. In addition, it displays potent anti-HIV-1 activity in cell culture against a range of laboratory-adapted and primary HIV-1 isolates.<p></p> Results: In this report, we expanded the study to i,i + 7 hydrocarbon-stapled peptides to delineate their mechanism of action and antiviral activity. We identified three potent inhibitors, NYAD-36, -66 and -67, which showed strong binding to CA in NMR and isothermal titration calorimetry (ITC) studies and disrupted the formation of mature-like particles. They showed typical α-helical structures and penetrated cells; however, the cell penetration was not as efficient as observed with the i,i + 4 peptides. Unlike NYAD-1, the i,i + 7 peptides did not have any effect on virus release; however, they impaired Gag precursor processing. HIV-1 particles produced in the presence of these peptides displayed impaired infectivity. Consistent with an effect on virus entry, selection for viral resistance led to the emergence of two mutations in the gp120 subunit of the viral envelope (Env) glycoprotein, V120Q and A327P, located in the conserved region 1 (C1) and the base of the V3 loop, respectively.<p></p> Conclusion: The i,i + 7 stapled peptides derived from CAI unexpectedly target both CA and the V3 loop of gp120. This dual-targeted activity is dependent on their ability to penetrate cells as well as their net charge. This mechanistic revelation will be useful in further modifying these peptides as potent anti-HIV-1 agents.<p></p&gt

Periodic harmonic functions on lattices and points count in positive characteristic

This survey addresses pluri-periodic harmonic functions on lattices with values in a positive characteristic field. We mention, as a motivation, the game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware, Barua-Ramakrishnan-Sarkar, Hunzikel-Machiavello-Park e.a.; see also 2 previous author's preprints for a more detailed account. Our approach explores harmonic analysis and algebraic geometry over a positive characteristic field. The Fourier transform allows us to interpret pluri-periods of harmonic functions on lattices as torsion multi-orders of points on the corresponding affine algebraic variety.Comment: These are notes on 13p. based on a talk presented during the meeting "Analysis on Graphs and Fractals", the Cardiff University, 29 May-2 June 2007 (a sattelite meeting of the programme "Analysis on Graphs and its Applications" at the Isaac Newton Institute from 8 January to 29 June 2007

Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems

We determine explicit orbit representatives of reducible Jordan algebras and of their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of N = 2, 4 locally supersymmetric theories of gravity coupled to an arbitrary number of Abelian vector multiplets in D = 4, 5 space-time dimensions.Comment: 18 pages. Updated to match published versio