New Reducible Five-brane Solutions in M-theory

We construct new M-theory solutions of M5 branes that are a realization of the fully localized ten dimensional NS5/D6 and NS5/D5 brane intersections. These solutions are obtained by embedding self-dual geometries lifted to M-theory. We reduce these solutions down to ten dimensions, obtaining new D-brane systems in type IIA/IIB supergravity. The worldvolume theories of the NS5-branes are new non-local, non-gravitational, six dimensional, T-dual little string theories with eight supersymmetries.Comment: 19 pages, 4 figures, two paragraphs added in conclusions, typos correcte

Gibbons-Hawking M-branes

We present new M2 and M5-brane solutions in M-theory based on transverse Gibbons-Hawking spaces. These solutions provide realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections. One novel feature of these solutions is that the metric functions depend on more than two transverse coordinates (unlike all the other previous known solutions). All the solutions have eight preserved supersymmetries and the world-volume theories of the NS5-branes are new non-local, non-gravitational, six dimensional, T-dual little string theories with eight supersymmetries. We discuss the limits in which the dynamics of the D2 and NS5-branes decouple from the bulk for these solutions.Comment: 32 pages, 7 figures, few sentences added, a couple of typos corrected, to appear in JHE

A stability version of H\"older's inequality

We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue 2, Pages 842-852. This version differs from the published one in that it contains a new reference, and a trivial improvement of Corollary 3.2. fo

Striving for humane deaths for laboratory mice: hypobaric hypoxia provides a potential alternative to carbon dioxide exposure

Killing is often an unavoidable and necessary procedure for laboratory mice involved in scientific research, and providing a humane death is vital for public acceptance. Exposure to carbon dioxide (CO2) gas is the most widely used methodology despite well proven welfare concerns. Consequently, the continued use of CO2 and its globally permitted status in legislation and guidelines presents an ethical dilemma for users. We investigated whether killing with hypobaric hypoxia via gradual decompression was associated with better welfare outcomes for killing laboratory mice. We compared the spontaneous behaviour of mice exposed to CO2, decompression or sham conditions, and used analgesic or anxiolytic interventions to determine their relative welfare impact. Gradual decompression resulted in longer times to unconsciousness and death and the pharmacological interventions support the notion of a minimally negative animal experience, while providing further evidence for pain and anxiety associated with exposure to CO2. Decompression resulted in moderate ear haemorrhage, but our welfare assessment suggests this may happen when mice are unconscious. Hence, gradual decompression could be the basis of significant refinement for killing laboratory mice. Future work should corroborate behaviour with neurobiological markers of loss of consciousness to verify the conscious phase of concern for animal welfare

Nuttier Bubbles

We construct new explicit solutions of general relativity from double analytic continuations of Taub-NUT spacetimes. This generalizes previous studies of 4-dimensional nutty bubbles. One 5-dimensional locally asymptotically AdS solution in particular has a special conformal boundary structure of $AdS_3\times S^1$. We compute its boundary stress tensor and relate it to the properties of the dual field theory. Interestingly enough, we also find consistent 6-dimensional bubble solutions that have only one timelike direction. The existence of such spacetimes with non-trivial topology is closely related to the existence of the Taub-NUT(-AdS) solutions with more than one NUT charge. Finally, we begin an investigation of generating new solutions from Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality, we provide new explicit time-dependent backgrounds in six dimensions.Comment: 32 pages, 1 figure; v.3. typos corrected. Matches the published versio

Experimental study of geometric t-spanners : a running time comparison

The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. We experimentally study the performance of the most common construction algorithms for points in the Euclidean plane. In a previous paper [10] we considered the properties of the produced graphs from five common algorithms. We consider several additional algorithms and focus on the running times. This is the first time an extensive comparison has been made between the running times of construction algorithms of t-spanners

Regularization of odd-dimensional AdS gravity: Kounterterms

As an alternative to the Dirichlet counterterms prescription, I introduce the concept of Kounterterms as the boundary terms with explicit dependence on the extrinsic curvature K_{ij} that regularize the AdS gravity action. Instead of a Dirichlet boundary condition on the metric, a suitable choice of the boundary conditions --compatible with any asymptotically AdS (AAdS) spacetime-- ensures a finite action principle for all odd dimensions. Background-independent conserved quantities are obtained as Noether charges associated to asymptotic symmetries and their general expression appears naturally split in two parts. The first one gives the correct mass and angular momentum for AAdS black holes and vanishes identically for globally AdS spacetimes. Thus, the second part is a covariant formula for the vacuum energy in AAdS spacetimes and reproduces the results obtained by the Dirichlet counterterms method in a number of cases. It is also shown that this Kounterterms series regularizes the Euclidean action and recovers the correct black hole thermodynamics in odd dimensions.Comment: 35+6 pages, 8 references and an appendix added, improved discussion on boundary conditions and geometrical origin of Kounterterms. Version accepted in JHE

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

The holographic superconductors in higher-dimensional AdS soliton

We explore the behaviors of the holographic superconductors at zero temperature for a charged scalar field coupled to a Maxwell field in higher-dimensional AdS soliton spacetime via analytical way. In the probe limit, we obtain the critical chemical potentials increase linearly as a total dimension $d$ grows up. We find that the critical exponent for condensation operator is obtained as 1/2 independently of $d$, and the charge density is linearly related to the chemical potential near the critical point. Furthermore, we consider a slightly generalized setup the Einstein-Power-Maxwell field theory, and find that the critical exponent for condensation operator is given as $1/(4-2n)$ in terms of a power parameter $n$ of the Power-Maxwell field, and the charge density is proportional to the chemical potential to the power of $1/(2-n)$.Comment: LaTeX, 16 pages, 5 figures, typos corrected, one reference added, version to appear in European Physical Journal