A volumetric Penrose inequality for conformally flat manifolds

We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to $\R^{n}\setminus \Omega, n\ge 3$, and so that their boundary is a minimal hypersurface. (Here, $\Omega\subset \R^{n}$ is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by $(V/\beta_{n})^{(n-2)/n}$, where $V$ is the Euclidean volume of $\Omega$ and $\beta_{n}$ is the volume of the Euclidean unit $n$-ball. This gives a partial proof to a conjecture of Bray and Iga \cite{brayiga}. Surprisingly, we do not require the boundary to be outermost.Comment: 7 page

Invisible pushdown languages

Context free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these properties by making the structure of the tree visible, such as is done by visibly pushdown languages, or finite automata on trees. In this paper, we show that the structure given by such approaches remains invisible when it is read by a finite automaton (on word). In particular, we show that separability with a regular language is undecidable for visibly pushdown languages, just as it is undecidable for general context free languages

Frequency shifts and depth dependence of premotor beta band activity during perceptual decision-making

Neural activity in the premotor and motor cortices shows prominent structure in the beta frequency range (13–30 Hz). Currently, the behavioral relevance of this beta band activity (BBA) is debated. The underlying source of motor BBA and how it changes as a function of cortical depth are also not completely understood. Here, we addressed these unresolved questions by investigating BBA recorded using laminar electrodes in the dorsal premotor cortex of 2 male rhesus macaques performing a visual reaction time (RT) reach discrimination task. We observed robust BBA before and after the onset of the visual stimulus but not during the arm movement. While poststimulus BBA was positively correlated with RT throughout the beta frequency range, prestimulus correlation varied by frequency. Low beta frequencies (∼12–20 Hz) were positively correlated with RT, and high beta frequencies (∼22–30 Hz) were negatively correlated with RT. Analysis and simulations suggested that these frequency-dependent correlations could emerge due to a shift in the component frequencies of the prestimulus BBA as a function of RT, such that faster RTs are accompanied by greater power in high beta frequencies. We also observed a laminar dependence of BBA, with deeper electrodes demonstrating stronger power in low beta frequencies both prestimulus and poststimulus. The heterogeneous nature of BBA and the changing relationship between BBA and RT in different task epochs may be a sign of the differential network dynamics involved in cue expectation, decision-making, motor preparation, and movement execution.Published versio

IUS guidance algorithm gamma guide assessment

The Gamma Guidance Algorithm which controls the inertial upper stage is described. The results of an independent assessment of the algorithm's performance in satisfying the NASA missions' targeting objectives are presented. The results of a launch window analysis for a Galileo mission, and suggested improvements are included

Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

Real space analysis of inherent structures

We study a generalization of the one-dimensional disordered Potts model, which exhibits glassy properties at low temperature. The real space properties of inherent structures visited dynamically are analyzed through a decomposition into domains over which the energy is minimized. The size of these domains is distributed exponentially, defining a characteristic length scale which grows in equilibrium when lowering temperature, as well as in the aging regime at a given temperature. In the low temperature limit, this length can be interpreted as the distance between `excited' domains within the inherent structures.Comment: 7 pages, 8 figures, final versio

Reply to "Comment on Evidence for the droplet picture of spin glasses"

Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.Comment: 1 page, 1 figur

Macro issues of Mikro Primary School

Mikro Primary School is an Afrikaans medium public school whose governing body refused to accede to an order of the Western Cape Department of Education to change the language policy of the school so as to convert it into a parallel medium Afrikaans/English school. The Supreme Court of Appeal held that section 29(2) of the Constitution of the Republic of South Africa, 1996, means that everyone has a right to be educated in an official language of his or her choice at a public educational institution to be provided by the State if reasonably practicable, but not the right to be so instructed at each and every public educational institution, subject only to it being reasonably practicable to do so. The court held that the language policy and admission policy of Mikro were not contrary to any provision of the Constitution, the South African Schools Act 84 of 1996, the Western Cape Provincial School Education Act 12 of 1997 or the Norms and Standards. The MEC and the department were prohibited and restrained from compelling or attempting to compel the school or its principal to admit learners for instruction otherwise than in compliance withits language policy and applicable provisions of the Schools Act and the Norms and Standards. The court declared the conduct of the department’s officials to be an unlawful interference with the government and professional management of the school in contravention of section 16 of the Schools Act and prohibited and restrained them from interfering unlawfully. The court rejected a previous interpretation of the term “organ of state” and relied on the Constitution which determines that any institution exercising a public power or performing a public function in terms of any legislation is an organ of state (section 239(b)(ii)). This means that the public school (acting through its governing body) is clearly an organ of state because as an institution it exercises a public-education power and performs public-education functions in terms of the Schools Act, for exampl

Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity, away from the cheetah, proportional to their distance from the cheetah, such that they tend to move away from the cheetah with increasing time. Using the backward Fokker-Planck equation we calculate, as a function of their initial separations, the probability that the cheetah has caught neither antelope after infinite time.Comment: 5 page