Yang-Mills fields on CR manifolds

We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.Comment: 52 page

Cooperation and the evolution of intelligence

The high levels of intelligence seen in humans, other primates, certain cetaceans and birds remain a major puzzle for evolutionary biologists, anthropologists and psychologists. It has long been held that social interactions provide the selection pressures necessary for the evolution of advanced cognitive abilities (the ‘social intelligence hypothesis’), and in recent years decision-making in the context of cooperative social interactions has been conjectured to be of particular importance. Here we use an artificial neural network model to show that selection for efficient decision-making in cooperative dilemmas can give rise to selection pressures for greater cognitive abilities, and that intelligent strategies can themselves select for greater intelligence, leading to a Machiavellian arms race. Our results provide mechanistic support for the social intelligence hypothesis, highlight the potential importance of cooperative behaviour in the evolution of intelligence and may help us to explain the distribution of cooperation with intelligence across taxa

Slutsky Matrix Norms and Revealed Preference Tests of Consumer Behaviour

Given any observed finite sequence of prices, wealth and demand choices, we characterize the relation between its underlying Slutsky matrix norm (SMN) and some popular discrete revealed preference (RP) measures of departures from rationality, such as the Afriat index. We show that testing rationality in the SMN aproach with finite data is equivalent to testing it under the RP approach. We propose a way to "summarize" the departures from rationality in a systematic fashion in finite datasets. Finally, these ideas are extended to an observed demand with noise due to measurement error; we formulate an appropriate modification of the SMN approach in this case and derive closed-form asymptotic results under standard regularity conditions

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Wild and laboratory exposure to cues of predation risk increases relative brain mass in male guppies

There is considerable diversity in brain size within and among species, and substantial dispute over the causes, consequences and importance of this variation. Comparative and developmental studies are essential in addressing this controversy. Predation pressure has been proposed as a major force shaping brain, behaviour and life history. The Trinidadian guppy, Poecilia reticulata, shows dramatic variation in predation pressure across populations. We compared the brain mass of guppies from high and low predation populations collected in the wild. Male but not female guppies exposed to high predation possessed heavier brains for their body size compared to fish from low predation populations. The brain is a plastic organ, so it is possible that the population differences we observed were partly due to developmental responses rather than evolved differences. In a follow‐up study, we raised guppies under cues of predation risk or in a control condition. Male guppies exposed to predator cues early in life had heavier brains relative to their body size than control males, while females showed no significant effect of treatment. Collectively our results suggest that male guppies exposed to predation invest more in neural tissue, and that these differences are at least partly driven by plastic responses

Does Diving Limit Brain Size in Cetaceans?

We test the longstanding hypothesis, known as the dive constraint hypothesis, that the oxygenation demands of diving pose a constraint on aquatic mammal brain size.Using a sample of 23 cetacean species we examine the relationship among six different measures of relative brain size, body size, and maximum diving duration. Unlike previous tests we include body size as a covariate and perform independent contrast analyses to control for phylogeny. We show that diving does not limit brain size in cetaceans and therefore provide no support for the dive constraint hypothesis. Instead, body size is the main predictor of maximum diving duration in cetaceans. Furthermore, our findings show that it is important to conduct robust tests of evolutionary hypotheses by employing a variety of measures of the dependent variable, in this case, relative brain size

Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators

We prove a quantitative unique continuation principle for infinite dimensional spectral subspaces of Schr\"odinger operators. Let $\Lambda_L = (-L/2,L/2)^d$ and $H_L = -\Delta_L + V_L$ be a Schr\"odinger operator on $L^2 (\Lambda_L)$ with a bounded potential $V_L : \Lambda_L \to \mathbb{R}^d$ and Dirichlet, Neumann, or periodic boundary conditions. Our main result is of the type $$\int_{\Lambda_L} \lvert \phi \rvert^2 \leq C_{\mathrm{sfuc}} \int_{W_\delta (L)} \lvert \phi \rvert^2,$$ where $\phi$ is an infinite complex linear combination of eigenfunctions of $H_L$ with exponentially decaying coefficients, $W_\delta (L)$ is some union of equidistributed $\delta$-balls in $\Lambda_L$ and $C_{\mathrm{sfuc}} > 0$ an $L$-independent constant. The exponential decay condition on $\phi$ can alternatively be formulated as an exponential decay condition of the map $\lambda \mapsto \lVert \chi_{[\lambda , \infty)} (H_L) \phi \rVert^2$. The novelty is that at the same time we allow the function $\phi$ to be from an infinite dimensional spectral subspace and keep an explicit control over the constant $C_{\mathrm{sfuc}}$ in terms of the parameters. Moreover, we show that a similar result cannot hold under a polynomial decay condition