Predicting Collaboration: Risk, Power, and Dependence in the Gulf of Maine

Collaboration among natural resource organizations and users is touted by researchers as an effective approach to managing common pool resources. To understand how collaboration works, previous studies in organizational theory have identified three variables: power, dependence, and risk. Relationships between actors can be represented by these qualifications of resources or threats and may predict if those relationships are in conflict or asymmetric in power. In this study, the Gulf of Maine transboundary fishery management network relied upon a dyadic influenced survey to quantitatively capture the perception of communication ties between organizations. Four kinds of dependence and three types of risk were captured by respondent responses to be used in predictive and descriptive analysis. The patterns presented a network with low risk and high levels of dependence. Dependence and risk were able to significantly predict whether a relationship was in conflict or whether a relationship had feelings of power, with legitimacy and performance as higher rated indicators. The results suggest that policy makers and network designers should foster legitimacy and shun performance failures when evaluating the relationships among management networks

On the Validity of the 0-1 Test for Chaos

In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics

Herman's Theory Revisited

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.Comment: 10 page

Fundamental Limits on the Speed of Evolution of Quantum States

This paper reports on some new inequalities of Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution between two orthogonal pure states. The clear determinant of the qualitative behavior of this time scale is the statistics of the energy spectrum. An often-overlooked correspondence between the real-time behavior of a quantum system and the statistical mechanics of a transformed (imaginary-time) thermodynamic system appears promising as a source of qualitative insights into the quantum dynamics.Comment: 6 pages, 1 eps figur

Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

A Tauberian Theorem for ℓ\ell-adic Sheaves on A1\mathbb A^1

Let $K\in L^1(\mathbb R)$ and let $f\in L^\infty(\mathbb R)$ be two functions on $\mathbb R$. The convolution $$(K\ast f)(x)=\int_{\mathbb R}K(x-y)f(y)dy$$ can be considered as an average of $f$ with weight defined by $K$. Wiener's Tauberian theorem says that under suitable conditions, if $$\lim_{x\to \infty}(K\ast f)(x)=\lim_{x\to \infty} (K\ast A)(x)$$ for some constant $A$, then $$\lim_{x\to \infty}f(x)=A.$$ We prove the following $\ell$-adic analogue of this theorem: Suppose $K,F, G$ are perverse $\ell$-adic sheaves on the affine line $\mathbb A$ over an algebraically closed field of characteristic $p$ ($p\not=\ell$). Under suitable conditions, if $$(K\ast F)|_{\eta_\infty}\cong (K\ast G)|_{\eta_\infty},$$ then $$F|_{\eta_\infty}\cong G|_{\eta_\infty},$$ where $\eta_\infty$ is the spectrum of the local field of $\mathbb A$ at $\infty$.Comment: To appear in Science in China, an issue dedicated to Wang Yuan on the occation of his 80th birthda

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Rigidity and Non-recurrence along Sequences

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page