Re-187-Os-187, Pt-190-Os-186 Isotopic and Highly Siderophile Element Systematics of Group IVA Irons

We have recently completed Re-187-Os-187 and Pt-190-Os-186 isotopic and elemental studies of the two largest magmatic iron meteorite groups, IIAB and IIIAB [1]. These studies revealed closed-system behavior of both isotopic systems, but complex trace element behavior for Re, Pt and Os in group IIIAB. Here we examine isotopic and trace elemental systematics of group IVA irons. The IVA irons are not as extensively fractionated as IIAB and IIIAB and their apparently less complex crystallization history may make for more robust interpretation of the relative partitioning behavior of Re, Pt and Os, as well as the other highly siderophile elements (HSE) measured here; Pd, Ru and Ir [e.g. 2]. An additional goal of our continuing research plan for iron meteorites is to assess the possibility of relating certain ungrouped irons with major groups via trace element modeling. Here, the isotopic and trace element systematics of the ungrouped irons Nedagolla and EET 83230 are compared with the IVA irons

Minimal supporting subtrees for the free energy of polymers on disordered trees

We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with respect to its localization behaviour. We show that, for high temperatures, the free energy is supported by a random tree of positive exponential growth rate, which is strictly smaller than that of the full tree. The growth rate of the minimal supporting subtree is decreasing to zero as the temperature decreases to the critical value. At the critical value and all lower temperatures, a single polymer suffices to support the free energy. Our proofs rely on elegant martingale methods adapted from the theory of branching random walks.Comment: 22 pages, 3 figures, to be published in the special issue of JMP, 'Statistical Mechanics on Random Structures

Information capacity in the weak-signal approximation

We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the optimality conditions in a convenient way. We show that input correlations in memoryless channels do not affect channel capacity since their effect decreases fast with vanishing input amplitude or power. On the other hand, for channels with memory, properly matching the input covariances to the dependence structure of the noise may lead to almost noiseless information transfer, even for intermediate values of the noise correlations. Since many model systems described in mathematical neuroscience and biophysics operate in the high noise regime and weak-signal conditions, we believe, that the described results are of potential interest also to researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review

Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur

Spin chains of Haldane-Shastry type and a generalized central limit theorem

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a nontrivial modification of the classical central limit theorem, and is especially suited to models whose partition function is explicitly known. In particular, we provide the first theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.Comment: RevTeX, 5 page

Sixteen years of Collaborative Learning through Active Sense-making in Physics (CLASP) at UC Davis

This paper describes our large reformed introductory physics course at UC Davis, which bioscience students have been taking since 1996. The central feature of this course is a focus on sense-making by the students during the five hours per week discussion/labs in which the students take part in activities emphasizing peer-peer discussions, argumentation, and presentations of ideas. The course differs in many fundamental ways from traditionally taught introductory physics courses. After discussing the unique features of CLASP and its implementation at UC Davis, various student outcome measures are presented showing increased performance by students who took the CLASP course compared to students who took a traditionally taught introductory physics course. Measures we use include upper-division GPAs, MCAT scores, FCI gains, and MPEX-II scores.Comment: Also submitted to American Journal of Physic

Large Deviations for a Non-Centered Wishart Matrix

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic potential theory, which in our case is a quadratic map involving the logarithmic energies, or Voiculescu's entropies, of two measures in the presence of an external field and an upper constraint. The proof is based on a two type particles Coulomb gas representation for the eigenvalue distribution, which gives a new insight on why such variational problems should describe the limiting spectral distribution. This representation is available because of a Nikishin structure satisfied by the weights of the multiple orthogonal polynomials hidden in the background.Comment: 40 page

Seeing the smart city on Twitter: Colour and the affective territories of becoming smart

This paper pays attention to the immense and febrile field of digital image files which picture the smart city as they circulate on the social media platform Twitter. The paper considers tweeted images as an affective field in which flow and colour are especially generative. This luminescent field is territorialised into different, emergent forms of becoming ‘smart’. The paper identifies these territorialisations in two ways: firstly, by using the data visualisation software ImagePlot to create a visualisation of 9030 tweeted images related to smart cities; and secondly, by responding to the affective pushes of the image files thus visualised. It identifies two colours and three ways of affectively becoming smart: participating in smart, learning about smart, and anticipating smart, which are enacted with different distributions of mostly orange and blue images. The paper thus argues that debates about the power relations embedded in the smart city should consider the particular affective enactment of being smart that happens via social media. More generally, the paper concludes that geographers must pay more attention to the diverse and productive vitalities of social media platforms in urban life and that this will require experiment with methods that are responsive to specific digital qualities