Discovery of a Dicephalic Western Diamondback Rattlesnake, Crotalus atrox (Serpentes: Viperidae), from Texas, with a Summary of Dicephalism Among Members of the Genus Crotalus

We document the fourth record of a dicephalic western diamondback rattlesnake, Crotalus atrox, collected on 17 September 2005 in Tom Green County, Texas, along with features of its external and internal anatomy, which are compared with normal C. atrox neonates. This is only the second reported case of complete anatomical duplication of the respiratory system and nearly complete duplication of the circulatory and digestive systems in dicephalic snakes. In addition, we present a summary of dicephalism among 10 species within the genus Crotalus

An Alternative Prior Process for Nonparametric Bayesian Clustering

Prior distributions play a crucial role in Bayesian approaches to clustering. Two commonly-used prior distributions are the Dirichlet and Pitman-Yor processes. In this paper, we investigate the predictive probabilities that underlie these processes, and the implicit "rich-get-richer" characteristic of the resulting partitions. We explore an alternative prior for nonparametric Bayesian clustering -- the uniform process -- for applications where the "rich-get-richer" property is undesirable. We also explore the cost of this process: partitions are no longer exchangeable with respect to the ordering of variables. We present new asymptotic and simulation-based results for the clustering characteristics of the uniform process and compare these with known results for the Dirichlet and Pitman-Yor processes. We compare performance on a real document clustering task, demonstrating the practical advantage of the uniform process despite its lack of exchangeability over orderings

Unitary derived functor modules with small spectrum

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The trace of the heat kernel on a compact hyperbolic 3-orbifold

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the discrete group \Ga contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.Comment: 11 page

Molecular evidence for Anaplasma phagocytophilum in Israel

Sequences from the Anaplasma phagocytophilum 16S rRNA gene were detected in 5 ticks representing 3 species (Hyalomma marginatum, Rhipicephalus turanicus, and Boophilus kohlsi) collected from roe deer (Capreolus capreolus) in Mount Carmel, Israel. The sequences were all identical to those of Ap-variant 1 strain

System of Complex Brownian Motions Associated with the O'Connell Process

The O'Connell process is a softened version (a geometric lifting with a parameter $a>0$) of the noncolliding Brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length $a$. This process is not determinantal. Under a special entrance law, however, Borodin and Corwin gave a Fredholm determinant expression for the expectation of an observable, which is a softening of an indicator of a particle position. We rewrite their integral kernel to a form similar to the correlation kernels of determinantal processes and show, if the number of particles is $N$, the rank of the matrix of the Fredholm determinant is $N$. Then we give a representation for the quantity by using an $N$-particle system of complex Brownian motions (CBMs). The complex function, which gives the determinantal expression to the weight of CBM paths, is not entire, but in the combinatorial limit $a \to 0$ it becomes an entire function providing conformal martingales and the CBM representation for the noncolliding Brownian motion is recovered.Comment: v3: AMS_LaTeX, 25 pages, no figure, minor corrections made for publication in J. Stat. Phy