The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

Kochen-Specker Theorem for Finite Precision Spin One Measurements

Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.Comment: 4 page

Existential Contextuality and the Models of Meyer, Kent and Clifton

It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.Comment: Revtex, 7 pages, 1 figure. Replaced with published versio

Bases for qudits from a nonstandard approach to SU(2)

Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for quantum information and quantum computation are constructed from angular momentum theory and su(2) Lie algebraic methods. We report on a formula for deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated application of the formula can be used for generating mutually unbiased bases in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection between mutually unbiased bases and the unitary group SU(d) is briefly discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of Theoretical Physics of the JINR and the ICAS at Yerevan State University

Variations on a theme of Heisenberg, Pauli and Weyl

The parentage between Weyl pairs, generalized Pauli group and unitary group is investigated in detail. We start from an abstract definition of the Heisenberg-Weyl group on the field R and then switch to the discrete Heisenberg-Weyl group or generalized Pauli group on a finite ring Z_d. The main characteristics of the latter group, an abstract group of order d**3 noted P_d, are given (conjugacy classes and irreducible representation classes or equivalently Lie algebra of dimension d**3 associated with P_d). Leaving the abstract sector, a set of Weyl pairs in dimension d is derived from a polar decomposition of SU(2) closely connected to angular momentum theory. Then, a realization of the generalized Pauli group P_d and the construction of generalized Pauli matrices in dimension d are revisited in terms of Weyl pairs. Finally, the Lie algebra of the unitary group U(d) is obtained as a subalgebra of the Lie algebra associated with P_d. This leads to a development of the Lie algebra of U(d) in a basis consisting of d**2 generalized Pauli matrices. In the case where d is a power of a prime integer, the Lie algebra of SU(d) can be decomposed into d-1 Cartan subalgebras.Comment: Dedicated to the memory of Mosh\'e Flato on the occasion of the tenth anniversary of his deat

Fetal Alcohol Syndrome: A Case Report of Neuropsychological, MRI, and EEG Assessment of Two Children

Neuropsychological, neuroanatomical, and electrophysiological data are presented on two subjects with fetal alcohol syndrome (FAS). Both boys had intelligence quotients in the mentally deficient range and were found to have several other severe, specific deficits. Magnetic resonance imaging showed abnormalities of the corpus callosum, and reductions in the size of the basal ganglia and thalamic structures. No focal abnormalities were noted in the electroencephalogram records, although the electroencephalograms of both boys were moderately abnormal for their age group. A multidisciplinary approach to the study of FAS, hopefully will lead to a more unified concept of the disorder and perhaps indicate specific areas of vulnerability

Face, body and speech cues independently predict judgments of attractiveness

Research on human attraction frequently makes use of single-modality stimuli such as neutral-expression facial photographs as proxy indicators of an individual’s attractiveness. However, we know little about how judgments of these single-modality stimuli correspond to judgments of stimuli that incorporate multi-modal cues of face, body and speech. In the present study, ratings of attractiveness judged from videos of participants introducing themselves were independently predicted by judgments of the participant’s facial attractiveness (a neutral-expression facial photograph masked to conceal the hairstyle), body attractiveness (a photograph of the upper body), and speech attractiveness (the soundtrack to the video). We also found that ratings of the face, body and speech were positively related to each other. Our results support the assumption that the single-modality stimuli used in much attractiveness research are valid proxy indicators of overall attractiveness in ecologically valid contexts, and complement literature showing cross-modality concordance of trait attractiveness, but also recommend that research relying on assessments of individual attractiveness take account of both visual and vocal attractiveness where possible

The Origin and Initial Rise of Pelagic Cephalopods in the Ordovician

BACKGROUND: During the Ordovician the global diversity increased dramatically at family, genus and species levels. Partially the diversification is explained by an increased nutrient, and phytoplankton availability in the open water. Cephalopods are among the top predators of today's open oceans. Their Ordovician occurrences, diversity evolution and abundance pattern potentially provides information on the evolution of the pelagic food chain. METHODOLOGY/PRINCIPAL FINDINGS: We reconstructed the cephalopod departure from originally exclusively neritic habitats into the pelagic zone by the compilation of occurrence data in offshore paleoenvironments from the Paleobiology Database, and from own data, by evidence of the functional morphology, and the taphonomy of selected cephalopod faunas. The occurrence data show, that cephalopod associations in offshore depositional settings and black shales are characterized by a specific composition, often dominated by orthocerids and lituitids. The siphuncle and conch form of these cephalopods indicate a dominant lifestyle as pelagic, vertical migrants. The frequency distribution of conch sizes and the pattern of epibionts indicate an autochthonous origin of the majority of orthocerid and lituitid shells. The consistent concentration of these cephalopods in deep subtidal sediments, starting from the middle Tremadocian indicates the occupation of the pelagic zone early in the Early Ordovician and a subsequent diversification which peaked during the Darriwilian. CONCLUSIONS/SIGNIFICANCE: The exploitation of the pelagic realm started synchronously in several independent invertebrate clades during the latest Cambrian to Middle Ordovician. The initial rise and diversification of pelagic cephalopods during the Early and Middle Ordovician indicates the establishment of a pelagic food chain sustainable enough for the development of a diverse fauna of large predators. The earliest pelagic cephalopods were slowly swimming vertical migrants. The appearance and early diversification of pelagic cephalopods is interpreted as a consequence of the increased food availability in the open water since the latest Cambrian