A delay logistic equation with variable growth rate

A logistic equation with distributed delay is considered in the case where the growth rate oscillates sinusoidally about a positive mean value. A delay kernel is chosen which admits bifurcation of the equilibrium state into a periodic solution when the growth rate is constant. It is shown that the fluctuations in growth rate modulate the bifurcation into a quasiperiodic solution. In certain circumstances, however, it is shown that frequency locking can occur but that this is a local phenomenon which does not persist outside the immediate vicinity of the bifurcation point

Gauge Mediated Mini-Split

We propose a simple model of split supersymmetry from gauge mediation. This model features gauginos that are parametrically a loop factor lighter than scalars, accommodates a Higgs boson mass of 125 GeV, and incorporates a simple solution to the $\mu-b_\mu$ problem. The gaugino mass suppression can be understood as resulting from collective symmetry breaking. Imposing collider bounds on $\mu$ and requiring viable electroweak symmetry breaking implies small $a$-terms and small $\tan \beta$ -- the stop mass ranges from $10^5$ to 10^8 \mbox{ GeV}. In contrast with models with anomaly + gravity mediation (which also predict a one-loop loop suppression for gaugino masses), our gauge mediated scenario predicts aligned squark masses and a gravitino LSP. Gluinos, electroweakinos and Higgsinos can be accessible at the LHC and/or future colliders for a wide region of the allowed parameter space.Comment: 16 pages, 1 figure. Journal version, references adde

Impaired recognition of social emotions following amygdala damage

Lesion, functional imaging, and single-unit studies in human and nonhuman animals have demonstrated a role for the amygdala in processing stimuli with emotional and social significance. We investigated the recognition of a wide variety of facial expressions, including basic emotions (e.g., happiness, anger) and social emotions (e.g., guilt, admiration, flirtatiousness). Prior findings with a standardized set of stimuli indicated that recognition of social emotions can be signaled by the eye region of the face and is disproportionately impaired in autism (Baron-Cohen, Wheelwright, & Jolliffe, 1997). To test the hypothesis that the recognition of social emotions depends on the amygdala, we administered the same stimuli to 30 subjects with unilateral amygdala damage (16 left, 14 right), 2 with bilateral amygdala damage, 47 brain-damaged controls, and 19 normal controls. Compared with controls, subjects with unilateral or bilateral amygdala damage were impaired when recognizing social emotions; moreover, they were more impaired in recognition of social emotions than in recognition of basic emotions, and, like previously described patients with autism, they were impaired also when asked to recognize social emotions from the eye region of the face alone. The findings suggest that the human amygdala is relatively specialized to process stimuli with complex social significance. The results also provide further support for the idea that some of the impairments in social cognition seen in patients with autism may result from dysfunction of the amygdala

Some applications of probability theory in statistical mechanics

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Seeing the Forest for the Trees: Using the Gene Ontology to Restructure Hierarchical Clustering

Motivation: There is a growing interest in improving the cluster analysis of expression data by incorporating into it prior knowledge, such as the Gene Ontology (GO) annotations of genes, in order to improve the biological relevance of the clusters that are subjected to subsequent scrutiny. The structure of the GO is another source of background knowledge that can be exploited through the use of semantic similarity. Results: We propose here a novel algorithm that integrates semantic similarities (derived from the ontology structure) into the procedure of deriving clusters from the dendrogram constructed during expression-based hierarchical clustering. Our approach can handle the multiple annotations, from different levels of the GO hierarchy, which most genes have. Moreover, it treats annotated and unannotated genes in a uniform manner. Consequently, the clusters obtained by our algorithm are characterized by significantly enriched annotations. In both cross-validation tests and when using an external index such as protein–protein interactions, our algorithm performs better than previous approaches. When applied to human cancer expression data, our algorithm identifies, among others, clusters of genes related to immune response and glucose metabolism. These clusters are also supported by protein–protein interaction data. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.Lynne and William Frankel Center for Computer Science; Paul Ivanier center for robotics research and production; National Institutes of Health (R01 HG003367-01A1

Identities for field extensions generalizing the Ohno-Nakagawa relations

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of `extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree l fields with Galois groups D_l and F_l respectively, for any odd prime l, and in particular we give another proof of the Ohno-Nakagawa relation without appealing to binary cubic forms.Comment: Version 2, 16 pages, to appear in Compositi

Spectroscopic Confirmation of the Dwarf Galaxies Hydra II and Pisces II and the Globular Cluster Laevens 1

We present Keck/DEIMOS spectroscopy of stars in the recently discovered Milky Way satellites Hydra II, Pisces II, and Laevens 1. We measured a velocity dispersion of 5.4 (+3.6 -2.4) km/s for Pisces II, but we did not resolve the velocity dispersions of Hydra II or Laevens 1. We marginally resolved the metallicity dispersions of Hydra II and Pisces II but not Laevens 1. Furthermore, Hydra II and Pisces II obey the luminosity-metallicity relation for Milky Way dwarf galaxies ( = -2.02 +/- 0.08 and -2.45 +/- 0.07, respectively), whereas Laevens 1 does not ( = -1.68 +/- 0.05). The kinematic and chemical properties suggest that Hydra II and Pisces II are dwarf galaxies, and Laevens 1 is a globular cluster. We determined that two of the previously observed blue stars near the center of Laevens 1 are not members of the cluster. A third blue star has ambiguous membership. Hydra II has a radial velocity = 303.1 +/- 1.4 km/s, similar to the leading arm of the Magellanic stream. The mass-to-light ratio for Pisces II is 370 (+310 -240) M_sun/L_sun. It is not among the most dark matter-dominated dwarf galaxies, but it is still worthy of inclusion in the search for gamma rays from dark matter self-annihilation.Comment: Accepted to ApJ. v2 has been revised in response to the referee's repor

NGC 2419 -- Another Remnant of Accretion by the Milky Way

We isolate a sample of 43 upper RGB stars in the extreme outer halo Galactic globular cluster NGC 2419 from two Keck/DEIMOS slitmasks. The probability that there is more than one contaminating halo field star in this sample is extremely low. Analysis of moderate resolution spectra of these cluster members, as well as of our Keck/HIRES high resolution spectra of a subsample of them, demonstrates that there is a small but real spread in Ca abundance of ~ 0.2 dex within this massive metal-poor globular cluster. This provides additional support to earlier suggestions that NGC 2419 is the remnant of a dwarf galaxy accreted long ago by the Milky Way.Comment: Accepted to the Astrophysical Journa