Spontaneous otogenic pneumocephalus and pneumatocoele

We report the case of a 33-year old woman with an otogenic pneumocephalus associated with pneumatocoele. To our knowledge only 2 other cases have been documented. We discuss the imaging, treatment and causes of otogenic pneumocephalus

Uniqueness of Bessel models: the archimedean case

In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.Comment: 22 page

A general form of Gelfand-Kazhdan criterion

We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion for a real reductive group in very general settings.Comment: 16 pages, to appear in Manuscripta Mathematic

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Depths and Thermal Habitat Used by Large versus Small Northern Pike in Three Minnesota Lakes

We monitored depths and temperatures used by large (>71‐cm) versus small Northern Pike Esox lucius in three north‐central Minnesota lakes with either acoustic telemetry or archival tags. Individual Northern Pike demonstrated flexibility in depths used within a season and between years. The fish had some tolerance for low levels of dissolved oxygen (<3 mg/L), but depth selection was generally constrained by low dissolved oxygen in summer and winter. The fish more fully exploited all available depths during winter and thermal turnover periods. During July and August, large Northern Pike tended to follow the thermocline into cooler water as upper water layers warmed. Selection ratios indicated that large Northern Pike preferred water temperatures of 16–21°C during August when temperatures up to 28°C were available. In two lakes providing dense overhead cover from water lilies in shallow water, small Northern Pike used warmer, shallower water compared with large fish during summer. In a third lake providing no such cover, small fish were more often in deeper, cooler water. For small Northern Pike, temperature seemed to be a secondary habitat consideration behind the presence of shallow vegetated cover. This study provided detailed temperature selection information that will be useful when considering temperature as an ecological resource for different sizes of Northern Pike.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141595/1/tafs1629.pd

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Behavioural syndrome in a solitary predator is independent of body size and growth rate.

Models explaining behavioural syndromes often focus on state-dependency, linking behavioural variation to individual differences in other phenotypic features. Empirical studies are, however, rare. Here, we tested for a size and growth-dependent stable behavioural syndrome in the juvenile-stages of a solitary apex predator (pike, Esox lucius), shown as repeatable foraging behaviour across risk. Pike swimming activity, latency to prey attack, number of successful and unsuccessful prey attacks was measured during the presence/absence of visual contact with a competitor or predator. Foraging behaviour across risks was considered an appropriate indicator of boldness in this solitary predator where a trade-off between foraging behaviour and threat avoidance has been reported. Support was found for a behavioural syndrome, where the rank order differences in the foraging behaviour between individuals were maintained across time and risk situation. However, individual behaviour was independent of body size and growth in conditions of high food availability, showing no evidence to support the state-dependent personality hypothesis. The importance of a combination of spatial and temporal environmental variation for generating growth differences is highlighted

Simulated Effects of Recruitment Variability, Exploitation, and Reduced Habitat Area on the Muskellunge Population in Shoepack Lake, Voyageurs National Park, Minnesota

The genetically unique population of muskellunge Esox masquinongy inhabiting Shoepack Lake in Voyageurs National Park, Minnesota, is potentially at risk for loss of genetic variability and long-term viability. Shoepack Lake has been subject to dramatic surface area changes from the construction of an outlet dam by beavers Castor canadensis and its subsequent failure. We simulated the long-term dynamics of this population in response to recruitment variation, increased exploitation, and reduced habitat area. We then estimated the effective population size of the simulated population and evaluated potential threats to long-term viability, based on which we recommend management actions to help preserve the long-term viability of the population. Simulations based on the population size and habitat area at the beginning of a companion study resulted in an effective population size that was generally above the threshold level for risk of loss of genetic variability, except when fishing mortality was increased. Simulations based on the reduced habitat area after the beaver dam failure and our assumption of a proportional reduction in population size resulted in an effective population size that was generally below the threshold level for risk of loss of genetic variability. Our results identified two potential threats to the long-term viability of the Shoepack Lake muskellunge population, reduction in habitat area and exploitation. Increased exploitation can be prevented through traditional fishery management approaches such as the adoption of no-kill, barbless hook, and limited entry regulations. Maintenance of the greatest possible habitat area and prevention of future habitat area reductions will require maintenance of the outlet dam built by beavers. Our study should enhance the long-term viability of the Shoepack Lake muskellunge population and illustrates a useful approach for other unique populations