220 research outputs found

    Uniqueness of Bessel models: the archimedean case

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    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

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    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

    Cone beam CT: non-dental applications

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    Initially Cone Beam CT was almost exclusively used to perform dental radiology. However, the first generation CBCT systems were later increasingly used to study sinuses, facial and nose fractures, temporomandibular joints etc. 3D-cephalometric head and neck studies became possible once CBCT systems were available that allowed scanning of the complete head. For this purpose a double rotation technique with stitching of the resulting two data sets was needed. CBCT systems on which the rotation could be stopped were needed to perform dynamic swallow or pharyngography studies. The advent of more powerful high-end CBCT systems led the way to temporal bone and skull base imaging. Finally, high-end “supine” CBCT systems using a “gantry” made small joint musculoskeletal imaging possible. These non-dental CBCT studies gradually replaced conventional X-rays and CT/MDCT studies because they allowed imaging with higher resolution, lower radiation dose and less metal artifacts. In this paper the most important non-dental CBCT indications will be discussed

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

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    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

    Crystal constructions in Number Theory

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    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

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

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    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

    The strong thirteen spheres problem

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    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

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

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    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

    Population Dynamics and Angler Exploitation of the Unique Muskellunge Population in Shoepack Lake, Voyageurs National Park, Minnesota

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    A unique population of muskellunge Esox masquinongy inhabits Shoepack Lake in Voyageurs National Park, Minnesota. Little is known about its status, dynamics, and angler exploitation, and there is concern for the long-term viability of this population. We used intensive sampling and mark–recapture methods to quantify abundance, survival, growth, condition, age at maturity and fecundity and angler surveys to quantify angler pressure, catch rates, and exploitation. During our study, heavy rain washed out a dam constructed by beavers Castor canadensis which regulates the water level at the lake outlet, resulting in a nearly 50% reduction in surface area. We estimated a population size of 1,120 adult fish at the beginning of the study. No immediate reduction in population size was detected in response to the loss of lake area, although there was a gradual, but significant, decline in population size over the 2-year study. Adults grew less than 50 mm per year, and relative weight (W r) averaged roughly 80. Anglers were successful in catching, on average, two fish during a full day of angling, but harvest was negligible. Shoepack Lake muskellunge exhibit much slower growth rates and lower condition, but much higher densities and angler catch per unit effort (CPUE), than other muskellunge populations. The unique nature, limited distribution, and location of this population in a national park require special consideration for management. The results of this study provide the basis for assessing the long-term viability of the Shoepack Lake muskellunge population through simulations of long-term population dynamics and genetically effective population size

    Black liquor and the hangover effect: fish assemblage recovery dynamics following a pulse disturbance

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    Anthropogenic perturbations impact aquatic systems causing wide-ranging responses, from assemblage restructuring to assemblage recovery. Previous studies indicate the duration and intensity of disturbances play a role in the dynamics of assemblage recovery. In August 2011, the Pearl River, United States, was subjected to a weak black liquor spill from a paper mill which resulted in substantial loss of fish in a large stretch of the main channel. We quantified resilience and recovery of fish assemblage structure in the impacted area following the event. We compared downstream (impacted) assemblages to upstream (unimpacted) assemblages to determine initial impacts on structure. Additionally, we incorporated historic fish collections (1988–2011) to examine impacts on assemblage structure across broad temporal scales. Based on NMDS, upstream and downstream sites generally showed similar assemblage structure across sample periods with the exception of the 2 months postdischarge, where upstream and downstream sites visually differed. Multivariate analysis of variance (PERMANOVA) indicated significant seasonal variation among samples, but found no significant interaction between impacted and unimpacted assemblages following the discharge event. However, multivariate dispersion (MVDISP) showed greater variance among assemblage structure following the discharge event. These results suggest that 2 months following the disturbance represent a time period of stochasticity in regard to assemblage structure dynamics, and this was followed by rapid recovery. We term this dynamic the “hangover effect” as it represents the time frame from the cessation of the perturbation to the assemblage's return to predisturbance conditions. The availability and proximity of tributaries and upstream refugia, which were not affected by the disturbance, as well as the rapid recovery of abiotic parameters likely played a substantial role in assemblage recovery. This study not only demonstrates rapid recovery in an aquatic system, but further demonstrates the value of continuous, long-term, data collections which enhance our understanding of assemblage dynamics.Ye
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