Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group

Let $U_n$ denote the group of $n\times n$ unipotent upper-triangular matrices over a fixed finite field \FF_q, and let U_\cP denote the pattern subgroup of $U_n$ corresponding to the poset \cP. This work examines the superclasses and supercharacters, as defined by Diaconis and Isaacs, of the family of normal pattern subgroups of $U_n$. After classifying all such subgroups, we describe an indexing set for their superclasses and supercharacters given by set partitions with some auxiliary data. We go on to establish a canonical bijection between the supercharacters of U_\cP and certain \FF_q-labeled subposets of \cP. This bijection generalizes the correspondence identified by Andr\'e and Yan between the supercharacters of $U_n$ and the \FF_q-labeled set partitions of $\{1,2,...,n\}$. At present, few explicit descriptions appear in the literature of the superclasses and supercharacters of infinite families of algebra groups other than \{U_n : n \in \NN\}. This work signficantly expands the known set of examples in this regard.Comment: 28 page

Acceleration of small astrophysical grains due to charge fluctuations

We discuss a novel mechanism of dust acceleration which may dominate for particles smaller than $\sim0.1~\mu$m. The acceleration is caused by their direct electrostatic interactions arising from fluctuations of grain charges. The energy source for the acceleration are the irreversible plasma processes occurring on the grain surfaces. We show that this mechanism of charge-fluctuation-induced acceleration likely affects the rate of grain coagulation and shattering of the population of small grains.Comment: 8 pages, 2 figures, revised version, submitted to Astrophysical Journa

On the Representation Theory of an Algebra of Braids and Ties

We consider the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for ${\cal E}_n(u)$ and show that this is faithful. We use it to give a basis for ${\cal E}_n(u)$ and to classify its irreducible representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic Combinatorics

Generalized Inverse Participation Numbers in Metallic-Mean Quasiperiodic Systems

From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers $Z_q \sim N^{-D_q(q-1)}$ with the system size $N$. In particular, we investigate $d$-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation $D_q^{d\mathrm{d}} = d D_q^\mathrm{1d}$ holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.Comment: 7 pages, 3 figure

Defensive behavior is linked to altered surface chemistry following infection in a termite society

The care-kill response determines whether a sick individual will be treated or eliminated from an insect society, but little is known about the physiological underpinnings of this process. We exploited the stepwise infection dynamics of an entomopathogenic fungus in a termite to explore how care-kill transitions occur, and identify the chemical cues behind these shifts. We found collective responses towards pathogen-injected individuals to vary according to severity and timing of pathogen challenge, with elimination, via cannibalism, occurring sooner in response to a severe active infection. However, injection with inactivated fungal blastospores also resulted in increased albeit delayed cannibalism, even though it did not universally cause host death. This indicates that the decision to eliminate an individual is triggered before pathogen viability or terminal disease status has been established. We then compared the surface chemistry of differently challenged individuals, finding increased amounts of long-chained methyl-branched alkanes with similar branching patterns in individuals injected with both dead and viable fungal blastospores, with the latter showing the largest increase. This coincided with the highest amounts of observed cannibalism as well as signs of severe moribundity. Our study provides new mechanistic insight into the emergent collective behaviors involved in the disease defense of a termite society

Deletion of hematopoietic Dectin-2 or CARD9 does not protect against atherosclerotic plaque formation in hyperlipidemic mice

Inflammatory reactions activated by pattern recognition receptors (PRRs) on the membrane of innate immune cells play an important role in atherosclerosis. Whether the PRRs of the C-type lectin receptor (CLR) family including Dectin-2 may be involved in the pathogenesis of atherosclerosis remains largely unknown. Recently, the CLR-adaptor molecule caspase recruitment domain family member 9 (CARD9) has been suggested to play a role in cardiovascular pathologies as it provides the link between CLR activation and transcription of inflammatory cytokines as well as immune cell recruitment. We therefore evaluated whether hematopoietic deletion of Dectin-2 or CARD9 reduces inflammation and atherosclerosis development. Low-density lipoprotein receptor (Ldlr)- knockout mice were transplanted with bone marrow from wild-type, Dectin-2- or Card9-knockout mice and fed a Western-type diet containing 0.1% (w/w) cholesterol. After 10 weeks, lipid and inflammatory parameters were measured and atherosclerosis development was determined. Deletion of hematopoietic Dectin-2 or CARD9 did not influence plasma triglyceride and cholesterol levels. Deletion of hematopoietic Dectin-2 did not affect atherosclerotic lesion area, immune cell composition, ex vivo cytokine secretion by peritoneal cells or bone marrow derived macrophages. Unexpectedly, deletion of hematopoietic CARD9 increased atherosclerotic lesion formation and lesion severity. Deletion of hematopoietic CARD9 did also not influence circulating immune cell composition and peripheral cytokine secretion. Besides a tendency to a reduced macrophage content within these lesions, plasma MCP-1 levels decreased upon WTD feeding. Deletion of hematopoietic Dectin-2 did not influence atherosclerosis development in hyperlipidemic mice. The absence of CARD9 unexpectedly increased atherosclerotic lesion size and severity, suggesting that the presence of CARD9 may protect against initiation of atherosclerosis development

An Interactive Bayesian Geostatistical Inverse Protocol for Hydraulic Tomography

Hydraulic tomography is a powerful technique for characterizing heterogeneous hydrogeologic parameters. An explicit trade-off between characterization based on measurement misfit and subjective characterization using prior information is presented. We apply a Bayesian geostatistical inverse approach that is well suited to accommodate a flexible model with the level of complexity driven by the data and explicitly considering uncertainty. Prior information is incorporated through the selection of a parameter covariance model characterizing continuity and providing stability. Often, discontinuities in the parameter field, typically caused by geologic contacts between contrasting lithologic units, necessitate subdivision into zones across which there is no correlation among hydraulic parameters. We propose an interactive protocol in which zonation candidates are implied from the data and are evaluated using cross validation and expert knowledge. Uncertainty introduced by limited knowledge of dynamic regional conditions is mitigated by using drawdown rather than native head values. An adjoint state formulation of MODFLOW-2000 is used to calculate sensitivities which are used both for the solution to the inverse problem and to guide protocol decisions. The protocol is tested using synthetic two-dimensional steady state examples in which the wells are located at the edge of the region of interest