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

Detecting Mandible Fractures in CBCT Scans Using a 3-Stage Neural Network

After nasal bone fractures, fractures of the mandible are the most frequently encountered injuries of the facial skeleton. Accurate identification of fracture locations is critical for effectively managing these injuries. To address this need, JawFracNet, an innovative artificial intelligence method, has been developed to enable automated detection of mandibular fractures in cone-beam computed tomography (CBCT) scans. JawFracNet employs a 3-stage neural network model that processes 3-dimensional patches from a CBCT scan. Stage 1 predicts a segmentation mask of the mandible in a patch, which is subsequently used in stage 2 to predict a segmentation of the fractures and in stage 3 to classify whether the patch contains any fracture. The final output of JawFracNet is the fracture segmentation of the entire scan, obtained by aggregating and unifying voxel-level and patch-level predictions. A total of 164 CBCT scans without mandibular fractures and 171 CBCT scans with mandibular fractures were included in this study. Evaluation of JawFracNet demonstrated a precision of 0.978 and a sensitivity of 0.956 in detecting mandibular fractures. The current study proposes the first benchmark for mandibular fracture detection in CBCT scans. Straightforward replication is promoted by publicly sharing the code and providing access to JawFracNet on grand-challenge.org

How is neck dissection performed in Oral and Maxillofacial Surgery? Results of a representative nationwide survey among university and non-university hospitals in Germany

Introduction Neck dissection (ND) is a surgical procedure addressing cervical lymph nodes and metastases in patients with oral squamous cell carcinoma (OSCC). The aim of this study was to analyze clinical decisions regarding indications and variations of ND in Oral and Maxillofacial Surgery (OMFS) in Germany. Material and methods A nationwide survey of the German Association of Oral and Maxillofacial Surgery was performed using dynamic online questionnaires including 38 questions. Data about oncological centers, case numbers, and staging procedures were collected. Relevant aspects, such as inclusion of level IIb and levels IV and V to ND, uni- vs. bilateral ND, and the influence of extra-nodal extension (ENE) of metastases on extension of ND were evaluated. Results Eighty-four OMFS of university and non-university hospitals participated in the study (responding rate 21.4%). Sixty-six (78.57%) stated to work at certified cancer centers and 53.57% of the hospitals treated between 50 and 100 OSCC cases per year. CT and/or MRI of the head and neck was performed in most of the staging procedures. Level IIb was included by 71 (93.42%) of the participants in selective ND. Levels IV and V were included by 53 (69.74%) in node-positive neck. In solitary ipsilateral metastases (ENE−), 49 participants (62.82%) stated to perform exclusively an ipsilateral ND and 40 (51.95%) stated to perform only an ipsilateral ND in ENE+. Conclusion This study demonstrated a high rate of certified cancer centers in Germany showing differences regarding staging procedures, indications, and extension of ND, especially in increasingly complex cases. Clinical relevance Clinical decisions regarding ND are dependent on case-individual aspects and must be decided individually