Algebraic and combinatorial aspects of sandpile monoids on directed graphs

The sandpile group of a graph is a well-studied object that combines ideas from algebraic graph theory, group theory, dynamical systems, and statistical physics. A graph's sandpile group is part of a larger algebraic structure on the graph, known as its sandpile monoid. Most of the work on sandpiles so far has focused on the sandpile group rather than the sandpile monoid of a graph, and has also assumed the underlying graph to be undirected. A notable exception is the recent work of Babai and Toumpakari, which builds up the theory of sandpile monoids on directed graphs from scratch and provides many connections between the combinatorics of a graph and the algebraic aspects of its sandpile monoid. In this paper we primarily consider sandpile monoids on directed graphs, and we extend the existing theory in four main ways. First, we give a combinatorial classification of the maximal subgroups of a sandpile monoid on a directed graph in terms of the sandpile groups of certain easily-identifiable subgraphs. Second, we point out certain sandpile results for undirected graphs that are really results for sandpile monoids on directed graphs that contain exactly two idempotents. Third, we give a new algebraic constraint that sandpile monoids must satisfy and exhibit two infinite families of monoids that cannot be realized as sandpile monoids on any graph. Finally, we give an explicit combinatorial description of the sandpile group identity for every graph in a family of directed graphs which generalizes the family of (undirected) distance-regular graphs. This family includes many other graphs of interest, including iterated wheels, regular trees, and regular tournaments.Comment: v2: Cleaner presentation, new results in final section. Accepted for publication in J. Combin. Theory Ser. A. 21 pages, 5 figure

K−K^--Nucleus Scattering at Low and Intermediate Energies

We calculate $K^-$-nucleus elastic differential, reaction and total cross sections for different nuclei ($^{12}$C,$^{40}$Ca and $^{208}$Pb) at several laboratory antikaon momenta, ranging from 127 MeV to 800 MeV. We use different antikaon-nucleus optical potentials, some of them fitted to kaonic atom data, and study the sensitivity of the cross sections to the considered antikaon-nucleus dynamics.Comment: Only 4 pages, Latex, 3 Figures. This version is much shorter than the previous one. Some details and references have been omitte

Reducción de los tiempos de observación en la evaluación del observación en la evaluación del comportamiento de conejas en producción. Análisis metodológico.

El objetivo de este trabajo fue evaluar diferentes técnicas de muestreo que redujeran el tiempo total de observación necesario para estimar el comportamiento de conejas alojadas en dos tipos de jaulas (convencionales vs. enriquecidas) y en dos estados fisiológicos distintos (gestantes vs. lactantes). Para ello, se compararon grabaciones completas de 24 h (método control de referencia) con estimaciones obtenidas a partir de grabaciones de diferente duración y frecuencia (métodos regular corto y regular largo y métodos irregulares de 6h y de 8h). A partir de los resultados obtenidos se observa que los métodos regulares se ajustaron mejor al método de referencia de 24h que los irregulares. Desde un punto de vista práctico el método regular corto sería el ideal, al reducir considerablemente el número total de horas de observación y análisi

Pion Cloud Contribution to K+ Nucleus Scattering

A careful reanalysis is done of the contribution to $K^{+}$ nucleus scattering from the interaction of the kaon with the virtual pion cloud. The usual approximations made in the evaluation of the related kaon selfenergy are shown to fail badly. We also find new interaction mechanisms which provide appreciable corrections to the kaon selfenergy. Some of these contribute to the imaginary part below pion creation threshold. The inclusion of these new mechanisms in the inelastic part of the optical potential produces a significant improvement in the differential and total $K^{+}$ nuclear cross sections. Uncertainties remain in the dispersive part of the optical potential.Comment: 27 pages, 17 figures (not all of them included, please request them), report UG-DFM-2/9

Connexins and the epithelial tissue barrier: a focus on Connexin 26

Epithelial tissue responds rapidly to environmental triggers and is constantly renewed. This tissue is also highly accessible for therapeutic targeting. This review highlights the role of connexin mediated communication in avascular epithelial tissue. These proteins form communication conduits with the extracellular space (hemichannels) and between neighboring cells (gap junctions). Regulated exchange of small metabolites less than 1kDa aide the co-ordination of cellular activities and in spatial communication compartments segregating tissue networks. Dysregulation of connexin expression and function has profound impact on physiological processes in epithelial tissue including wound healing. Connexin 26, one of the smallest connexins, is expressed in diverse epithelial tissue and mutations in this protein are associated with hearing loss, skin and eye conditions of differing severity. The functional consequences of dysregulated connexin activity is discussed and the development of connexin targeted therapeutic strategies highlighted

Ectopic third molar in the mandibular condyle: a review of the literature

Objectives: To evaluate the etiopathogenesis, clinical features, therapeutic options, and surgical approaches for removal of ectopic third molars in the mandibular condyle. Study design: MEDLINE search of articles published on ectopic third molars in the mandibular condyle from 1980 to 2011. 14 well-documented clinical cases from the literature were evaluated together with a new clinical case provided by the authors, representing a sample of 15 patients. Results: We found a mean age at diagnosis of 48.6 years and a higher prevalence in women. In 14 patients, associated radiolucent lesions were diagnosed on radiographic studies and confirmed histopathologically as odontogenic cysts. Clinical symptoms were pain and swelling in the jaw or preauricular region, trismus, difficulty chewing, cutaneous fistula and temporomandibular joint dysfunction. Treatment included conservative management in one case and in the other cases, surgical removal by intra- or extraoral approaches, the latter being the most common approach carried out. In most reported cases, serious complications were not outlined. Conclusions: The etiopathogenic theory involving odontogenic cysts in the displacement of third molars to the mandibular condyle seems to be the most relevant. They must be removed if they cause symptoms or are associated with cystic pathology. The surgical route must be planned according to the location and position of the ectopic third molar, and the possible morbidity associated with surgery

Efecto del tipo de jaula sobre el comportamiento de conejas

El objetivo de este ensayo fue evaluar el efecto del tipo de jaula (convencional vs. enriquecida) y el estado fisiológico de las conejas (gestación vs. lactación) sobre su comportamiento. Se realizaron grabaciones de 12 conejas multíparas durante 24 h en dos momentos distintos. Los comportamientos observados se clasificaron en tres grupos independientes (localización, locomoción y acciones). Se observó una predominancia clara por el uso del reposapatas (principalmente en la fase de lactación), pero este tiempo disminuyó significativamente en jaulas enriquecidas debido al uso de la plataforma (67,1 vs. 48,2%; Pmenor que0,05). Las conejas permanecieron tumbadas y sentadas el 78,4 y 20,7% del día, respectivamente, sin tener efecto ni el tipo de jaula ni el estado fisiológico. Las conejas se ponían de pie únicamente para comer u oler las heces retenidas sobre la plataforma. Las conejas se mostraron más nerviosas en la fase de lactación tratando de huir de los gazapos, siendo esta huida exitosa cuando las conejas tenían la posibilidad de utilizar la plataforma. Las conejas gestantes estuvieron significativamente más tiempo que las lactantes acicalándose, mordiendo barrotes e interaccionando con las vecinas (Pmenor que0,01; 0,05 y 0,05, respectivamente). Las conejas lactantes dedicaron más tiempo a beber (Pmenor que0,05) que las gestantes. De este trabajo se desprende que el aumento del espacio disponible con la colocación de una plataforma elevada podría ser una buena alternativa para la mejora del bienestar de las conejas, sobre todo en la fase final de la lactación, aunque la retención de heces sobre la plataforma y las deyecciones pueden ocasionar problemas de higiene

The Zagros Epipalaeolithic revisited: New excavations and ¹⁴C dates from Palegawra cave in Iraqi Kurdistan

Palegawra cave, alongside its neighbouring Zarzi, has been an emblematic site of the Epipalaeolithic (Zarzian) cultural horizon in the NW Zagros of Southwest Asia ever since its first exploration in 1951 by Bruce Howe and Robert Braidwood in the context of the Iraq-Jarmo project. At the time scientific excavation, sampling and analysis methods were either under-developed or did not exist. In this paper we present the first results of new excavations at Palegawra conducted in 2016-2017 by the Eastern Fertile Crescent (EFEC) project, a research collaboration of the University of Liverpool and the Sulaymaniyah Directorate of Antiquities and Heritage. Our research has produced the first radiometric evidence pushing back the chronology of the NW Zagros Epipalaeolithic to the Last Glacial Maximum, thus fully aligning it with Epipalaeolithic facies until now known only from the Levant and the south Anatolian coast. We have also unearthed, for the first time in the Palaeolithic of the Zagros, direct archaeobotanical evidence for hitherto elusive Zarzian plant exploitation and the vegetation of the NW Zagros piedmont zone from the LGM to the end of the Lateglacial (~19,600-13,000 cal BP). The new Palegawra chronology alongside our detailed studies of its material culture and faunal and botanical assemblages suggest that the prevailing Epipalaeolithic habitation pattern in the NW Zagros (centred on generalised persistent occupations of small caves and rock-shelters alongside task-oriented ephemeral open-air campsites) remained an enduring characteristic of the Zarzian horizon throughout this period. The Palegawra data clearly show that neither resource levels and climate conditions nor geographic and/or cultural isolation provide adequate explanations for the stability and longevity of Zarzian lifeways during this long timespan. More fieldwork is required, including the discovery, excavation and intensive sampling of other Zarzian sites, for reaching a data-informed understanding of the nature and evolution of the NW Zagros Epipalaeolithic