Affine descents and the Steinberg torus

Abstract. Let W ⋉ L be an irreducible affine Weyl group with Coxeter complex Σ, where W denotes the associated finite Weyl group and L the translation subgroup. The Steinberg torus is the Boolean cell complex obtained by taking the quotient of Σ by the lattice L. We show that the ordinary and flag h-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over W for a descent-like statistic first studied by Cellini. We also show that the ordinary h-polynomial has a nonnegative γ-vector, and hence, symmetric and unimodal coefficients. In the classical cases, we also provide expansions, identities, and generating functions for the h-polynomials of Steinberg tori. Résumé. Nous considérons un groupe de Weyl affine irréductible W ⋉ L avec complexe de Coxeter Σ, où W désigne le groupe de Weyl fini associé et L le sous-groupe des translations. Le tore de Steinberg est le complexe cellulaire Booléen obtenu comme le quotient de Σ par L. Nous montrons que les h-polynômes, ordinaires et de drapeaux, du tore de Steinberg (sans la face vide) sont des fonctions génératrices sur W pour une statistique de type descente, étudiée en premier lieu par Cellini. Nous montrons également qu’un h-polynôme ordinaire possède un γ-vecteur positif, et par conséquent, a des coéfficients symétriques et unimodaux. Dans les cas classiques, nous donnons également des développements, des identités et des fonctions génératrices pour les h-polynômes des tores de Steinberg

Seismicity and fault interaction, Southern San Jacinto Fault Zone and adjacent faults, southern California: Implications for seismic hazard

The southern San Jacinto fault zone is characterized by high seismicity and a complex fault pattern that offers an excellent setting for investigating interactions between distinct faults. This fault zone is roughly outlined by two subparallel master fault strands, the Coyote Creek and Clark-San Felipe Hills faults, that are located 2 to 10 km apart and are intersected by a series of secondary cross faults. Seismicity is intense on both master faults and secondary cross faults in the southern San Jacinto fault zone. The seismicity on the two master strands occurs primarily below 10 km; the upper 10 km of the master faults are now mostly quiescent and appear to rupture mainly or solely in large earthquakes. Our results also indicate that a considerable portion of recent background activity near the April 9, 1968, Borrego Mountain rupture zone (M_L=6.4) is located on secondary faults outside the fault zone. We name and describe the Palm Wash fault, a very active secondary structure located about 25 km northeast of Borrego Mountain that is oriented subparallel to the San Jacinto fault system, dips approximately 70° to the northeast, and accommodates right-lateral shear motion. The Vallecito Mountain cluster is another secondary feature delineated by the recent seismicity and is characterized by swarming activity prior to nearby large events on the master strand. The 1968 Borrego Mountain and the April 28, 1969, Coyote Mountain (M_L=5.8) events are examples of earthquakes with aftershocks and subevents on these secondary and master faults. Mechanisms from those earthquakes and recent seismic data for the period 1981 to 1986 are not simply restricted to strike-slip motion; dipslip motion is also indicated. Teleseismic body waves (long-period P and SH) of the 1968 and 1969 earthquakes were inverted simultaneously for source mechanism, seismic moment, rupture history, and centroid depth. The complicated waveforms of the 1968 event (M_o=1.2 × 10^(19) Nm) are interpreted in terms of two subevents; the first caused by right-lateral strike-slip motion in the mainshock along the Coyote Creek fault and the second by a rupture located about 25 km away from the master fault. Our waveform inversion of the 1969 event indicates that strike-slip motion predominated, releasing a seismic moment of 2.5 × 10^(17) Nm. Nevertheless, the right-lateral nodal plane of the focal mechanism is significantly misoriented (20°) with respect to the master fault, and hence the event is not likely to be associated with a rupture on that fault. From this and other examples in southern California, we conclude that cross faults may contribute significantly to seismic hazard and that interaction between faults has important implications for earthquake prediction

Virulence difference between the prototypic Schu S4 strain (A1a) and Francisella tularensisA1a, A1b, A2 and type B strains in a murine model of infection

BACKGROUND: The use of prototypic strains is common among laboratories studying infectious agents as it promotes consistency for data comparability among and between laboratories. Schu S(4) is the prototypic virulent strain of Francisella tularensis and has been used extensively as such over the past six decades. Studies have demonstrated virulence differences among the two clinically relevant subspecies of F. tularensis, tularensis (type A) and holarctica (type B) and more recently between type A subpopulations (A1a, A1b and A2). Schu S(4) belongs to the most virulent subspecies of F. tularensis, subspecies tularensis. METHODS: In this study, we investigated the relative virulence of Schu S(4) in comparison to A1a, A1b, A2 and type B strains using a temperature-based murine model of infection. Mice were inoculated intradermally and a hypothermic drop point was used as a surrogate for death. Survival curves and the length of temperature phases were compared for all infections. Bacterial burdens were also compared between the most virulent type A subpopulation, A1b, and Schu S(4) at drop point. RESULTS: Survival curve comparisons demonstrate that the Schu S(4) strain used in this study resembles the virulence of type B strains, and is significantly less virulent than all other type A (A1a, A1b and A2) strains tested. Additionally, when bacterial burdens were compared between mice infected with Schu S(4) or MA00-2987 (A1b) significantly higher burdens were present in the blood and spleen of mice infected with MA00-2987. CONCLUSIONS: The knowledge gained from using Schu S(4) as a prototypic virulent strain has unquestionably advanced the field of tularemia research. The findings of this study, however, indicate that careful consideration of F. tularensis strain selection must occur when the overall virulence of the strain used could impact the outcome and interpretation of results

Differential respiratory health effects from the 2008 northern California wildfires: A spatiotemporal approach

AbstractWe investigated health effects associated with fine particulate matter during a long-lived, large wildfire complex in northern California in the summer of 2008. We estimated exposure to PM2.5 for each day using an exposure prediction model created through data-adaptive machine learning methods from a large set of spatiotemporal data sets. We then used Poisson generalized estimating equations to calculate the effect of exposure to 24-hour average PM2.5 on cardiovascular and respiratory hospitalizations and ED visits. We further assessed effect modification by sex, age, and area-level socioeconomic status (SES). We observed a linear increase in risk for asthma hospitalizations (RR=1.07, 95% CI=(1.05, 1.10) per 5µg/m3 increase) and asthma ED visits (RR=1.06, 95% CI=(1.05, 1.07) per 5µg/m3 increase) with increasing PM2.5 during the wildfires. ED visits for chronic obstructive pulmonary disease (COPD) were associated with PM2.5 during the fires (RR=1.02 (95% CI=(1.01, 1.04) per 5µg/m3 increase) and this effect was significantly different from that found before the fires but not after. We did not find consistent effects of wildfire smoke on other health outcomes. The effect of PM2.5 during the wildfire period was more pronounced in women compared to men and in adults, ages 20–64, compared to children and adults 65 or older. We also found some effect modification by area-level median income for respiratory ED visits during the wildfires, with the highest effects observed in the ZIP codes with the lowest median income. Using a novel spatiotemporal exposure model, we found some evidence of differential susceptibility to exposure to wildfire smoke

Affine descents and the Steinberg torus

Let $W \ltimes L$ be an irreducible affine Weyl group with Coxeter complex $\Sigma$, where $W$ denotes the associated finite Weyl group and $L$ the translation subgroup. The Steinberg torus is the Boolean cell complex obtained by taking the quotient of $\Sigma$ by the lattice $L$. We show that the ordinary and flag $h$-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over $W$ for a descent-like statistic first studied by Cellini. We also show that the ordinary $h$-polynomial has a nonnegative $\gamma$-vector, and hence, symmetric and unimodal coefficients. In the classical cases, we also provide expansions, identities, and generating functions for the $h$-polynomials of Steinberg tori

Transfusion burden in non-dialysis chronic kidney disease patients with persistent anemia treated in routine clinical practice: a retrospective observational study

Background: Transfusion patterns are not well characterized in non-dialysis (ND) chronic kidney disease (CKD) patients. This study describes the proportion of patients transfused, units of blood transfused and trigger-hemoglobin (Hb) levels for transfusions in severe anemic, ND-CKD patients in routine practice. Methods. A retrospective cohort study of electronic medical record data from the Henry Ford Health identified 374 adult, ND-CKD patients with severe anemia (Hb \u3c 10 g/dL and subsequent use of erythropoiesis-stimulating agents [ESA] therapy, blood transfusions, or a second Hb \u3c 10 g/dL) between January 2004 and June 2008. Exclusions included those with prior diagnoses of cancer, renal or liver transplant, end-stage renal disease, acute bleeding, trauma, sickle cell disease, or aplastic anemia. A gap of ≥1 days between units of blood transfused was counted as a separate transfusion. Results: At least 1 transfusion (mean of 2 units; range, 1-4) was administered to 20% (75/374) of ND-CKD patients with mean (±SD) follow-up of 459 (±427) days. The mean (±SD) Hb level closest and prior to a transfusion was 8.8 (±1.5) g/dL. Patients who were hospitalized in the 6 months prior to their first anemia diagnosis were 6.3 times more likely to receive a blood transfusion than patients who were not hospitalized (p \u3c 0.0001). Patients with peripheral vascular disease (PVD) were twice as likely to have a transfusion as patients without PVD (p = 0.04). Conclusions: Transfusions were prevalent and the trigger hemoglobin concentration was approximately 9 g/dL among ND-CKD patients with anemia. To reduce the transfusion burden, clinicians should consider other anemia treatments including ESA therapy. © 2012 Fox et al; licensee BioMed Central Ltd

Brain function distinguishes female carriers and non-carriers of familial risk for autism

BACKGROUND: Autism spectrum disorder (ASD) is characterized by high population-level heritability and a three-to-one male-to-female ratio that occurs independent of sex linkage. Prior research in a mixed-sex pediatric sample identified neural signatures of familial risk elicited by passive viewing of point light motion displays, suggesting the possibility that both resilience and risk of autism might be associated with brain responses to biological motion. To confirm a relationship between these signatures and inherited risk of autism, we tested them in families enriched for genetic loading through undiagnosed ( carrier ) females. METHODS: Using functional magnetic resonance imaging, we examined brain responses to passive viewing of point light displays-depicting biological versus non-biological motion-in a sample of undiagnosed adult females enriched for inherited susceptibility to ASD on the basis of affectation in their respective family pedigrees. Brain responses in carrier females were compared to responses in age-, SRS-, and IQ-matched non-carrier-females-i.e., females unrelated to individuals with ASD. We conducted a hypothesis-driven analysis focused on previously published regions of interest as well as exploratory, brain-wide analyses designed to characterize more fully the rich responses to this paradigm. RESULTS: We observed robust responses to biological motion. Notwithstanding, the 12 regions implicated by prior research did not exhibit the hypothesized interaction between group (carriers vs. controls) and point light displays (biological vs. non-biological motion). Exploratory, brain-wide analyses identified this interaction in three novel regions. Post hoc analyses additionally revealed significant variations in the time course of brain activation in 20 regions spanning occipital and temporal cortex, indicating group differences in response to point light displays (irrespective of the nature of motion) for exploration in future studies. LIMITATIONS: We were unable to successfully eye-track all participants, which prevented us from being able to control for potential differences in eye gaze position. CONCLUSIONS: These methods confirmed pronounced neural signatures that differentiate brain responses to biological and scrambled motion. Our sample of undiagnosed females enriched for family genetic loading enabled discovery of numerous contrasts between carriers and non-carriers of risk of ASD that may index variations in visual attention and motion processing related to genetic susceptibility and inform our understanding of mechanisms incurred by inherited liability for ASD