On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms $\rho: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism $\mathcal{N}_r(G) \cong |G|$ to arbitrary infinitesimal unipotent supergroup schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and 3.3. Simplified the proof of Proposition 3.3.

Cohomology for infinitesimal unipotent algebraic and quantum groups

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its unipotent radical $U_J$, we determine the ring structure of the cohomology ring $H^\bullet((U_J)_1,k)$. We also obtain new results on computing $H^\bullet((P_J)_1,L(\lambda))$ as an $L_J$-module where $L(\lambda)$ is a simple $G$-module with high weight $\lambda$ in the closure of the bottom $p$-alcove. Finally, we provide generalizations of all our results to the quantum situation.Comment: 18 pages. Some proofs streamlined over previous version. Additional details added to some proofs in Section

Validation of Different Combination of Three Reversing Half-Hitches Alternating Posts (RHAPs) Effects on Arthroscopic Knot Integrity

Introduction. With arthroscopic techniques being used, the importanceof knot tying has been examined. Previous literaturehas examined the use of reversing half-hitches on alternatingposts (RHAPs) on knot security. Separately, there has been researchregarding different suture materials commonly used inthe operating room. The specific aim of this study was to validatethe effect of different stacked half-hitch configuration anddifferent braided suture materials on arthroscopic knot integrity. Methods. Three different suture materials tied withfive different RHAPs in arthroscopic knots were compared.A single load-to-failure test was performed andthe mean ultimate clinical failure load was obtained. Results. Significant knot holding strength improvement wasfound when one half-hitch was reversed as compared to baselineknot. When two of the half-hitches were reversed, therewas a greater improvement with all knots having a mean ultimateclinical failure load greater than 150 newtons (N). Comparisonof the suture materials demonstrated a higher meanultimate clinical failure load when Force Fiber® was used andat least one half-hitch was reversed. Knots tied with eitherForce Fiber® or Orthocord® showed 0% chance of knot slippagewhile knots tied with FiberWire® or braided fishing linehad about 10 and 30% knot slippage chances, respectively. Conclusion. A significant effect was observed in regards to bothstacked half-hitch configuration and suture materials used onknot loop and knot security. Caution should be used with tyingthree RHAPs in arthroscopic surgery, particularly witha standard knot pusher and arthroscopic cannulas. The findingsof this study indicated the importance of three RHAPsin performing arthroscopic knot tying and provided evidenceregarding discrepancies of maximum clinical failure loads observedbetween orthopaedic surgeons, thereby leading to bettersurgical outcomes in the future. KS J Med 2017;10(2):35-39

Does the PI3K pathway promote or antagonize regulatory T cell development and function?

Regulatory T cells (Tregs) prevent autoimmunity and inflammation by suppressing the activation of other T cells and antigen presenting cells. The role of phosphoinositide 3-kinase (PI3K) signaling in Treg is controversial. Some studies suggest that inhibition of the PI3K pathway is essential for the development of Tregs whereas other studies have shown reduced Treg numbers and function when PI3K activity is suppressed. Here we attempt to reconcile the different studies that have explored PI3K and the downstream effectors Akt, Foxo, and mTOR in regulatory T cell development and function and discuss the implications for health and therapeutic intervention

Regulators of complement activity mediate inhibitory mechanisms through a common C3b‐binding mode

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Fluid Dynamics in a Thrust Fault Inferred from Petrology and Geochemistry of Calcite Veins: An Example from the Southern Pyrenees

Petrographic and geochemical analyses (δ18O, δ13C, 87Sr/86Sr, clumped isotopes, and elemental composition) coupled with field structural data of synkinematic calcite veins, fault rocks, and host rocks are used to reconstruct the episodic evolution of an outstanding exposed thrust zone in the Southern Pyrenees and to evaluate the fault behavior as a conduit or barrier to fluid migration. The selected thrust displaces the steeply dipping southern limb of the Sant Corneli-Bóixols anticline, juxtaposing a Cenomanian-Turonian carbonate unit against a Coniacian carbonate sequence. Successive deformation events are recorded by distinct fracture systems and related calcite veins, highlighting (i) an episodic evolution of the thrust zone, resulting from an upward migration of the fault tip (process zone development) before growth of the fault (thrust slip plane propagation), and (ii) compartmentalization of the thrust fault zone, leading to different structural and fluid flow histories in the footwall and hanging wall. Fractures within the footwall comprise three systematically oriented fracture sets (F1, F2, and F3), each sealed by a separate generation calcite cement, and a randomly oriented fracture system (mosaic to chaotic breccia), cemented by the same cements as fracture sets F1 and F2. The formation of fractures F1 and F2 and the mosaic to chaotic breccia is consistent with dilatant fracturing within the process zone (around the fault tip) during initial fault growth, whereas the formation of the latest fracture system points to hybrid shear-dilational failure during propagation of the fault. The continuous formation of different fracture systems and related calcite cementation phases evidences that the structural permeability in the footwall was transient and that the fluid pathways and regime evolved due to successive events of fracture opening and calcite cementation. Clumped isotopes evidence a progressive increase in precipitation temperatures from around 50°C to 117°C approximately, interpreted as burial increase linked to thrust sheet emplacement. During this period, the source of fluid changed from meteoric fluids to evolved meteoric fluids due to the water-rock interaction at increasing depths and temperatures. Contrary to the footwall, within the hanging wall, only randomly oriented fractures are recognized and the resulting crackle proto-breccia is sealed by a later and different calcite cement, which is also observed in the main fault plane and in the fault core. This cement precipitated from formation fluids, at around 95°C, that circulated along the fault core and in the hanging wall block, again supporting the interpretation of compartmentalization of the thrust structure. The integration of these data reveals that the studied thrust fault acted as a transverse barrier, dividing the thrust zone into two separate fluid compartments, and a longitudinal drain for migration of fluids. This study also highlights the similarity in deformation processes and mechanisms linked to the evolution of fault zones in compressional and extensional regimes involving carbonate rocks

Impact of Scottish smoke-free legislation on smoking quit attempts and prevalence

<p><b>Objectives:</b> In Scotland, legislation was implemented in March 2006 prohibiting smoking in all wholly or partially enclosed public spaces. We investigated the impact on attempts to quit smoking and smoking prevalence.</p> <p><b>Methods:</b> We performed time series models using Box-Jenkins autoregressive integrated moving averages (ARIMA) on monthly data on the gross ingredient cost of all nicotine replacement therapy (NRT) prescribed in Scotland in 2003–2009, and quarterly data on self-reported smoking prevalence between January 1999 and September 2010 from the Scottish Household Survey.</p> <p><b>Results:</b> NRT prescription costs were significantly higher than expected over the three months prior to implementation of the legislation. Prescription costs peaked at £1.3 million in March 2006; £292,005.9 (95% CI £260,402.3, £323,609, p<0.001) higher than the monthly norm. Following implementation of the legislation, costs fell exponentially by around 26% per month (95% CI 17%, 35%, p<0.001). Twelve months following implementation, the costs were not significantly different to monthly norms. Smoking prevalence fell by 8.0% overall, from 31.3% in January 1999 to 23.7% in July–September 2010. In the quarter prior to implementation of the legislation, smoking prevalence fell by 1.7% (95% CI 2.4%, 1.0%, p<0.001) more than expected from the underlying trend.</p> <p><b>Conclusions:</b> Quit attempts increased in the three months leading up to Scotland's smoke-free legislation, resulting in a fall in smoking prevalence. However, neither has been sustained suggesting the need for additional tobacco control measures and ongoing support.</p&gt

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Gestational age at delivery and special educational need: retrospective cohort study of 407,503 schoolchildren

<STRONG>Background</STRONG> Previous studies have demonstrated an association between preterm delivery and increased risk of special educational need (SEN). The aim of our study was to examine the risk of SEN across the full range of gestation. <STRONG>Methods and Findings</STRONG> We conducted a population-based, retrospective study by linking school census data on the 407,503 eligible school-aged children resident in 19 Scottish Local Authority areas (total population 3.8 million) to their routine birth data. SEN was recorded in 17,784 (4.9%) children; 1,565 (8.4%) of those born preterm and 16,219 (4.7%) of those born at term. The risk of SEN increased across the whole range of gestation from 40 to 24 wk: 37–39 wk adjusted odds ratio (OR) 1.16, 95% confidence interval (CI) 1.12–1.20; 33–36 wk adjusted OR 1.53, 95% CI 1.43–1.63; 28–32 wk adjusted OR 2.66, 95% CI 2.38–2.97; 24–27 wk adjusted OR 6.92, 95% CI 5.58–8.58. There was no interaction between elective versus spontaneous delivery. Overall, gestation at delivery accounted for 10% of the adjusted population attributable fraction of SEN. Because of their high frequency, early term deliveries (37–39 wk) accounted for 5.5% of cases of SEN compared with preterm deliveries (<37 wk), which accounted for only 3.6% of cases. <STRONG>Conclusions</STRONG> Gestation at delivery had a strong, dose-dependent relationship with SEN that was apparent across the whole range of gestation. Because early term delivery is more common than preterm delivery, the former accounts for a higher percentage of SEN cases. Our findings have important implications for clinical practice in relation to the timing of elective delivery