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关键词： Finite tensor category   Module category   Modular tensor category   Hochschild cohomology  

摘要： Let C be a finite tensor category, and letMbe an exact left C-module category. The action of C onMinduces a functor. : C. Rex(M), where Rex(M) is the category of k-linear right exact endofunctors onM. Our key observation is that. has a right *** given by the *** ( F) = similar to M.M Hom( M, F( M)) (F. Rex(M)). As an application, we establish the following results: (1) We give a description of the composition of the induction functor C* M. Z(C* M) and Schauenburg's equivalenceZ(C* M) similar to Z(C). (2) We introduce the space CF(M) of `class functions' ofMand initiate the character theory for pivotal module categories. (3) We introduce a filtration for CF(M) and discuss its relation with some ring-theoretic notions, such as the Reynolds ideal and its generalizations. (4) We show that Ext similar to C(1,.ra(idM)) is isomorphic to the Hochschild cohomology ofM. As an application, we showthat themodular group acts projectively on the Hochschild cohomology of a modular tensor category.

关键词： Economic policy uncertainty   Exchange rate volatility   Japan   Spillovers   Stock market volatility   United States   Vector autoregression  

摘要： Using generalised variance decompositions from vector autoregressions, we analyse cross-country, cross-category spillovers of economic policy uncertainty (EPU) and financial market volatility between the US and Japan. Our model includes indices of monetary, fiscal and trade policy uncertainty for each country, as well as three measures of option-implied stock market and exchange rate volatility, respectively. We find that the financial market volatility indices are usually substantial net spillover transmitters towards the total group of EPU measures. However, the Japanese equity and especially the FX volatility index are typically more affected by EPU spillovers than the US VXO. Our results also reveal that, compared to within-country spillovers, cross-country spillovers of EPU are relatively small and less volatile. Finally, we show that the direction of net EPU spillovers between the US and Japan is both time- and category-dependent with different EPU categories acting as strong sources of uncertainty spillovers throughout the sample period.

关键词： Modular tensor categories   monoidal auto-equivalences   quantum algebra  

摘要： In this short note we investigate the process of using invertible objects to construct auto-equivalences of modular tensor categories. We derive conditions on the invertible object for the resulting auto-equivalence to be either monoidal, braided, or pivotal. We also discuss the composition of these auto-equivalences constructed from invertible objects. To demonstrate the practicality of this construction, we construct auto-equivalences of several real-world examples of modular tensor categories.

关键词： Bartter syndrome   CASR   congenital chloride diarrhea   Gitelman syndrome   HNF1B   pseudo-Bartter syndrome   pseudo-Gitelman syndrome  

摘要： Bartter syndrome (BS) and Gitelman syndrome (GS) are syndromes associated with congenital tubular dysfunction, characterized by hypokalemia and metabolic alkalosis. Clinically, BS is classified into two types: the severe antenatal/neonatal type, which develops during the fetal period with polyhydramnios and preterm delivery;and the relatively mild classic type, which is usually found during infancy with failure to thrive. GS can be clinically differentiated from BS by its age at onset, usually after school age, or laboratory findings of hypomagnesemia and hypocalciuria. Recent advances in molecular biology have shown that these diseases can be genetically classified into type 1 to 5 BS and GS. As a result, it has become clear that the clinical classification of antenatal/neonatal BS, classic BS, and GS does not always correspond to the clinical symptoms associated with the genotypes in a one-to-one manner;and there is clinically no clear differential border between type 3 BS and GS. This has caused confusion among clinicians in the diagnosis of these diseases. It has been proposed that the disease name "inherited salt-losing tubulopathy" can be used for cases of tubulopathies accompanied by hypokalemia and metabolic alkalosis. It is reasonable to use this term prior to genetic typing into type 1-5 BS or GS, to avoid confusion in a clinical setting. In this article, we review causative genes and phenotypic correlations, diagnosis, and treatment strategies for salt-losing tubulopathy as well as the clinical characteristics of pseudo-BS/GS, which can also be called a "salt-losing disorder".

关键词： Emerging market categories   Innovation   Socio-cognitive approach  

摘要： Industries with emerging market categories offer greater opportunities for firms to innovate. However, such opportunities are not a matter of "the more, the better." An increasing number of emerging market categories poses a dilemma. While more emerging market categories arguably bring about increasing growth opportunities, they can also generate greater ambiguity for incumbent firms, which may hinder their innovation efforts. This study attempts to address this dilemma by proposing that the number of emerging market categories in an industry will have an inverted U-shaped relationship with incumbent firms' innovation efforts. We further argue that this curvilinear relationship will be influenced by the socio-cognitive context of a firm's focal industry, in the sense that the degree of collective identity incoherence at the industry level will intensify the proposed inverted U-shaped relationship, whereas the prevalence of trade associations in the industry will depress this relationship. We test our hypotheses by examining research and development (R&D) investments of a sample of U.S. high-technology manufacturing firms and find support for our main prediction and the hypothesized effect of collective identity incoherence. We also find a surprising but intriguing moderating effect of trade associations.

关键词： Simple-minded system   simple-minded mutation pair   Calabi-Yau triangulated category   Calabi-Yau reduction  

摘要： We develop the basic properties of w-simple-minded systems in (-w)-Calabi-Yau triangulated categories for w >= 1. We show that the theory of simple-minded systems exhibits striking parallels with that of cluster-tilting objects. The main result is a reduction technique for negative Calabi-Yau triangulated categories. Our construction provides an inductive technique for constructing simple-minded systems.

摘要： OBJECTIVE Most individuals with two or more islet autoantibodies progress to clinical type 1 diabetes. However, in some individuals, autoantibodies are subsequently lost. Here, our objectives were to determine the frequency of autoantibody loss (reversion) in multiple-autoantibody-positive individuals and to determine the association between reversion and progression to clinical disease. RESEARCH DESIGN AND METHODS We analyzed multiple-autoantibody-positive individuals participating in TrialNet's Pathway to Prevention Study for reversion and determined the effect of reversion on progression to clinical disease using a Cox regression analysis. RESULTS Of 3,284 multiple-autoantibody-positive subjects, reversion occurred in 134 (4.1%) and was associated with reduced incidence of clinical disease. Reversion occurred more frequently with older age, lower autoantibody titers, and fewer positive autoantibodies. CONCLUSIONS Although reversion of multiple-autoantibody positivity is rare, when it occurs, the risk of progressing to clinical disease is reduced. This suggests unknown mechanisms promoting immune remission in some individuals.

关键词： child   infant   polysomnography   sleep stages   guidelines   sleep   sleep spindles   eye tracking   data analysis  

摘要： Introduction A growing body of research suggests that sleep has an important role in consolidating newly learnt information and generalising this knowledge to novel instances (e.g. Djonlagic et al., 2009). The effects of sleep on early categorisation abilities haven’t been investigated so far and thus the aim of this study is to examine the role of sleep in formation of category representations. Two experiments were conducted. Experiment 1 set out to determine 4-months-old infants’ ability to form novel visual categories when category formation test immediately followed learning. Experiment 2 investigated the impact of sleep on category consolidation by testing category formation after a 2 hours delay. Methods Both experiments employed eye-tracking familiarisation-novelty-preference paradigm. In Experiment 1, infants were familiarised with a set of exemplars from a novel category. Immediately after the familiarisation phase, infants’ category formation was tested and their looking references were used as an index of category learning. Experiment 2 tested consolidation of the newly acquired categories by introducing a delay between the familiarisation and the test phase. Half of the participants took a nap during the delay, whereas the other half remained awake. Polysomnography was recorded using a standard PSG protocol. Sleep stages were scored according to the AASM guidelines, and sleep spindles were detected using an adapted algorithm for children. Results Results of the Experiment 1 revealed that infants were able to learn novel visual categories when category formation was tested immediately after learning suggesting therefore that infants are able to extract relevant information and generalise to novel instances. Preliminary results of Experiment 2 (data analysis ongoing) suggested that infants who napped performed better than infants who stayed awake. Conclusion The present study suggests that infants are able to rapidly form novel categories, and that consoli