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关键词： Scheme   Sheaf   Pure-exact sequence   Ziegler spectrum  

摘要： We consider categorical and geometric purity for sheaves of modules over a scheme satisfying some mild conditions, both for the category of all sheaves and for the category of quasicoherent sheaves. We investigate the relations between these four purities;for example, we give a characterisation of geometric pure-injectives in both the quasicoherent and non-quasicoherent case. We also compute a number of examples, in particular describing both the geometric and categorical Ziegler spectra for the category of quasicoherent sheaves over the projective line over a field.

关键词： Homological mirror symmetry   Fukaya categories   Aoo-categories  

摘要： We construct an Aoo-structure of the Fukaya category explicitly for any flat symplectic two-torus. The structure constants of the non-transversal Aoo-products are obtained as derivatives of those of transversal Aoo-products. (C) 2020 Elsevier B.V. All rights reserved.

关键词： atypia of undetermined significance (AUS)   fine-needle aspiration (FNA)   mucin   risk of malignancy (ROM)   risk of neoplasm (RON)   salivary gland   The Milan System for Reporting Salivary Gland Cytopathology (MSRSGC)  

摘要： Background Atypia of undetermined significance (AUS) is a category of the Milan System for Reporting Salivary Gland Cytopathology that refers to salivary gland fine-needle aspiration (FNA) specimens that cannot be definitively diagnosed as neoplastic or nonneoplastic. Methods The AUS FNA samples were selected from a large academic institution from 2008 through 2018. The AUS cases were divided into 6 subgroups. The risk of malignancy (ROM), risk of neoplasm (RON), and clinical outcomes for each subgroup were evaluated. Results A total of 123 cases were found (76 males and 47 females with a mean age of 62 years [range, 6-94 years]). The parotid gland was the most common FNA site (103 cases), followed by the submandibular gland (9 cases). The overall RON and ROM were 63% and 47%, respectively. Among the subgroups, salivary gland lymph nodes or lymphoid lesions was the most common diagnosis (42%), whereas mucinous cystic lesions with no or a scant epithelial component was the least common (2%). The specimens with preparation artifacts category had the highest RON and ROM (100% for both), whereas the reactive and reparative atypia indefinite for a neoplasm category had the lowest RON and ROM (7% for both). The salivary gland lymph nodes or lymphoid lesions indefinite for a lymphoproliferative disorder category had the second highest RON and ROM at 77% and 74%, respectively. Conclusions The overall RON and ROM for the AUS category were 63% and 47%, respectively. The RON and ROM varied among the different AUS subgroups, being highest in the specimens with preparation artifacts category and lowest in the reactive and reparative atypia category, thereby demonstrating the importance of subgrouping in the AUS specimens.

关键词： Finite length categories   Uniserial categories   Iterated extensions   Noncommutative deformations  

摘要： In this paper, we study length categories using iterated extensions. We fix a field k, and for any family S of orthogonal k-rational points in an Abelian k-category A, we consider the category Ext(S) of iterated extensions of S in A, equipped with the natural forgetful functor Ext(S) -> A(S) into the length category A(S). There is a necessary and sufficient condition for a length category to be uniserial, due to Gabriel, expressed in terms of the Gabriel quiver (or Ext-quiver) of the length category. Using Gabriel's criterion, we give a complete classification of the indecomposable objects in A(S) when it is a uniserial length category. In particular, we prove that there is an obstruction for a path in the Gabriel quiver to give rise to an indecomposable object. The obstruction vanishes in the hereditary case, and can in general be expressed using matric Massey products. We discuss the close connection between this obstruction, and the noncommutative deformations of the family S in A. As an application, we classify all graded holonomic D-modules on a monomial curve over the complex numbers, obtaining the most explicit results over the affine line, when D is the first Weyl algebra. We also give a non-hereditary example, where we compute the obstructions and show that they do not vanish.

关键词： Thermal conductivity   Thermal diffusivity   Material category identification   Time delay   Electrical analogy modelling  

摘要： Material identification based on thermal properties is a commonly used approach of classifying materials into different categories. In this paper, an analytical approach for estimation of two thermal properties under the transient condition and arbitrary ambient temperature is presented for material category identification. The thermal properties are estimated by exploiting the analogy between the one-dimensional thermal conduction in material with the voltage distribution in resistance-capacitance (RC) ladder network. The concept of time delay in the RC ladder network has been used in the thermal domain for deriving simple analytical expressions of thermal diffusivity and thermal conductivity. The proposed approach is simple, has less data related concerns and can identify the material category based on two thermal properties for better certainty. This approach has been verified by simulations and experiments performed on materials of different categories. The approach would be helpful in automated applications related to material identification or handling.

关键词： Anecic   Endogeic   Epigeic   Ecological traits   Burrow   Cast   Earthworms  

摘要： Seven earthworm ecological categories, including anecics, endogeics and epigeics, were defined by Marcel Bouche in 1972 based only on morpho-anatomical characteristics measured on European lumbricids. These categories had an outstanding success, and their use was generalized even outside of Europe. However, most of the time, only the three main categories are used, and over two decades, these categories have been considered functional groups, i.e. to presume how earthworms influence the soil functioning. Moreover, this relationship between ecological categories and functional groups is seldom tested and often uncritically accepted by soil biology researchers. It is then not surprising to observe unexpected trends when earthworm species are gathered in ecological categories to, for instance, analyze burrow systems or cast properties. We believe it is time to acknowledge that ecological categories are not functional, because they were not made for this purpose. We also propose three future directions in order to either improve our knowledge on the functional effects of earthworms or to build new authentically functional groups: (i) going back to the seven initial ecological categories to provide greater accuracy than the usage of the simplified three-level classification;(ii) testing, for a set of selected species, the functionality of the groups, being ecological categories or new tailored ones;and (iii) using trait-based approach in order to study the correlation between some earthworm traits and main soil functions.

关键词： Coquasi-bialgebra   Preantipode   Coquasi-Hopf algebra   Rigid monoidal category   Tensor functor   Reconstruction  

摘要： By a theorem of Majid, every monoidal category with a neutral quasi-monoidal functor to finitely generated and projective k-modules gives rise to a coquasi-bialgebra. We prove that if the category is also rigid, then the associated coquasi-bialgebra admits a preantipode, providing in this way an analogue for coquasi-bialgebras of Ulbrich's reconstruction theorem for Hopf algebras. When k is a field, this allows us to characterize coquasi-Hopf algebras as well in terms of rigidity of finite-dimensional corepresentations.

关键词： Immigration   South Africa   Racial classification   New categories   Refugees   Immigrants  

摘要： Scholars examining the South African racial classification system have suggested that apartheid-era racial categories continue to officially classify the South African population. However, there is little discussion about the extent to which the South African racial classification configuration is relevant to new immigrants and refugees (or their descendants) and whether the system will endure or undergo transformation in the face of a growing immigration-induced racial and ethnic diversity. It is palpable that new immigrants and refugees will continue to find apartheid-era South African racial categories incompatible with identities they brought from their home countries. I draw on some empirical works conducted in South Africa and examples in other national contexts such as the USA to argue that the rigid quaternary South African racial classification system, which is based on White, Black, Indian, and Colored racial categories, might be transformed or re-configured due to shifts and transformations in the racial and ethnic makeup of the South African population owing to immigration. Furthermore, such re-configuration might occur if immigrant and refugee communities or their descendants lobby the South African state to create identities for them. Currently, and in the context of widespread public and institutional xenophobia and exclusion of non-citizens, it is paramount to create categories that refer to "foreign-origin" to tackle systemic discrimination based on foreign origin and accelerate institutional integration of refugees and immigrants.

关键词： Categorical spatial variable   Conditional simulation   Gibbs sampler   Implicit function   Principal component analysis  

摘要： This paper introduces a method to generate conditional categorical simulations, given an ensemble of partially conditioned (or unconditional) categorical simulations derived from any simulation process. The proposed conditioning method relies on implicit functions (signed distance functions) for representing the categorical spatial variable of interest. Thus, the conditioning problem is reformulated in terms of signed distance functions. The proposed approach combines aspects of principal component analysis and Gibbs sampling to achieve the conditioning of the unconditional categorical realizations to the data. It is applied to synthetic and real-world datasets and compared to the traditional sequential indicator simulation. It appears that the proposed simulation technique is an effective method to generate conditional categorical simulations from a set of unconditional categorical simulations.