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关键词： Cotorsion pairs   Quiver representations   Abelian categories  

摘要： Given a complete hereditary cotorsion pair (A, B) in an abelian category C satisfying certain conditions, we study the completeness of the induced cotorsion pairs (Phi(A), Phi(A)(perpendicular to)) and ((perpendicular to)Psi(B), Psi(B)) in the category Rep (Q, C) of C-valued representations of a given quiver Q. We show that if Q is left rooted, then the cotorsion pair (Phi(A), Phi(A)(perpendicular to)) is complete, and if Q is right rooted, then the cotorsion pair ((perpendicular to)Psi(B), Psi(B)) is complete. Besides, we work on the infinite line quiver A(infinity)(infinity), which is neither left rooted nor right rooted. We prove that these cotorsion pairs in Rep(A(infinity)(infinity), R) are complete, as well. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Bayesian network   Categorical spatial variable   Conditional independence   Markov chain random field   Sequential Bayesian updating  

摘要： The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies among nearest data and the central random variable can be described by a probabilistic directed acyclic graph that conforms to a neighborhood-based Bayesian network on spatial data. By selecting different neighborhood sizes and structures, applying the spatial conditional independence assumption to nearest neighbors, or incorporating ancillary information, one may construct specific MCRF models based on the MCRF general solution for various application purposes. Simplified MCRF models based on assuming the spatial conditional independence of nearest data involve only spatial transition probabilities, and one can implement them easily in sequential simulations. In this article, we prove the spatial Bayesian network characteristic of MCRFs, and test the optimal neighborhoods under the spatial conditional independence assumption. The testing results indicate that the quadrantal (i.e., one nearest datum per quadrant) neighborhood is generally the best choice for the simplified MCRF solution, performing better than other sectored neighborhoods and non-sectored neighborhoods with regard to simulation accuracy and pattern rationality.

关键词： 03B30   03D60   03F15 (primary)  

摘要： Peter Aczel has given a categorical construction for fixed points of normal functors, that is, dilators which preserve initial segments. For a general dilator X -> TX, we cannot expect to obtain a well-founded fixed point, as the order type of TX may always exceed the order type of X. In the present paper, we show how to construct a Bachmann-Howard fixed point of T, that is, an order BH(T) with an 'almost' order preserving collapse upsilon : TBH(T) -> BH(T). Building on previous work, we show that pi 11-comprehension is equivalent to the assertion that BH(T) is well-founded for any dilator T.

关键词： colour categorization   colour constancy   colour vision   LED light source   real scenes  

摘要： Some previous studies have investigated the influence of the lighting time course and viewing background on the colour constancy using two-dimensional flat stimuli simulated on a monitor. In the present study, we investigated the categorical colour constancy in real scenes by manipulating (a) the lighting time course, that is, adaptation period to the illuminant (brief adaptation or complete adaptation) and (b) the background structure of a stimulus (a uniform gray background with an approximately 25% spectral reflectance or a multicolour background consisting of the Macbeth ColorChecker and some fruit models). The neutral (u ' = 0.1994, v ' = 0.4671), red (u ' = 0.2433, v ' = 0.4622), green (u ' = 0.1525, v ' = 0.4697), blue (u ' = 0.2049, v ' = 0.4198), and yellow (u ' = 0.1892, v ' = 0.5112) illuminants were produced by an RGB-LED lamp. For each chromatic illumination condition, subjects categorized 240 surfaces with Munsell Value 5/ in four viewing conditions with different combinations of the lighting time course and the background structure. A total of seven subjects participated in experiments with red and green illuminants and five subjects with blue and yellow illuminants. The results showed that the constancy index was the lowest (0.66) in the brief adaptation and gray background condition and the highest (0.74) in the complete adaptation and multicolour background condition. The results suggest that increasing the adaptation period alone or adding chromatic cues in the background with a brief adaptation can help to improve the colour constancy, and a time-taking reference to surrounding coloured objects with the long presentation of the illuminant may also contribute to obtaining colour constancy.

关键词： Giardiasis   Assemblage   Genotyping   PCR-RFLP   gdh   bg   tpi  

摘要： Background: Giardiasis is one of the commonest intestinal parasitic diseases that affects wide range of age groups. We aimed to detect the pattern of Giardia intestinalis assemblages among symptomatic patients at the age of 2 up to 40 years. Methods: Stool samples were collected from 278 patients and examined microscopically and genetically for giardiasis. Giardia was diagnosed using wet mount examination and subjected to molecular assays targeting three genes, glutamate dehydrogenase (gdh) using semi-nested PCR (nPCR), beta-giardin (bg) and triose phosphate isomerase (tpi) using nPCR. Amplified products were subjected to genotyping using PCR-restriction fragment length polymorphism (PCR-RFLP) targeting gdh and bg genes. Results: Among 48 samples positive by microscopy and by a minimum of one of the three used genes, genotyping was successful among 23 samples (47.9%). Assemblage B was more prevalent (16/23, 69.6%), than assemblage A (4/23, 17.4%) and 3 (13%) isolates were identified as assemblage B at gdh locus which later were identified as assemblage A at bg locus. Sub-assemblage AII (3/4, 75%) and sub-assemblage BIII (12/15, 66.7%) were predominate at gdh locus. Age groups was an estimated risk factor for infection with assemblage B with a peak (87.5%) during 6 to 12 years (P<0.05), diarrhea and abdominal pain (OR (95%CI) = .654 (.094, .963);.201 (.048, 1.009), respectively) were significantly associated with assemblage B. Conclusion: It is recommended to suspect infection with giardiasis assemblage B by physicians during late childhood presenting with diarrhea and abdominal pain.

关键词： Differential categories   Differential algebras   Hurwitz series rings   Faa di Bruno formula  

摘要： Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since led to abstract formulations of many notions involving differentiation such as the directional derivative, differential forms, smooth manifolds, De Rham cohomology, etc. In this paper we study the generalization of differential algebras to the context of differential categories by introducing T-differential algebras, which can be seen as special cases of Blute, Lucyshyn-Wright, and O'Neill's notion of T-derivations. As such, T-differential algebras are axiomatized by the chain rule and as a consequence we obtain both the higher-order Leibniz rule and the Faa di Bruno formula for the higher-order chain rule. We also construct both free and cofree T-differential algebras for suitable codifferential categories and discuss power series of T-algebras. (C) 2019 Elsevier B.V. All rights reserved.

摘要： We establish a correspondence among simple objects of the relative commutant of a full fusion subcategory in a larger fusion category in the sense of Drinfeld, irreducible half-braidings of objects in the larger fusion category with respect to the fusion subcategory, and minimal central projections in the relative tube algebra. Based on this, we explicitly compute certain relative Drinfeld commutants of fusion categories arising from alpha-induction for braided subfactors. We present examples arising from chiral conformal field theory.

关键词： functional magnetic resonance imaging   semantics   visual cortex   visual perception  

摘要： Introduction How do multiple sources of information interact to form mental representations of object categories? It is commonly held that object categories reflect the integration of perceptual features and semantic/knowledge-based features. To explore the relative contributions of these two sources of information, we used functional magnetic resonance imaging (fMRI) to identify regions involved in the representation object categories with shared visual and/or semantic features. Methods Participants (N = 20) viewed a series of objects that varied in their degree of visual and semantic overlap in the MRI scanner. We used a blocked adaptation design to identify sensitivity to visual and semantic features in a priori visual processing regions and in a distributed network of object processing regions with an exploratory whole-brain analysis. Results Somewhat surprisingly, within higher-order visual processing regions-specifically lateral occipital cortex (LOC)-we did not obtain any difference in neural adaptation for shared visual versus semantic category membership. More broadly, both visual and semantic information affected a distributed network of independently identified category-selective regions. Adaptation was seen a whole-brain network of processing regions in response to visual similarity and semantic similarity;specifically, the angular gyrus (AnG) adapted to visual similarity and the dorsomedial prefrontal cortex (DMPFC) adapted to both visual and semantic similarity. Conclusions Our findings suggest that perceptual features help organize mental categories throughout the object processing hierarchy. Most notably, visual similarity also influenced adaptation in nonvisual brain regions (i.e., AnG and DMPFC). We conclude that category-relevant visual features are maintained in higher-order conceptual representations and visual information plays an important role in both the acquisition and neural representation of conceptual object categories.

关键词： Ternion support vector machine   One-versus-one-versus-rest tree   Multi-category classification   Handwritten digit recognition   Image classification  

摘要： This paper proposes a three-class classifier termed as 'Ternion support vector machine' (TerSVM) and its tree based multi-category classification approach termed as 'Multi-category ternion support vector machine' (M-TerSVM). The proposed classifier, TerSVM, is motivated by twin multi-class support vector classification (Twin-KSVC) and evaluates the data patterns for three outputs (+1,-1,0). Twin-KSVC has very high computational complexity, which makes it infeasible for real-world problems. Our proposed classifier, TerSVM, overcomes this limitation, as it formulates three unconstrained minimization problems (UMPs), instead of quadratic programming problems as solved by Twin-KSVC. The UMPs of TerSVM are solved as systems of linear equations which determine three proximal nonparallel hyperplanes. TerSVM can also be used as a binary classifier. This work also proposes a multi-category classification algorithm, M-TerSVM, that extents our three-class classifier (TerSVM) into multi-category framework. For a K-class problem, M-TerSVM constructs a classifier model in the form of a ternion tree of height left perpendicularK/2right perpendicular, where the data is partitioned into three groups at each level. Our algorithm uses a novel procedure to identify a reduced training set which improves its learning time. Numerical experiments performed on synthetic and benchmark datasets indicate that M-TerSVM outperforms other classical multi-category approaches like one-against-all and Twin-KSVC, in terms of generalization ability and learning time. This paper proposes the application of M-TerSVM for handwritten digit recognition and color image classification.

关键词： association strength   autism spectrum disorders   categorical relatedness   fMRI   semantic knowledge  

摘要： Impaired language and communication are commonly observed in youths with autism spectrum disorders (ASDs). However, the organization of semantic knowledge in youths with ASD remains unclear compared to typically developing (TD) youths. The present study addresses this issue by using functional magnetic resonance imaging (fMRI) to examine the distinction between association strength and categorical relatedness of semantic knowledge. A sample of 31 male youths with ASD (mean age = 12.1 years, SD = 1.2) and 38 TD youths (mean age = 11.9 years, SD = 1.0) was recruited with matched age, gender, and handedness. Participants decided if two visually presented Chinese characters were semantically related during fMRI scanning. For weaker association strength, the ASD group showed greater left cuneus activation, which was positively correlated with the picture completion for visual perception, whereas the TD group showed greater middle temporal gyrus and inferior frontal gyrus activation. For higher categorical relatedness, the TD group showed greater activation than the ASD group in the occipitotemporal cortex and left precuneus, which was positively correlated with the similarities for concept formulation. Findings imply that the ASD group may use lower-level visual information for both association strength and categorical relatedness. The TD group showed higher-level controlled processes of more elaborate semantic representations for association strength and more elaborate features of categorical knowledge for semantic selection and integration. Autism Res 2019, 00: 1-11. (c) 2019 International Society for Autism Research, Wiley Periodicals, Inc. Lay Summary Individuals with autism spectrum disorder (ASD) often present language/communication impairments. Exploring the difference of semantic processing between youths with ASD and typically developing (TD) youths is crucial for understanding the organization of semantic knowledge. We found different neural substrates of seman