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The polygroup theory is a natural generalization of the group theory. In a group the composition of two elements is an element, while in a polygroup the composition of two elements is a set. Polygroups have been applied in many area, such as geometry, lattices, combinatorics, and color scheme. Also, Crossed modules and its applications play very important roles in category theory, homology and cohomology of groups, homotopy theory, algebra, k-theory, etc. In this paper, we have definition of a polyfunctor and transformation for polygroups. Also, we introduce the concept of the symmetric crossed module to the symmetric crossed polymodules. Our results extend the classical results of crossed modules to crossed polymodules of polygroups. [ABSTRACT FROM AUTHOR]

We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how dense subcategories let one compute isotropy in the presence of binary coproducts, unifying various known one-dimensional results and providing tractable computational tools in the two-dimensional setting. In particular, we show that the isotropy 2-group of a monoidal category coincides with its Picard 2 -group , i.e., the 2-group on its weakly invertible objects. [ABSTRACT FROM AUTHOR]

In category theory circles it is well-known that the Schreier theory of group extensions can be understood in terms of the Grothendieck construction on indexed categories. However, it is seldom discussed how this relates to extensions of monoids. We provide an introduction to the generalised Grothendieck construction and apply it to recover classifications of certain classes of monoid extensions (including Schreier and weakly Schreier extensions in particular). [ABSTRACT FROM AUTHOR]

Based on a formalization of open formulas as statements in context, the paper presents a freshly new and abstract view of logics and specification formalisms. Generalizing concepts like sets of generators in Group Theory, underlying graph of a sketch in Category Theory, sets of individual names in Description Logic and underlying graph-based structure of a software model in Software Engineering, we coin an abstract concept of context. We show how to define, in a category independent way, arbitrary first-order statements in arbitrary contexts. Examples of those statements are defining relations in Group Theory, commutative, limit and colimit diagrams in Category Theory, assertional axioms in Description Logic and constraints in Software Engineering. To validate the appropriateness of the newly proposed abstract framework, we prove that our category independent definitions and constructions give us a very broad spectrum of Institutions of Statements at hand. For any Institution of Statements, a specification (presentation) is given by a context together with a set of first-order statements in that context. Since many of our motivating examples are variants of sketches, we will simply use the term sketch for those specifications. We investigate exhaustively different kinds of arrows between sketches and their interrelations. To pave the way for a future development of category independent deduction calculi for sketches, we define arbitrary first-order sketch conditions and corresponding sketch constraints as a generalization of graph conditions and graph constraints, respectively. Sketch constraints are the crucial conceptual tool to describe and reason about the structure of sketches. We close the paper with some vital observations, insights and ideas related to future deduction calculi for sketches. Moreover, we outline that our universal method to define sketch constraints enables us to establish and to work with conceptual hierarchies of sketches. [ABSTRACT FROM AUTHOR]

The study of social inequality and stratification (e.g., ethnoracial and gender) has long been at the core of sociology and the social sciences. In this article, I argue that certain tendencies have become entrenched in our dominant paradigm that leave many researchers pursuing coarse-grained analyses of how difference relates to inequality. Centrally, despite the importance of categories and categorization for how researchers study social inequality, contemporary (as opposed to classical) theories of categories are poorly integrated into conventional research. I contend that the widespread and often unquestioned use of state categories as categories of analysis reinforces these tendencies. Using research on colorism as an inspiration, I highlight several components of what I call the infracategorical model of inequalit y, which urges researchers to disaggregate difference by shifting our focus from membership in (nominal) categories to the cues of categories, membership in subcategories, and perceived typicality. [ABSTRACT FROM AUTHOR]

We study the categorical properties of preordered groups. We first give a description of limits and colimits in this category, and study some classical exactness properties. Then we point out a strong analogy between the algebraic behaviour of preordered groups and monoids, and we apply two different recent approaches to relative categorical algebra to obtain some homological properties of preordered groups. [ABSTRACT FROM AUTHOR]

Abstract The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the Gray -category of 2-categories and the tricategory of bicategories. We show that – far from requiring the full weakness provided by the definitions of tricategory theory – this adjunction can be strictly enriched over the symmetric closed multicategory of bicategories defined by Verity. Moreover, we show that this adjunction underlies an adjunction of bicategory-enriched symmetric multicategories. An appendix introduces the symmetric closed multicategory of pseudo double categories, into which Verity's symmetric multicategory of bicategories embeds fully. [ABSTRACT FROM AUTHOR]

We explain how the nilpotent singular support condition introduced into the geometric Langlands conjecture by Arinkin and Gaitsgory arises naturally from the point of view of 4-dimensional N = 4 supersymmetric gauge theory. We define what it means in topological quantum field theory to restrict a category of boundary conditions to the full subcategory of objects compatible with a fixed choice of vacuum, both in functorial field theory and in the language of factorization algebras. For B-twisted N = 4 gauge theory with gauge group G, the moduli space of vacua is equivalent to h ∗ / W , and the nilpotent singular support condition arises by restricting to the vacuum 0 ∈ h ∗ / W . We then investigate the categories obtained by restricting to points in larger strata, and conjecture that these categories are equivalent to the geometric Langlands categories with gauge symmetry broken to a Levi subgroup, and furthermore that by assembling such for the groups GL n with n ≥ 1 one finds a hidden factorization algebra structure for the geometric Langlands theory. [ABSTRACT FROM AUTHOR]

Abstract We give simple characterizations of the category PAsm (A) of partitioned assemblies , and of the realizability topos RT (A) over a partial combinatory algebra A. This answers the question for an 'extensional characterization' of realizability toposes. [ABSTRACT FROM AUTHOR]

Abstract We establish a connection between two settings of representation stability for the symmetric groups S n over C. One is the symmetric monoidal category Rep (S ∞) of algebraic representations of the infinite symmetric group S ∞ = ⋃ n S n , related to the theory of FI -modules. The other is the family of rigid symmetric monoidal Deligne categories Rep _ (S t) , t ∈ C , together with their abelian versions Rep _ a b (S t) , constructed by Comes and Ostrik. We show that for any t ∈ C the natural functor Rep (S ∞) → Rep _ a b (S t) is an exact symmetric faithful monoidal functor, and compute its action on the simple representations of S ∞. Considering the highest weight structure on Rep _ a b (S t) , we show that the image of any object of Rep (S ∞) has a filtration with standard objects in Rep _ a b (S t). As a by-product of the proof, we give answers to the questions posed by P. Deligne concerning the cohomology of some complexes in the Deligne category Rep _ (S t) , and their specializations at non-negative integers n. [ABSTRACT FROM AUTHOR]

Abstract We introduce the notion of syzygy for a set of reduction operators and relate it to the notion of syzygy for presentations of algebras. We give a method for constructing a linear basis of the space of syzygies for a set of reduction operators. We interpret these syzygies in terms of the confluence property from rewriting theory. This enables us to optimise the completion procedure for reduction operators based on a criterion for detecting useless reductions. We illustrate this criterion with an example of construction of commutative Gröbner basis. [ABSTRACT FROM AUTHOR]

It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the group of points of a localic group object, called the localic isotropy group, which also acts on every object, and in fact also on every internal locales and on every T-topos. This new localic isotropy group has better functoriality and stability property than the original version and shed some lights on the phenomenon of higher isotropy observed for the ordinary isotropy group. We prove in particular using a localic version of the isotropy quotient that any geometric morphism can be factored uniquely as a connected atomic geometric morphism followed by a so called "essentially anisotropic" geometric morphism, and that connected atomic morphism are exactly the quotient by an open isotropy action. [ABSTRACT FROM AUTHOR]

The Faa di Bruno construction, introduced by Cockett and Seely, constructs a comonad Faa whose coalgebras are precisely Cartesian differential categories. In other words, for a Cartesian left additive category X, Faa(X) is the cofree Cartesian differential category over X. Composition in these cofree Cartesian differential categories is based on the Faa di Bruno formula, and corresponds to composition of differential forms. This composition, however, is somewhat complex and difficult to work with. In this paper we provide an alternative construction of cofree Cartesian differential categories inspired by tangent categories. In particular, composition defined here is based on the fact that the chain rule for Cartesian differential categories can be expressed using the tangent functor, which simplifies the formulation of the higher order chain rule. [ABSTRACT FROM AUTHOR]

Let S and T be automorphisms of a probability space whose powers S ⊗ S and T ⊗ T isomorphic. Are the automorphisms S and T isomorphičThis question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows St ⊗ St and Tt ⊗ Tt are isomorphic, then so are the flows St and Tt, provided that one of them has a weak integral limit. [ABSTRACT FROM AUTHOR]

Let C be a smooth irreducible projective curve and let (L , H 0 (L)) be a complete and generated linear series on C. Denote by M L the kernel of the evaluation map H 0 (L) ⊗ 𝒪 C → L. The exact sequence 0 → M L → H 0 (L) ⊗ 𝒪 C → L → 0 fits into a commutative diagram that we call the Butler's diagram. This diagram induces in a natural way a multiplication map on global sections m W : W ∨ ⊗ H 0 (K C) → H 0 (S ∨ ⊗ K C) , where W ⊆ H 0 (L) is a subspace and S ∨ is the dual of a subbundle S ⊂ M L . When the subbundle S is a stable bundle, we show that the map m W is surjective. When C is a Brill–Noether general curve, we use the surjectivity of m W to give another proof of the semistability of M L , moreover, we fill up a gap in some incomplete argument by Butler: With the surjectivity of m W we give conditions to determine the stability of M L , and such conditions imply the well-known stability conditions for M L stated precisely by Butler. Finally we obtain the equivalence between the (semi)stability of M L and the linear (semi)stability of (L , H 0 (L)) on k -gonal curves. [ABSTRACT FROM AUTHOR]

In the paper Triangulations, orientals, and skew monoidal categories , the free skew monoidal category Fsk on a single generating object was described. We sharpen this by giving a completely explicit description of Fsk , and so of the free skew monoidal category on any category. As an application we describe adjunctions between the operad for skew monoidal categories and various simpler operads. For a particular such operad L , we identify skew monoidal categories with certain colax L -algebras. [ABSTRACT FROM AUTHOR]

The Q-matrix of a cognitively diagnostic test is said to be complete if it guarantees the identifiability of all possible proficiency classes among examinees. An incomplete Q-matrix causes examinees to be assigned to proficiency classes to which they do not belong. Completeness of the Q-matrix is therefore a key requirement of any cognitively diagnostic test. The importance of the completeness property of the Q-matrix of a test as a fundamental condition to guarantee a reliable estimate of an examinee’s attribute profile has only recently been realized by researchers. In fact, inspection of extant assessments based on the cognitive diagnosis framework often revealed that, in hindsight, the Q-matrices used with these tests were not complete. Thus, the availability of rules for building a complete Q-matrix at the early stages of test development is perhaps at least as desirable as rules for identifying the completeness of a given Q-matrix. This article presents procedures for constructing Q-matrices that are complete. The famous Fraction-Subtraction test problems by K. K. Tatsuoka (1984) are used throughout for illustration. [ABSTRACT FROM AUTHOR]

The Ehresmann-Schein-Nambooripad (ESN) Theorem asserts an equivalence between the category of inverse semigroups and the category of inductive groupoids. In this paper, we consider the category of inverse categories and functors - a natural generalization of inverse semigroups and semigroup homomorphisms - and extend the ESN Theorem to an equivalence between this category and the category of locally complete inductive groupoids and locally inductive functors. From the proof of this extension, we also generalize the ESN Theorem to an equivalence between the category of inverse semicategories and the category of locally inductive groupoids and to an equivalence between the category of inverse categories with oplax functors and the category of locally complete inductive groupoids and ordered functors. [ABSTRACT FROM AUTHOR]

The main idea of this paper is to introduce the notion of a Schreier 2-category and of a crossed semimodule over categories and to prove the categorical equivalence between their categories. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notions of quasi-entwining structure and cleft extension for a quasi-entwining structure. We prove that if (A, C, ψ) is a quasi-entwining structure and the associated extension to the submagma of coinvariants AC is cleft, there exists an isomorphism Wa between Ac ⊗ C and A. Moreover, we define two unital but not necessarily associative products on Ac ⊗ C. For these structures we obtain the necessary and sufficient conditions to assure that ωa is a magma isomorphism, giving some examples fulfilling these conditions. [ABSTRACT FROM AUTHOR]

The formation of the "strict" span category Span(C) of a category C with pullbacks is a standard organizational tool of category theory. Unfortunately, limits or colimits in Span(C) are not easily computed in terms of constructions in C. This paper shows how to form the pullback in Span(C) for many, but not all, pairs of spans, given the existence of some speci-c so-called lax pullback complements in C of the "left legs" of at least one of the two given spans. For some types of spans we require the ambient category to be adhesive to be able to form at least a weak pullback in Span(C). The existence of all lax pullback complements in C along a given morphism is equivalent to the exponentiability of that morphism. Since exponentiability is a rather restrictive property of a morphism, the paper first develops a comprehensive framework of rules for individual lax pullback complement diagrams, which resembles the set of pasting and cancellation rules for pullback diagrams, including their behaviour under pullback. We also present examples of lax pullback complements along non-exponentiable morphisms, obtained via lifting along a fibration. [ABSTRACT FROM AUTHOR]

For certain roots of unity, we consider the categories of weight modules over three quantum groups: small, unrestricted and unrolled. The first main theorem of this paper is to show that there is a modified trace on the projective modules of the first two categories. The second main theorem is to show that category over the unrolled quantum group is ribbon. Partial results related to these theorems were known previously. [ABSTRACT FROM AUTHOR]

We classify up an isomorphism all rings having expressed their elements by at most three commuting idempotents. Our main result consider- ably extends certain important achievements established by Hirano-Tominaga [3], Ying et al. [6] and Tang et al. [5] as well as it somewhat strengthens recent results proved by the author in [1] and [2]. [ABSTRACT FROM AUTHOR]

We solve a problem posed by Goncharov and Knight (Problem 4 in [S. Goncharov and J. Knight, Computable structure and antistructure theorems, Algebra Logika 41(6) (2002) 639-681, 757]). More specifically, we produce an effective Friedberg (i.e. injective) enumeration of computable equivalence structures, up to isomorphism. We also prove that there exists an effective Friedberg enumeration of all isomorphism types of infinite computable equivalence structures. [ABSTRACT FROM AUTHOR]

Let R be a semiprime *-ring, α and β be automorphisms of R and let D: R→ R be additive mapping satisfying any one of the following condition [ (i)] D(xyx) = D(xy)α(x*)+β(xy)D(x) or D(xyx) = D(x)α(y*x*)+β(x)D(yx) for all pairs x,y ∈ R, [ (ii)] D(xn) = D(xn-1)α(x*) + β(xn-1)D(x) or D(xn) = D(x)α((x*)n-1)+β(x)D(xn-1) for all x ∈ R, [ (iii)] 2D(xn) = D(xn-1)α(x*)+β(xn-1)D(x)+D(x)α((x*)n-1)+β(x)D(xn-1) for all x ∈ R. Then D is a Jordan (α,β)*-derivation. [ABSTRACT FROM AUTHOR]

Let t1, . . . , tn be ℓ-group terms in the variables X1, . . . , Xm. Let t̂1, . . . , t̂n be their associated piecewise homogeneous linear functions. Let G be the ℓ-group generated by t̂1, . . . , t̂n in the free m-generator ℓ-group Am. We prove: (i) the problem whether G is ℓ-isomorphic toAn is decidable; (ii) the problem whether G is ℓ-isomorphic to Al (l arbitrary) is undecidable; (iii) for m = n, the problem whether {t̂1, . . . , tt̂n} is a free generating set is decidable. In view of the Baker-Beynon duality, these theorems yield recognizability and unrecognizability results for the rational polyhedron associated to the ℓ-group G. We make pervasive use of fans and their stellar subdivisions. [ABSTRACT FROM AUTHOR]

Voskresenskii conjectured that stably rational tori are rational. Klyachko proved this assertion for a wide class of tori by general principles. We re-prove Klyachko's result by providing simple explicit birational isomorphisms, and elaborate on some links to torus-based cryptography. [ABSTRACT FROM AUTHOR]

We study projective dimension and graded length of structural modules in parabolic-singular blocks of the BGG category O. Some of these are calculated explicitly, others are expressed in terms of two functions. We also obtain several partial results and estimates for these two functions and relate them to monotonicity properties for quasi-hereditary algebras. The results are then applied to study blocks of O in the context of Guichardet categories, in particular, we show that blocks of O are not always weakly Guichardet. [ABSTRACT FROM AUTHOR]

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the embedding of the canonical abelian subring of functions supported on the unit space. We deduce that diagonal-preserving ring isomorphism of Leavitt path algebras implies C*-isomorphism of C*-algebras for graphs E and F in which every cycle has an exit. [ABSTRACT FROM AUTHOR]

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called “flexibility” whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena. [ABSTRACT FROM AUTHOR]

Let X be a smooth, complex projective variety, and Y be a very general, sufficiently ample hypersurface in X . A conjecture of M.V. Nori states that the natural restriction map CH p ( X ) Q → CH p ( Y ) Q is an isomorphism for all p < dim ⁡ Y and an injection for p = dim ⁡ Y . This is the generalized Noether–Lefschetz conjecture . We prove an infinitesimal version of this conjecture. [ABSTRACT FROM AUTHOR]

The purpose of this note is to study the Maulik-Okounkov K-theoretic stable basis for the Hilbert scheme of points on the plane, which depends on a 'slope' $$m \in {\mathbb {R}}$$ . When $$m = \frac{a}{b}$$ is rational, we study the change of stable matrix from slope $$m-\varepsilon $$ to $$m+\varepsilon $$ for small $$\varepsilon >0$$ , and conjecture that it is related to the Leclerc-Thibon conjugation in the q-Fock space for $$U_q\widehat{{\mathfrak {gl}}}_b$$ . This is part of a wide framework of connections involving derived categories of quantized Hilbert schemes, modules for rational Cherednik algebras and Hecke algebras at roots of unity. [ABSTRACT FROM AUTHOR]

Let A be either a simplicial complex K or a small category C with V (A) as its set of vertices or objects. We define a twisted structure on A with coefficients in a simplicial group G as a function δ : V (A) → End(G), v → δv, such that δv o δw = δw o δv if there exists an edge in A joining v with w or an arrow either from v to w or from w to v. We give a canonical construction of twisted simplicial groups as well as twisted homology for A with a given twisted structure. Also we determine the homotopy type of this simplicial group as the loop space over certain twisted smash product. [ABSTRACT FROM AUTHOR]

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let be a non-trivial finite linear space with points, where and are two primes. We prove that if is line-transitive point-imprimitive, then is solvable. [ABSTRACT FROM AUTHOR]

We extend the notion of test module filtration introduced by Blickle for Cartier modules. We then show that this naturally defines a filtration on unit F -modules and prove that this filtration coincides with the notion of V -filtration introduced by Stadnik in the cases where he proved existence of his filtration. We also show that these filtrations do not coincide in general. Moreover, we show that for a smooth morphism f : X → Y test modules are preserved under f ! . We also give examples to show that this is not the case if f is finite flat and tamely ramified along a smooth divisor. [ABSTRACT FROM AUTHOR]

We construct exceptional collections of line bundles of maximal length 4 on S = ( C × D ) / G which is a surface isogenous to a higher product with p g = q = 0 where G = G ( 32 , 27 ) is a finite group of order 32 having number 27 in the list of Magma library. From these exceptional collections, we obtain new examples of quasiphantom categories as their orthogonal complements. [ABSTRACT FROM AUTHOR]

We propose a new unifying framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application, we prove a theorem which implies that planar or symmetric or braided operads with transformations satisfying some finiteness conditions yield operad groups of type F ∞ . This unifies and extends existing proofs that certain Thompson-like groups are of type F ∞ . [ABSTRACT FROM AUTHOR]

A class of abelian topological groups was previously defined to be a variety of topological groups with coproducts if it is closed under forming subgroups, quotients, products and coproducts in the category of all abelian topological groups and continuous homomorphisms. This extended research on varieties of topological groups initiated by the second author. The key to describing varieties of topological groups generated by various classes was proving that all topological groups in the variety are a quotient of a subgroup of a product of groups in the generating class. This paper analyses generating varieties of topological groups with coproducts. It focuses on the interplay between forming products and coproducts. It is proved that the variety of topological groups with coproducts generated by all discrete groups contains topological groups which cannot be expressed as a quotient of a subgroup of a product of a coproduct of discrete groups. It is proved that the variety of topological groups with coproducts generated by any infinite-dimensional Hilbert space contains all infinite-dimensional Hilbert spaces, answering an open question. This contrasts with the result that a variety of topological groups generated by a topological group does not contain any infinite-dimensional Hilbert space of greater cardinality. [ABSTRACT FROM PUBLISHER]

We give a description of the isomorphism classes of matrix groups over commutative rings with 1 and that have dimension more than 3 and containing the group of elementary transvections. We characterize those ho- momorphisms of matrix groups, which satisfy the so-called (*) condition. Such homomorphisms can be constructed with the help of the standard homomor- phism. We apply the characterization obtained to the description of the above class of matrix groups. [ABSTRACT FROM AUTHOR]

We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear in the existing literature. We start with a discussion of graded spaces, passing through graded bundles and their linearisation to end with weighted (graded) Lie groupoids/algebroids. [ABSTRACT FROM AUTHOR]

The Hochschild cohomology groups are calculated for the algebras of semidihedral type that form the family $$ SD\left(3\mathcal{K}\right) $$ (from the famous K. Erdmann's classification). In the calculation, the bimodule resolution previously constructed for the algebras belonging to the family under discussion is used. [ABSTRACT FROM AUTHOR]

We provide a general formula for Müger's centralizer of any fusion subcategory of a braided fusion category containing a Tannakian subcategory. This entails a description for Müger's centralizer of all fusion subcategories of a group theoretical braided fusion category. [ABSTRACT FROM AUTHOR]

Fisher Determination Dictionary Learning (FDDL) has shown to be effective in image classification. However, the Original FDDL (O-FDDL) method is time-consuming. To address this issue, a fast Simplified FDDL (S-FDDL) method was proposed. But S-FDDL ignores the role of collaborative reconstruction, thus having an unstable performance in classification tasks with unbalanced changes in different classes. This paper focuses on developing an Efficient FDDL (E-FDDL) method, which is more suitable for such classification problems. Precisely, instead of solving the original Fisher Discrimination based Sparse Representation (FDSR) problem, we propose to solve an Approximate FDSR (A-FDSR) problem whose objective function is an upper bound of that of FDSR. A-FDSR considers the role of both the discriminative reconstruction and the collaborative reconstruction. This makes E-FDDL stable when dealing with classification tasks with unbalanced changes in different classes. Furthermore, fast optimization strategies are applicable to A-FDSR, thus leading to the high efficiency of E-FDDL which can be explained by analysis on convergence rate and computational complexity. We also use E-FDDL to accelerate the Shared Domain-adapted Dictionary Learning (SDDL) algorithm which is a FDDL based new method for domain adaptation. Experimental results on face and object recognition demonstrate the stable and fast performance of E-FDDL. [ABSTRACT FROM AUTHOR]

We consider the problem of unsupervised classification of hidden Markov models (HMC) with dependent noise. Time is discrete, the hidden process takes its values in a finite set of classes, while the observed process is continuous. We adopt an extended HMC model in which the rich possibilities of different kinds of dependence in the noise are modelled via copulas. A general model identification algorithm, in which different noise margins and copulas corresponding to different classes are selected in given families and estimated in an automated way, from the sole observed process, is proposed. The interest of the whole procedure is shown via experiments on simulated data and on a real SAR image. [ABSTRACT FROM AUTHOR]

We study the partition properties enjoyed by the “next best thing to a P-point” ultrafilters introduced recently in joint work with Dobrinen and Raghavan. That work established some finite-exponent partition relations, and we now analyze the connections between these relations for different exponents and the notion of conservativity introduced much earlier by Phillips. In addition, we establish some infinite-exponent partition relations for these ultrafilters and also for sums of non-isomorphic selective ultrafilters indexed by selective ultrafilters. [ABSTRACT FROM AUTHOR]

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent 'internal' renditions of the famous categoricity arguments for arithmetic and set theory. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new example of Hopf group coalgebras by considering Radford's biproduct Hopf algebra in the Turaev category. Furthermore, we find some sufficient and necessary conditions for such Radford's biproduct Hopf algebra to admit quasitriangular structures in the sense of Turaev group coalgebras. [ABSTRACT FROM AUTHOR]