Objective: Some adolescents and young adults who do not fulfill criteria for DSM-IV alcohol abuse (AA) report symptoms of DSM-IV alcohol dependence (AD) below the diagnostic threshold (diagnostic orphans, DOs; 1 or 2 symptoms). Contemporarily, little is known on the long-term stability, risk of progression to AD, impairment, and drinking patterns possibly associated with this status in the first decades of life. Aim: (1) To identify prevalence rates of the DO status from adolescence to early adulthood. To investigate (2) stability and variability of the DO status over time and (3) associations between DO status, drinking patterns and impairment in comparison to subjects with AA, with AD, or without any symptoms. Method: N = 2039 community subjects (aged 14–24 years at baseline) were assessed at baseline and at about four and ten years after baseline. DSM-IV AUD diagnoses were obtained with the DIA-X/M-CIDI. Results: About 11–12% of the sample was classified as DOs at all waves. Over a period of ten years, 18% of DOs were stable in their diagnosis and additional 10% progressed to AD. DOs were comparable to subjects with AA in drinking patterns, impairment and stability of diagnostic status. DOs progressed to AD significantly more often than AA. AD was associated with highest levels in all outcomes of interest. Conclusions: The DO status in adolescence and early adulthood is associated with considerable stability, risk of progression and problematic alcohol intake. In consequence, it can be meaningful for the timely identification of early stages of clinically relevant alcohol problems. For subjects with DO status early specific interventions are required.

In this article we establish a bridge between dynamical systems, including topological and measurable dynamical systems as well as continuous skew product flows and nonautonomous dynamical systems; and coalgebras in categories having all finite products. We introduce a straightforward unifying definition of abstract dynamical system on finite product categories. Furthermore, we prove that such systems are in a unique correspondence with monadic algebras whose signature functor takes products with the time space. We substantiate that the categories of topological spaces, metrisable and uniformisable spaces have exponential objects w.r.t. locally compact Hausdorff, σ-compact or arbitrary time spaces as exponents, respectively. Exploiting the adjunction between taking products and exponential objects, we demonstrate a one-to-one correspondence between monadic algebras (given by dynamical systems) for the left-adjoint functor and comonadic coalgebras for the other. This, finally, provides a new, alternative perspective on dynamical systems.

Objective: Some adolescents and young adults who do not fulfill criteria for DSM-IV alcohol abuse (AA) report symptoms of DSM-IV alcohol dependence (AD) below the diagnostic threshold (diagnostic orphans, DOs; 1 or 2 symptoms). Contemporarily, little is known on the long-term stability, risk of progression to AD, impairment, and drinking patterns possibly associated with this status in the first decades of life. Aim: (1) To identify prevalence rates of the DO status from adolescence to early adulthood. To investigate (2) stability and variability of the DO status over time and (3) associations between DO status, drinking patterns and impairment in comparison to subjects with AA, with AD, or without any symptoms. Method: N = 2039 community subjects (aged 14–24 years at baseline) were assessed at baseline and at about four and ten years after baseline. DSM-IV AUD diagnoses were obtained with the DIA-X/M-CIDI. Results: About 11–12% of the sample was classified as DOs at all waves. Over a period of ten years, 18% of DOs were stable in their diagnosis and additional 10% progressed to AD. DOs were comparable to subjects with AA in drinking patterns, impairment and stability of diagnostic status. DOs progressed to AD significantly more often than AA. AD was associated with highest levels in all outcomes of interest. Conclusions: The DO status in adolescence and early adulthood is associated with considerable stability, risk of progression and problematic alcohol intake. In consequence, it can be meaningful for the timely identification of early stages of clinically relevant alcohol problems. For subjects with DO status early specific interventions are required.

In this article we establish a bridge between dynamical systems, including topological and measurable dynamical systems as well as continuous skew product flows and nonautonomous dynamical systems; and coalgebras in categories having all finite products. We introduce a straightforward unifying definition of abstract dynamical system on finite product categories. Furthermore, we prove that such systems are in a unique correspondence with monadic algebras whose signature functor takes products with the time space. We substantiate that the categories of topological spaces, metrisable and uniformisable spaces have exponential objects w.r.t. locally compact Hausdorff, σ-compact or arbitrary time spaces as exponents, respectively. Exploiting the adjunction between taking products and exponential objects, we demonstrate a one-to-one correspondence between monadic algebras (given by dynamical systems) for the left-adjoint functor and comonadic coalgebras for the other. This, finally, provides a new, alternative perspective on dynamical systems.:1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Preliminaries and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Preliminaries related to topology and measure theory . . . . . . . . 4 2.2 Basic notions from category theory . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Classical dynamical systems theory . . . . . . . . . . . . . . . . . . . . . . 23 3 Dynamical Systems in Abstract Categories . . . . . . . . . . . . . . . . . . 30 3.1 Monoids and monoid actions in abstract categories . . . . . . . . . . 31 3.2 Abstract dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Nonautonomous dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4 Dynamical Systems as Algebras and Coalgebras . . . . . . . . . . . . . .38 4.1 From monoids to monads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 From abstract dynamical systems to monadic algebras . . . . . . . 48 4.3 Connections to coalgebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.4 Exponential objects in Top for locally compact Hausdorff spaces . . 52 4.5 (Co)Monadic (co)algebras and adjoint functors . . . . . . . . . . . . . .56

Der Begriff des ›Prototypen‹ ist der deutschsprachigen Musiktheorie nicht fremd, ohne dass jedoch seine Implikationen umfassend rezipiert worden wären. Für die Entwicklung der cognitive sciences hat die Prototypentheorie seit den 1970er Jahren eine wichtige Rolle gespielt, indem sie Prozesse der Kategorisierung untersuchte und diese ins Zentrum der Kognition stellte: »We have categories for everything we can think about. To change the concept of category itself is to change our understanding of the world.« (Lakoff) Ausgehend von einer kurzen Einführung in das Prinzip einer Kategorienbildung mit unscharfen Grenzen, nichtäquivalenten Exemplaren und flexibler Gewichtung von Merkmalen, skizziert der Beitrag das Potenzial der Prototypentheorie für die Klärung bzw. Weiterentwicklung musiktheoretischer Begriffe und schlägt Kriterien zur Beurteilung ihrer Nützlichkeit vor. / The term ›prototype‹ is not unknown in German music theory. Its implications, however, haven’t been thoroughly adopted yet. Prototype theory has played an important part in the development of cognitive sciences since the 1970s by enabling researchers to examine processes of categorization and place them in the center of cognition: »We have categories for everything we can think about. To change the concept of category itself is to change our understanding of the world.« (Lakoff) The article begins with a brief introduction into the concept of categories with vague boundaries, non-equivalent samples and adjustable emphasis of characteristics. It outlines the potential of prototype theory to clarify or further develop music theory terms. Finally, there are suggestions for criteria to evaluate their usefulness.

No description available.

Pairs in involution are a Hopf algebraic structure with applications to category theory, cyclic homology and knot theory. In the present dissertation we will answer the question whether every finite-dimensional Hopf algebra admits such pairs, construct and investigate their categorical analogues, and develop, based on our previous findings, the theory of pairs in involutions for Hopf monads.

Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how tomultiply two ε-hermitian forms to obtain a quadratic form over the base field. This allows to define a commutative graded ring structure by taking together bilinear forms and ε-hermitian forms, which we call the mixedWitt ring of an algebra with involution. We also describe a less powerful version of this construction for unitary involutions, which still defines a ring, but with a grading over Z instead of the Klein group. We first describe a general framework for defining graded rings out of monoidal functors from monoidal categories with strong symmetry properties to categories of modules. We then give a description of such a strongly symmetric category Brₕ(K, ι) which encodes the usual hermitian Morita theory of algebras with involutions over a field K. We can therefore apply the general framework to Brₕ(K, ι) and theWitt group functors to define our mixed Witt rings, and derive their basic properties, including explicit formulas for products of diagonal forms in terms of involution trace forms, explicit computations for the case of quaternion algebras, and reciprocity formulas relative to scalar extensions. We intend to describe in future articles further properties of those rings, such as a λ-ring structure, and relations with theMilnor conjecture and the theory of signatures of hermitian forms.

No description available.

No description available.