Abstract:
Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with arbitrary (possibly uncountable) state spaces. We consider the sub-probability monad and the probability monad (Giry monad) on the category of measurable spaces and measurable functions. Our main contribution is that the existence of a final coalgebra in the Kleisli category of these monads is closely connected to the measure-theoretic extension theorem for sigma-finite pre-measures. In fact, we obtain a practical definition of the trace measure for both finite and infinite traces of PTS that subsumes a well-known result for discrete probabilistic transition systems. Finally we consider two example systems with uncountable state spaces and apply our theory to calculate their trace measures.

Abstract:
In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows us to introduce fine-scale correctors that are not subject to a cumbersome divergence-free constraint and which can hence easily be implemented. To analyze the method, we first revisit classical homogenization theory for time-harmonic Maxwell equations and derive a new homogenization result that makes use of the divergence-regularization in the two-scale homogenized equation. We then show that the HMM is equivalent to a discretization of this equation. In particular, writing both problems in a fully coupled two-scale formulation is the crucial starting point for a corresponding numerical analysis of the method. With this approach we are able to prove rigorous a priori error estimates in the $\mathbf{H}(\mbox{curl})$- and the $H^{-1}$-norm and we derive reliable and efficient localized residual-based a posteriori error estimates.

Abstract:
In this paper, we combine polynomial functions, Generalized Estimating
Equations, and bootstrap-based model selection to test for signatures of linear
or nonlinear relationships between body surface temperature and ambient
temperature in endotherms. Linearity or nonlinearity is associated with the
absence or presence of cutaneous vasodilation and vasoconstriction, respectively.
We obtained experimental data on body surface temperature variation from a
mammalian model organism as a function of ambient temperature using infrared
thermal imaging. The statistical framework of model estimation and selection
successfully detected linear and nonlinear relationships between body surface
temperature and ambient temperature for different body regions of the model
organism. These results demonstrate that our statistical approach is
instrumental to assess the complexity of thermoregulation in endotherms.

Abstract:
We study behavioral metrics in an abstract coalgebraic setting. Given a coalgebra alpha: X -> FX in Set, where the functor F specifies the branching type, we define a framework for deriving pseudometrics on X which measure the behavioral distance of states. A first crucial step is the lifting of the functor F on Set to a functor in the category PMet of pseudometric spaces. We present two different approaches which can be viewed as generalizations of the Kantorovich and Wasserstein pseudometrics for probability measures. We show that the pseudometrics provided by the two approaches coincide on several natural examples, but in general they differ. Then a final coalgebra for F in Set can be endowed with a behavioral distance resulting as the smallest solution of a fixed-point equation, yielding the final coalgebra in PMet. The same technique, applied to an arbitrary coalgebra alpha: X -> FX in Set, provides the behavioral distance on X. Under some constraints we can prove that two states are at distance 0 if and only if they are behaviorally equivalent.

Abstract:
We investigate the possibility of deriving metric trace semantics in a coalgebraic framework. First, we generalize a technique for systematically lifting functors from the category Set of sets to the category PMet of pseudometric spaces, showing under which conditions also natural transformations, monads and distributive laws can be lifted. By exploiting some recent work on an abstract determinization, these results enable the derivation of trace metrics starting from coalgebras in Set. More precisely, for a coalgebra on Set we determinize it, thus obtaining a coalgebra in the Eilenberg-Moore category of a monad. When the monad can be lifted to PMet, we can equip the final coalgebra with a behavioral distance. The trace distance between two states of the original coalgebra is the distance between their images in the determinized coalgebra through the unit of the monad. We show how our framework applies to nondeterministic automata and probabilistic automata.

Abstract:
We are looking for a mathematical model of monophonic sounds with independent time and phase dimensions. With such a model we can resynthesise a sound with arbitrarily modulated frequency and progress of the timbre. We propose such a model and show that it exactly fulfils some natural properties, like a kind of timeinvariance, robustness against non-harmonic frequencies, envelope preservation, and inclusion of plain resampling as a special case. The resulting algorithm is efficient and allows to process data in a streaming manner with phase and shape modulation at sample rate, what we demonstrate with an implementation in the functional language Haskell. It allows a wide range of applications, namely pitch shifting and time scaling, creative FM synthesis effects, compression of monophonic sounds, generating loops for sampled sounds, synthesise sounds similar to wavetable synthesis, or making ultrasound audible.

Abstract:
In official Norwegian government reports’ prison statistics, it is claimed that the prevalence of Dissocial Personality Disorder (DPD) or Antisocial Personality Disorder (APD) among inmates in preventive detention is approximately 50%. Furthermore, previous findings have described a practice in which forensic examiners use the DSM SCID axis II for APD to confirm an ICD 10 diagnosis of DPD. Clinical investigation supported by the use of SCID Axis II for quality assurance was performed on almost half the population of inmates (46.4%) in preventive detention at a high security prison. The inmates had all committed severe violent acts including murder. All the information obtained by applying the DSM IV-TR criteria was tested against the ICD-10 Research Criteria (ICD-10-RC) for Dissocial Personality Disorder (ICD-10, DPD). It was found that all inmates met the ICD-10-RC for (DPD) and the DSM-IV-TR definition for Adult Antisocial Behavior (AAB). On the other hand, none met the DSM-IV-TR criteria for (APD). The SCID Axis II failed to identify inmates with APD because the DSM-IV-TR C-criteria, referring to symptoms of childhood Conduct Disorder (CD), were not met. These findings raise important questions since the choice of diagnostic system may influence whether a person’s clinically described antisocial behaviour should be classified as a personality disorder or not. For the inmates, a diagnosis of APD or DPD may compromise their legal rights and affect decisions on prolongation of the preventive detention. Studies have shown that combining the DSM and the ICD diagnostic systems may have consequences for the reliability of the diagnosis.

Abstract:
We have coupled an upright HG mode into a fiber-optic waveguide and used the application of stress to generate a Laguerre-Gaussian laser mode. We have generalized previous results by McGloin et al. by using a polarized input beam, a true 3-mode fiber and by applying the stress on a stripped piece of the optical waveguide. These generalizations are necessary in order to perform quantum information experiments and obtain reliable information on the stress imposed on the optical fiber.

We consider the solution of matching problems with a
convex cost function via a network flow algorithm. We review the general
mapping between matching problems and flow problems on skew symmetric networks
and revisit severalresults on optimality of network flows. We use these results to
derive a balanced capacity scaling algorithm for matching problems with
a linear cost function. The latter is later generalized to a balanced capacity
scaling algorithm also for a convex cost function. We prove the correctness and
discuss the complexity of our solution.

We analyse the
proximity effect in hybrid nanoscale junctions involving superconducting leads.
We develop a general framework for the analysis of the proximity effect using
the same theoretical methods typically employed for the analysis of conductance
properties. We apply our method to a normal-superconductor tunnel contact and
compare our results to previous results.