Natural Topologies on Colombeau Algebras

We define natural topologies on the Colombeau algebras which are compatible with the algebraic structure. These topologies reduces do Scarpalezos sharp topologies when restricted. with this we take a positive step towards topological methods of solving P.D. Equations in Colombeau algebras. Applications will appear elsewhere.Comment: 20 page

Sex differences in the influence of social context, salient social stimulation and amphetamine on ultrasonic vocalizations in prairie voles

Prairie voles ( Microtus ochrogaster ) are a socially monogamous rodent species and their cooperative behaviors require extensive communication between conspecifics. Rodents use ultrasonic vocalizations (USVs) to communicate and because a prairie vole breeder pair must engage in extensive cooperation for successful reproduction, auditory communication may be critical for this species. Therefore, we sought to characterize USVs in adult male and female prairie voles, and to determine how these calls are influenced by social context, salient social stimuli and the psychostimulant drug of abuse amphetamine (AMPH). Here, we characterize prairie vole USVs by showing the range of frequencies of prairie vole USVs, the proportion of various call types, how these call types compare between males and females, and how they are influenced by social stimulation and AMPH. AMPH caused a robust increase in the number of USVs in both males and females and there was a dramatic sex difference in the complexity of call structures of AMPH‐induced USVs, with males emitting more elaborate calls. Moreover, we show that novel (i.e. salient) social cues evoked differential increases in USVs across sex, with males showing a much more robust increase in USV production, both with respect to the frequency and complexity of USV production. Exposure to an estrous female in particular caused an extraordinary increase in USVs in male subjects. These data suggest that USVs may be a useful measure of social motivation in this species, including how social behaviors can be impacted by drugs of abuse.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107527/1/inz212071.pd

Isomorphisms of algebras of Colombeau generalized functions

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generalized functions on X to the ring of Colombeau generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page

Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Distributional energy momentum tensor of the extended Kerr geometry

We generalize previous work on the energy-momentum tensor-distribution of the Kerr geometry by extending the manifold structure into the negative mass region. Since the extension of the flat part of the Kerr-Schild decomposition from one sheet to the double cover develops a singularity at the branch surface we have to take its non-smoothness into account. It is however possible to find a geometry within the generalized Kerr-Schild class that is in the Colombeau-sense associated to the maximally analytic Kerr-metric.Comment: 12 pages, latex2e, amslatex and epsf macro

Development of behavioral preferences for the optimal choice following unexpected reward omission is mediated by a reduction of D 2‐like receptor tone in the nucleus accumbens

To survive in a dynamic environment, animals must identify changes in resource availability and rapidly apply adaptive strategies to obtain resources that promote survival. We have utilised a behavioral paradigm to assess differences in foraging strategy when resource (reward) availability unexpectedly changes. When reward magnitude was reduced by 50% (receive one reward pellet instead of two), male and female rats developed a preference for the optimal choice by the second session. However, when an expected reward was omitted (receive no reward pellets instead of one), subjects displayed a robust preference for the optimal choice during the very first session. Previous research shows that, when an expected reward is omitted, dopamine neurons phasically decrease their firing rate, which is hypothesised to decrease dopamine release preferentially affecting D 2‐like receptors. As robust changes in behavioral preference were specific to reward omission, we tested this hypothesis and the functional role of D 1‐ and D 2‐like receptors in the nucleus accumbens in mediating the rapid development of a behavioral preference for the rewarded option during reward omission in male rats. Blockade of both receptor types had no effect on this behavior; however, holding D 2‐like, but not D 1‐like, receptor tone via infusion of dopamine receptor agonists prevented the development of the preference for the rewarded option during reward omission. These results demonstrate that avoiding an outcome that has been tagged with aversive motivational properties is facilitated through decreased dopamine transmission and subsequent functional disruption of D 2‐like, but not D 1‐like, receptor tone in the nucleus accumbens. This study investigates the role of dopamine receptors in the nucleus accumbens in altering behavior in response to the omission of an expected reward. Similarly to controls, multiple doses of a D 1‐like receptor agonist, D 1‐like receptor antagonist, and D 2‐like receptor antagonist do not prevent subjects from developing a robust behavioral preference for the rewarded lever and avoiding the omitted‐reward lever during the first session of reward omission. However, the D 2‐like agonist quinpirole dose‐dependently blocks a behavioral preference for the rewarded lever, suggesting that reductions in D 2‐like receptor tone are necessary for altering behavior away from an aversive option and toward the optimal choice.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99645/1/ejn12253.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/99645/2/ejn12253-sup-0001-Supplement.pd

An algebraic approach to manifold-valued generalized functions

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.Comment: 7 page

Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities

In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so called "`infinite quantities"' make sense unambiguously (but are not classical real numbers). The perturbation series does not make sense. A novelty appears when one starts to compute the transition probabilities. The transition probabilities have to be computed in a nonperturbative way which, at least in simplified mathematical examples (even those looking like nonrenormalizable series), gives real values between 0 and 1 capable to represent probabilities. However these calculations should be done numerically and we have only been able to compute simplified mathematical examples due to the fact these calculations appear very demanding in the physically significant situation with an infinite dimensional Fock space and the QFT operators