Complete Positivity for Mixed Unitary Categories

In this article we generalize the \CP^\infty-construction of dagger monoidal categories to mixed unitary categories. Mixed unitary categories provide a setting, which generalizes (compact) dagger monoidal categories and in which one may study quantum processes of arbitrary (infinite) dimensions. We show that the existing results for the \CP^\infty-construction hold in this more general setting. In particular, we generalize the notion of environment structures to mixed unitary categories and show that the \CP^\infty-construction on mixed unitary categories is characterized by this generalized environment structure.Comment: Lots of figure

Faint star counts in the near-infrared

We discuss near-infrared star counts at the Galactic pole with a view to guiding the NGST and ground-based NIR cameras. Star counts from deep K-band images from the CFHT are presented, and compared with results from the 2MASS survey and some Galaxy models. With appropriate corrections for detector artifacts and galaxies, the data agree with the models down to K~18, but indicate a larger population of fainter red stars. There is also a significant population of compact galaxies that extend to the observational faint limit of K=20.5. Recent Galaxy models agree well down to K$\sim$19, but diverge at fainter magnitudes.Comment: 14 pages and 4 diagrams; to appear in PAS

On the creation of networks and knowledge

This paper examines the evolution of networks when innovation takes place as a result of agents bringing together their knowledge endowments. Agents freely form pairs creating a globally stable matching. paired agents combine their existing knowledge to create new knowledge. We study the properties of the dynamic network formed by these interactions, and the resultant knowledge dynamics. Each agent carries an amount of knowledge of a certain type, and the innovative output of a pair is a function of the partners'' endowments and types. We find evidence that the pattern of substitution between quantity and type of knowledge in the innovation function is vital in determining the growth of knowledge, the emergence of expertise and the stability of a number of network structures. Network structure itself exhibits a phase change when the relative importance of diversity compared to quantity increases beyond a threshold value.economics of technology ;

Networks as Emergent Structures from Bilateral Collaboration

In this paper we model the formation of innovation networks as they emerge from bilateral actions. The effectiveness of a bilateral collaboration is determined by cognitive, relational and structural embeddedness. Innovation results from the recombination of knowledge held by the partners to the collaboration, and the extent to which agents’ knowledge complement each others is an issue of cognitive embeddedness. Previous collaborations (relational embeddedness) increase the probability of a successful collaboration; as does information gained from common third parties (structural embeddedness). As a result of repeated alliance formation, a network emerges whose properties are studied, together with those of the process of knowledge creation. Two features are central to the innovation process: how agents pool their knowledge resources; and how agents derive information about potential partners. We focus on the interplay between these two dimensions, and find that they both matter. The networks that emerge are not random, but in certain parts of the parameter space have properties of small worlds. (JEL Classification: L14, Z13, O3 Keywords: Networks, Innovation, Network Formation, Knowledge)industrial organization ;

Spectral pitch distance and microtonal melodies

We present an experiment designed to test the effectiveness of spectral pitch distance at modeling the degree of “affinity” or “fit” of pairs of successively played tones or chords (spectral pitch distance is the cosine distance between salience-weighted, Gaussian-smoothed, pitch domain embeddings of spectral pitches—typically the first eight to ten partials of a tone). The results of a previously conducted experiment, which collected ratings of the perceived similarity and fit of root-position major and minor triads, suggest the model works well for pairs of triads in standard 12-tone equal temperament tunings. The new experiment has been designed to test the effectiveness of spectral pitch distance at modeling the affinity of tones in microtonal melodies where the partials of the tones can be variably tempered between being perfectly harmonic and perfectly matched to the underlying microtonal tuning. The use of microtonal tunings helps to disambiguate innate perceptual (psychoacoustical) responses from learned (cultural) responses. Participants are presented with a software synthesizer containing two unlabeled controls: one adjusts the precise tuning of the tones; the other adjusts the extent to which the spectrum is tempered to match the tuning (as set by the first control). A selection of microtonal melodies are played in different tunings, and the participants adjust one, or both, controls until they find a “sweet spot” at which the music sounds most “in-tune” and the notes best “fit” together. The results of these experiments will be presented and discussed

Metrics for pitch collections

Models of the perceived distance between pairs of pitch collections are a core component of broader models of the perception of tonality as a whole. Numerous different distance measures have been proposed, including voice-leading, psychoacoustic, and pitch and interval class distances; but, so far, there has been no attempt to bind these different measures into a single mathematical framework, nor to incorporate the uncertain or probabilistic nature of pitch perception (whereby tones with similar frequencies may, or may not, be heard as having the same pitch). To achieve these aims, we embed pitch collections in novel multi-way expectation arrays, and show how metrics between such arrays can model the perceived dissimilarity of the pitch collections they embed. By modeling the uncertainties of human pitch perception, expectation arrays indicate the expected number of tones, ordered pairs of tones, ordered triples of tones and so forth, that are heard as having any given pitch, dyad of pitches, triad of pitches, and so forth. The pitches can be either absolute or relative (in which case the arrays are invariant with respect to transposition). We provide a number of examples that show how the metrics accord well with musical intuition, and suggest some ways in which this work may be developed

Issues concerning centralized versus decentralized power deployment

The results of a study of proposed lunar base architectures to identify issues concerning centralized and decentralized power system deployment options are presented. The power system consists of the energy producing system (power plant), the power conditioning components used to convert the generated power into the form desired for transmission, the transmission lines that conduct this power from the power sources to the loads, and the primary power conditioning hardware located at the user end. Three power system architectures, centralized, hybrid, and decentralized, were evaluated during the course of this study. Candidate power sources were characterized with respect to mass and radiator area. Two electrical models were created for each architecture to identify the preferred method of power transmission, dc or ac. Each model allowed the transmission voltage level to be varied at assess the impact on power system mass. The ac power system models also permitted the transmission line configurations and placements to determine the best conductor construction and installation location. Key parameters used to evaluate each configuration were power source and power conditioning component efficiencies, masses, and radiator areas; transmission line masses and operating temperatures; and total system mass

Biases in Expansion Distances of Novae Arising from the Prolate Geometry of Nova Shells

(abridged) Expansion distances (or expansion parallaxes) for classical novae are based on comparing a measurement of the shell expansion velocity, multiplied by the time since outburst, with some measure of the angular size of the shell. We review and formalize this method in the case of prolate spheroidal shells. We present expressions for the maximum line-of-sight velocity from a complete, expanding shell and for its projected major and minor axes, in terms of the intrinsic axis ratio and the inclination of the polar axis to the line of sight. For six distinct definitions of ``angular size'', we tabulate the error in distance that is introduced under the assumption of spherical symmetry (i.e., without correcting for inclination and axis ratio). The errors can be significant and systematic, affecting studies of novae whether considered individually or statistically. Each of the six estimators overpredicts the distance when the polar axis is close to the line of sight, and most underpredict the distance when the polar axis is close to the plane of the sky. The straight mean of the projected semimajor and semiminor axes gives the least distance bias for an ensemble of randomly oriented prolate shells. The best individual expansion distances, however, result from a full spatio-kinematic modeling of the nova shell. We discuss several practical complications that affect expansion distance measurements of real nova shells. Nova shell expansion distances be based on velocity and angular size measurements made contemporaneously if possible, and the same ions and transitions should be used for the imaging and velocity measurements. We emphasize the need for complete and explicit reporting of measurement procedures and results, regardless of the specific method used.Comment: 21 pages, LaTeX, uses aasms4.sty, to be published in Publ. Astron. Soc. of the Pacific, May 200