Positivity of rational functions and their diagonals

The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szeg\H{o} as well as Askey and Gasper, who inspired more recent work. It is well known that the diagonal coefficients of rational functions are $D$-finite. This note is motivated by the observation that, for several of the rational functions whose positivity has received special attention, the diagonal terms in fact have arithmetic significance and arise from differential equations that have modular parametrization. In each of these cases, this allows us to conclude that the diagonal is positive. Further inspired by a result of Gillis, Reznick and Zeilberger, we investigate the relation between positivity of a rational function and the positivity of its diagonal.Comment: 16 page

On the nature of bias and defects in the software specification process

Implementation bias in a specification is an arbitrary constraint in the solution space. This paper describes the problem of bias. Additionally, this paper presents a model of the specification and design processes describing individual subprocesses in terms of precision/detail diagrams and a model of bias in multi-attribute software specifications. While studying how bias is introduced into a specification we realized that software defects and bias are dual problems of a single phenomenon. This was used to explain the large proportion of faults found during the coding phase at the Software Engineering Laboratory at NASA/GSFC

Anterograde Signalling by Nitric Oxide: Characterisation and In Vitro Reconstitution of an Identified Nitrergic Synapse

Nitric oxide (NO) is recognized as a signaling molecule in the CNS where it is a candidate retrograde neurotransmitter. Here we provide direct evidence that NO mediates slow excitatory anterograde transmission between the NO synthase (NOS)-expressing B2 neuron and an NO-responsive follower neuron named B7nor. Both are motoneurons located in the buccal ganglia of the snail Lymnaea stagnalis where they participate in feeding behavior. Transmission between B2 and B7nor is blocked by inhibiting NOS and is suppressed by extracellular scavenging of NO. Furthermore, focal application of NO to the cell body of the B7nor neuron causes a depolarization that mimics the effect of B2 activity. The slow interaction between the B2 and B7nor neurons can be re-established when the two neurons are cocultured, and it shows the same susceptibility to NOS inhibition and NO scavenging. In cell culture we have also examined spatial aspects of NO signaling. We show that before the formation of an anatomical connection, the presynaptic neuron can cause depolarizing potentials in the follower neuron at distances up to 50 micro(m). The strength of the interaction increases when the distance between the cells is reduced. Our results suggest that NO can function as both a synaptic and a nonsynaptic signaling molecul

A magnetized torus for modeling Sgr A* millimeter images and spectra

Context. The supermassive black hole, Sagittarius (Sgr) A*, in the centre of our Galaxy has the largest angular size in the sky among all astrophysical black holes. Its shadow, assuming no rotation, spans ~ 50 microarcsec. Resolving such dimensions has long been out of reach for astronomical instruments until a new generation of interferometers being operational during this decade. Of particular interest is the Event Horizon Telescope (EHT) with resolution ~ 20 microarcsec in the millimeter-wavelength range 0.87 mm - 1.3 mm. Aims. We investigate the ability of the fully general relativistic Komissarov (2006) analytical magnetized torus model to account for observable constraints at Sgr A* in the centimeter and millimeter domains. The impact of the magnetic field geometry on the observables is also studied. Methods. We calculate ray-traced centimeter- and millimeter-wavelength synchrotron spectra and images of a magnetized accretion torus surrounding the central black hole in Sgr A*. We assume stationarity, axial symmetry, constant specific angular momentum and polytropic equation of state. A hybrid population of thermal and non-thermal electrons is considered. Results. We show that the torus model is capable of reproducing spectral constraints in the millimeter domain, and in particular in the observable domain of the EHT. However, the torus model is not yet able to fit the centimeter spectrum. 1.3 mm images at high inclinations are in agreement with observable constraints. Conclusions. The ability of the torus model to account for observations of Sgr A* in the millimeter domain is interesting in the perspective of the future EHT. Such an analytical model allows very fast computations. It will thus be a suitable test bed for investigating large domains of physical parameters, as well as non-black-hole compact object candidates and alternative theories of gravity.Comment: Major changes wrt the June 2014 version. Accepted by A&

Associative memory stored by functional novel pathway rather than modifications of preexisting neuronal pathways

Associative conditioning involves changes in the processing pathways activated by sensory information to link the conditioned stimulus (CS) to the conditioned behavior. Thus, conditioning can recruit neuronal elements to form new pathways for the processing of the CS and/or can change the strength of existing pathways. Using a behavioral and systems level electrophysiological approach on a tractable invertebrate circuit generating feeding in the mollusk Lymnaea stagnalis, we identified three independent pathways for the processing of the CS amyl acetate used in appetitive conditioning. Two of these pathways, one suppressing and the other stimulating feeding, mediate responses to the CS in naive animals. The effects ofthese two pathways on feeding behavior are unaltered by conditioning. In contrast, the CS response ofa third stimulatory pathway is significantly enhanced after conditioning, becoming an importantcontributor to the overall CS response. This is unusual because, in most of the previous examples in which naive animals already respond to the CS, memory formation results from changes in the strength of pathways that mediate the existing response. Here, we show that, in the molluscan feeding system, both modified and unmodified pathways are activated in parallel by the CS after conditioning, and it is their integration that results in the conditioned respons

A comparison of foot-eye coordination of boys and girls 7, 9, and 11 years of age on a tracking task

The purpose of this study was to determine the foot-eye coordination of boys and girls at 7,9, and 11 years of age. [This is an excerpt from the abstract. For the complete abstract, please see the document.