Categorical orthodoxy has it that collections of ordinary mathematical structures such as groups, rings, or spaces, form categories (such as the category of groups); collections of 1-dimensional categorical structures, such as categories, monoidal categories, or categories with finite limits, form 2-categories; and collections of 2-dimensional categorical structures, such as 2-categories or bicategories, form 3-categories. We describe a useful way in which to regard bicategories as objects of a 2-category. This is a bit surprising both for technical and for conceptual reasons. The 2-cells of this 2-category are the crucial new ingredient; they are the icons of the title. These can be thought of as ``the oplax natural transformations whose components are identities'', but we shall also give a more elementary description. We describe some properties of these icons, and give applications to monoidal categories, to 2-nerves of bicategories, to 2-dimensional Lawvere theories, and to bundles of bicategories.

We have added a simplified neuromorphic model of Spike Time Dependent Plasticity (STDP) to the Synapto-dendritic Kernel Adapting Neuron (SKAN). The resulting neuron model is the first to show synaptic encoding of afferent signal to noise ratio in addition to the unsupervised learning of spatio temporal spike patterns. The neuron model is particularly suitable for implementation in digital neuromorphic hardware as it does not use any complex mathematical operations and uses a novel approach to achieve synaptic homeostasis. The neurons noise compensation properties are characterized and tested on noise corrupted zeros digits of the MNIST handwritten dataset. Results show the simultaneously learning common patterns in its input data while dynamically weighing individual afferent channels based on their signal to noise ratio. Despite its simplicity the interesting behaviors of the neuron model and the resulting computational power may offer insights into biological systems.

The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of normal and disjunctive programs under the general stable model semantics. A translation from disjunctive programs to normal programs is proposed for infinite structures. Over finite structures, some disjunctive programs are proved to be intranslatable to normal programs if the arities of auxiliary predicates and functions are bounded in a certain way. The equivalence of the expressiveness of normal programs and disjunctive programs over arbitrary structures is also shown to coincide with that over finite structures, and coincide with whether NP is closed under complement. Moreover, to capture the exact expressiveness, some intertranslatability results between logic program classes and fragments of second-order logic are obtained.

We present the results of a systematic search for point-like and moderately extended soft (0.1-2.4 keV) X-ray sources in a raster of nine pointings covering a field of 8.95 deg^2 and performed with the ROSAT PSPC between October 1991 and October 1993 in the direction of the Small Magellanic Cloud. We detect 248 objects which we include in the first version of our SMC catalogue of soft X-ray sources. We set up seven source classes defined by selections in the count rate, hardness ratio and source extent. We find five high luminosity super-soft sources (1E 0035.4-7230, 1E 0056.8-7146, RX J0048.4-7332, RX J0058.6-7146 and RX J0103-7254), one low-luminosity super-soft source RX J0059.6-7138 correlating with the planetary nebula L357, 51 candidate hard X-ray binaries including eight bright hard X-ray binary candidates, 19 supernova remnants, 19 candidate foreground stars and 53 candidate background active galactic nuclei (and quasars). We give a likely classification for ~60% of the catalogued sources. The total count rate of the detected point-like and moderately extended sources in our catalogue is 6.9+/-0.3 s^-1, comparable to the background subtracted total rate from the integrated field of ~6.1+/-0.1 s^-1.

In this paper, we study online double auctions, where multiple sellers and multiple buyers arrive and depart dynamically to exchange one commodity. We show that there is no deterministic online double auction that is truthful and competitive for maximising social welfare in an adversarial model. However, given the prior information that sellers are patient and the demand is not more than the supply, a deterministic and truthful greedy mechanism is actually 2-competitive, i.e. it guarantees that the social welfare of its allocation is at least half of the optimal one achievable offline. Moreover, if the number of incoming buyers is predictable, we demonstrate that an online double auction can be reduced to an online one-sided auction, and the truthfulness and competitiveness of the reduced online double auction follow that of the online one-sided auction. Notably, by using the reduction, we find a truthful mechanism that is almost 1-competitive, when buyers arrive randomly. Finally, we argue that these mechanisms also have a promising applicability in more general settings without assuming that sellers are patient, by decomposing a market into multiple sub-markets.

Models of the very early universe, including inflationary models, are argued to produce varying universe domains with different values of fundamental constants and cosmic parameters. Using the cosmological hydrodynamical simulation code from the eagle collaboration, we investigate the effect of the cosmological constant on the formation of galaxies and stars. We simulate universes with values of the cosmological constant ranging from Lambda = 0 to Lambda_0 = 300, where Lambda_0 is the value of the cosmological constant in our Universe. Because the global star formation rate in our Universe peaks at t = 3.5 Gyr, before the onset of accelerating expansion, increases in Lambda of even an order of magnitude have only a small effect on the star formation history and efficiency of the universe. We use our simulations to predict the observed value of the cosmological constant, given a measure of the multiverse. Whether the cosmological constant is successfully predicted depends crucially on the measure. The impact of the cosmological constant on the formation of structure in the universe does not seem to be a sharp enough function of Lambda to explain its observed value alone.

Representing defeasibility is an important issue in common sense reasoning. In reasoning about action and change, this issue becomes more difficult because domain and action related defeasible information may conflict with general inertia rules. Furthermore, different types of defeasible information may also interfere with each other during the reasoning. In this paper, we develop a prioritized logic programming approach to handle defeasibilities in reasoning about action. In particular, we propose three action languages {\cal AT}^{0}, {\cal AT}^{1} and {\cal AT}^{2} which handle three types of defeasibilities in action domains named defeasible constraints, defeasible observations and actions with defeasible and abnormal effects respectively. Each language with a higher superscript can be viewed as an extension of the language with a lower superscript. These action languages inherit the simple syntax of {\cal A} language but their semantics is developed in terms of transition systems where transition functions are defined based on prioritized logic programs. By illustrating various examples, we show that our approach eventually provides a powerful mechanism to handle various defeasibilities in temporal prediction and postdiction. We also investigate semantic properties of these three action languages and characterize classes of action domains that present more desirable solutions in reasoning about action within the underlying action languages.

Data Release 5 (DR5) of the Radial Velocity Experiment (RAVE) is the fifth data release from a magnitude-limited (9< I < 12) survey of stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra ($R\sim7500$) covering the Ca-triplet region (8410-8795\AA) span the complete time frame from the start of RAVE observations in 2003 to their completion in 2013. Radial velocities from 520,781 spectra of 457,588 unique stars are presented, of which 255,922 stellar observations have parallaxes and proper motions from the Tycho-Gaia astrometric solution (TGAS) in Gaia DR1. For our main DR5 catalog, stellar parameters (effective temperature, surface gravity, and overall metallicity) are computed using the RAVE DR4 stellar pipeline, but calibrated using recent K2 Campaign 1 seismic gravities and Gaia benchmark stars, as well as results obtained from high-resolution studies. Also included are temperatures from the Infrared Flux Method, and we provide a catalogue of red giant stars in the dereddened color $(J-Ks)_0$ interval (0.50,0.85) for which the gravities were calibrated based only on seismology. Further data products for sub-samples of the RAVE stars include individual abundances for Mg, Al, Si, Ca, Ti, Fe, and Ni, and distances found using isochrones. Each RAVE spectrum is complemented by an error spectrum, which has been used to determine uncertainties on the parameters. The data can be accessed via the RAVE Web site or the Vizier database.

The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then solve for a regression or classification output by means of a mathematical pseudoinverse operation. In the field of neuromorphic engineering, these methods are increasingly popular for synthesizing biologically plausible neural networks, but the "learning method" - computation of the pseudoinverse by singular value decomposition - is problematic both for biological plausibility and because it is not an online or an adaptive method. We present an online or incremental method of computing the pseudoinverse, which we argue is biologically plausible as a learning method, and which can be made adaptable for non-stationary data streams. The method is significantly more memory-efficient than the conventional computation of pseudoinverses by singular value decomposition.

This dissertation is based on a project co-founded by the Health Market Quality Program (now Rozetta Institute) and the Australian Institute of Health and Welfare. The overall objective of this work is to provide a framework and a tool for classification and clustering of homogeneous geographic areas based on aggregated population data. Thus, to enable the presentation and reporting of comparable information of individual units with peers, I develop the Homogeneity and Location indices to measure respectively the dispersion and central tendency of a categorical ordinal distribution. The advantages of such indices include statistical efficiency and a simple presentation of results. Our approach is founded on the general theory of probability distributions, and our aim is to provide a natural benchmark for a homogeneity measure in terms of what is a "high" and "low" concentration of a probability distribution. Currently, there is no accepted benchmark that could be used to assess the homogeneity of a categorical ordinal variable. In this work, the proposed statistical indices are used to assess the socioeconomic homogeneity of the commonly used SA3 Australia census geography and analyse the variation of GP attenders in the metropolitan area of Sydney. The approach can be used to classify any geographic area and explore variation across any specified geographical boundaries. The SA3 dataset and scripts (R/Python) to develop these indices have been made available on my GitHub account: this https URL

Let $\mathcal M_{mn}=\mathcal M_{mn}(\mathbb F)$ denote the set of all $m\times n$ matrices over a field $\mathbb F$, and fix some $n\times m$ matrix $A\in\mathcal M_{nm}$. An associative operation $\star$ may be defined on $\mathcal M_{mn}$ by $X\star Y=XAY$ for all $X,Y\in\mathcal M_{mn}$, and the resulting \emph{sandwich semigroup} is denoted $\mathcal M_{mn}^A=\mathcal M_{mn}^A(\mathbb F)$. These semigroups are closely related to Munn rings, which are fundamental tools in the representation theory of finite semigroups. In this article, we study $\mathcal M_{mn}^A$ as well as its subsemigroups $\operatorname{Reg}(\mathcal M_{mn}^A)$ and $\mathcal E_{mn}^A$ (consisting of all regular elements and products of idempotents, respectively), as well as the ideals of $\operatorname{Reg}(\mathcal M_{mn}^A)$. Among other results, we: characterise the regular elements, determine Green's relations and preorders, calculate the minimal number of matrices (or idempotent matrices, if applicable) required to generate each semigroup we consider, and classify the isomorphisms between finite sandwich semigroups $\mathcal M_{mn}^A(\mathbb F_1)$and$\mathcal M_{kl}^B(\mathbb F_2)$. Along the way, we develop a general theory of sandwich semigroups in a suitably defined class of \emph{partial semigroups} related to Ehresmann-style "arrows only" categories, we hope this framework will be useful in studies of sandwich semigroups in other categories. We note that all our results have applications to the \emph{variants} $\mathcal M_n^A$of the full linear monoid$\mathcal M_n$(in the case$m=n$), and to certain semigroups of linear transformations of restricted range or kernel (in the case that $\operatorname{rank}(A)$ is equal to one of $m,n$).

Let $\mathcal P_X$ and $\mathcal S_X$ be the partition monoid and symmetric group on an infinite set $X$. We show that $\mathcal P_X$ may be generated by $\mathcal S_X$ together with two (but no fewer) additional partitions, and we classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal S_X\cup\{\alpha,\beta\}$. We also show that $\mathcal P_X$may be generated by the set$\mathcal E_X$ of all idempotent partitions together with two (but no fewer) additional partitions. In fact, $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$ if and only if it is generated by $\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}$. We also classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$. Among other results, we show that any countable subset of $\mathcal P_X$ is contained in a $4$-generated subsemigroup of $\mathcal P_X$, and that the length function on $\mathcal P_X$ is bounded with respect to any generating set.

Humans and other animals behave as if we perform fast Bayesian inference underlying decisions and movement control given uncertain sense data. Here we show that a biophysically realistic model of the subthreshold membrane potential of a single neuron can exactly compute the numerator in Bayes rule for inferring the Poisson parameter of a sensory spike train. A simple network of spiking neurons can construct and represent the Bayesian posterior density of a parameter of an external cause that affects the Poisson parameter, accurately and in real time.

Most of the classical approaches to straight line detection only deal with a binary edge image and need to use 2D interpolation operation. This paper proposes a new transform method figuratively named as funnel transform which can efficiently and rapidly detect straight lines. The funnel transform consists of three 1D Fourier transforms and one nonlinear variable-metric transform (NVMT). It only needs to exploit 1D interpolation operation for achieving its NVMT, and can directly handle grayscale images by using its high-pass filter property, which significantly improves the performance of the closely-related approaches. Based on the slope-intercept line equation, the funnel transform can more uniformly turn the straight lines formed by ridge-typical and step-typical edges into the local maximum points (peaks). The parameters of each line can be uniquely extracted from its corresponding peak coordinates. Additionally, each peak can be theoretically specified by a 2D delta function, which makes the peaks and lines more easily identified and detected, respectively. Theoretical analysis and experimental results demonstrate that the funnel transform has advantages including smaller computational complexity, lower hardware cost, higher detection probability, greater location precision, better parallelization properties, stronger anti-occlusion and noise robustness.

The dust emissivity spectral index, $\beta$, is a critical parameter for deriving the mass and temperature of star-forming structures, and consequently their gravitational stability. The $\beta$ value is dependent on various dust grain properties, such as size, porosity, and surface composition, and is expected to vary as dust grains evolve. Here we present $\beta$, dust temperature, and optical depth maps of the star-forming clumps in the Perseus Molecular Cloud determined from fitting SEDs to combined Herschel and JCMT observations in the 160 $\mu$m, 250 $\mu$m, 350 $\mu$m, 500 $\mu$m, and 850 $\mu$m bands. Most of the derived $\beta$, and dust temperature values fall within the ranges of 1.0 - 2.7 and 8 - 20 K, respectively. In Perseus, we find the $\beta$ distribution differs significantly from clump to clump, indicative of grain growth. Furthermore, we also see significant, localized $\beta$ variations within individual clumps and find low $\beta$ regions correlate with local temperature peaks, hinting at the possible origins of low $\beta$ grains. Throughout Perseus, we also see indications of heating from B stars and embedded protostars, as well evidence of outflows shaping the local landscape.

The development of cooperative relations within and between firms plays an important role in the successful implementation of business strategy. How to produce such relations is less well understood. We build on work in relational contract theory and the evolution of cooperation to examine the conditions under which group based incentives outperform individual based incentives and how they produce more cooperative behavior. Group interactions are modeled as iterated games in which individuals learn optimal strategies under individual and group based reward mechanisms. The space of possible games is examined and it is found that, when individual and group interests are not aligned, group evaluation and reward systems lead to higher group performance and, counter-intuitively, higher individual performance. Such groups include individuals who, quite differently to free-riders, sacrifice their own performance for the good of the group. We discuss the implications of these results for the design of incentive systems.

Mediation is an important method in dispute resolution. We implement a case based reasoning approach to mediation integrating analogical and commonsense reasoning components that allow an artificial mediation agent to satisfy requirements expected from a human mediator, in particular: utilizing experience with cases in different domains; and structurally transforming the set of issues for a better solution. We utilize a case structure based on ontologies reflecting the perceptions of the parties in dispute. The analogical reasoning component, employing the Structure Mapping Theory from psychology, provides a flexibility to respond innovatively in unusual circumstances, in contrast with conventional approaches confined into specialized problem domains. We aim to build a mediation case base incorporating real world instances ranging from interpersonal or intergroup disputes to international conflicts.

It is thought that neutron stars in low-mass binary systems can accrete matter and angular momentum from the companion star and be spun-up to millisecond rotational periods. During the accretion stage, the system is called a low-mass X-ray binary, and bright X-ray emission is observed. When the rate of mass transfer decreases in the later evolutionary stages, these binaries host a radio millisecond pulsar whose emission is powered by the neutron star's rotating magnetic field. This evolutionary model is supported by the detection of millisecond X-ray pulsations from several accreting neutron stars and also by the evidence for a past accretion disc in a rotation-powered millisecond pulsar. It has been proposed that a rotation-powered pulsar may temporarily switch on during periods of low mass inflow in some such systems. Only indirect evidence for this transition has hitherto been observed. Here we report observations of accretion-powered, millisecond X-ray pulsations from a neutron star previously seen as a rotation-powered radio pulsar. Within a few days after a month-long X-ray outburst, radio pulses were again detected. This not only shows the evolutionary link between accretion and rotation-powered millisecond pulsars, but also that some systems can swing between the two states on very short timescales.

We use Vessiot theory and exterior calculus to solve partial differential equations(PDEs) of the type uyy = F(x, y,u,ux,uy,uxx,uxy) and associated evolution equations. These equations are represented by the Vessiot distribution of vector fields. We develop and apply an algorithm to find the largest integrable sub-distributions and hence solutions of the PDEs. We then apply the integrating factor technique [19] to integrate this integrable Vessiot sub-distribution. The method is successfully applied to a large class of linear and non-linear PDEs.

We present ten new radio continuum (RC) detections at catalogued planetary nebula (PN) positions in the Small Magellanic Cloud (SMC): SMPS6, LIN 41, LIN 142, SMP S13, SMP S14, SMP S16, J18, SMP S18, SMP S19 and SMP S22. Additionally, six SMC radio PNe previously detected, LIN 45, SMP S11, SMPS17, LIN321, LIN339 and SMPS24 are also investigated (re-observed) here making up a population of 16 radio detections of catalogued PNe in the SMC. These 16 radio detections represent ~15 % of the total catalogued PN population in the SMC. We show that six of these objects have characteristics that suggest that they are PN mimics: LIN 41, LIN 45, SMP S11, LIN 142, LIN 321 and LIN 339. We also present our results for the surface brightness - PN radius relation ({\Sigma}-D) of the SMC radio PN population. These are consistent with previous SMC and LMC PN measurements of the ({\Sigma}-D) relation.