The Farm Apprenticeship Scheme in Australia: How Different Groups Look at it

ABSTRAC

Matching Dynamics with Constraints

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.Comment: Conference Version in WINE 201

High Probability Analysis of the Condition Number of Sparse Polynomial Systems

Let F:=(f_1,...,f_n) be a random polynomial system with fixed n-tuple of supports. Our main result is an upper bound on the probability that the condition number of f in a region U is larger than 1/epsilon. The bound depends on an integral of a differential form on a toric manifold and admits a simple explicit upper bound when the Newton polytopes (and underlying covariances) are all identical. We also consider polynomials with real coefficients and give bounds for the expected number of real roots and (restricted) condition number. Using a Kahler geometric framework throughout, we also express the expected number of roots of f inside a region U as the integral over U of a certain {\bf mixed volume} form, thus recovering the classical mixed volume when U = (C^*)^n.Comment: 29 pages, no figures. Extensive revision and streamlining of math.NA/0012104. In particular, new theorem with explicit high probability estimate of the condition number of a random sparse polynomial system (Theorem 1) has been adde

Vestibular, auditory, and somatic input to the posterior thalamus of the cat

The responses of 157 neural units in the magnocellular (mc) and parvocellular (pc) components of the medial geniculate nucleus (MG) and other nuclei of the posterior (PO) thalamic group were recorded and analyzed. Units were tested for a response to electrical stimulation of the vestibular nerve, natural auditory and electrical cochlear nerve stimulation, and natural stimulation of joint, muscle, and cutaneous receptors of the limbs, trunk, and neck (somatic stimulation). Only 45% of the units responded to these stimuli. Twenty-four percent of the responsive units were multimodal, responding to more than one stimulus. All multimodal units were activated by auditory stimuli. More units responding to vestibular stimulation were found in mcMG than in pcMG or other components of the PO group. Potentials evoked by vestibular nerve stimulation were recorded in all 3 regions with latencies of 5–25 msec. No evidence was found for a thalamic relay from vestibular nerve to cortex in the area investigated, since the recorded latency for activity from vestibular nerve stimulation was longer than the latency of responses recorded in the cortex. This region of the thalamus appears to be important for reception of auditory information and integration with vestibular and somatic modalities.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46549/1/221_2004_Article_BF00238337.pd

GEMINI near-infrared spectroscopic observations of young massive stars embedded in molecular clouds

K-band spectra of young stellar candidates in four southern hemisphere clusters have been obtained with the near-infrared spectrograph GNIRS in Gemini South. The clusters are associated with IRAS sources that have colours characteristic of ultracompact HII regions. Spectral types were obtained by comparison of the observed spectra with those of a NIR library; the results include the spectral classification of nine massive stars and seven objects confirmed as background late-type stars. Two of the studied sources have K-band spectra compatible with those characteristic of very hot stars, as inferred from the presence of Civ, Niii, and Nv emission lines at 2.078 micron, 2.116 micron, and 2.100 micron respectively. One of them, I16177 IRS1, has a K-band spectrum similar to that of Cyg OB2 7, an O3If* supergiant star. The nebular K-band spectrum of the associated UC Hii region shows the s-process [Kriii] and [Seiv] high excitation emission lines, previously identified only in planetary nebula. One young stellar object (YSO) was found in each cluster, associated with either the main IRAS source or a nearby resolved MSX component, confirming the results obtained from previous NIR photometric surveys. The distances to the stars were derived from their spectral types and previously determined JHK magnitudes; they agree well with the values obtained from the kinematic method, except in the case of IRAS15408-5356, for which the spectroscopic distance is about a factor two smaller than the kinematic value.Comment: This is the version that will be published by the Montly Notices of the Royal Astronomical Societ

Is the dynamics of open quantum systems always linear?

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.Comment: 19 pages, 3 figures, minor changes to improve readability, discussion on Mori's linear regime and references adde

Radiation Damping of a BPS Monopole; an Implication to S-duality

The radiation reaction of a BPS monopole in the presence of incident electromagnetic waves as well as massless Higgs waves is analyzed classically. The reactive forces are compared to those of $W$ boson that is interpreted as a dual partner of the BPS monopole. It is shown that the damping of acceleration is dual to each other, while in the case of finite size effects the duality is broken explicitly. Their implications on the duality are discussed.Comment: 20 pages, uses revtex, changes in reference

The spiral structure of the Galaxy revealed by CS sources and evidence for the 4:1 resonance

We present a map of the spiral structure of the Galaxy, as traced by molecular CS emission associated with IRAS sources which are believed to be compact HII regions. The CS line velocities are used to determine the kinematic distances of the sources, in order to investigate their distribution in the galactic plane. This allows us to use 870 objects to trace the arms, a number larger than that of previous studies based on classical HII regions. The distance ambiguity of the kinematic distances, when it exists, is solved by different procedures, including the latitude distribution and an analysis of the longitude-velocity diagram. The well defined spiral arms are seen to be confined inside the co-rotation radius, as is often the case in spiral galaxies. We identify a square-shaped sub-structure in the CS map with that predicted by stellar orbits at the 4:1 resonance (4 epicycle oscillations in one turn around the galactic center). The sub-structure is found at the expected radius, based on the known pattern rotation speed and epicycle frequency curve. An inner arm presents an end with strong inward curvature and intense star formation that we tentatively associate with the region where this arm surrounds the extremity of the bar, as seen in many barred galaxies. Finally, a new arm with concave curvature is found in the Sagitta to Cepheus region of the sky