A multipole-Taylor expansion for the potential of gravitational lens MG J0414+0534

We employ a multipole-Taylor expansion to investigate how tightly the gravitational potential of the quadruple-image lens MG J0414+0534 is constrained by recent VLBI observations. These observations revealed that each of the four images of the background radio source contains four distinct components, thereby providing more numerous and more precise constraints on the lens potential than were previously available. We expand the two-dimensional lens potential using multipoles for the angular coordinate and a modified Taylor series for the radial coordinate. After discussing the physical significance of each term, we compute models of MG J0414+0534 using only VLBI positions as constraints. The best-fit model has both interior and exterior quadrupole moments as well as exterior m=3 and m=4 multipole moments. The deflector centroid in the models matches the optical galaxy position, and the quadrupoles are aligned with the optical isophotes. The radial distribution of mass could not be well constrained. We discuss the implications of these models for the deflector mass distribution and for the predicted time delays between lensed components.Comment: 44 pages, 5 figures, 11 tables, accepted for publication in Ap

Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as $Sr_3 CuPt_{1-x} Ir_x O_6$. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of $Sr_3 CuPt_{1-x} Ir_x O_6$ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.Comment: 7 pages, 5 eps-figures included, typeset using JPSJ.sty, accepted for publication in J. Phys. Soc. Jpn. 68, Vol. 3. (1999

Listening and learning : the reciprocal relationship between worker and client

The relationship between worker and client has for the best part of 100 years been the mainstay of probation, and yet has recently been eroded by an increased emphasis on punishment, blame and managerialism. The views of offenders are in direct contradiction to these developments within the criminal justice system and this article argues that only by taking account of the views of those at the 'coal face' will criminologists, policy makers and practitioners be able to effect real change in crime rates. The article thus focuses on the views of a sample of previously persistent offenders in Scotland about offending, desistance and how the system can help them. It explores not only their need for friendship and support in youth but also the close association between relationships and the likelihood of offending. It also demonstrates the views of offenders themselves about the importance of the working relationship with supervising officers in helping them desist from crime. The article concludes that the most effective way of reducing offending is to re-engage with the message of the Probation Act of 100 years ago, namely, to 'advise, assist and befriend' offenders rather than to 'confront, challenge and change' offending behaviour

Robust Chauvenet Outlier Rejection

Sigma clipping is commonly used in astronomy for outlier rejection, but the number of standard deviations beyond which one should clip data from a sample ultimately depends on the size of the sample. Chauvenet rejection is one of the oldest, and simplest, ways to account for this, but, like sigma clipping, depends on the sample's mean and standard deviation, neither of which are robust quantities: Both are easily contaminated by the very outliers they are being used to reject. Many, more robust measures of central tendency, and of sample deviation, exist, but each has a tradeoff with precision. Here, we demonstrate that outlier rejection can be both very robust and very precise if decreasingly robust but increasingly precise techniques are applied in sequence. To this end, we present a variation on Chauvenet rejection that we call "robust" Chauvenet rejection (RCR), which uses three decreasingly robust/increasingly precise measures of central tendency, and four decreasingly robust/increasingly precise measures of sample deviation. We show this sequential approach to be very effective for a wide variety of contaminant types, even when a significant -- even dominant -- fraction of the sample is contaminated, and especially when the contaminants are strong. Furthermore, we have developed a bulk-rejection variant, to significantly decrease computing times, and RCR can be applied both to weighted data, and when fitting parameterized models to data. We present aperture photometry in a contaminated, crowded field as an example. RCR may be used by anyone at https://skynet.unc.edu/rcr, and source code is available there as well.Comment: 62 pages, 48 figures, 7 tables, accepted for publication in ApJ

Resummation of fermionic in-medium ladder diagrams to all orders

A system of fermions with a short-range interaction proportional to the scattering length $a$ is studied at finite density. At any order $a^n$, we evaluate the complete contributions to the energy per particle $\bar E(k_f)$ arising from combined (multiple) particle-particle and hole-hole rescatterings in the medium. This novel result is achieved by simply decomposing the particle-hole propagator into the vacuum propagator plus a medium-insertion and correcting for certain symmetry factors in the $(n-1)$-th power of the in-medium loop. Known results for the low-density expansion up to and including order $a^4$ are accurately reproduced. The emerging series in $a k_f$ can be summed to all orders in the form of a double-integral over an arctangent function. In that representation the unitary limit $a\to \infty$ can be taken and one obtains the value $\xi= 0.5067$ for the universal Bertsch parameter. We discuss also applications to the equation of state of neutron matter at low densities and mention further extensions of the resummation method.Comment: 12 pages, 7 figures, submitted to Nuclear Physics

Efficiency of symmetric targeting for finite-T DMRG

Two targeting schemes have been known for the density matrix renormalization group (DMRG) applied to non-Hermitian problems; one uses an asymmetric density matrix and the other uses symmetric density matrix. We compare the numerical efficiency of these two targeting schemes when they are used for the finite temperature DMRG.Comment: 4 pages, 3 Postscript figures, REVTe

On FO2 quantifier alternation over words

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels

A 23 GHz Survey of GRB Error Boxes

The Haystack 37-meter telescope was used in a pilot project in May 1995 to observe GRB error boxes at 23~GHz. Seven BATSE error boxes and two IPN arcs were scanned by driving the beam of the telescope rapidly across their area. For the BATSE error boxes, the radio observations took place two to eighteen days after the BATSE detection, and several boxes were observed more than once. Total power data were recorded continuously as the telescope was driven at a rate of 0.2~degrees/second, yielding Nyquist sampling of the beam with an integration time of 50~milliseconds, corresponding to a theoretical rms sensitivity of 0.5~Jy. Under conditions of good weather, this sensitivity was achieved. In a preliminary analysis of the data we detect only two sources, 3C273 and 0552+398, both catalogued sources that are known to be variable at 23~GHz. Neither had a flux density that was unusally high or low at the time of our observations.Comment: 5 pages, 1 postscript figure. To appear in Proceedings of the Third Huntsville Symposium on Gamma-Ray Bursts (eds. C. Kouveliotou, M. S. Briggs, and G. J. Fishman

Chiral Dynamics and Nuclear Matter

We calculate the equation of state of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The contributions to the energy per particle $\bar E(k_f)$ from one- and two-pion exchange diagrams are ordered in powers of the Fermi momentum $k_f$ (modulo functions of $k_f /m_\pi$). It is demonstrated that, already at order ${\cal O}(k_f^4)$, two-pion exchange produces realistic nuclear binding. The underlying saturation mechanism is surprisingly simple (in the chiral limit), namely the combination of an attractive $k_f^3$-term and a repulsive $k_f^4$-term. The empirical saturation point and the nuclear compressibility $K\simeq 250$MeV are well reproduced at order ${\cal O}(k_f^5)$ with a momentum cut-off of $\Lambda \simeq 0.65$ GeV which parametrizes short-range dynamics. No further short-distance terms are required in our calculation of nuclear matter. In the same framework we calculate the density-dependent asymmetry energy and find $A_0\simeq 34$MeV at the saturation point, in good agreement with the empirical value. The pure neutron matter equation of state is also in fair qualitative agreement with sophisticated many-body calculations and a resummation result of effective field theory, but only for low neutron densities $\rho_n <0.25$fm$^{-3}$.Comment: 18 pages, 8 figure

Applying proximity sensors to monitor beef cattle social behaviour as an indicator of animal welfare

There are currently no approved monitoring programs in the beef industry that use paddock based behaviour as an indicator of animal welfare. Current animal welfare assessments are conducted at a single point in time, such as supplying food and water and treating illnesses as these needs arise. These aspects comply with the five freedoms that animals should have when addressing animal welfare, however, the assessments are infrequent. Of the five freedoms, the freedom to express normal behaviour can be a subjective measure, due to differences in the way individual animals express certain behaviours. There is a need for continual monitoring of welfare indicators in modern animal assessment methods to objectively measure behaviour and address public concerns about the welfare state of animals. The experiment commenced in June 2017 to assess changes in cattle social interaction patterns in response to social stress created by regrouping four groups of eight heifers. Previous research with cattle has provided evidence that social contact and spatial behaviour differ when novel individuals are introduced (Patison et al., 2010b), and re-grouped animals continue to experience stress until the social hierarchy is re-established after regrouping (Kondo and Hurnik, 1990). Proximity sensors that record the frequency and duration of close proximity contacts (<4 m) will be used to remotely collect animal association data, while blood cortisol concentrations will be used as an independent measure of stress. Responses to stress will be compared with a group of heifers where re-grouping does not occur. This paper outlines the background and methodology to explore the potential for proximity sensors as a continual welfare monitoring device, related to an animal’s freedom to express normal behaviour. Preliminary results of the project will be presented at The International Tri-Conference for Precision Agriculture held in New Zealand in October, 2017