Branching on multi-aggregated variables

open5siopenGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, DomenicoGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, Domenic

The subdivision of large simplicial cones in Normaliz

Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two main computational goals are (i) finding a system of generators of the set of lattice points and (ii) counting elements degree-wise in a generating function, the Hilbert Series. In the homogeneous case, in which the polyhedron is a cone, the set of generators is the Hilbert basis of the intersection of the cone and the lattice, an affine monoid. We will present some improvements to the Normaliz algorithm by subdividing simplicial cones with huge volumes. In the first approach the subdivision points are found by integer programming techniques. For this purpose we interface to the integer programming solver SCIP to our software. In the second approach we try to find good subdivision points in an approximating overcone that is faster to compute.Comment: To appear in the proceedings of the ICMS 2016, published by Springer as Volume 9725 of Lecture Notes in Computer Science (LNCS

Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum

We use kinetic simulations of diffusive shock acceleration (DSA) to study the time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified shocks. Thermal leakage injection of low energy CRs and finite Alfv\'en wave propagation and dissipation are included. Bohm diffusion as well as the diffusion with the power-law momentum dependence are modeled. As long as the acceleration time scale to relativistic energies is much shorter than the dynamical evolution time scale of the shocks, the precursor and subshock transition approach the time-asymptotic state, which depends on the shock sonic and Alfv\'enic Mach numbers and the CR injection efficiency. For the diffusion models we employ, the shock precursor structure evolves in an approximately self-similar fashion, depending only on the similarity variable, x/(u_s t). During this self-similar stage, the CR distribution at the subshock maintains a characteristic form as it evolves: the sum of two power-laws with the slopes determined by the subshock and total compression ratios with an exponential cutoff at the highest accelerated momentum, p_{max}(t). Based on the results of the DSA simulations spanning a range of Mach numbers, we suggest functional forms for the shock structure parameters, from which the aforementioned form of CR spectrum can be constructed. These analytic forms may represent approximate solutions to the DSA problem for astrophysical shocks during the self-similar evolutionary stage as well as during the steady-state stage if p_{max} is fixed.Comment: 38 pages, 12 figures, ApJ accepte

The European Union's Ambient and Assisted Living Joint Programme: An evaluation of its impact on population health and well-being

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Targeting women as agents of (climate) change: a human rights based approach

PURPOSE: To review the available evidence-based literature on the components of brief inpatient psychiatric hospital admission as an intervention for patients with borderline personality disorder. DESIGN AND METHOD: Systematic literature search, narrative literature review. Content analysis. FINDINGS: Five key components of brief admission as an intervention were identified: discussion of goals; organization of Brief Admission; clear admission procedure; specification of any other interventions during Brief Admission; and stipulation of conditions for premature (i.e., forced) discharge. RESEARCH AND PRACTICE IMPLICATIONS: Brief Admission can be effectively used to prevent self-harm and suicide in patients with borderline personality disorder. During the Brief Admission, psychiatric nurses can support these patients achieving an active coping in dealing with their symptoms

Potential for classical biological control of the potato bug Closterotomus norwegicus (Hemiptera: Miridae): description, parasitism and host specificity of Peristenus closterotomae sp. n. (Hymenoptera: Braconidae)

The potato bug, Closterotomus norwegicus (Gmelin) (Hemiptera: Miridae) is an introduced pest of lucerne, white clover and lotus seed crops in New Zealand and a key pest of pistachios in California, USA. Efforts were made to identify potential biological control agents of C. norwegicus in Europe. A total of eight parasitoids, including six primary parasitoids from the genus Peristenus (Hymenoptera: Braconidae) and two hyperparasitoids from the genus Mesochorus (Hymenoptera: Ichneumonidae), were reared from C. norwegicus nymphs collected in various habitats in northern Germany. With a proportion of more than 85% of all C. norwegicus parasitoids, Peristenus closterotomae (Hymenoptera: Braconidae), a new species, was the most dominant parasitoid, whereas other parasitoid species only occurred sporadically. Peristenus closterotomae did not fit in the keys to any described species and is described as new to science. Parasitism caused by P. closterotomae was on average 24% (maximum 77%). To assess the host specificity of parasitoids associated with C. norwegicus, the parasitoid complexes of various Miridae occurring simultaneously with C. norwegicus were studied. Peristenus closterotomae was frequently reared from Calocoris affinis (Herrich-Schaeffer), and a few specimens were reared from Calocoris roseomaculatus (De Geer) and the meadow plant bug, Leptopterna dolobrata (Linnaeus) (all Hemiptera: Miridae). The remaining primary parasitoids associated with C. norwegicus were found to be dominant in hosts other than C. norwegicus. Whether nymphal parasitoids may potentially be used in a classical biological control initiative against the potato bug in countries where it is introduced and considered to be a pest is discusse

Fermi gamma-ray `bubbles' from stochastic acceleration of electrons

Gamma-ray data from Fermi-LAT reveal a bi-lobular structure extending up to 50 degrees above and below the galactic centre, which presumably originated in some form of energy release there less than a few million years ago. It has been argued that the gamma-rays arise from hadronic interactions of high energy cosmic rays which are advected out by a strong wind, or from inverse-Compton scattering of relativistic electrons accelerated at plasma shocks present in the bubbles. We explore the alternative possibility that the relativistic electrons are undergoing stochastic 2nd-order Fermi acceleration by plasma wave turbulence through the entire volume of the bubbles. The observed gamma-ray spectral shape is then explained naturally by the resulting hard electron spectrum and inverse Compton losses. Rather than a constant volume emissivity as in other models, we predict a nearly constant surface brightness, and reproduce the observed sharp edges of the bubbles.Comment: 4 pages, 4 figures; REVTeX4-1; discussion amended and one figure added; to appear in PR

Nonlinear shock acceleration beyond the Bohm limit

We suggest a physical mechanism whereby the acceleration time of cosmic rays by shock waves can be significantly reduced. This creates the possibility of particle acceleration beyond the knee energy at ~10^15eV. The acceleration results from a nonlinear modification of the flow ahead of the shock supported by particles already accelerated to the knee momentum at p ~ p_*. The particles gain energy by bouncing off converging magnetic irregularities frozen into the flow in the shock precursor and not so much by re-crossing the shock itself. The acceleration rate is thus determined by the gradient of the flow velocity and turns out to be formally independent of the particle mean free path (m.f.p.). The velocity gradient is, in turn, set by the knee-particles at p ~ p_* as having the dominant contribution to the CR pressure. Since it is independent of the m.f.p., the acceleration rate of particles above the knee does not decrease with energy, unlike in the linear acceleration regime. The reason for the knee formation at p ~ p_* is that particles with $p > p_*$ are effectively confined to the shock precursor only while they are within limited domains in the momentum space, while other particles fall into ``loss-islands'', similar to the ``loss-cone'' of magnetic traps. This structure of the momentum space is due to the character of the scattering magnetic irregularities. They are formed by a train of shock waves that naturally emerge from unstably growing and steepening magnetosonic waves or as a result of acoustic instability of the CR precursor. These losses steepen the spectrum above the knee, which also prevents the shock width from increasing with the maximum particle energy.Comment: aastex, 13 eps figure

On the mechanism for breaks in the cosmic ray spectrum

The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on full consistency of the CR acceleration theory with the observations; direct proof is impossible because of the orbit stochasticity of CR particles. Recent observations of a number of galactic SNR strongly support the SNR-CR connection in general and the Fermi mechanism of CR acceleration, in particular. However, many SNR expand into weakly ionized dense gases, and so a significant revision of the mechanism is required to fit the data. We argue that strong ion-neutral collisions in the remnant surrounding lead to the steepening of the energy spectrum of accelerated particles by \emph{exactly one power}. The spectral break is caused by a partial evanescence of Alfven waves that confine particles to the accelerator. The gamma-ray spectrum generated in collisions of the accelerated protons with the ambient gas is also calculated. Using the recent Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that the parent proton spectrum is a classical test particle power law $\propto E^{-2}$, steepening to $E^{-3}$ at $E_{br}\approx7GeV$.Comment: APS talk to appear in PoP, 4 figure

Constraints On the Diffusive Shock Acceleration From the Nonthermal X-ray Thin Shells In SN1006 NE Rim

Characteristic scale lengths of nonthermal X-rays from the SN1006 NE rim, which are observed by Chandra, are interpreted in the context of the diffusive shock acceleration on the assumption that the observed spatial profile of nonthermal X-rays corresponds to that of accelerated electrons with energies of a few tens of TeV. To explain the observed scale lengths, we construct two simple models with a test particle approximation, where the maximum energy of accelerated electrons is determined by the age of SN1006 (age-limited model) or the energy loss (energy loss-limited model), and constrain the magnetic field configuration and the diffusion coefficients of accelerated electrons. When the magnetic field is nearly parallel to the shock normal, the magnetic field should be in the range of 20-85 micro Gauss and highly turbulent both in upstream and downstream, which means that the mean free path of accelerated electrons is on the order of their gyro-radius (Bohm limit). This situation can be realized both in the age-limited and energy loss-limited model. On the other hand, when the magnetic field is nearly perpendicular to the shock normal, which can exist only in the age-limited case, the magnetic field is several micro Gauss in the upstream and 14-20 micro Gauss in the downstream, and the upstream magnetic field is less turbulent than the downstream.Comment: 9 pages, 4 figures, accepted for publication in A&