A Recipe for State-and-Effect Triangles

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The current paper exploits a classical result in category theory, part of Jon Beck's monadicity theorem, to systematically construct such a state-and-effect triangle from an adjunction. The power of this construction is illustrated in many examples, covering many monads occurring in program semantics, including (probabilistic) power domains

Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

On the Kennicutt-Schmidt relation of low-metallicity high-redshift galaxies

We present results of self-consistent, high-resolution cosmological simulations of galaxy formation at z~3. The simulations employ recently developed recipe for star formation based on the local abundance of molecular hydrogen, which is tracked self-consistently during the course of simulation. The phenomenological H2 formation model accounts for the effects of dissociating UV radiation of stars in each galaxy, as well as self-shielding and shielding of H2 by dust, and therefore allows us to explore effects of lower metallicities and higher UV fluxes prevalent in high redshift galaxies on their star formation. We compare stellar masses, metallicities, and star formation rates of the simulated galaxies to available observations of the Lyman Break Galaxies (LBGs) and find a reasonable agreement. We find that the Kennicutt-Schmidt (KS) relation exhibited by our simulated galaxies at z~3 is substantially steeper and has a lower amplitude than the z=0 relation at Sigma_gas < 100 Msun/pc^2. The predicted relation, however, is consistent with existing observational constraints for the z~3 Damped Lyman $\alpha$ (DLA) and LBGs. Our tests show that the main reason for the difference from the local KS relation is lower metallicity of the ISM in high redshift galaxies. We discuss several implications of the metallicity-dependence of the KS relation for galaxy evolution and interpretation of observations.Comment: Submitted to Ap

The density profile of equilibrium and non-equilibrium dark matter halos

We study the diversity of the density profiles of dark matter halos based on a large set of high-resolution cosmological simulations of 256^3 particles. The cosmological models include four scale-free models and three representative cold dark matter models. The simulations have good force resolution, and there are about 400 massive halos with more than 10^4 particles within the virial radius in each cosmological model. Our unbiased selection of all massive halos enables to quantify how well the bulk of dark matter halos can be described by the Navarro, Frenk & White (NFW) profile which was established for equilibrium halos. We find that about seventy percent of the halos can be fitted by the NFW profile with a fitting residual dvi_{max} less than 30% in Omega_0=1 universes. This percentage is higher in lower density cosmological models. The rest of the halos exhibits larger deviations from the NFW profile for more significant internal substructures. There is a considerable amount of variation in the density profile even for the halos which can be fitted by the NFW profile (i.e. dvi_{max}<0.30). The distribution of the profile parameter, the concentration $c$, can be well described by a lognormal function with the mean value \bar c slightly smaller (15%) than the NFW result and the dispersion \sigma_c in \ln c about 0.25. The more virialized halos with dvi_{max}<0.15 have the mean value \bar c in good agreement with the NFW result and a slightly smaller dispersion \sigma_c (about 0.2). Our results can alleviate some of the conflicts found recently between the theoretical NFW profile and observational results. Implications for theoretical and observational studies of galaxy formation are discussed.Comment: The final version accepted for publication in ApJ; one figure and one paragraph added to demonstrate that all the conclusions of the first version are solid to the resoltuion effects; 19 pages with 6 figure

Strangeness dynamics and transverse pressure in relativistic nucleus-nucleus collisions

We investigate hadron production as well as transverse hadron spectra from proton-proton, proton-nucleus and nucleus-nucleus collisions from 2 $A\cdot$GeV to 21.3 $A\cdot$TeV within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. The comparison to experimental data on transverse mass spectra from $pp$, $pA$ and C+C (or Si+Si) reactions shows the reliability of the transport models for light systems. For central Au+Au (Pb+Pb) collisions at bombarding energies above $\sim$ 5 A$\cdot$GeV, furthermore, the measured $K^{\pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the default calculations. We investigate various scenarios to explore their potential effects on the $K^\pm$ spectra. In particular the initial state Cronin effect is found to play a substantial role at top SPS and RHIC energies. However, the maximum in the $K^+/\pi^+$ ratio at 20 to 30 A$\cdot$GeV is missed by ~40% and the approximately constant slope of the $K^\pm$ spectra at SPS energies is not reproduced either. Our systematic analysis suggests that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential $\mu_q$ and temperature $T$- should be generated by strong interactions in the early pre-hadronic/partonic phase of central Au+Au (Pb+Pb) collisions.Comment: 20 pages, 15 figures, Phys. Rev. C, in pres

Kaon photoproduction: background contributions, form factors and missing resonances

The photoproduction p(gamma, K+)Lambda process is studied within a field-theoretic approach. It is shown that the background contributions constitute an important part of the reaction dynamics. We compare predictions obtained with three plausible techniques for dealing with these background contributions. It appears that the extracted resonance parameters drastically depend on the applied technique. We investigate the implications of the corrections to the functional form of the hadronic form factor in the contact term, recently suggested by Davidson and Workman (Phys. Rev. C 63, 025210). The role of background contributions and hadronic form factors for the identification of the quantum numbers of ``missing'' resonances is discussed.Comment: 11 pages, 7 eps figures, submitted to Phys. Rev.

Symmetry of k·p Hamiltonian in pyramidal InAs/GaAs quantum dots: Application to the calculation of electronic structure

A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the C-4 symmetry of the 8-band k·p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasiangular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type, and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer's double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands