The variety generated by order algebras

Every ordered set can be considered as an algebra in a natural way. We investigate the variety generated by order algebras. We prove, among other things, that this variety is not finitely based and, although locally finite, it is not contained in any finitely generated variety; we describe the bottom of the lattice of its subvarieties

Isometries between the spaces of L^1 holomorphic quadratic differentials on Riemann surfaces of finite type

By applying the methods of V. Markovic [7] to the special case of Riemann surfaces of finite type, we obtain a transparent new proof of a classical result about isometries between the spaces of L^1 holomorphic quadratic differentials on such surfaces

Testing the Warm Dark Matter paradigm with large-scale structures

We explore the impact of a LWDM cosmological scenario on the clustering properties of large-scale structure in the Universe. We do this by extending the halo model. The new development is that we consider two components to the mass density: one arising from mass in collapsed haloes, and the second from a smooth component of uncollapsed mass. Assuming that the nonlinear clustering of dark matter haloes can be understood, then from conservation arguments one can precisely calculate the clustering properties of the smooth component and its cross-correlation with haloes. We then explore how the three main ingredients of the halo calculations, the mass function, bias and density profiles are affected by WDM. We show that, relative to CDM: the mass function is suppressed by ~50%, for masses ~100 times the free-streaming mass-scale; the bias of low mass haloes can be boosted by up to 20%; core densities of haloes can be suppressed. We also examine the impact of relic thermal velocities on the density profiles, and find that these effects are constrained to scales r<1 kpc/h, and hence of little importance for dark matter tests, owing to uncertainties in the baryonic physics. We use our modified halo model to calculate the non-linear matter power spectrum, and find significant small-scale power in the model. However, relative to the CDM case, the power is suppressed. We then calculate the expected signal and noise that our set of LWDM models would give for a future weak lensing mission. We show that the models should in principle be separable at high significance. Finally, using the Fisher matrix formalism we forecast the limit on the WDM particle mass for a future full-sky weak lensing mission like Euclid or LSST. With Planck priors and using multipoles l<5000, we find that a lower limit of 2.6 keV should be easily achievable.Comment: Replaced with version accepted for publication in PRD. Inclusion of: new figure showing dependence of predictions on cut-off mass; new discussion of mass function; updated refs. 18 pages, 10 Figure

Microlensing, structure of the galactic halo and determination of dark objects' mass function

We study the accuracy of inference of the massive halo objects' (MHO or `Macho') mass function from microlensing events observed toward LMC. Assuming the spatial distribution and kinematics of the objects are known, the slope and the range of the MHO mass function (modeled here by a simple power law) will be possible to determine from 100-1000 detected events if the slope \alpha is in the range [-2.5, -0.5], with the statistical errors reaching their minima at \alpha =-1.5. Outside this range the errors grow rapidly making the inference difficult even at very large numbers of events (N\approx 10000). On the other hand, the average mass of the MHOs will be determined to better than about 30% accuracy from N\approx 100 events for any slope. We find that the accuracy of inference at fixed N will not be strongly affected by the presently available detection efficiencies if the typical MHO masses are in the range indicated by the events detected so far. We also estimate the effects of uncertainty of the MHOs' spatial distribution and kinematics on the determination of their mass function. The halo models considered are all spherical but we allow for various density profiles and a radius-dependent, anisotropic velocity dispersion. We find that, while the mass function slope and range are weakly affected for -2 < \alpha < 0, the error in the average mass due to the halo uncertainties could be reduced to less than 50% only through the detection of about 1000 or more events. Reliable estimates of the halo structure itself [density profile and velocity dispersion profile] can start only at very large numbers of detections (N ~ 10000).Comment: MNRAS LaTeX style, 14 pages, 11 figures embedded; some changes in the estimates of the last section; a few references added. Also available from http://www.tac.dk/~draza/papers/macho1.ps.

Stability Analysis of Converter Control Modes in Low-Inertia Power Systems

This paper deals with the small-signal stability analysis of converter control modes in low-inertia power systems. For this purpose, a detailed differential-algebraic equation model of the voltage source converter and its control scheme is developed. Both grid-forming and grid-feeding concepts have been considered, as well as different active power controllers based on traditional droop and virtual inertia emulation. An eigenvalue analysis of the linearized state-space system is conducted and the performance of different control configurations is compared. Furthermore, various bifurcation studies have been completed and conclusions on stability margins have been drawn with respect to control sensitivity and robustness

Large-scale retrospective relative spectro-photometric self-calibration in space

We consider the application of relative self-calibration using overlap regions to spectroscopic galaxy surveys that use slit-less spectroscopy. This method is based on that developed for the SDSS by Padmanabhan at al. (2008) in that we consider jointly fitting and marginalising over calibrator brightness, rather than treating these as free parameters. However, we separate the calibration of the detector-to-detector from the full-focal-plane exposure-to-exposure calibration. To demonstrate how the calibration procedure will work, we simulate the procedure for a potential implementation of the spectroscopic component of the wide Euclid survey. We study the change of coverage and the determination of relative multiplicative errors in flux measurements for different dithering configurations. We use the new method to study the case where the flat-field across each exposure or detector is measured precisely and only exposure-to-exposure or detector-to-detector variation in the flux error remains. We consider several base dither patterns and find that they strongly influence the ability to calibrate, using this methodology. To enable self-calibration, it is important that the survey strategy connects different observations with at least a minimum amount of overlap, and we propose an "S"-pattern for dithering that fulfills this requirement. The final survey strategy adopted by Euclid will have to optimise for a number of different science goals and requirements. The large-scale calibration of the spectroscopic galaxy survey is clearly cosmologically crucial, but is not the only one.Comment: 23 pages, 19 figures, Accepted for publication in MNRAS, 201

Vertex routing models

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.Comment: 12 pages, 6 figure