Dichotomy for tree-structured trigraph list homomorphism problems

Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while digraph list homomorphism problems enjoy dichotomy (each problem is NP-complete or polynomial time solvable), such dichotomy is not necessarily expected for trigraph list homomorphism problems. However, in this paper, we identify a large class of trigraphs for which list homomorphism problems do exhibit a dichotomy. They consist of trigraphs with a tree-like structure, and, in particular, include all trigraphs whose underlying graphs are trees. In fact, we show that for these tree-like trigraphs, the trigraph list homomorphism problem is polynomially equivalent to a related digraph list homomorphism problem. We also describe a few examples illustrating that our conditions defining tree-like trigraphs are not unnatural, as relaxing them may lead to harder problems

Mosaic multi-state scenario vs. one-state description of supercooled liquids

According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.Comment: 4 pages, 3 figures, final version accepted in PR

Proposals of a procedure to asses Pollutographs. Application to Murcia's Combined Sewer Overflows (CSOs). Póster

Directives 91/271/EEC and 93/481/EEC set norms regarding the management of Combined Sewer Overflows. European Commission monitors the implementation status and implementation programmes. In fact, during the year 2019 all the utilities should be able to quantify the pollution spilled during storm events. And afterwards, plans have to be developed in order to reduce the impact of such events. In this paper, we proposed a method to estimate the transported pollution during events as well as to serve as a tool for developing plans to lessen the corresponding pollution. The procedure is divided into three steps: A. Periodical measurements of all relevant pollutants, e.g. total suspended solids and chemical oxygen demand, in wet and dry weather. Such pollutant “concentrations” are correlated with the turbidity, updating the relation among them [1]. B. Continuous measures of the turbidity. Turbidity is continously register in the sewer areas near overflow spillways. Turbidimeters are a very convenient equipment for this purpose [2]. Actually, it is reliable, its measures are very correlated with the total suspended solid concentration and its maintenance is easy. In this way, combining A. and B. turbidity measures provide us a real-time estimation of the pollutant concentration. on real time. C. Assesment of each catchment hydrograph. Depending on the available data, this step could be based on a design, a measured or a simulated hydrograph. In order to apply this methodology to Murcia’s Combined Sewer System, we have used simulated hydrographs based on real measured rainfall. Murcia’s utility has developed a calibrated SWMM model, and therefore, using the rainfall data, it is possible to estimate hydrographs for all the relevant points of the system. D. Estimation of each catchment pollutograph. Combining the pollutant concentration, estimated in the previous steps, with the hydrographs, we can asses how the mass of pollutants are transported. This information allows us to comply with EU Directives, but it will also be useful to design Murcia’s strategy to minimize environmental impacts

Evaluating energy recovery potential in Murcia's water supply system

Murcia is the 7th most populated city in Spain. Its water supply system is extensively monitored through a large number of pressure gauges and flow meters. Murcia’s water supply network is fed from distribution reservoirs at enough elevation to avoid needing pumping stations for most of the city districts. Hydraulic resources have been evaluated throughout the water supply system. Besides the pressure reducing valves, where the assessment is quite straight forward [1], District Metered Areas (DMA) inlets have been evaluated. In these areas despite the hydraulic resources are not as great as in pressure reducing valves locations, their location is quite convenient. Actually, these positions are located inside the city, therefore making easy to use the produced energy in municipal self consumption or to provide facilities to the citizens. In order to perform such evaluation, a detailed model of the water supply network has been implemented in EPANET parting from a GIS model. The first step of the evaluation has consisted in the optimizing and validation of the model. Initially, the model was reviewed by comparing pressure and flow rate measurements in the main pipes. Then, an extensive experimental campaign was designed. In that campaign valves were switched so that each day a set of District Metered Areas (DMA) have just one metered inlet or at the most a very short number of metered inlets, whereas having a set of pressure measurements within the DMA. The obtained data was used to minimize errors in pressure time series, optimising roughness of the main pipes through Levenberg/Marquardt BFGS algorithm using EPANET ToolKit through Epanet-Octave [2]. Important roughness proposed changes tended to be located surrounding particular points, where errors in the GIS were located (mainly wrong diameter assignement). After patching all the errors the algorithm eased to localise, model errors were mostly below measures uncertainty, and therefore, the model was considered validated. Then, the hydraulic potential at the DMAs inlets has been evaluated by tracking the “instantaneous” minimum pressure and head within each DMA, as well as the flow rate entering the DMA. So that, the maximum head and the range of flow rates is established for the turbine. At the moment, once that all of these potentials have been assessed, a turbine prototype is being designed

Side-pumping Nd:YAG solar laser by six Fresnel lenses

To obtain a good compromise between collection efficiency and brightness figure of merit of solar-pumped lasers, a new side-pumping scheme is proposed. Firstly the solar radiations are collected and concentrated by six 700 mm diameter Fresnel lenses. The concentrated solar radiations are subsequently reflected by six plane folding mirrors with 95% reflectivity, into a common focal spot. This allows the concentration of 1740 W solar power with about 6.4 W/mm2 peak solar flux. A secondary concentrator is composed of six aspheric fused silica lenses, positioned around a 40 mm radius fused silica sphere, compressing all the concentrated solar radiation from the six Fresnel lenses into an 8 mm diameter by 9 mm length Nd:YAG single-crystal rod. By positioning the spherical concentrator slightly above the aspherical lenses, a more uniform absorption profile is achieved. Mechanical support with a water cooling system ensures an efficient cooling to the laser medium. Optimal laser parameters are found through ZEMAXTM and LASCADTM numerical analysis software. Only 16% of the solar power is absorbed by Nd:YAG medium. Solar laser power of 42.6 W is numerically calculated, reaching a collection efficiency of 18.5 W/m2. For a 400 mm plane-concave resonance cavity with -5m radius of curvature, M2 x = M2 y = 22 beam quality factors are numerically predicted. A near uniform pump absorption profile can be achieved by increasing the number of Fresnel lens and folding mirrors.authorsversionpublishe

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the Chemical Master Equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provide the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually-inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species are order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.Comment: 33 pages, 9 figures, accepted for publication in the Journal of Chemical Physic

Transverse mode coupling instability in the SPS: Headtail simulation and moses calculation

Since 2003, single bunches of protons with high intensity (~ 1.2 1011 protons) and low longitudinal emittance (~ 0.2 eVs) have been observed to suffer from heavy losses in less than one synchrotron period after injection at 26 GeV/c in the CERN Super Proton Synchrotron (SPS) when the vertical chromaticity is corrected (ξy ~ 0). Understanding the mechanisms underlying this instability is crucial to assess the feasibility of an anticipated upgrade of the SPS, which requires bunches of 4 1011 protons. Analytical calculations and particle tracking simulations had already agreed in predicting the intensity threshold of a fast instability. The aim of the present paper is to present a sensitive frequency analysis of the HEADTAIL simulations output using SUSSIX, which brought to light the fine structure of the mode spectrum of the bunch coherent motion. Coupling between the azimuthal modes “-2” and “-3” was clearly observed to be the reason for this fast instability

PS Booster Orbit Correction

At the end of the 2007 run, orbit measurements were carried out in the 4 rings of the PS Booster (PSB) for different working points and beam energies. The aim of these measurements was to provide the necessary input data for a PSB realignment campaign during the 2007/2008 shutdown. Currently, only very few corrector magnets can be operated reliably in the PSB; therefore the orbit correction has to be achieved by displacing (horizontally and vertically) and/or tilting some of the defocusing quadrupoles (QDs). In this report we first describe the orbit measurements, followed by a detailed explanation of the orbit correction strategy. Results and conclusions are presented in the last section