Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

One- and two-center physical space partitioning of the energy in the density functional theory

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (Hartree-Fock) exchange for the same Kohn-Sham orbitals

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

Carbon and nitrogen partitioning during post-anthesis is conditioned by N fertilization and sink strength in three cereals

Further knowledge of the processes conditioning nitrogen use efficiency (NUE) is of great relevance to crop productivity. The aim of this paper was characterise C and N partitioning during grain filling and their implications for NUE. Cereals such as bread wheat (Triticum aestivum L. cv Califa sur), triticale (× Triticosecale Wittmack cv. Imperioso) and tritordeum (× Tritordeum Asch. & Graebn line HT 621) were grown under low (LN, 5 mm NH4NO3) and high (HN, 15 mm NH4NO3) N conditions. We conducted simultaneous double labelling (12CO2 and 15NH415NO3) in order to characterise C and N partitioning during grain filling. Although triticale plants showed the largest total and ear dry matter values in HN conditions, the large investment in shoot and root biomass negatively affected ear NUE. Tritordeum was the only genotype that increased NUE in both N treatments (NUEtotal), whereas in wheat, no significant effect was detected. N labelling revealed that N fertilisation during post-anthesis was more relevant for wheat and tritordeum grain filling than for triticale. The study also revealed that the investments of C and N in flag leaves and shoots, together with the"waste" of photoassimilates in respiration, conditioned the NUE of plants, and especially under LN. These results suggest that C and N use by these plants needs to be improved in order to increase ear C and N sinks, especially under LN. It is also remarkable that even though tritordeum shows the largest increase in NUE, the low yield of this cereal limits its agronomic value.

Stable isotopes unveil habitat partitioning among the marine mammals off NW Africa and reveal unique trophic niches for two globally threatened species.

Stable isotope abundances of carbon (δ13C) and nitrogen (δ15N) in the bone of 13 species of marine mammals from the northwest coast of Africa were investigated to assess their positions in the local trophic web and their preferred habitats. Also, samples of primary producers and potential prey species from the study area were collected to characterise the local isotopic landscape. This characterisation indicated that δ13C values increased from offshore to nearshore and that δ15N was a good proxy for trophic level. Therefore, the most coastal species were Monachus monachus and Sousa teuszii, whereas the most pelagic were Physeter macrocephalus and Balaenoptera acutorostrata. δ15N values indicated that marine mammals located at the lowest trophic level were B. acutorostrata, Stenella coeruleoalba and Delphinus sp., and those occupying the highest trophic level were M. monachus and P. macrocephalus. The trophic level of Orcinus orca was similar to that of M. monachus, suggesting that O. orca preys on fish. Conservation of coastal and threatened species (M. monachus and S. teuszii) off NW Africa should be a priority because these species, as the main apex predators, cannot be replaced by other marine mammals.

Effects of a nursery CO2 enriched atmosphere on the germination and seedling morphology of two Mediterranean oaks with contrasting leaf habit

Abstract: The use of an enriched CO2 atmosphere in tree nurseries has been envisaged as a promising technique to increase productivity and to obtain seedlings with a higher root/shoot ratio, an essential trait to respond to water stress in Mediterranean-type ecosystems. In that framework, we have analyzed the effects of three levels of atmospheric CO2 concentration (350, 500 and 700 ppm) on the germination rate, growth and morphology of seedlings of two Mediterranean oaks used in reforestation programs: the evergreen Quercus ilex L. and the deciduous Quercus cerrioides Wilk. et Costa. CO2 enrichment increased the germination rate of Q. cerrioides (from 70±7 to 81±3 %) while it decreased that of Q. ilex (from 71±10 to 41±12 %). Seedlings of both species increased approximately 60% their total biomass in response to CO2 enrichment but at two different CO2 concentrations: 500 ppm for Q. cerrioides and 700 ppm for Q. ilex. This increase in seedlings biomass was entirely due to an augmentation of root biomass. Considering germination and biomass partitioning, an enriched CO2 atmosphere might not be appropriate for growing Mediterranean evergreen oaks, such as Q. ilex, since it reduces acorn germination and the only gains in root biomass occur at a high concentration (700 ppm). On the other hand, a moderate CO2 enrichment (500 ppm) appears as a promising nursery technique to stimulate the germination, growth and root/shoot ratio of deciduous oaks, such as Q. cerrioides. Resumen: El uso de una atmósfera enriquecida en CO2 durante la fase de vivero puede contribuir a aumentar la producción viverística, a la vez que ayudar a conseguir plántulas con una mayor relación biomasa subterránea/biomasa aérea, más adecuadas para hacer frente al severo estrés hídrico que generalmente limita el éxito de las repoblaciones en el clima Mediterráneo. En este estudio hemos analizado el efecto de tres niveles de abonado carbónico atmosférico (350, 500 y 750 ppm) en la germinación y morfología de plántulas de encina (Quercus ilex) y roble cerrioide (Quercus cerrioides). Una atmósfera enriquecida en CO2 incrementó la germinación de Q. cerrioides (de 70±7 a 81±3 %) mientras que disminuyó la de Q. ilex (de 71±10 a 41±12 %). Las plántulas de ambas especies incrementaron aproximadamente un 60% su biomasa en respuesta a una mayor concentración de CO2, aunque esta respuesta se produjo a diferentes dosis: 500 ppm en Q. cerrioides y 700 ppm en Q. ilex. El aumento en la biomasa total de las plántulas se debió enteramente a un mayor desarrollo de su sistema radical, Considerando tanto la germinación como los efectos sobre la relación biomasa subterránea/biomasa aérea, una atmósfera enriquecida en CO2 no parece ser un tratamiento adecuado para la producción en vivero de plántulas de Q.ilex, puesto que diminuye su germinación y solo aumenta su sistema radicular a dosis muy elevadas (700 ppm). Por el contrario, un aumento moderado en la concentración de CO2 (500 ppm) aparece como una técnica interesante para estimular el crecimiento y obtener plántulas de Q. cerrioides con un sistema radical más desarrollado.

An information theoretic framework for image segmentation

In this paper, an information theoretic framework for image segmentation is presented. This approach is based on the information channel that goes from the image intensity histogram to the regions of the partitioned image. It allows us to define a new family of segmentation methods which maximize the mutual information of the channel. Firstly, a greedy top-down algorithm which partitions an image into homogeneous regions is introduced. Secondly, a histogram quantization algorithm which clusters color bins in a greedy bottom-up way is defined. Finally, the resulting regions in the partitioning algorithm can optionally be merged using the quantized histogram

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing theHarmonized European Time Use Surveys system. Under such a unified framework,the first Time Use Survey of national scope was conducted in Spain during 2002–03. The aim of these surveys is to understand human behavior and the lifestyle ofpeople. Time allocation data are of compositional nature in origin, that is, they aresubject to non-negativity and constant-sum constraints. Thus, standard multivariatetechniques cannot be directly applied to analyze them. The goal of this work is toidentify homogeneous Spanish Autonomous Communities with regard to the typicalactivity pattern of their respective populations. To this end, fuzzy clustering approachis followed. Rather than the hard partitioning of classical clustering, where objects areallocated to only a single group, fuzzy method identify overlapping groups of objectsby allowing them to belong to more than one group. Concretely, the probabilistic fuzzyc-means algorithm is conveniently adapted to deal with the Spanish Time Use Surveymicrodata. As a result, a map distinguishing Autonomous Communities with similaractivity pattern is drawn.Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

Critical analysis and extension of the Hirshfeld atoms in molecules

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Optimum power allocation for multiuser OFDM with arbitrary signal constellations

This paper formulates power allocation policies that maximize the region of mutual informationsachievable in multiuser downlink OFDM channels. Arbitrary partitioning ofthe available tones among users and arbitrary modulation formats, possibly different forevery user, are considered. Two distinct policies are derived, respectively for slow fadingchannels tracked instantaneously by the transmitter and for fast fading channels knownonly statistically thereby. With instantaneous channel tracking, the solution adopts theform of a multiuser mercury/waterfilling procedure that generalizes the single-user mercury/waterfilling introduced in [1, 2]. With only statistical channel information, in contrast,the mercury/waterfilling interpretation is lost. For both policies, a number of limitingregimes are explored and illustrative examples are provided.

Silver space-time trellis-coded modulation

Silver Code (SilC) was originally discovered in [1–4] for 2×2 multiple-input multiple-output (MIMO) transmission. It has non-vanishing minimum determinant 1/7, slightly lower than Golden code, but is fast-decodable, i.e., it allows reduced-complexity maximum likelihood decoding [5–7]. In this paper, we present a multidimensional trellis-coded modulation scheme for MIMO systems [11] based on set partitioning of the Silver Code, named Silver Space-Time Trellis Coded Modulation (SST-TCM). This lattice set partitioning is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions. Viterbi algorithm is applied for trellis decoding, while the branch metrics are computed by using a sphere-decoding algorithm. It is shown that the proposed SST-TCM performs very closely to the Golden Space-Time Trellis Coded Modulation (GST-TCM) scheme, yetwith a much reduced decoding complexity thanks to its fast-decoding property.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Identification and prospective validation of clinically relevant chronic obstructive pulmonary disease (COPD) subtypes.

Background Chronic obstructive pulmonary disease (COPD) is increasingly considered a heterogeneous condition. It was hypothesised that COPD, as currently defined, includes different clinically relevant subtypes. Methods To identify and validate COPD subtypes, 342 subjects hospitalised for the first time because of a COPD exacerbation were recruited. Three months after discharge, when clinically stable, symptoms and quality of life, lung function, exercise capacity, nutritional status, biomarkers of systemic and bronchial inflammation, sputum microbiology, CT of the thorax and echocardiography were assessed. COPD groups were identified by partitioning cluster analysis and validated prospectively against cause-specific hospitalisations and all-cause mortality during a 4 year follow-up. Results Three COPD groups were identified: group 1 (n ¼ 126, 67 years) was characterised by severe airflow limitation (postbronchodilator forced expiratory volume in 1 s (FEV 1 ) 38% predicted) and worse performance in most of the respiratory domains of the disease; group 2 (n ¼ 125, 69 years) showed milder airflow limitation (FEV 1 63% predicted); and group 3 (n ¼ 91, 67 years) combined a similarly milder airflow limitation (FEV 1 58% predicted) with a high proportion of obesity, cardiovascular disorders, iabetes and systemic inflammation. During follow-up, group 1 had more frequent hospitalisations due to COPD (HR 3.28, p < 0.001) and higher all-cause mortality (HR 2.36, p ¼ 0.018) than the other two groups, whereas group 3 had more admissions due to cardiovascular disease (HR 2.87, p ¼ 0.014). Conclusions In patients with COPD recruited at their first hospitalisation, three different COPD subtypes were identified and prospectively validated:"severe respiratory COPD","moderate respiratory COPD", and"systemic COPD'