997 resultados para DEPTH DOSE DISTRIBUTIONS


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En aquest treball s'explora el camp de la identificació facial de subjectes utilitzant tècniques d'anàlisi multimodal. Això és utilitzant imatges RGB i imatges de profunditat (3D) amb l'objecte de validar les diverses tècniques emprades en el reconeixement facial i aprofundir en sistemes que incorporen informació tridimensional als algorismes de detecció i identificació facial.

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The top soil of a 14.5 km(2) region at la Chaux-de-Fonds in the Swiss Jura is exceptionally rich in cadmium. It contains an average of 1.3 mg per kg of soil. The spatial distribution of the metal has no simple pattern that could be explained by atmospheric deposition or agricultural practices. Thin soil contained most of its Cd at the surface; in thicker soil Cd is mainly concentrated between 60 and 80 cm depth. No specific minerals or soil fractions could account for these accumulation, and the vertical distribution of Cd is best explained by leaching from the topsoil and further adsorption within layers of nearly neutral pH. The local Jurassic sedimentary rocks contained too little Cd to account for the Cd concentrations in the soil. Alpine gravels from glacial till were too sparse in soils to explain such a spreading of Cd. Moreover this origin is contradictory with the fact that Cd is concentrated in the sand fraction of soils. The respective distributions of Fe and Cd in soils, and soil fractions, suggested that the spreading of iron nodules accumulated during the siderolithic period (Eocene) was not the main source of Cd. Atmospheric deposition, and spreading of fertiliser or waste from septic tanks seem the only plausible explanation for the Cd concentrations, but at present few factors allow us to differentiate between them.

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Résumé Le but de cette étude est d'évaluer la faisabilité et l'efficacité d'un traitement des carcinomes pharyngo-laryngés avancés par combinaison de chimiothérapie intensive associé à une radiothérapie accélérée. Vingt-trois patients ont été inclus (age médian 54 ans, entre 35 et 70 ans). Les localisations tumorales étaient l'hypopharynx (n=7), base de langue (n=10), nasopharynx (n=2) ou l'oesophage proximal (n.1), ou sans porte d'entrée (n=3). Le traitement comprend trois cycles de chimiothérapie (cisplatin 100mg/m2 à J1 ; 5-FU 1000mg/m2 par jour pendant 5 jours en perfusion continue, précédé par de l'amifostine 910mg/m2 ; répété toutes les trois semaines). La radiothérapie concomitante, accélérée (dose totale de 70Gy en 6 semaines) a été débuté au premier jour du deuxième cycle de chimiothérapie. Vingt et un patients ont pu achever la radiothérapie. Dix-huit patients étaient en rémission complète à la fin du traitement. Avec un suivi médian de 45 mois, le taux de survie globale atteint 56% (95% Cl, 32-79%). Le contrôle loco-régional était de 71% (95% CI, 52-91%). La toxicité associée au traitement consistait en une insuffisance rénale réversible (≥grade II) chez 9 patients (43%) et une agranulocytose fébrile chez 9 patients (43%). Tous les patients ont présenté une mucite modérée à sévère (grade II/III) et 19 patients ont montré une toxicité cutanée de grade III. En conclusion, le traitement combiné de radiothérapie accélérée avec une chimiothérapie concomitante à base de Cisplatin/5-FU full-dose avec amifostine est faisable. La toxicité est importante mais reste maîtrisable dans le cadre d'un centre multidisciplinaire. Le taux de survie globale à 4 ans est prometteur, la recherche en vue de traitements moins toxiques doit se poursuivre. Abstract The purpose of this study was to evaluate the feasibility and efficacy of a treatment concept combining three cycles of full-dose chemotherapy (CT) with concomitant accelerated uninterrupted radiotherapy (RI). Twenty- three patients (median age: 54 years, range: 35-70) with locally advanced squamous cell carcinoma of the head and neck (SCCHN) were included. The primary tumor involved the hypopharynx (n=7), base of the tongue (n=10), nasopharynx (n=2) or upper esophagus (n=1) or its location was unknown (n=3). Treatment consisted of three cycles of chemotherapy (cisplatin 100 mg/m2 on day 1; 5-FU 1,000 mg/m2 per day for 5 days as a continuous infusion, preceded by amifostine 910 mg/m2). repeated every 3 weeks. Uninterrupted concomitant boost-accelerated RI (total dose of 70 Gy in 6 weeks) started together on day 1 of the second cycle. All but two patients received the full course of RT. Eighteen patients achieved complete remission (78%). At a median follow-up of 45 months the overall survival was 56% (95% c.i. 32-79%) and the loco-regional control 71% (95% c.i. 52-91%). Toxicity involved reversible renal insufficiency of grade II in 9 patients (39%) and neutropenic fever in 9 patients (39%). All patients suffered from moderate to severe mucositis (grade HMI), and 19 patients presented cutaneous toxicity grade III. Concomitant boost-accelerated RI combined with concurrent full-dose cisplatin/5-FU chemotherapy and amifostine is feasible with manageable, although substantial, toxicity. The overall survival of 4 years is promising. Newer regimens causing less acute mucosal and skin toxicity are needed.

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In the ornamental plant production region of Girona (Spain), which is one of the largest of its kind in southern Europe, most of the surface is irrigated using wide blocked-end furrows. The objectives of this paper were: (1) to evaluate the irrigation scheduling methods used by ornamental plant producers; (2) to analyse different scenarios inorder to assess how they affect irrigation performance; (3) to evaluate the risk of deep percolation; and (4) to calculategross water productivity. A two-year study in a representative commercial field, planted with Prunus cerasifera ‘Nigra’, was carried out. The irrigation dose applied by the farmers was slightly smaller than the required water dose estimated by the use of two different methods: the first based on soil water content, and the second based on evapotranspiration. Distribution uniformity and application efficiency were high, with mean values above 87%. Soil water contentmeasurements revealed that even at the end of the furrow, where the infiltrated water depth was greatest, more than 90% of the infiltrated water was retained in the shallowest 40 cm of the soil; accordingly, the risk of water loss due to deep percolation was minimal. Gross water productivity for ornamental tree production was € 11.70 m–3, approximately 20 times higher than that obtained with maize in the same region

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SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

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BACKGROUND: Antiretroviral therapy (ART) containing tenofovir disoproxil fumarate (TDF) and didanosine (ddI) has been associated with poor immune recovery despite virologic success. This effect might be related to ddI toxicity since ddI exposure is substantially increased by TDF. OBJECTIVE: To analyze whether immune recovery during ART with TDF and ddI is ddI-dose dependent. DESIGN AND METHODS: A retrospective longitudinal analysis of immune recovery measured by the CD4 T-cell slope in 614 patients treated with ART containing TDF with or without ddI. Patients were stratified according to the tertiles of their weight-adjusted ddI dose: low dose (< 3.3 mg/kg), intermediate dose (3.3-4.1 mg/kg) and high dose (> 4.1 mg/kg). Cofactors modifying the degree of immune recovery after starting TDF-containing ART were identified by univariable and multivariable linear regression analyses. RESULTS: CD4 T-cell slopes were comparable between patients treated with TDF and a weight-adjusted ddI-dose of < 4.1 mg/kg per day (n = 143) versus TDF-without-ddI (n = 393). In the multivariable model the slopes differed by -13 CD4 T cells/mul per year [95% confidence interval (CI), -42 to 17; P = 0.40]. In contrast, patients treated with TDF and a higher ddI dose (> 4.1 mg/kg per day, n = 78) experienced a significantly impaired immune recovery (-47 CD4 T cells/microl per year; 95% CI, -82 to -12; P = 0.009). The virologic response was comparable between the different treatment groups. CONCLUSIONS: Immune recovery is impaired, when high doses of ddI (> 4.1 mg/kg) are given in combination with TDF. If the dose of ddI is adjusted to less than 4.1 mg/kg per day, immune recovery is similar to other TDF-containing ART regimen.

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INTRODUCTION: We report the impact of canakinumab, a fully human anti-interleukin-1β monoclonal antibody, on inflammation and health-related quality of life (HRQoL) in patients with difficult-to-treat Gouty Arthritis. METHODS: In this eight-week, single-blind, double-dummy, dose-ranging study, patients with acute Gouty Arthritis flares who were unresponsive or intolerant to--or had contraindications for--non-steroidal anti-inflammatory drugs and/or colchicine were randomized to receive a single subcutaneous dose of canakinumab (10, 25, 50, 90, or 150 mg) (N = 143) or an intramuscular dose of triamcinolone acetonide 40 mg (N = 57). Patients assessed pain using a Likert scale, physicians assessed clinical signs of joint inflammation, and HRQoL was measured using the 36-item Short-Form Health Survey (SF-36) (acute version). RESULTS: At baseline, 98% of patients were suffering from moderate-to-extreme pain. The percentage of patients with no or mild pain was numerically greater in most canakinumab groups compared with triamcinolone acetonide from 24 to 72 hours post-dose; the difference was statistically significant for canakinumab 150 mg at these time points (P < 0.05). Treatment with canakinumab 150 mg was associated with statistically significant lower Likert scores for tenderness (odds ratio (OR), 3.2; 95% confidence interval (CI), 1.27 to 7.89; P = 0.014) and swelling (OR, 2.7; 95% CI, 1.09 to 6.50, P = 0.032) at 72 hours compared with triamcinolone acetonide. Median C-reactive protein and serum amyloid A levels were normalized by seven days post-dose in most canakinumab groups, but remained elevated in the triamcinolone acetonide group. Improvements in physical health were observed at seven days post-dose in all treatment groups; increases in scores were highest for canakinumab 150 mg. In this group, the mean SF-36 physical component summary score increased by 12.0 points from baseline to 48.3 at seven days post-dose. SF-36 scores for physical functioning and bodily pain for the canakinumab 150 mg group approached those for the US general population by seven days post-dose and reached norm values by eight weeks post-dose. CONCLUSIONS: Canakinumab 150 mg provided significantly greater and more rapid reduction in pain and signs and symptoms of inflammation compared with triamcinolone acetonide 40 mg. Improvements in HRQoL were seen in both treatment groups with a faster onset with canakinumab 150 mg compared with triamcinolone acetonide 40 mg. TRIAL REGISTRATION: clinicaltrials.gov: NCT00798369.

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Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

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Radiotherapy with concomitant and adjuvant TMZ is the standard of care for newly diagnosed GBM. MGMT methylation status may be an important determinant of treatment response. This trial, conducted by the RTOG, EORTC, and NCCTG, determined if intensified TMZ improves survival (OS) or progression free survival (PFS) in all patients or specific to MGMT status. Eligibility criteria included age . 18 yrs, KPS ≥ 60, and existence of a tissue block with . 1cm2 tumor for prospective MGMT and retrospective molecular analysis. Patients were randomized to Arm 1: standard TMZ (150-200 mg/m2 x 5 d) or Arm 2: dd TMZ (75-100 mg/m2 x 21 d) q 4 wks for 6-12 cycles. Symptom burden, quality of life (QOL), and neurocognition were prospectively and longitudinally assessed in a patient subset. 833 patients were randomized (1173 registered). Inadequate tissue (n ¼ 144) was the most frequent reason for nonrandomization.No statistical difference was observed between Arms 1 and 2 for median OS (16.6, 14.9 mo, p ¼ 0.63), median PFS (5.5, 6.7 mo, p ¼ 0.06), or methylation status. MGMT methylation was associated with improved OS (21.2, 14 mo, p , 0.0001), PFS (8.7, 5.7 mo, p , 0.0001), and treatment response (p ¼ 0.012). Cox modeling identifiedMGMT status and RPA class as significant predictors of OS; treatment arm and radiation technique (EORTC vs. RTOG) were not. There was increased grade ≥ 3 toxicity in Arm 2 (19%, 27%, p ¼ 0.008), which was mostly lymphopenia and fatigue. This study did not demonstrate improved efficacy for dd TMZ for newly diagnosed GBM regardless of methylation status. However, it confirmed the prognostic significance of MGMT methylation in GBM, demonstrated the feasibility of tumor tissue collection, molecular stratification, and collection of patient outcomes in a large transatlantic intergroup trial, thereby establishing a viable clinical trial paradigm. Support: NCI U10 CA 21661 and U10 CA37422.

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It is well documented that reducing blood pressure (BP) in hypertensive individuals reduces the risk of cardiovascular (CV) events. Despite this, many patients with hypertension remain untreated or inadequately treated, and fail to reach the recommended BP goals. Suboptimal BP control, whilst arising from multiple causes, is often due to poor patient compliance and/or persistence, and results in a significant health and economic burden on society. The use of fixed-dose combinations (FDCs) for the treatment of hypertension has the potential to increase patient compliance and persistence. When compared with antihypertensive monotherapies, FDCs may also offer equivalent or better efficacy, and the same or improved tolerability. As a result, FDCs have the potential to reduce both the CV event rates and the non-drug healthcare costs associated with hypertension. When FDCs are adopted for the treatment of hypertension, issues relating to copayment, formulary restrictions and therapeutic reference pricing must be addressed.

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Purpose/Objective(s): To implement a carotid dose sparing protocol using helical Tomotherapy in T1N0 squamous cell laryngeal carcinoma.Materials/Methods: Between July and August 2010, 7 men with stage T1N0 laryngeal carcinoma were included in this study. Age ranged from 47 - 74 years. Staging included endoscopic examination, CT-scan and MRI when indicated. Planned irradiation dose was 70 Gy in 35 fractions over 7 weeks. A simple treatment planning algorithm for carotid sparing was used: maximum point dose to the carotids 35 Gy, to the spinal cord 30 Gy, and 100% PTV volume to be covered with 95% of the prescribed dose. Carotid volume of interest extended to 1 cm above and below of the PTV. Doses to the carotid arteries, to the critical organs, and to the planned target volume (PTV) with our standard laryngeal irradiation protocol was compared. Daily megavoltage scans were obtained before each fraction. When necessary, the Planned Adaptive software (TomoTherapy Inc., Madison, WI) was used to evaluatethe need for a re-planning, which has never been indicated. Dose data were extracted using the VelocityAI software (Atlanta, GA), and data normalization and dose-volume histogram (DVH) interpolation were realized using the Igor Pro software (Portland, OR).Results:A significant (p\0.05) carotid dose sparing compared to our standard protocol with an average maximum point dose of 38.3 Gy (standard deviation [SD] 4.05 Gy), average mean dose of 18.59 Gy (SD 0.83 Gy) was achieved. In all patients, 95% of the carotid volume received less than 28.4 Gy (SD 0.98 Gy). The average maximum point dose to the spinal cord was 25.8 Gy (SD 3.24 Gy). PTV was fully covered with more than 95% of the prescribed dose for all patients with an average maximum point dose of 74.1 Gy and the absolute maximum dose in a single patient of 75.2 Gy. To date, the clinical outcomes have been excellent. Three patients (42%) developed stage 1 mucositis that was conservatively managed, and all the patients presented a mild to moderate dysphonia. All adverse effects resolved spontaneously in the month following the end of treatment. Early local control rate is 100% considering a 4 - 5 months post treatment follow-up.Conclusions: Helical Tomotherapy allows a clinically significant decrease of carotid irradiation dose compared to standard irradiation protocols with an acceptable spinal cord dose tradeoff. Moreover, this technique allows the PTV to be homogenously covered with a curative irradiation dose. Daily control imaging brings added security margins especially when working with high dose gradients. Further investigations and follow-up are underway to better evaluate the late clinical outcomes especially the local control rate, late laryngeal and vascular toxicity, and expected potential impact on cerebrovascular events.

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Objectifs: Comparer la qualité d'image entre des protocoles dose-standard avec rétroprojection filtrée et basse-dose avec reconstruction itérative en scanner du rachis cervical. Matériels et méthodes: 40 patients ont été investigués par scanner du rachis cervical et prospectivement randomisés en 2 groupes: dose-standard (120kV, 275mAs) avec rétroprojection filtrée, basse-dose (120kV, 150mAs) avec reconstruction itérative. Mesure du bruit, signal-sur-bruit et contraste-sur-bruit. Analyse semi-quantitative (4 points) par 2 observateurs indépendants des disques, foramens, cordon médullaire, ligaments, parties molles et vertèbres, en C3-C4 et C6-C7. Evaluation semi-quantitative (10 points) de la qualité d'image globale. Les paramètres de dose ont été mesurés. Résultats: Il n'y avait aucune différence significative de bruit, signal-sur-bruit ou contraste-sur-bruit entre les 2 protocoles (p≥0.39). En basse-dose avec reconstruction itérative, la visibilité était significativement meilleure pour les disques, foramens et ligaments (p≤0.05), égale pour le cordon médullaire et moins bonne pour les parties molles et vertèbres (p≤0.02). La qualité d'image globale était meilleure, avec une réduction de dose de 41%. Conclusion: Le scanner du rachis cervical basse-dose avec reconstruction itérative fournit des images égales ou meilleures pour les disques, foramens et ligaments, tout en réduisant la dose d'environ 40%.

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The importance of competition between similar species in driving community assembly is much debated. Recently, phylogenetic patterns in species composition have been investigated to help resolve this question: phylogenetic clustering is taken to imply environmental filtering, and phylogenetic overdispersion to indicate limiting similarity between species. We used experimental plant communities with random species compositions and initially even abundance distributions to examine the development of phylogenetic pattern in species abundance distributions. Where composition was held constant by weeding, abundance distributions became overdispersed through time, but only in communities that contained distantly related clades, some with several species (i.e., a mix of closely and distantly related species). Phylogenetic pattern in composition therefore constrained the development of overdispersed abundance distributions, and this might indicate limiting similarity between close relatives and facilitation/complementarity between distant relatives. Comparing the phylogenetic patterns in these communities with those expected from the monoculture abundances of the constituent species revealed that interspecific competition caused the phylogenetic patterns. Opening experimental communities to colonization by all species in the species pool led to convergence in phylogenetic diversity. At convergence, communities were composed of several distantly related but species-rich clades and had overdispersed abundance distributions. This suggests that limiting similarity processes determine which species dominate a community but not which species occur in a community. Crucially, as our study was carried out in experimental communities, we could rule out local evolutionary or dispersal explanations for the patterns and identify ecological processes as the driving force, underlining the advantages of studying these processes in experimental communities. Our results show that phylogenetic relations between species provide a good guide to understanding community structure and add a new perspective to the evidence that niche complementarity is critical in driving community assembly.

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The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

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A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented