975 resultados para Magnus V Erlingsson, king of Norway, 1154-1184.
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Sentinel lymph node biopsy (SLNB) is an appropriate method for the evaluation of axillary status in cases of early breast cancer. We report our experience in treating cases evaluated using SLNB. We analyzed a total of 1192 cases assessed by means of SLNB from July 1999 to December 2007. SLNB processing was successfully completed in 1154 cases with the use of blue dye or radiolabeled 99mTc-Dextran-500, or both. Of these 1154 patients, 857 were N0(i-) (no regional lymph node metastasis, negative immunohistochemistry, IHC), 96 were N0(i+) (no regional lymph node metastasis histologically, positive IHC, no IHC cluster greater than 0.2 mm) and 201 were N1mi (greater than 0.2 mm, none greater than 2.0 mm). Most of the tumors (70%) were invasive ductal carcinomas and tumors were staged as T1 in 770 patients (65%). A total of 274 patients underwent SLNB and axillary dissections up to April 2003. The inclusion criteria were tumor size equal to or less than 3 cm in diameter, no clinically palpable axillary lymph nodes, no neoadjuvant therapy. In 19 cases, the SLN could not be identified intraoperatively. A false-negative rate of 11% and a negative predictive value of 88.2% were obtained for the 255 assessable patients. The overall concordance between SLNB and axillary lymph node status was 92%. SLNB sensitivity for nodes was 81% and specificity was 100%. The higher sensitivity, specificity, accuracy, and lower false-negative rates of SLNB suggest that this method may be an appropriate alternative to total axillary dissection in early breast cancer patients.
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Surficial sediments east of Dunnville, Ontario representing a limited deltaic/lacustrine/aeolian system are investigated with the aim of defining and interpreting their geological history by means of exarrrrning their sedimentology and interrelationships. The Folk and \oJard grain size statistics of samples fran the area were calculated. These sample parameters were e1en plotted on maps to detennine regional patterns. The strongest pattern observed was one of distinct fining to the east, away fran the sand source. Aeolian deposits were fourrl to be better sorted than the surrcunding sediments. The grain size parameter values were also plotted on bivariate graphs in an attempt to separate the samples according to depositional environment. This exercise met with little success, as rrost of the sediments sampled in the area have similar grain size parameters. This is believed to be because the sediment sources for the different environments (delta, distal delta, aeolian dune) are intimately related, to the point that nnst dunes appear to have been sourcErl fran immediately local sediments. It is FOstulated that in such a srrall sedimentological sub-system, sediments were not involved in active transport for a length of time sufficient for the rraterial to cane to equilibritnn with its transporting medium. Thus, fe..v distinctive patterns of parameters were developed that would enable one to differentiate between various environments of neposition. The i.rnTaturity of rrany dune forms and the i.Imaturity of mineralogical composition of all deposits support the above hyt:XJthesis of limited transport time. Another hypothesis proposen is that eadh geologically or geographically distinct area or "sub-system" rray have its o,.m "signature" of grain size relationships as plotted on bivariate graphs. Thus, the emphasis, concerning graphs of this type, should not be placErl on attempting to nifferentiate between various environnents of deposition, hut raB1er on investigating the interrelationships between sanples am environments within that "sub-system". Through the course of this investigation, the existence of nelta plain distributary Channels in the thesis area is SUG0ested, and the mscovery of significantly mfferent sub-units within the TUnnville dune sediments is documented. It is inferred by reference to other authors interpretations of the glacial history of the area, that the tirre of effective aeolian acti vi ty in the Dunnville area was between 12,300 to 12,100 years R.p.
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The purpose of this thesis is to examine the impact of 2 recent legal events, specifically the Fair Access to Regulated Professions Act (2006) and Siadat v. Ontario College of Teachers (2007) decision, with regards to the opportunity of foreign trained teachers to practice their profession in Ontario. The emphasis is on the case of Fatima Siadat, who was a teacher in Iran but was unable to satisfy all the licensing requirements of the Ontario College of Teachers and consequently was unable to practise her profession in Ontario. When the Ontario College of Teachers Appeals Committee upheld the previous decision of the Ontario College of Teachers Registrar to refuse to issue her a teacher's certificate, Ms. Fatima Siadat decided to initiate a lawsuit. Ms. Fatima Siadat challenged the decision ofthe Ontario College of Teachers Appeals Committee by raising a question of applicability of human rights legislation (i.e., The Ontario Human Rights Code, 1990) on the Ontario College of Teachers' decisions. The Ontario Superior Court of Justice decided in January of2007 in favour of Ms. Fatima Siadat (Siadat v. Ontario College of Teachers , 2007) and ordered that her licensing application be reconsidered by the Ontario College of Teachers Appeals Committee. In this thesis the author argues that the Fatima Siadat decision, together with the Fair Access to Regulated Professions Act, 2006, will likely make a significant contribution to enhancing the access of foreign trained teachers and other professionals to practice their regulated professions in Ontario.
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The site of present-day St. Catharines was settled by 3000 United Empire Loyalists at the end of the 18th century. From 1790, the settlement (then known as "The Twelve") grew as an agricultural community. St. Catharines was once referred to Shipman's Corners after Paul Shipman, owner of a tavern that was an important stagecoach transfer point. In 1815, leading businessman William Hamilton Merritt abandoned his wharf at Queenston and set up another at Shipman's Corners. He became involved in the construction and operation of several lumber and gristmills along Twelve Mile Creek. Shipman's Corners soon became the principal milling site of the eastern Niagara Peninsula. At about the same time, Merritt began to develop the salt springs that were discovered along the river which subsequently gave the village a reputation as a health resort. By this time St. Catharines was the official name of the village; the origin of the name remains obscure, but is thought to be named after Catharine Askin Robertson Hamilton, wife of the Hon. Robert Hamilton, a prominent businessman. Merritt devised a canal scheme from Lake Erie to Lake Ontario that would provide a more reliable water supply for the mills while at the same time function as a canal. He formed the Welland Canal Company, and construction took place from 1824 to 1829. The canal and the mills made St. Catharines the most important industrial centre in Niagara. By 1845, St. Catharines was incorporated as a town, with the town limits extending in 1854. Administrative and political functions were added to St. Catharines in 1862 when it became the county seat of Lincoln. In 1871, construction began on the third Welland Canal, which attracted additional population to the town. As a consequence of continual growth, the town limits were again extended. St. Catharines attained city status in 1876 with its larger population and area. Manufacturing became increasingly important in St. Catharines in the early 1900s with the abundance of hydro-electric power, and its location on important land and water routes. The large increase in population after the 1900s was mainly due to the continued industrialization and urbanization of the northern part of the city and the related expansion of business activity. The fourth Welland Canal was opened in 1932 as the third canal could no longer accommodate the larger ships. The post war years and the automobile brought great change to the urban form of St. Catharines. St. Catharines began to spread its boundaries in all directions with land being added five times during the 1950s. The Town of Merritton, Village of Port Dalhousie and Grantham Township were all incorporated as part of St. Catharines in 1961. In 1970 the Province of Ontario implemented a regional approach to deal with such issues as planning, pollution, transportation and services. As a result, Louth Township on the west side of the city was amalgamated, extending the city's boundary to Fifteen Mile Creek. With its current population of 131,989, St. Catharines has become the dominant centre of the Niagara region. Source: City of St. Catharines website http://www.stcatharines.ca/en/governin/HistoryOfTheCity.asp (January 27, 2011)
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This letter authorizes William Hamilton of Portmollart to repair to Edinburgh notwithstanding the acts discharging the Hamiltons from being within six miles of the King’s person. James VI and James I (June 19, 1566 – March 27, 1625) was King of Scots as James VI from July 24th, 1567 and King of England and Ireland as James I from the union of the English and Scottish crowns on March 24, 1603 after the passing of Elizabeth I.
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Detailing what the Prince had to say about his travels.
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In 1361, at Hotel St-Pol, the future king of France, Charles the Fifth, received a book entitled Livret des elections universelles des 12 maisons from his astrologer, Pèlerin de Prusse. Written in old French during the translatio studii period, the book contains two books and describes several astrological theories along with precise descriptions of the twelve houses. Charles the Fifth is widely known as Charles the Wise in our present day. This is due to his vast contributions to the Louvre library as well as his impulse of translations from Latin to the French of the auctoritates and his passion for astrology. The significance imparted on astrology prior and during Charles the Fifth’s reign is apparent in Pèlerin de Prusse’s text Traité des elections, commissioned by Charles during a time of political unrest. The defeat of Poitiers, the États of 1356 to 1358 as well as the Jacquerie define the political landscape of 14th century France. Located at Oxford and the Vatican, two copies are extant, and neither have been edited from the original or subjected to detailed examination and study. This master will present a transcription of the first part of the Livret des elections universelles des 12 maisons.
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This thesis Entitled Bayesian inference in Exponential and pareto populations in the presence of outliers. The main theme of the present thesis is focussed on various estimation problems using the Bayesian appraoch, falling under the general category of accommodation procedures for analysing Pareto data containing outlier. In Chapter II. the problem of estimation of parameters in the classical Pareto distribution specified by the density function. In Chapter IV. we discuss the estimation of (1.19) when the sample contain a known number of outliers under three different data generating mechanisms, viz. the exchangeable model. Chapter V the prediction of a future observation based on a random sample that contains one contaminant. Chapter VI is devoted to the study of estimation problems concerning the exponential parameters under a k-outlier model.
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The present study consists of nine chapters including the introductory chapter. Chapter II makes a brief review of environmental literature and examines various measures adopted at the global level to protect the environment. The environmental problems often transgress national sovereignity and geographical boundaries. Therefore, attempts must be made at the national and international levels to protect the environment, the resources of which are the common property of mankind. The protection of the national environment from the ancient till the present forms the content of Chapter III. These chapters together provide a background to understand the issues analysed in the subsequent chapters. Carefully worked out theoretical framework is a pre-requisite for the successful study of a complex subject. Some of the theoretical issues of ‘environomics’ are examined in Chapter IV. The theoretical issues involved in estimating the costs and benefits of environmental protection constitute the theme of Chapter V. The state of environment in Eloor-Edayar Industrial belt andthe impact analysis of pollution of the area are discussed in Chapter VI and VII respectively. Chapter VIII makes the financial estimate of environmental protection of the project And finally, Chapter IX presents the findings of the study
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The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.
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The resurgence of the enteric pathogen Vibrio cholerae, the causative organism of epidemic cholera, remains a major health problem in many developing countries like India. The southern Indian state of Kerala is endemic to cholera. The outbreaks of cholera follow a seasonal pattern in regions of endemicity. Marine aquaculture settings and mangrove environments of Kerala serve as reservoirs for V. cholerae. The non-O1/non-O139 environmental isolates of V. cholerae with incomplete ‘virulence casette’ are to be dealt with caution as they constitute a major reservoir of diverse virulence genes in the marine environment and play a crucial role in pathogenicity and horizontal gene transfer. The genes coding cholera toxin are borne on, and can be infectiously transmitted by CTXΦ, a filamentous lysogenic vibriophages. Temperate phages can provide crucial virulence and fitness factors affecting cell metabolism, bacterial adhesion, colonization, immunity, antibiotic resistance and serum resistance. The present study was an attempt to screen the marine environments like aquafarms and mangroves of coastal areas of Alappuzha and Cochin, Kerala for the presence of lysogenic V. cholerae, to study their pathogenicity and also gene transfer potential. Phenotypic and molecular methods were used for identification of isolates as V. cholerae. The thirty one isolates which were Gram negative, oxidase positive, fermentative, with or without gas production on MOF media and which showed yellow coloured colonies on TCBS (Thiosulfate Citrate Bile salt Sucrose) agar were segregated as vibrios. Twenty two environmental V. cholerae strains of both O1 and non- O1/non-O139 serogroups on induction with mitomycin C showed the presence of lysogenic phages. They produced characteristic turbid plaques in double agar overlay assay using the indicator strain V. cholerae El Tor MAK 757. PCR based molecular typing with primers targeting specific conserved sequences in the bacterial genome, demonstrated genetic diversity among these lysogen containing non-O1 V. cholerae . Polymerase chain reaction was also employed as a rapid screening method to verify the presence of 9 virulence genes namely, ctxA, ctxB, ace, hlyA, toxR, zot,tcpA, ninT and nanH, using gene specific primers. The presence of tcpA gene in ALPVC3 was alarming, as it indicates the possibility of an epidemic by accepting the cholera. Differential induction studies used ΦALPVC3, ΦALPVC11, ΦALPVC12 and ΦEKM14, underlining the possibility of prophage induction in natural ecosystems, due to abiotic factors like antibiotics, pollutants, temperature and UV. The efficiency of induction of prophages varied considerably in response to the different induction agents. The growth curve of lysogenic V. cholerae used in the study drastically varied in the presence of strong prophage inducers like antibiotics and UV. Bacterial cell lysis was directly proportional to increase in phage number due to induction. Morphological characterization of vibriophages by Transmission Electron Microscopy revealed hexagonal heads for all the four phages. Vibriophage ΦALPVC3 exhibited isometric and contractile tails characteristic of family Myoviridae, while phages ΦALPVC11 and ΦALPVC12 demonstrated the typical hexagonal head and non-contractile tail of family Siphoviridae. ΦEKM14, the podophage was distinguished by short non-contractile tail and icosahedral head. This work demonstrated that environmental parameters can influence the viability and cell adsorption rates of V. cholerae phages. Adsorption studies showed 100% adsorption of ΦALPVC3 ΦALPVC11, ΦALPVC12 and ΦEKM14 after 25, 30, 40 and 35 minutes respectively. Exposure to high temperatures ranging from 50ºC to 100ºC drastically reduced phage viability. The optimum concentration of NaCl required for survival of vibriophages except ΦEKM14 was 0.5 M and that for ΦEKM14 was 1M NaCl. Survival of phage particles was maximum at pH 7-8. V. cholerae is assumed to have existed long before their human host and so the pathogenic clones may have evolved from aquatic forms which later colonized the human intestine by progressive acquisition of genes. This is supported by the fact that the vast majority of V. cholerae strains are still part of the natural aquatic environment. CTXΦ has played a critical role in the evolution of the pathogenicity of V. cholerae as it can transmit the ctxAB gene. The unusual transformation of V. cholerae strains associated with epidemics and the emergence of V. cholera O139 demonstrates the evolutionary success of the organism in attaining greater fitness. Genetic changes in pathogenic V. cholerae constitute a natural process for developing immunity within an endemically infected population. The alternative hosts and lysogenic environmental V. cholerae strains may potentially act as cofactors in promoting cholera phage ‘‘blooms’’ within aquatic environments, thereby influencing transmission of phage sensitive, pathogenic V. cholerae strains by aquatic vehicles. Differential induction of the phages is a clear indication of the impact of environmental pollution and global changes on phage induction. The development of molecular biology techniques offered an accessible gateway for investigating the molecular events leading to genetic diversity in the marine environment. Using nucleic acids as targets, the methods of fingerprinting like ERIC PCR and BOX PCR, revealed that the marine environment harbours potentially pathogenic group of bacteria with genetic diversity. The distribution of virulence associated genes in the environmental isolates of V. cholerae provides tangible material for further investigation. Nucleotide and protein sequence analysis alongwith protein structure prediction aids in better understanding of the variation inalleles of same gene in different ecological niche and its impact on the protein structure for attaining greater fitness of pathogens. The evidences of the co-evolution of virulence genes in toxigenic V. cholerae O1 from different lineages of environmental non-O1 strains is alarming. Transduction studies would indicate that the phenomenon of acquisition of these virulence genes by lateral gene transfer, although rare, is not quite uncommon amongst non-O1/non-O139 V. cholerae and it has a key role in diversification. All these considerations justify the need for an integrated approach towards the development of an effective surveillance system to monitor evolution of V. cholerae strains with epidemic potential. Results presented in this study, if considered together with the mechanism proposed as above, would strongly suggest that the bacteriophage also intervenes as a variable in shaping the cholera bacterium, which cannot be ignored and hinting at imminent future epidemics.
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Soil organic matter (SOM) vitally impacts all soil functions and plays a key role in the global carbon (C) cycle. More than 70% of the terrestric C stocks that participate in the active C cycle are stored in the soil. Therefore, quantitative knowledge of the rates of C incorporation into SOM fractions of different residence time is crucial to understand and predict the sequestration and stabilization of soil organic carbon (SOC). Consequently, there is a need of fractionation procedures that are capable of isolating functionally SOM fractions, i.e. fractions that are defined by their stability. The literature generally refers to three main mechanisms of SOM stabilization: protection of SOM from decomposition by (i) its structural composition, i.e. recalcitrance, (ii) spatial inaccessibility and/or (iii) interaction with soil minerals and metal ions. One of the difficulties in developing fractionation procedures for the isolation of functional SOM fractions is the marked heterogeneity of the soil environment with its various stabilization mechanisms – often several mechanisms operating simultaneously – in soils and soil horizons of different texture and mineralogy. The overall objective of the present thesis was to evaluate present fractionation techniques and to get a better understanding of the factors of SOM sequestration and stabilization. The first part of this study is attended to the structural composition of SOM. Using 13C cross-polarization magic-angle spinning (CPMAS) nuclear magnetic resonance (NMR) spectroscopy, (i) the effect of land use on SOM composition was investigated and (ii) examined whether SOM composition contributes to the different stability of SOM in density and aggregate fractions. The second part of the present work deals with the mineral-associated SOM fraction. The aim was (iii) to evaluate the suitability of chemical fractionation procedures used in the literature for the isolation of stable SOM pools (stepwise hydrolysis, treatments using oxidizing agents like Na2S2O8, H2O2, and NaOCl as well as demineralization of the residue obtained by the NaOCl treatment using HF (NaOCl+HF)) by pool sizes, 13C and 14C data. Further, (iv) the isolated SOM fractions were compared to the inert organic matter (IOM) pool obtained for the investigated soils using the Rothamsted Carbon Model and isotope data in order to see whether the tested chemical fractionation methods produce SOM fractions capable to represent this pool. Besides chemical fractionation, (v) the suitability of thermal oxidation at different temperatures for obtaining stable SOC pools was evaluated. Finally, (vi) the short-term aggregate dynamics and the factors that impact macroaggregate formation and C stabilization were investigated by means of an incubation study using treatments with and without application of 15N labeled maize straw of different degradability (leaves and coarse roots). All treatments were conducted with and without the addition of fungicide. Two study sites with different soil properties and land managements were chosen for these investigations. The first one, located at Rotthalmünster, is a Stagnic Luvisol (silty loam) under different land use regimes. The Ah horizons of a spruce forest and continuous grassland and the Ap and E horizons of two plots with arable crops (continuous maize and wheat cropping) were examined. The soil of the second study site, located at Halle, is a Haplic Phaeozem (loamy sand) where the Ap horizons of two plots with arable crops (continuous maize and rye cropping) were investigated. Both study sites had a C3-/C4-vegetational change on the maize plot for the purpose of tracing the incorporation of the younger, maize-derived C into different SOM fractions and the calculation of apparent C turnover times of these. The Halle site is located near a train station and industrial areas, which caused a contamination with high amounts of fossil C. The investigation of aggregate and density fractions by 13C CPMAS NMR spectroscopy revealed that density fractionation isolated SOM fractions of different composition. The consumption of a considerable part (10–20%) of the easily available O-alkyl-C and the selective preservation of the more recalcitrant alkyl-C when passing from litter to the different particulate organic matter (POM) fractions suggest that density fractionation was able to isolate SOM fractions with different degrees of decomposition. The spectra of the aggregate fractions resembled those of the mineral-associated SOM fraction obtained by density fractionation and no considerable differences were observed between aggregate size classes. Comparison of plant litter, density and aggregate size fractions from soil under different land use showed that the type of land use markedly influenced the composition of SOM. While SOM of the acid forest soil was characterized by a large content (> 50%) of POM, which contained high amounts of spruce-litter derived alkyl-C, the organic matter in the biologically more active grassland and arable soils was dominated by mineral-associated SOM (> 95%). This SOM fraction comprised greater proportions of aryl- and carbonyl-C and is considered to contain a higher amount of microbially-derived organic substances. Land use can alter both, structure and stability of SOM fractions. All applied chemical treatments induced considerable SOC losses (> 70–95% of mineral-associated SOM) in the investigated soils. The proportion of residual C after chemical fractionation was largest in the arable Ap and E horizons and increased with decreasing C content in the initial SOC after stepwise hydrolysis as well as after the oxidative treatments with H2O2 and Na2S2O8. This can be expected for a functional stable pool of SOM, because it is assumed that the more easily available part of SOC is consumed first if C inputs decrease. All chemical treatments led to a preferential loss of the younger, maize-derived SOC, but this was most pronounced after the treatments with Na2S2O8 and H2O2. After all chemical fractionations, the mean 14C ages of SOC were higher than in the mineral-associated SOM fraction for both study sites and increased in the order: NaOCl < NaOCl+HF ≤ stepwise hydrolysis << H2O2 ≈ Na2S2O8. The results suggest that all treatments were capable of isolating a more stable SOM fraction, but the treatments with H2O2 and Na2S2O8 were the most efficient ones. However, none of the chemical fractionation methods was able to fit the IOM pool calculated using the Rothamsted Carbon Model and isotope data. In the evaluation of thermal oxidation for obtaining stable C fractions, SOC losses increased with temperature from 24–48% (200°C) to 100% (500°C). In the Halle maize Ap horizon, losses of the young, maize-derived C were considerably higher than losses of the older C3-derived C, leading to an increase in the apparent C turnover time from 220 years in mineral-associated SOC to 1158 years after thermal oxidation at 300°C. Most likely, the preferential loss of maize-derived C in the Halle soil was caused by the presence of the high amounts of fossil C mentioned above, which make up a relatively large thermally stable C3-C pool in this soil. This agrees with lower overall SOC losses for the Halle Ap horizon compared to the Rotthalmünster Ap horizon. In the Rotthalmünster soil only slightly more maize-derived than C3-derived SOC was removed by thermal oxidation. Apparent C turnover times increased slightly from 58 years in mineral-associated SOC to 77 years after thermal oxidation at 300°C in the Rotthalmünster Ap and from 151 to 247 years in the Rotthalmünster E horizon. This led to the conclusion that thermal oxidation of SOM was not capable of isolating SOM fractions of considerably higher stability. The incubation experiment showed that macroaggregates develop rapidly after the addition of easily available plant residues. Within the first four weeks of incubation, the maximum aggregation was reached in all treatments without addition of fungicide. The formation of water-stable macroaggregates was related to the size of the microbial biomass pool and its activity. Furthermore, fungi were found to be crucial for the development of soil macroaggregates as the formation of water-stable macroaggregates was significantly delayed in the fungicide treated soils. The C concentration in the obtained aggregate fractions decreased with decreasing aggregate size class, which is in line with the aggregate hierarchy postulated by several authors for soils with SOM as the major binding agent. Macroaggregation involved incorporation of large amounts maize-derived organic matter, but macroaggregates did not play the most important role in the stabilization of maize-derived SOM, because of their relatively low amount (less than 10% of the soil mass). Furthermore, the maize-derived organic matter was quickly incorporated into all aggregate size classes. The microaggregate fraction stored the largest quantities of maize-derived C and N – up to 70% of the residual maize-C and -N were stored in this fraction.
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A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table
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Xeroderma pigmentosum (XP) is a rare autosomal recessive disorder haracterized by extreme sensitivity to actinic pigmentation changes in the skin and increased incidence of skin cancer. In some cases, patients are affected by neurological alterations. XP is caused by mutations in 8 distinct genes (XPA through XPG and XPV). The XP-V (variant) subtype of the disease results from mutations in a gene (XPV, also named POLH) which encodes for Polg, a member of the Y-DNA polymerase family. Although the presence and severity of skin and neurological dysfunctions differ between XP subtypes, there are overlapping clinical features among subtypes such that the sub-type cannot be deduced from the clinical features. In this study, in order to overcome this drawback, we undertook whole-exome sequencing in two XP sibs and their father. We identified a novel homozygous nonsense mutation (c.897T.G, p.Y299X) in POLH which causes the disease. Our results demonstrate that next generation sequencing is a powerful approach to rapid determination of XP genetic etiology.