Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

A Modest Proposal to Clarify the Status of Coca in the United Nations Conventions

The implementation of anti-drug policies that focus on illicit crops in the Andean countries faces many significant obstacles, one of which is the cultural clash it generates between the main stakeholders. On the one hand one finds the governments and agencies that attempt to implement crop substitution and eradication policies and on the other the peasant and natives communities that have traditionally grown and used coca or those peasants who have found in coca an instrument of power and political leverage that they never had before. The confrontation about coca eradication, alternative development and other anti-drug policies in coca growing areas transcends drug related issues and is part of a wider and deeper confrontation that reflects the long-term unsolved conflicts of the Andean societies. All Andean countries have stratified and fragmented societies in which peasants and Indians have been excluded from power. In Bolivia, Ecuador and Peru most peasants belong to native communities many of which have remained segregated from “white” society. The mixing of the races (mestizaje) in Colombia occurred early during the Conquest and Colony. Those of Indian descent became subservient to the Spanish and Creoles. The society that evolved was (and still is) highly hierarchical, authoritarian, and has subjacent racist values. The resulting political system has been exclusionary of large portions of the population. Among Indian communities coca has been used for millennia and its use has become an identity symbol of their resistance against what may be looked at as foreign invasion. “The Andean Indian chews coca because that way he affirms his identity as son and owner of the land that yesterday the Spaniard took away and today the landowner keeps away from him. To chew coca is to be Indian...and to quietly and obstinately challenge the contemporary lords that descend from the old encomenderos and the older conquistadors” (Vidart, 1991: 61, author’s translation). In Andean literature on illegal drugs as well as in seminars, colloquia and other meetings where drug policies are debated, complaints are frequently expressed about the treatment of coca in the same category as cocaine, heroin, morphine amphetamines and other “hard” drugs. The complainants assert that “coca is not cocaine” and that it is unfair to classify coca, a nature given plant which has been used for millennia in the Andes without significant negative effects on users, in the same category as man made psychotropic drugs. They also argue that coca has manifold social and religious meanings in indigenous cultures, that coca is sacred and that the requirement of the1961 Single Convention demanding that Bolivia and Peru completely eradicate coca within 25 years is limiting Indigenous communities in their freedom to practice their religions. In most debates about drug interdiction, the views of those who oppose that approach are not accepted as legitimate. Indeed, “prohibitionists” demonize drugs and those who oppose drug policies in Latin America frequently demonize the United States as the imperialist power that imposes them. This dual polarization is a main obstacle to establish a meaningful policy debate aimed at broadening the policy consensus necessary for successful policy implementation. This essay surveys the status of coca in the United Nations Conventions, explains why it is confusing, and how a few changes would eliminate some of the sources of conflict and help organize and control licit coca markets in the Andes. The current disorganized and weakly controlled legal coca market in Peru has been analyzed to demonstrate its deficiencies and to illustrate possible improvements in international drug control policies.

Correlación entre saturación venosa, ruptura de anastomosis y formación de fístulas en pacientes con trauma abdominal en el Hospital Occidente de Kennedy

El manejo del trauma abdominal supone el reto de realizar una anastomosis o sutura intestinal en pacientes comprometidos hemodinámicamente. La decisión de cirugía de control de daños ante la presencia de acidosis, hipotermia y coagulopatía es evidente, sin embargo la situación no siempre es tan clara. En individuos con trauma se desarrollan cambios moleculares e inflamatorios por inadecuado balance entre aporte y demanda de oxígeno, que afectan el proceso de reparación de los tejidos con el riesgo de aparición de fístulas. Una forma rápida y práctica de detectar esta hipoperfusión es midiendo la saturación venosa de oxígeno (SVO2) y el Lactato Sérico. OBJETIVOS: Establecer correlación entre los valores de SVO2 transoperatorio y la aparición de fístulas intestinales en pacientes intervenidos por trauma abdominal. MATERIALES Y METODOS: Estudio de cohorte prospectivo que analiza diferentes variables en relación con la aparición de fistulas en pacientes con trauma abdominal que requieren suturas en el tracto gastrointestinal, haciendo énfasis en los niveles de SVO2. RESULTADOS: Los pacientes con falla anastomótica, presentaron un promedio de SVO2 más baja (60.0% ± 2.94%), versus los no fistulizados (69.89% ± 7.21%) (p =0.010). Todos los pacientes de la cohorte expuesta (SVO2<65%), presentaron dehiscencia de la anastomosis (RR =39.8, IC95%: 2.35,659.91, p<0.001, Test exacto de Fisher). El valor predictivo positivo de la saturación (<65%) fue de 57.14% (IC 95%: 13.34%, 100%) y el valor predictivo negativo fue de 100% (IC 95%:81.75%, 100%). La sensibilidad fue de 100% (IC 95%:87.50%, 100%) y especificidad de 91.89% (IC 95%: 81.75%, 100%). En el análisis bivariante determinó que el índice de trauma abdominal, el nivel de hemoglobina y el requerimiento de transfusión de glóbulos rojos, son factores de riesgo directamente relacionados con la falla de la anastomosis en pacientes con trauma abdominal CONCLUSIONES: - Hay una fuerte relación entre la falla en la reparación intestinal y SVO2 < 65%. - El pronóstico de una anastomosis intestinal está directamente relacionada con el estado hemodinámico y la perfusión tisular al momento de la intervención quirúrgica. - El nivel de SVO2 puede apoyar al cirujano en la decisión de realizar o no una reparación en víscera hueca al momento de intervención quirúrgica en un paciente con trauma abdominal.

Reajuste de derechos de propiedad del suelo urbano en las ciudades de Japón y de Colombia

Los instrumentos de la reforma urbana se han concebido para disciplinar el funcionamiento de los mercados inmobiliarios. Este artículo trata sobre uno de estos instrumentos, el reajuste de tierras. En la primera parte se esbozan, de manera sucinta, algunos rasgos de las formaciones sociales y territoriales del Japón y de Colombia con relación a la propiedad y el uso del suelo urbano. En la segunda presentamos tres experiencias en el empleo del reajuste tierras, comenzando por la restauración posguerra de Nagoya por ser, según nuestro parecer, la más emblemática y original de las múltiples que se pueden encontrar en el Japón. Las otras dos corresponden al proceso de reconstrucción posterremoto de la ciudad de Armenia en Colombia: una de ellas fracasada y otra exitosa.-----The instruments of the Urban Reform have been conceived to discipline the operation of the real estate markets. This work deals with on one these instruments, the Land Readjustment. In the first part they are outlined, of way succinct, some social and territorial characteristics of the formation of Japan and Colombia in relation to the property and the use of the urban land. In second we displayed three experiences in the use of the readjustment land, beginning by the one of the restoration postwar period of Nagoya to be, according to ours to seem, most emblematic and original of the manifold that can be found in Japan. The other two correspond to the reconstruction process post-earthquake of the city of Armenia in Colombia: one of them failed and another successful one.

Feminist Debate around ‘Trafficking’ in Women for the Purpose of Sexual Exploitation in Prostitution

Women trafficking, as a widespread phenomenon, is a complex topic with manifold consequences which have a direct bearing on the way in which the problem of trafficking is understood by regulatory institutions and their proposed solutions. The governmental strategy must respond to this multidimensional phenomenon through state tools to counteract the effects of crime and recognize that women, men, children and adolescents may be indiscriminately vulnerable to this scourge. Nevertheless, we must recognize that, due to cultural facts, women and girls constitute the majority of its victims and specific actions are required for them.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Carbon suboxide: the vibrational dependence of the v7 bending potential function

Data on the vibrational energy levels and rotational constants of carbon suboxide for the low-wavenumber bending mode ν7 are reviewed, in the ground-state manifold, and in the ν2-, ν3-, ν4-, and ν2 + ν4-state manifolds. Following the procedure developed by Duckett, Mills, and Robiette [J. Mol. Spectrosc. 63, 249 (1976)] the data have been inverted to give the effective bending potential in ν7 for each of these five states. Values are obtained for various other parameters in the effective vibration-rotation Hamiltonian. The potential and rotational constants in ν2 + ν4 are given to a close approximation by linear extrapolation from the ground state through the ν2 and ν4 states.

Microwave spectrum of deuterated silyl isocyanate, SiD3NCO

The microwave spectrum of SiD3NCO has been observed and analyzed for 18 different vibrational states in the ν10 manifold. Some accidental resonances have been observed and analyzed. The vibrational dependence of the rotational and l-doubling constant and centrifugal distortion constant DJK has been successfully interpreted in terms of the two-dimensional anharmonic oscillator model.

Composite control of non-linear singularly perturbed systems: meeting a design objective

Using the integral manifold approach, a composite control—the sum of a fast control and a slow control—is derived for a particular class of non-linear singularly perturbed systems. The fast control is designed completely at the outset, thus ensuring the stability of the fast transients of the system and, furthermore, the existence of the integral manifold. A new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy. Though this approach is, by its very nature, ad hoc, the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Convective quasi–equilibrium

The concept of convective quasi–equilibrium (CQE) is a key ingredient in order to understand the role of deep moist convection in the atmosphere. It has been used as a guiding principle to develop almost all convective parameterizations and provides a basic theoretical framework for large–scale tropical dynamics. The CQE concept as originally proposed by Arakawa and Schubert [1974] is systematically reviewed from wider perspectives. Various interpretations and extensions of Arakawa and Schubert’s CQE are considered in terms of both a thermodynamic analogy and as a dynamical balance. The thermodynamic interpretations can be more emphatically embraced as a homeostasis. The dynamic balance interpretations can be best understood by analogy with the slow manifold. Various criticisms of CQE can be avoided by taking the dynamic balance interpretation. Possible limits of CQE are also discussed, including the importance of triggering in many convective situations, as well as the possible self–organized criticality of tropical convection. However, the most intriguing aspect of the CQE concept is that, in spite of many observational tests supporting and interpreting it in many different senses, it has 1never been established in a robust manner based on a systematic analysis of the cloud–work function budget by observations as was originally defined.

Chaucer's presence in songes and sonettes

In an elegy to Wyatt published in Tottel’s Miscellany, Surrey claims that Wyatt ‘reft Chaucer the glory of his wit’. This statement, which both lauds and resists Chaucer, is a microcosm of the way Chaucer is treated throughout the Miscellany. In examining the collection’s paradoxical attitude to Chaucer, this essay focuses particularly on the Squire’s Tale, the Franklin’s Tale, Anelida and Arcite, the Legend of Good Women, and several short lyrics. In its interest in courtly love poetry and Petrarch, the Miscellany follows a trajectory in English poetry set by Chaucer. Its courtly verse is saturated with words, phrases, and tropes from his poetry. Rhyme royal, which he introduced into English poetry, is widely used. The Canterbury Tales has been fully assimilated and can be referred to allusively with the same confidence of the audience’s knowledge as is the case when referring to classical myth; in Wyatt’s ‘Myne owne Jhon Poins’, the speaker, disclaiming deceitfulness, says that he cannot ‘say that Pan/ Passeth Appollo in musike manifold:/ Praise syr Topas for a noble tale,/ And scorne the story that the knight tolde’ (lines 48-50). However, Chaucer’s poetry is also downplayed and contested in the Miscellany. ‘Truth’, the only poem of his which appears in the volume, is disingenuously placed in the ‘Uncertain Authors’ section. In addition, some of the most important elements of his work are strongly resisted in the Miscellany, either ignored, dismissed or challenged. These elements include Chaucer’s interest in variety of voice, his sympathetic engagement with women, particularly wronged women, and his interest in female speech and particularly female complaint. The Miscellany, by contrast, is dominated by male-voiced lyrics preoccupied with the pain inflicted on the lover by a lady who is frequently unfeeling, cruel, or faithless. Chaucer’s frequent focus on the cynical seduction and betrayal of female by male is reversed in the Miscellany, and the language and metaphors he uses to express male cruelty (e.g. the word ‘newfangleness’ and images of hooks, nets and traps) are usurped to describe the lady’s cruelty to the suffering lover. On occasion, poems in the Miscellany challenge specific Chaucerian texts; ‘On His Love Named White’ throws down a gauntlet to The Book of the Duchess, while two of Surrey’s poems implicitly take issue with the female falcon’s voice in the Squire’s Tale, giving the deceitful tercelet the opportunity to shout down the falcon’s charges. The essay thus shows that in many respects Tottel’s Miscellany is only superficially Chaucerian, and that it both passively and actively takes issue with Chaucer’s work.

A unified theory of balance in the extratropics

Many physical systems exhibit dynamics with vastly different time scales. Often the different motions interact only weakly and the slow dynamics is naturally constrained to a subspace of phase space, in the vicinity of a slow manifold. In geophysical fluid dynamics this reduction in phase space is called balance. Classically, balance is understood by way of the Rossby number R or the Froude number F; either R ≪ 1 or F ≪ 1. We examined the shallow-water equations and Boussinesq equations on an f -plane and determined a dimensionless parameter _, small values of which imply a time-scale separation. In terms of R and F, ∈= RF/√(R^2+R^2 ) We then developed a unified theory of (extratropical) balance based on _ that includes all cases of small R and/or small F. The leading-order systems are ensured to be Hamiltonian and turn out to be governed by the quasi-geostrophic potential-vorticity equation. However, the height field is not necessarily in geostrophic balance, so the leading-order dynamics are more general than in quasi-geostrophy. Thus the quasi-geostrophic potential-vorticity equation (as distinct from the quasi-geostrophic dynamics) is valid more generally than its traditional derivation would suggest. In the case of the Boussinesq equations, we have found that balanced dynamics generally implies hydrostatic balance without any assumption on the aspect ratio; only when the Froude number is not small and it is the Rossby number that guarantees a timescale separation must we impose the requirement of a small aspect ratio to ensure hydrostatic balance.