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. Centralnotations 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 understoodeasily 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 weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces 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 functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

An Automatic Approach for Learning and Tuning Gaussian Interval Type-2 Fuzzy Membership Functions Applied to Lung CAD Classification System

The potential of type-2 fuzzy sets for managing high levels of uncertainty in the subjective knowledge of experts or of numerical information has focused on control and pattern classification systems in recent years. One of the main challenges in designing a type-2 fuzzy logic system is how to estimate the parameters of type-2 fuzzy membership function (T2MF) and the Footprint of Uncertainty (FOU) from imperfect and noisy datasets. This paper presents an automatic approach for learning and tuning Gaussian interval type-2 membership functions (IT2MFs) with application to multi-dimensional pattern classification problems. T2MFs and their FOUs are tuned according to the uncertainties in the training dataset by a combination of genetic algorithm (GA) and crossvalidation techniques. In our GA-based approach, the structure of the chromosome has fewer genes than other GA methods and chromosome initialization is more precise. The proposed approach addresses the application of the interval type-2 fuzzy logic system (IT2FLS) for the problem of nodule classification in a lung Computer Aided Detection (CAD) system. The designed IT2FLS is compared with its type-1 fuzzy logic system (T1FLS) counterpart. The results demonstrate that the IT2FLS outperforms the T1FLS by more than 30% in terms of classification accuracy.

Market and institutional determinants in the regulation of conveyancers

Demand for law professionals in the conveyancing of property is decreasing because of market and institutional changes. On the market side, many transactions feature large, well-known parties and standardized transactions, which make professionals less effective or necessary for protecting the parties to private contracts. On the institutional side, public titling makes it possible to dispense with a broadening set of their former functions. Recording of deeds made professionals redundant as depositories of deeds and reduced demand for them to design title guarantees. Effective registration of rights increasingly substitutes professionals for detecting title conflicts with third parties and gathering their consent. Market changes undermine the information asymmetry rationale for regulating conveyancing, while institutional changes facilitate liberalizing not only conduct but also license regulations. These arguments are supported here by disentangling the logic of titling systems and presenting empirical evidence from the European and USA markets.

Catholic Loyalism, Service and Careerism: Lewes Lewkenor's Quest for Favour

This article discusses one of Lewkenor's more obscure works, The Resolved Gentleman (1594 - STC 15139), in the context of Elizabethan court politics in the 1590s, with a particular emphasis on the author's own experience of dissent, exile to Catholic Spain in the 1580s and return to England in the early 1590s. A translation of Hernando de Acuña's El Caballero Determinado, itself a reworking of Olivier de la Marche's Chevalier Délibéré (1483), the Resolved Gentleman bends the conventions of medieval chivalric allegory to articulate Lewkenor's own experience of alienation and dissent in the specific context of the factionalism of the 1590s. Beneath Lewkenor's seemingly self-effacing, 'humanist' translation it is in fact possible to discern a complex set of criticisms of Elizabeth's court. The knight's 'wandering' and 'errance' thus becomes a complex, multivalent figure that reverberates with a number of autobiographical meanings: the knight's exile becomes in Lewkenor's hands a figure of his own forced exile to Catholic Spain, and the account of the knight's quest functions as an oblique allusion to his own efforts to make his way back to Elizabeth's court. More importantly, however, these 'personal' meanings acquire a wider, political valence in the context of the allegory, and the narrative as a whole thus becomes a subtle, perceptive but scathing criticism of the Elizabethan court in the 1590's and the 'contraction' of royal favour that resulted in particular in the exclusion of capable, experienced but Catholic counsellors like Lewkenor himself. Articulating the frustration of this younger generation of alienated but fundamentally loyalist Catholics, Lewkenor paints a picture of a failed quest for favour, where the questing knight is finally forced to retire from the active life and withdraw to a rustic hermitage that is not only incompatible with his own ideal of the vita activa, but also dangerously smacks of unregenerate, and potentially seditious Catholicism.

A tractable consideration set structure for network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing from an offerset, have recently become popular in assortment optimization and revenue management. The dynamicprogram for these models is intractable and approximated by a deterministic linear program called theCDLP which has an exponential number of columns. When there are products that are being consideredfor purchase by more than one customer segment, CDLP is difficult to solve since column generationis known to be NP-hard. However, recent research indicates that a formulation based on segments withcuts imposing consistency (SDCP+) is tractable and approximates the CDLP value very closely. In thispaper we investigate the structure of the consideration sets that make the two formulations exactly equal.We show that if the segment consideration sets follow a tree structure, CDLP = SDCP+. We give acounterexample to show that cycles can induce a gap between the CDLP and the SDCP+ relaxation.We derive two classes of valid inequalities called flow and synchronization inequalities to further improve(SDCP+), based on cycles in the consideration set structure. We give a numeric study showing theperformance of these cycle-based cuts.

Natural killer cell receptor-repertoire and functions after induction therapy by polyclonal rabbit anti-thymocyte globulin in unsensitized kidney transplant recipients.

Polyclonal rabbit anti-thymocyte globulin (rATG) is widely used in solid organ transplantation (SOT) as induction therapy or to treat corticosteroid-resistant rejection. In vivo, the effect of rATG on natural killer (NK) cells has not been studied. These cells are of particular relevance after SOT because classical immunosuppressive drugs do not inhibit or even can activate NK cells. A cohort of 20 recipients at low immunological risk, that had been receiving rATG as induction therapy, was analyzed for receptor repertoire, cytotoxicity and capacity of NK cells to secrete IFN-γ before kidney transplantation and at different time points thereafter. NK cells expressed fewer killer-cell immunoglobulin-like receptors (KIR), fewer activating receptors NKG2D, but more inhibitory receptor NKG2A compatible with an immature phenotype in the first 6 months post transplantation. Both cytotoxicity of NK cells and the secretion of IFN-γ were preserved over time after transplantation.

Solving two production scheduling problems with sequence-dependent set-up times

In today’s competitive markets, the importance of goodscheduling strategies in manufacturing companies lead to theneed of developing efficient methods to solve complexscheduling problems.In this paper, we studied two production scheduling problemswith sequence-dependent setups times. The setup times areone of the most common complications in scheduling problems,and are usually associated with cleaning operations andchanging tools and shapes in machines.The first problem considered is a single-machine schedulingwith release dates, sequence-dependent setup times anddelivery times. The performance measure is the maximumlateness.The second problem is a job-shop scheduling problem withsequence-dependent setup times where the objective is tominimize the makespan.We present several priority dispatching rules for bothproblems, followed by a study of their performance. Finally,conclusions and directions of future research are presented.

Evaluating predictive densities of U.S. output growth and inflation in a large macroeconomic data set

We evaluate conditional predictive densities for U.S. output growth and inflationusing a number of commonly used forecasting models that rely on a large number ofmacroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly used normality assumption fit actual realizationsout-of-sample. Our focus on predictive densities acknowledges the possibility that, although some predictors can improve or deteriorate point forecasts, they might have theopposite effect on higher moments. We find that normality is rejected for most modelsin some dimension according to at least one of the tests we use. Interestingly, however,combinations of predictive densities appear to be correctly approximated by a normaldensity: the simple, equal average when predicting output growth and Bayesian modelaverage when predicting inflation.

A fish-specific transposable element shapes the repertoire of p53 target genes in zebrafish.

Transposable elements, as major components of most eukaryotic organisms' genomes, define their structural organization and plasticity. They supply host genomes with functional elements, for example, binding sites of the pleiotropic master transcription factor p53 were identified in LINE1, Alu and LTR repeats in the human genome. Similarly, in this report we reveal the role of zebrafish (Danio rerio) EnSpmN6_DR non-autonomous DNA transposon in shaping the repertoire of the p53 target genes. The multiple copies of EnSpmN6_DR and their embedded p53 responsive elements drive in several instances p53-dependent transcriptional modulation of the adjacent gene, whose human orthologs were frequently previously annotated as p53 targets. These transposons define predominantly a set of target genes whose human orthologs contribute to neuronal morphogenesis, axonogenesis, synaptic transmission and the regulation of programmed cell death. Consistent with these biological functions the orthologs of the EnSpmN6_DR-colonized loci are enriched for genes expressed in the amygdala, the hippocampus and the brain cortex. Our data pinpoint a remarkable example of convergent evolution: the exaptation of lineage-specific transposons to shape p53-regulated neuronal morphogenesis-related pathways in both a hominid and a teleost fish.

The functions of sleep.

Here we report on The Satellite Symposium on Sleep Function that was held in Lausanne during 6(th) FENS forum and brought together neuroscientists from basic and clinical sleep research. We illustrate the principal questions that arose during this interdisciplinary gathering and introduce the contents of nine review articles on aspects of sleep that are contained in this Special Issue of the European Journal of Neuroscience.

Gene expression profiling in the human pathogenic dermatophyte Trichophyton rubrum during growth on proteins.

Dermatophytes are highly specialized filamentous fungi which cause the majority of superficial mycoses in humans and animals. The high secreted proteolytic activity of these microorganisms during growth on proteins is assumed to be linked to their particular ability to exclusively infect keratinized host structures such as the skin stratum corneum, hair, and nails. Individual secreted dermatophyte proteases were recently described and linked with the in vitro digestion of keratin. However, the overall adaptation and transcriptional response of dermatophytes during protein degradation are largely unknown. To address this question, we constructed a cDNA microarray for the human pathogenic dermatophyte Trichophyton rubrum that was based on transcripts of the fungus grown on proteins. Profiles of gene expression during the growth of T. rubrum on soy and keratin protein displayed the activation of a large set of genes that encode secreted endo- and exoproteases. In addition, other specifically induced factors potentially implicated in protein utilization were identified, including heat shock proteins, transporters, metabolic enzymes, transcription factors, and hypothetical proteins with unknown functions. Of particular interest is the strong upregulation of key enzymes of the glyoxylate cycle in T. rubrum during growth on soy and keratin, namely, isocitrate lyase and malate synthase. This broad-scale transcriptional analysis of dermatophytes during growth on proteins reveals new putative pathogenicity-related host adaptation mechanisms of these human pathogenic fungi.

A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.