Empirical Similarity

An agent is asked to assess a real-valued variable Y_{p} based on certain characteristics X_{p} = (X_{p}^{1},...,X_{p}^{m}), and on a database consisting (X_{i}^{1},...,X_{i}^{m},Y_{i}) for i = 1,...,n. A possible approach to combine past observations of X and Y with the current values of X to generate an assessment of Y is similarity-weighted averaging. It suggests that the predicted value of Y, Y_{p}^{s}, be the weighted average of all previously observed values Y_{i}, where the weight of Y_{i}, for every i =1,...,n, is the similarity between the vector X_{p}^{1},...,X_{p}^{m}, associated with Y_{p}, and the previously observed vector, X_{i}^{1},...,X_{i}^{m}. We axiomatize this rule. We assume that, given every database, a predictor has a ranking over possible values, and we show that certain reasonable conditions on these rankings imply that they are determined by the proximity to a similarity-weighted average for a certain similarity function. The axiomatization does not suggest a particular similarity function, or even a particular functional form of this function. We therefore proceed to suggest that the similarity function be estimated from past observations. We develop tools of statistical inference for parametric estimation of the similarity function, for the case of a continuous as well as a discrete variable. Finally, we discuss the relationship of the proposed method to other methods of estimation and prediction.Similarity, estimation

Generalizations of the DERHAM Complex with Applications to Duality Theory and the Cohomology of Singular Varieties

Paper by David Lieberma

Physical and geometric constraints explain the labyrinth-like shape of the nasal cavity

The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, but their overall shape is restricted only by the geometry of the head. Our theory explains the geometric variations of natural nasal cavities quantitatively and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations.Comment: 7 pages, 4 figure

Valid Asymptotic Expansions for the Maximum Likelihood Estimator of the Parameter of a Stationary, Gaussian, Strongly Dependent Process

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin’s (1980) general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood derivatives; (ii) appeal to a simple result of Skovgaard (1986) to obtain from this an Edgeworth expansion for the joint distribution of the log-likelihood derivatives; (iii) appeal to and extension of arguments of Bhattacharya and Ghosh (1978) to accomplish the passage from the result on the log-likelihood derivatives to the result for the maximum likelihood estimators. We develop and make extensive use of a uniform version of Dahlhaus’s (1989) Theorem~5.1 on products of Toeplitz matrices; the extension of Dahlhaus’s result is of interest in its own right. A small numerical study of the efficacy of the Edgeworth expansion is presented for the case of fractional Gaussian noise

Integration of the Head and Forelimb in Bipedal Hominids

Integration, a fundamental property of organisms, occurs via multiple mechanisms and for diverse reasons. Although there has been substantial work on the genetic and epigenetic mechanisms by which developmental integration occurs, we have less of an understanding of the evolutionary relationships between functional and developmental integration. In this respect, human evolution provides an interesting test case. In quadrupedal mammals, there is considerable functional integration among and between the limbs, but little functional integration between the limbs and the skull. The evolution of bipedalism in hominids, however, provided new opportunities for novel forms of integration by emancipating the forelimbs from any major role in locomotion. Here we consider how the forelimb and head become increasingly integrated in the genus Homo because of the biomechanical challenges of running. While the arm and the head interact little during walking, we have found that, during running, the stance side arm acts as a counterbalance to the head, stabilizing it against impulsive pitching forces generated by the heel strike transient. Moreover, the functional properties of this linkage may have driven several developmental changes in the proportions of the arm and the anatomy of the shoulder girdle during human evolution. Thus, evolutionary changes in arm and head morphology during human evolution may be more integrated than previously considered.AnthropologyHuman Evolutionary Biolog

Testosterone Influence on Gene Expression in Lacrimal Glands of Mouse Models of Sjögren Syndrome

Purpose: Sjögren syndrome is an autoimmune disorder that occurs almost exclusively in women and is associated with extensive inflammation in lacrimal tissue, an immune-mediated destruction and/or dysfunction of glandular epithelial cells, and a significant decrease in aqueous tear secretion. We discovered that androgens suppress the inflammation in, and enhance the function of, lacrimal glands in female mouse models (e.g., MRL/MpJ-Tnfrsf6lpr [MRL/lpr]) of Sjögren syndrome. In contrast, others have reported that androgens induce an anomalous immunopathology in lacrimal glands of nonobese diabetic/LtJ (NOD) mice. We tested our hypothesis that these hormone actions reflect unique, strain- and tissue-specific effects, which involve significant changes in the expression of immune-related glandular genes. Methods: Lacrimal glands were obtained from age-matched, adult, female MRL/lpr and NOD mice after treatment with vehicle or testosterone for up to 3 weeks. Tissues were processed for analysis of differentially expressed mRNAs using CodeLink Bioarrays and Affymetrix GeneChips. Data were analyzed with bioinformatics and statistical software. Results: Testosterone significantly influenced the expression of numerous immune-related genes, ontologies, and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways in lacrimal glands of MRL/lpr and NOD mice. The nature of this hormone-induced immune response was dependent upon the autoimmune strain, and was not duplicated within lacrimal tissues of nonautoimmune BALB/c mice. The majority of immune-response genes regulated by testosterone were of the inflammatory type. Conclusions: Our findings support our hypothesis and indicate a major role for the lacrimal gland microenvironment in mediating androgen effects on immune gene expression