Densities, spectral densities and modality

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the local adaptivity of the procedures and the method is extended to spectral densities.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000036

Nonparametric Regression, Confidence Regions and Regularization

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in that region where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler

Confidence sets and non-parametric regression

--Nonparametric regression , shape regularization , confidence bounds

Different models and single-nucleotide polymorphisms signal the simulated weak gene-gene interaction for a quantitative trait using haplotype-based and mixed models testing

Knowledge of simulated genetic effects facilitates interpretation of methodological studies. Genetic interactions for common disorders are likely numerous and weak. Using the 200 replicates of the Genetic Analysis Workshop 16 (GAW16) Problem 3 simulated data, we compared the statistical power to detect weak gene-gene interactions using a haplotype-based test in the UNPHASED software with genotypic mixed model (GMM) and additive mixed model (AMM) mixed linear regression model in SAS. We assumed a candidate-gene approach where a single-nucleotide polymorphism (SNP) in one gene is fixed and multiple SNPs are at the second gene. We analyzed the quantitative low-density lipoprotein trait (heritability 0.7%), modulated by simulated interaction of rs4648068 from 4q24 and another gene on 8p22, where we analyzed seven SNPs. We generally observed low power calculated per SNP (≤ 37% at the 0.05 level), with the haplotype-based test being inferior. Over all tests, the haplotype-based test performed within chance, while GMM and AMM had low power (~10%). The haplotype-based and mixed models detected signals at different SNPs. The haplotype-based test detected a signal in 50 unique replicates; GMM and AMM featured both shared and distinct SNPs and replicates (65 replicates shared, 41 GMM, 27 AMM). Overall, the statistical signal for the weak gene-gene interaction appears sensitive to the sample structure of the replicates. We conclude that using more than one statistical approach may increase power to detect such signals in studies with limited number of loci such as replications. There were no results significant at the conservative 10-7 genome-wide level

Cholinergic suppression: A postsynaptic mechanism of long-term associative learning

Food avoidance learning in the mollusc Pleurobranchaea entails reduction in the responsiveness of key brain interneurons in the feeding neural circuitry, the paracerebral feeding command interneurons (PCNs), to the neurotransmitter acetylcholine (AcCho). Food stimuli applied to the oral veil of an untrained animal depolarize the PCNs and induce the feeding motor program (FMP). Atropine (a muscarinic cholinergic antagonist) reversibly blocks the food-induced depolarization of the PCNs, implicating AcCho as the neurotransmitter mediating food detection. AcCho applied directly to PCN somata depolarizes them, indicating that the PCN soma membrane contains AcCho receptors and induces the FMP in the isolated central nervous system preparation. The AcCho response of the PCNs is mediated by muscariniclike receptors, since comparable depolarization is induced by muscarinic agonists (acetyl-ß -methylcholine, oxotremorine, pilocarpine), but not nicotine, and blocked by muscarinic antagonists (atropine, trifluoperazine). The nicotinic antagonist hexamethonium, however, blocked the AcCho response in four of six cases. When specimens are trained to suppress feeding behavior using a conventional food-avoidance learning paradigm (conditionally paired food and shock), AcCho applied to PCNs in the same concentration as in untrained animals causes little or no depolarization and does not initiate the FMP. Increasing the concentration of AcCho 10-100 times, however, induces weak PCN depolarization in trained specimens, indicating that learning diminishes but does not fully abolish AcCho responsiveness of the PCNs. This study proposes a cellular mechanism of long-term associative learning -- namely, postsynaptic modulation of neurotransmitter responsiveness in central neurons that could apply also to mammalian species

Neck atonia with a focal stimulation-induced seizure arising from the SMA: pathophysiological considerations.

A 28-year-old patient with pharmacoresistant non-lesional right frontal epilepsy underwent extra-operative intracranial EEG recordings and electrical cortical stimulation (ECS) to map eloquent cortex. Right supplementary motor area (SMA) ECS induced a brief seizure with habitual symptoms involving neck tingling followed by asymmetric tonic posturing. An additional feature was neck atonia. During atonia and sensory aura, discharges were seen in the mesial frontal electrodes and precentral gyrus. Besides motor signs, atonia, although rare and not described in the neck muscles, and sensations have been reported with SMA stimulation. The mechanisms underlying neck atonia in seizures arising from the SMA can be explained by supplementary negative motor area (SNMA) - though this was not mapped in electrodes overlying the ictal onset zone in our patient - or primary sensorimotor cortex activation through rapid propagation. Given the broad spectrum of signs elicited by SMA stimulation and rapid spread of seizures arising from the SMA, caution should be taken to not diagnose these as non-epileptic, as had previously occurred in this patient

Increased alpha-actinin-1 destabilizes E-cadherin-based adhesions and associates with poor prognosis in basal-like breast cancer

The controlled formation and stabilization of E-cadherin-based adhesions is vital for epithelial integrity. This requires co-operation between the E-cadherin-based adhesions and the associated actin cytoskeleton. In cancer, this co-operation often fails, predisposing cells to migration through molecular mechanisms that have only been partially characterized. Here, we demonstrate that the actin filament cross-linker alpha-actinin-1 is frequently increased in human breast cancer. In mammary epithelial cells, the increased alpha-actinin-1 levels promote cell migration and induce disorganized acini-like structures in Matrigel. This is accompanied by a major reorganization of the actin cytoskeleton and the associated E-cadherin-based adhesions. Increased expression of alpha-actinin-1 is particularly noted in basal-like breast cancer cell lines, and in breast cancer patients it associates with poor prognosis in basal-like subtypes. Downregulation of alpha-actinin-1 in E-cadherin expressing basal-like breast cancer cells demonstrate that alpha-actinin-1-assembled actin fibers destabilize E-cadherin-based adhesions. Taken together, these results indicate that increased alpha-actinin-1 expression destabilizes E-cadherin-based adhesions, which is likely to promote the migratory potential of breast cancer cells. Furthermore, our results identify alpha-actinin-1 as a candidate prognostic biomarker in basal-like breast cancer.Peer reviewe

A massive, distant proto-cluster at z=2.47 caught in a phase of rapid formation?

Numerical simulations of cosmological structure formation show that the Universe's most massive clusters, and the galaxies living in those clusters, assemble rapidly at early times (2.5 < z < 4). While more than twenty proto-clusters have been observed at z > 2 based on associations of 5-40 galaxies around rare sources, the observational evidence for rapid cluster formation is weak. Here we report observations of an asymmetric, filamentary structure at z = 2.47 containing seven starbursting, submillimeter-luminous galaxies and five additional AGN within a comoving volume of 15000 Mpc$^{3}$. As the expected lifetime of both the luminous AGN and starburst phase of a galaxy is ~100 Myr, we conclude that these sources were likely triggered in rapid succession by environmental factors, or, alternatively, the duration of these cosmologically rare phenomena is much longer than prior direct measurements suggest. The stellar mass already built up in the structure is $\sim10^{12}M_{\odot}$ and we estimate that the cluster mass will exceed that of the Coma supercluster at $z \sim 0$. The filamentary structure is in line with hierarchical growth simulations which predict that the peak of cluster activity occurs rapidly at z > 2.Comment: 7 pages, 3 figures, 2 tables, accepted in ApJL (small revisions from previous version

Confidence regions, non-parametric regression

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region An which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in An where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler. Although the procedure makes no attempt to minimize any loss function such as MISE the resulting estimates have optimal rates of convergence in the supremum norm both for shape and smoothness regularization. We show that rates of convergence can be misleading even for samples of size n = 10^6 and propose a different form of asymptotics which allows model complexity to increase with sample size