On visual distances for spectrum-type functional data

A functional distance (H), based on the Hausdorff metric between the function hypographs, is proposed for the space Ɛ of non-negative real upper semicontinuous functions on a compact interval. The main goal of the paper is to show that the space (Ɛ,H) is particularly suitable in some statistical problems with functional data which involve functions with very wiggly graphs and narrow, sharp peaks. A typical example is given by spectrograms, either obtained by magnetic resonance or by mass spectrometry. On the theoretical side, we show that (Ɛ,H) is a complete, separable locally compact space and that the H-convergence of a sequence of functions implies the convergence of the respective maximum values of these functions. The probabilistic and statistical implications of these results are discussed, in particular regarding the consistency of k-NN classifiers for supervised classification problems with functional data in H. On the practical side, we provide the results of a small simulation study and check also the performance of our method in two real data problems of supervised classification involving mass spectraA. Cuevas and R. Fraiman have been partially supported by Spanish Grant MTM2013-44045-

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Exploratory Analysis of Functional Data via Clustering and Optimal Segmentation

We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of segments in the prototypes, $P$, is chosen by the user and optimally distributed among the clusters via two dynamic programming algorithms. The practical relevance of the method is shown on two real world datasets

Neurocognitive profiles in autism spectrum disorder

textThe current research project examines the performance of a group of high functioning young adult males with autism spectrum disorders on standardized measures of neurocognitive functioning to determine whether distinct cognitive profiles of strengths and weaknesses emerge. Neuropsychological test data across various domains: general cognitive ability, visuospatial processing, verbal learning and memory, visual learning and memory, working memory, reasoning, cognitive flexibility, attention, receptive language, expressive language, social and emotional processing, and fine motor skills was examined. Data were analyzed using cluster analysis to assess for the presence and nature of unique clusters/subgroups based on neuropsychological test performance. Three unique clusters were derived from the analyses. This study highlights the well-documented heterogeneity across the spectrum of autism and suggests a method for parsing a heterogeneous sample of ASD subjects into smaller and more meaningful homogeneous groups using standardized neuropsychological assessments.Educational Psycholog

Valence-programmable nanoparticle architectures.

Nanoparticle-based clusters permit the harvesting of collective and emergent properties, with applications ranging from optics and sensing to information processing and catalysis. However, existing approaches to create such architectures are typically system-specific, which limits designability and fabrication. Our work addresses this challenge by demonstrating that cluster architectures can be rationally formed using components with programmable valence. We realize cluster assemblies by employing a three-dimensional (3D) DNA meshframe with high spatial symmetry as a site-programmable scaffold, which can be prescribed with desired valence modes and affinity types. Thus, this meshframe serves as a versatile platform for coordination of nanoparticles into desired cluster architectures. Using the same underlying frame, we show the realization of a variety of preprogrammed designed valence modes, which allows for assembling 3D clusters with complex architectures. The structures of assembled 3D clusters are verified by electron microcopy imaging, cryo-EM tomography and in-situ X-ray scattering methods. We also find a close agreement between structural and optical properties of designed chiral architectures

Conformational effects on the Circular Dichroism of Human Carbonic Anhydrase II: a multilevel computational study

Circular Dichroism (CD) spectroscopy is a powerful method for investigating conformational changes in proteins and therefore has numerous applications in structural and molecular biology. Here a computational investigation of the CD spectrum of the Human Carbonic Anhydrase II (HCAII), with main focus on the near-UV CD spectra of the wild-type enzyme and it seven tryptophan mutant forms, is presented and compared to experimental studies. Multilevel computational methods (Molecular Dynamics, Semiempirical Quantum Mechanics, Time-Dependent Density Functional Theory) were applied in order to gain insight into the mechanisms of interaction between the aromatic chromophores within the protein environment and understand how the conformational flexibility of the protein influences these mechanisms. The analysis suggests that combining CD semi empirical calculations, crystal structures and molecular dynamics (MD) could help in achieving a better agreement between the computed and experimental protein spectra and provide some unique insight into the dynamic nature of the mechanisms of chromophore interactions

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

Coordinated optimization of visual cortical maps : 2. Numerical studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations

The Benchmark Ultracool Subdwarf HD 114762B: A Test of Low-Metallicity Atmospheric and Evolutionary Models

We present a near-infrared spectroscopic study of HD 114762B, the latest-type metal-poor companion discovered to date and the only ultracool subdwarf with a known metallicity, inferred from the primary star to be [Fe/H] = -0.7. We obtained a medium-resolution Keck/OSIRIS J-band spectrum and a low-resolution IRTF/SpeX 0.8-2.4 um spectrum of HD 114762B. HD 114762B exhibits spectral features common to both late-type dwarfs and subdwarfs, and we assign it a spectral type of d/sdM9 +/- 1. We use a Monte Carlo technique to fit PHOENIX/GAIA synthetic spectra to the observations, accounting for the coarsely-gridded nature of the models. Fits to the entire OSIRIS J-band and to the metal-sensitive J-band atomic absorption features (Fe I, K I, and Al I lines) yield model parameters that are most consistent with the metallicity of the primary star and the high surface gravity expected of old late-type objects. The effective temperatures and radii inferred from the model atmosphere fitting broadly agree with those predicted by the evolutionary models of Chabrier & Baraffe, and the model color-absolute magnitude relations accurately predict the metallicity of HD 114762B. We conclude that current low-mass, mildly metal-poor atmospheric and evolutionary models are mutually consistent for spectral fits to medium-resolution J-band spectra of HD 114762B, but are inconsistent for fits to low-resolution near-infrared spectra of mild subdwarfs. Finally, we develop a technique for estimating distances to ultracool subdwarfs based on a single near-infrared spectrum. We show that this "spectroscopic parallax" method enables distance estimates accurate to < 10% of parallactic distances for ultracool subdwarfs near the hydrogen burning minimum mass. (abridged)Comment: Accepted by ApJ; 23 pages, 20 figure