Center for Statistical Sciences Seminar
Abstract: One of the most important techniques in learning about the functioning of the brain has involved examining neuronal activity in laboratory animals under varying experimental conditions. Neural information is represented and communicated through series of action potentials, or spike trains, and the central scientific issue in many studies concerns the physiological significance that should be attached to a particular neuron firing pattern in a particular part of the brain. In addition, a major comparatively new effort in neurophysiology involves the use of multi-electrode recording, in which responses from dozens of neurons are recorded simultaneously. Among other things, this has made possible the construction of brain-controlled robotic devices, which could benefit people whose movement has been severely impaired.
In my talk I will briefly outline the progress made, by many people, over the past 10 years, highlighting some of the work my colleagues and I have contributed. Part of my perspective comes from the evolution of the international workshops ``Statistical Analysis of Neural Data," which I co-organized in 2002, 2004, 2006, and 2008. I will try to emphasize general statistical ideas, but will also indicate current status and future challenges.
Lefschetz Center for Dynamical Systems Seminar
Abstract: I shall discuss some properties of solutions of the Navier-Stokes system written in the Fourier space.
Brown Analysis Seminar
Abstract: I will discuss planar analogues of the Lebesgue differentiation theorem, with averages over rectangles (or line segments) rather than averages over balls. Averages of a function along short line segments converge a.e. may not converge unless we restrict the orientation of the segments to a "small" set of directions. I will describe exactly what kind of "smallness" is required. More technically: I will characterize those sets of directions E that have an unbounded (on L^p) directional maximal operator by characterizing those sets of directions E for which one can construct Kakeya-type sets of rectangles, each of whose slope is in E.
Division of Applied Mathematics and the Department of Egyptology and Ancient Western Asian Studies
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Abstract: Did Nilakantha (c. 1444-1544) anticipate Copernicus's heliocentric model !?
Center for Computational Molecular Biology
Hosted by: Sorin Istrail (Refreshments will be served at 3:45pm) |
Abstract: Among the many popular techniques for reconstructing evolutionary trees from molecular sequences, distance-matrix methods such as UPGMA and Neighbor Joining are known to be the fastest. This speed stems from a straightforward, intuitive approach: the repeated agglomeration of the closest clusters of species. However, unlike more elaborate techniques such as maximum likelihood, distance methods only exploit correlations between pairs of sequences (a.k.a. the distance matrix). This limited use of the data is often cited as a serious weakness, as it is thought to affect the convergence rate in the large-sample limit. In this talk, I will discuss recent surprising results shedding some light on this question.
Bio: Sebastien Roch is a postdoctoral researcher at Microsoft Research. He earned his Ph.D. from the University of California, Berkeley under the guidance of Elchanan Mossel. His research interests include Markov models on trees, Markov chains, interacting particle systems, random graphs, and randomized algorithms -- with an emphasis on biological applications.
Department of Mathematics Colloquium
Abstract: Frobenius number for $n$ coprime numbers $a=(a_1,...,a_n)$ is the smallest number $F(a)$ such that beginning with $F(a)$ any integer can be written as $x_1a_1 + ... + x_n a_n$. We shall discuss the problem of limiting distributions of $F(a)/N^(1+1/n-1)$
CCMB Seminar Series
Abstract: Computational protein structure modeling plays an important role in molecular biological research. In addition to well-established algorithms for the interpretation of experimental data (such as X-ray crystal diffraction and NMR), homology-based protein structure prediction tools have become accurate enough to significantly contribute to the understanding of a protein's structure, function, and interactions. Unfortunately, many protein families, such as transmembrane beta-barrels (found in the outer membrane of Gram-negative bacteria, mitochondria, and chloroplasts), are experimentally difficult to study using crystallography or NMR, and few homologues are fully characterized, rendering existing methods insufficient. In this talk, Jerome Waldispuhl and Charles O'Donnell introduce a new family of algorithms, implemented as the tool "partiFold," for investigating the folding landscape of transmembrane beta-barrel proteins based only on sequence information, broad investigator knowledge, and a statistical-mechanical approach using the Boltzmann partition function. This provides predictions of all possible structural conformations that might arise in-vivo, along with their relative likelihood of occurrence. Using a parameterizable grammatical model, these algorithms incorporate high-level information, such as membrane thickness, with an energy function based on stacked amino-acid pair statistical potentials to predicted ensemble properties, such as the likelihood of two residues pairing in a beta-sheet, or the per-residue X-ray crystal structure B-value. Complete conformations can also be sampled from the ensemble, providing a good picture of the subset of low-energy structures [1]. This framework has also been extended in more recent work to combine these same ensemble prediction with classical sequence alignment algorithms to obtain high-quality alignments for non-homologous transmembrane beta-barrel protein pairs [2]. To conclude the talk, ongoing research is presented which generalizes this methodology to incorporate more expansive sets of beta-sheet forming proteins, such as amyloid fibrils and prions. By broadening the grammatical models, and incorporating additional energetic functions and features, this work better incorporates experimentalist knowledge, and provides more tangible hypotheses that can help guide experimentation in a semi-automated manner.
Pattern Theory Seminar
Abstract: Visual object recognition is one of the most poorly understood mental faculties. Theories of object recognition are underspecified with respect to both the functional roles ascribed to different neural structures in the inferior-temporal (IT) cortex and the range of visual recognition behaviors exhibited by humans. The inadequacies of current theories stem from a theoretical status quo combined with methodological limitations inherent in both psychophysics and neurophysiology. To better understand object recognition we must discard both standard feed-forward, hierarchical models that bear little resemblance to the facts as we know them and the behavioral studies that test such narrow models. We must also develop new neuroimaging methods to complement neurophysiology, which severely under-samples object representation space and typically relies on ad hoc/a theoretic strategies for determining which features/objects yield maximal neural responses. In this talk I outline ideas for developing new tools for mapping feature and object selectivity across human visual cortex using functional Magnetic Resonance Imaging (fMRI). The effort is motivated by neurophysiological studies with similar objectives. However, the informativeness and generality of visual physiology has been limited by the low number of samples (~103 recordings) relative to the size of the neural representational space (~109 neurons). fMRI, which measures brain responses in voxels (~106 neurons), enables the study of neural codes at a macro level, yet at a resolution fine enough to capture meaningful functional differences between brain regions. To explore the feature selectivity of localized regions of IT, visual stimulation will be driven by real-time fMRI, in which accruing neural contrasts between conditions are computed instantaneously. This mapping approach will be enhanced by employing at least two principled strategies for moving through feature space: an a priori method that relies on an algorithm for automatically segmenting objects into features (which has been validated against human segmentations); and, an a posteriori method that relies on "mutual information" to identify features that carry more or less task-relevant information.
<--- 2008 Index