Faculty Bibliography

Image denoising methods are often designed to minimize mean-squared error (MSE) within the subbands of a multiscale decomposition. However, most high-quality denoising results have been obtained with overcomplete representations, for which minimization of MSE in the subband domain does not guarantee optimal MSE performance in the image domain. We prove that, despite this suboptimality, the expected image-domain MSE resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions (e.g., cycle spinning) is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation. In addition, we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image-domain MSE. We develop an extended version of Stein's unbiased risk estimate (SURE) that allows us to perform this optimization adaptively, for each observed noisy image. We demonstrate this methodology using a new class of estimator formed from linear combinations of localized 'bump' functions that are applied either pointwise or on local neighborhoods of subband coefficients. We show through simulations that the performance of these estimators applied to overcomplete subbands and optimized for image-domain MSE is substantially better than that obtained when they are optimized within each subband. This performance is, in turn, substantially better than that obtained when they are optimized for use on a nonredundant representation

We present a mathematical model and provide an analysis of optical beam director systems composed of adaptive arrays of fiber collimators (subapertures), referred to here as conformal optical systems. Performances of the following two system architectures are compared: A conformal-beam director with mutually incoherent output laser beams transmitted through fiber collimators (beamlets), and a corresponding coherent system whose beamlets can be coherently combined (phase locked) at a remote target plane. The effect of the major characteristics of the conformal systems on the efficiency of laser beam projection is evaluated both analytically and through numerical simulations. The characteristics considered here are the number of fiber collimators and the subaperture and conformal aperture fill factors, as well as the accuracy of beamlet pointing

Next-generation sequencing is limited to short read lengths and by high error rates. We systematically analyzed sources of noise in the Illumina Genome Analyzer that contribute to these high error rates and developed a base caller, Alta-Cyclic, that uses machine learning to compensate for noise factors. Alta-Cyclic substantially improved the number of accurate reads for sequencing runs up to 78 bases and reduced systematic biases, facilitating confident identification of sequence variants

Here analytical and simulation results are presented characterizing the recoding arising when overlapping patterns of sensor input impinge on an array of model neurons with branched thresholded dendritic trees. Thus, the neural units employed are intended to capture the integrative behavior of pyramidal cells that sustain isolated Na(+) or NMDA spikes in their branches. Given a defined set of sensor vectors, equations were derived for the probability of firing of both branches and neurons and for the expected overlap between the neural firing patterns triggered by two afferent patterns of given overlap. Thus, both the sparseness of the neural representation and the orthogonalization of overlapping vectors were computed. Simulations were then performed with an array of 1000 neurons comprising 30,000 branches to verify the analytical results and confirm their applicability to systems (which include any practicable artificial system) in which the combinatorically possible branches and neurons are severely subsampled. A means of readout and a measure of discrimination performance were provided so that the accuracy of discrimination among overlapping sensor vectors could be optimized as a function of neuron structure parameters. Good performance required both orthogonalization of the afferent patterns, so that discrimination was accurate and free of interference, and maintenance of a minimum level of neural activity, so that some neurons fired in response to each sensor pattern. It is shown that the discrimination performance achieved by arrays of neurons with branched dendritic trees could not be reached with single-compartment units, regardless of how many of the latter are used. The analytical results furnish a benchmark against which to measure further enhancements in the performance of subsequent simulated systems incorporating local neural mechanisms which, while often less amenable to closed-form analysis, are ubiquitous in biological neural circuitry

Determining how a particular neuron, or population of neurons, encodes information in their spike trains is not a trivial problem, because multiple coding schemes exist and are not necessarily mutually exclusive. Coding schemes generally fall into one of two broad categories, which we refer to as rate and temporal coding. In rate coding schemes, information is encoded in the variations of the average firing rate of the spike train. In contrast, in temporal coding schemes, information is encoded in the specific timing of the individual spikes that comprise the train. Here, we describe a method for testing the presence of temporal encoding of information. Suppose that a set of original spike trains is given. First, surrogate spike trains are generated by randomizing each of the original spike trains subject to the following constraints: the local average firing rate is approximately preserved, while the overall average firing rate and the distribution of primary interspike intervals are perfectly preserved. These constraints ensure that any rate coding of information present in the original spike trains is preserved in the members of the surrogate population. The null-hypothesis is rejected when additional information is found to be present in the original spike trains, implying that temporal coding is present. The method is validated using artificial data, and then demonstrated using real neuronal data.

The precision with which motor neurons innervate target muscles depends on a regulatory network of Hox transcription factors that translates neuronal identity into patterns of connectivity. We show that a single transcription factor, FoxP1, coordinates motor neuron subtype identity and connectivity through its activity as a Hox accessory factor. FoxP1 is expressed in Hox-sensitive motor columns and acts as a dose-dependent determinant of columnar fate. Inactivation of Foxp1 abolishes the output of the motor neuron Hox network, reverting the spinal motor system to an ancestral state. The loss of FoxP1 also changes the pattern of motor neuron connectivity, and in the limb motor axons appear to select their trajectories and muscle targets at random. Our findings show that FoxP1 is a crucial determinant of motor neuron diversification and connectivity, and clarify how this Hox regulatory network controls the formation of a topographic neural map

Specificity of sensory neurons requires restricted expression of one sensory receptor gene and the exclusion of all others within a given cell. In the Drosophila retina, functional identity of photoreceptors depends on light-sensitive Rhodopsins (Rhs). The much simpler larval eye (Bolwig organ) is composed of about 12 photoreceptors, eight of which are green-sensitive (Rh6) and four blue-sensitive (Rh5). The larval eye becomes the adult extraretinal 'eyelet' composed of four green-sensitive (Rh6) photoreceptors. Here we show that, during metamorphosis, all Rh6 photoreceptors die, whereas the Rh5 photoreceptors switch fate by turning off Rh5 and then turning on Rh6 expression. This switch occurs without apparent changes in the programme of transcription factors that specify larval photoreceptor subtypes. We also show that the transcription factor Senseless (Sens) mediates the very different cellular behaviours of Rh5 and Rh6 photoreceptors. Sens is restricted to Rh5 photoreceptors and must be excluded from Rh6 photoreceptors to allow them to die at metamorphosis. Finally, we show that Ecdysone receptor (EcR) functions autonomously both for the death of larval Rh6 photoreceptors and for the sensory switch of Rh5 photoreceptors to express Rh6. This fate switch of functioning, terminally differentiated neurons provides a novel, unexpected example of hard-wired sensory plasticity.

A concise synthesis of rubioncolin B is described, which features an unprecedented intramolecular Diels-Alder reaction involving an ortho-quinone methide and a naphthofuran moiety. The ortho-quinone methide is generated through a surprisingly facile tautomerization of a para-quinone.

The macroevolutionary events leading to neural innovations for social communication, such as vocalization, are essentially unexplored. Many fish vocalize during female courtship and territorial defense, as do amphibians, birds, and mammals. Here, we map the neural circuitry for vocalization in larval fish and show that the vocal network develops in a segment-like region across the most caudal hindbrain and rostral spinal cord. Taxonomic analysis demonstrates a highly conserved pattern between fish and all major lineages of vocal tetrapods. We propose that the vocal basis for acoustic communication among vertebrates evolved from an ancestrally shared developmental compartment already present in the early fishes.