How to cluster in parallel with neural networks

Partitioning a set of N patterns in a d-dimensional metric space into K clusters - in a way that those in a given cluster are more similar to each other than the rest - is a problem of interest in astrophysics, image analysis and other fields. As there are approximately K(N)/K (factorial) possible ways of partitioning the patterns among K clusters, finding the best solution is beyond exhaustive search when N is large. Researchers show that this problem can be formulated as an optimization problem for which very good, but not necessarily optimal solutions can be found by using a neural network. To do this the network must start from many randomly selected initial states. The network is simulated on the MPP (a 128 x 128 SIMD array machine), where researchers use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also by starting the network from many initial states at once, thus obtaining many solutions in one run. Researchers obtain speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of speedups comensurate with human perceptual abilities

Amyloid Aggregation Behavior of Human Calcitonin

Under appropriate conditions, certain peptides and proteins, both intrinsically disordered and misfolded from their native state, can self-associate to form long proteinaceous fibrils known as amyloids. This transition forms the molecular basis of several pathologies, through both losses of native functions and cytotoxic effects. Calcitonin (CT) is a 32 amino acid therapeutic hormone peptide that can be considered a molecular paradigm for the central events associated with amyloid misfolding. CT’s biological activity is limited by its aggregation along the canonical amyloid aggregation pathway. A better understanding of the misfolding process would not only provide a structural basis to improve CT’s long-term stability and activity as a therapeutic, but also provide valuable insights into the pathological aggregation of other amyloids. As such, the aggregation of human CT (hCT) has been studied in this dissertation using a range of biophysical techniques, with a particular focus on native modulators of kinetic behavior. A direct relationship between human calcitonin (hCT) concentration and aggregation lag time was observed for the first time, contrary to the conventional understanding of amyloid aggregation. This kinetic trend was found to persist over a range of aggregation conditions, as confirmed by Thioflavin-T kinetics assays, CD spectroscopy, and transmission EM. On the basis of kinetics modeling and experimental results, a mechanism whereby structural conversion of hCT monomers is needed before incorporation into the fibril was proposed. Comparative studies of hCT and the canonically aggregating salmon CT (sCT) using experimental and computational techniques suggested that alpha-helical monomers represent a growth-competent species, whereas unstructured random coil monomers represent a growth-incompetent species. The kinetic mechanism proposed represents a novel mechanism in amyloid aggregation, and synthesizes several previously disparate amyloid behaviors. The determinants of hCT lag time were further investigated in a membrane environment, providing the first systematic study of the effect of membranes on CT aggregation. The direct relationship between peptide concentration and lag phase was found to persist in the presence of large unilamellar vesicles (LUVs), and was shown to be dependent on membrane composition. Specifically, lipid compositions encouraging stronger surface interactions increased the concentration dependent differences in lag time. CD experiments suggested adsorption and sequestration of growth-competent helical monomers to play a role in this behavior. An apparent reformatting of mature hCT fibrils was also observed, in a process which appears dependent on not only lipid composition but also the peptide to lipid ratio. The ability of LUVs to remodel fibers grown in solution suggests that interactions between mature fibrils and lipid bilayers are causative in the behavior, rather than membrane-peptide interactions during fiber growth. The results of this thesis, particularly as they relate to monomer growth competence, represent significant contributions to the amyloid field and CT therapy. The novel kinetic mechanism proposed reveals that intramolecular interactions in disordered monomers, while often transient and weak compared to intermolecular interactions, can play crucial roles in mediating amyloid aggregation. Additionally, the elucidated effects of monomer structure and lipid interactions on hCT aggregation kinetics present possible means by which aggregation kinetics can be modulating while maintaining peptide sequence and thus therapeutic efficacy, a key goal in hCT therapies. Such results present a richer picture of hCT aggregation than had previously been available, and potentially provide novel insights as to more general mechanisms of amyloid aggregation.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144023/1/kkamgar_1.pd

Discrete spherical means of directional derivatives and Veronese maps

We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a general construction for obtaining discrete spherical means of directional derivatives. The construction is based on using the Minkowski's existence theorem and Veronese maps. Approximating the directional derivatives by appropriate finite differences allows one to obtain finite difference operators with good rotation invariance properties. In particular, we use discrete circular and spherical means to derive discrete approximations of various linear and nonlinear first- and second-order differential operators, including discrete Laplacians. A practical potential of our approach is demonstrated by considering applications to nonlinear filtering of digital images and surface curvature estimation

Multiple-Point and Multiple-Time Correlations Functions in a Hard-Sphere Fluid

A recent mode coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multi-point and multi-time correlation functions of the densities of conserved variables are calculated in the hydrodynamic limit and compared to results obtained from event-based molecular dynamics simulations. It is demonstrated that the mode coupling theory results are in excellent agreement with the simulation results provided that dissipative couplings are included in the vertices appearing in the theory. In contrast, simplified mode coupling theories in which the densities obey Gaussian statistics neglect important contributions to both the multi-point and multi-time correlation functions on all time scales.Comment: Second one in a sequence of two (in the first, the formalism was developed). 12 pages REVTeX. 5 figures (eps). Submitted to Phys.Rev.

A generalisable framework for saliency-based line segment detection

Here we present a novel, information-theoretic salient line segment detector. Existing line detectors typically only use the image gradient to search for potential lines. Consequently, many lines are found, particularly in repetitive scenes. In contrast, our approach detects lines that define regions of significant divergence between pixel intensity or colour statistics. This results in a novel detector that naturally avoids the repetitive parts of a scene while detecting the strong, discriminative lines present. We furthermore use our approach as a saliency filter on existing line detectors to more efficiently detect salient line segments. The approach is highly generalisable, depending only on image statistics rather than image gradient; and this is demonstrated by an extension to depth imagery. Our work is evaluated against a number of other line detectors and a quantitative evaluation demonstrates a significant improvement over existing line detectors for a range of image transformation

Generalized Boltzmann Equation for Lattice Gas Automata

In this paper, for the first time a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy for the $n$-particle distribution functions, cluster expansion techniques are used to derive approximate kinetic equations. In zeroth approximation the standard nonlinear Boltzmann equation is obtained; the next approximation yields the ring kinetic equation, similar to that for hard sphere systems, describing the time evolution of pair correlations. As a quantitative test we calculate equal time correlation functions in equilibrium for two models that violate semi-detailed balance. One is a model of interacting random walkers on a line, the other one is a two-dimensional fluid type model on a triangular lattice. The numerical predictions agree very well with computer simulations.Comment: 31 pages LaTeX, 12 uuencoded tar-compressed Encapsulated PostScript figures (`psfig' macro), hardcopies available on request, 78kb + 52k

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure