7,036 research outputs found
Semantic distillation: a method for clustering objects by their contextual specificity
Techniques for data-mining, latent semantic analysis, contextual search of
databases, etc. have long ago been developed by computer scientists working on
information retrieval (IR). Experimental scientists, from all disciplines,
having to analyse large collections of raw experimental data (astronomical,
physical, biological, etc.) have developed powerful methods for their
statistical analysis and for clustering, categorising, and classifying objects.
Finally, physicists have developed a theory of quantum measurement, unifying
the logical, algebraic, and probabilistic aspects of queries into a single
formalism. The purpose of this paper is twofold: first to show that when
formulated at an abstract level, problems from IR, from statistical data
analysis, and from physical measurement theories are very similar and hence can
profitably be cross-fertilised, and, secondly, to propose a novel method of
fuzzy hierarchical clustering, termed \textit{semantic distillation} --
strongly inspired from the theory of quantum measurement --, we developed to
analyse raw data coming from various types of experiments on DNA arrays. We
illustrate the method by analysing DNA arrays experiments and clustering the
genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence,
Springer-Verla
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
Symbolic and Visual Retrieval of Mathematical Notation using Formula Graph Symbol Pair Matching and Structural Alignment
Large data collections containing millions of math formulae in different formats are available on-line. Retrieving math expressions from these collections is challenging. We propose a framework for retrieval of mathematical notation using symbol pairs extracted from visual and semantic representations of mathematical expressions on the symbolic domain for retrieval of text documents. We further adapt our model for retrieval of mathematical notation on images and lecture videos. Graph-based representations are used on each modality to describe math formulas. For symbolic formula retrieval, where the structure is known, we use symbol layout trees and operator trees. For image-based formula retrieval, since the structure is unknown we use a more general Line of Sight graph representation. Paths of these graphs define symbol pairs tuples that are used as the entries for our inverted index of mathematical notation. Our retrieval framework uses a three-stage approach with a fast selection of candidates as the first layer, a more detailed matching algorithm with similarity metric computation in the second stage, and finally when relevance assessments are available, we use an optional third layer with linear regression for estimation of relevance using multiple similarity scores for final re-ranking. Our model has been evaluated using large collections of documents, and preliminary results are presented for videos and cross-modal search. The proposed framework can be adapted for other domains like chemistry or technical diagrams where two visually similar elements from a collection are usually related to each other
Retrieving Infinite Numbers of Patterns in a Spin-Glass Model of Immune Networks
The similarity between neural and immune networks has been known for decades,
but so far we did not understand the mechanism that allows the immune system,
unlike associative neural networks, to recall and execute a large number of
memorized defense strategies {\em in parallel}. The explanation turns out to
lie in the network topology. Neurons interact typically with a large number of
other neurons, whereas interactions among lymphocytes in immune networks are
very specific, and described by graphs with finite connectivity. In this paper
we use replica techniques to solve a statistical mechanical immune network
model with `coordinator branches' (T-cells) and `effector branches' (B-cells),
and show how the finite connectivity enables the system to manage an extensive
number of immune clones simultaneously, even above the percolation threshold.
The system exhibits only weak ergodicity breaking, so that both multiple
antigen defense and homeostasis can be accomplished.Comment: Editor's Choice 201
Phase Transitions in Phase Retrieval
Consider a scenario in which an unknown signal is transformed by a known
linear operator, and then the pointwise absolute value of the unknown output
function is reported. This scenario appears in several applications, and the
goal is to recover the unknown signal -- this is called phase retrieval. Phase
retrieval has been a popular subject of research in the last few years, both in
determining whether complete information is available with a given linear
operator, and in finding efficient and stable phase retrieval algorithms in the
cases where complete information is available. Interestingly, there are a few
ways to measure information completeness, and each way appears to be governed
by a phase transition of sorts. This chapter will survey the state of the art
with some of these phase transitions, and identify a few open problems for
further research.Comment: Book chapter, survey of recent literature, submitted to Excursions in
Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Cente
MATHEMATICAL LANGUAGE PROCESSING: DEEP LEARNING REPRESENTATIONS AND INFERENCE OVER MATHEMATICAL TEXT
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