In this paper, we propose a new representation of the cortical surface that may be used to study the cortex folding process and to recover some putative stable anatomical landmarks called sulcal roots usually burried in the depth of adult brains. This representation is a primal sketch derived from a scale space computed for the mean curvature of the cortical surface. This scale-space stems from a diffusion equation geodesic to the cortical surface. The primal sketch is made up of objects defined from mean curvature minima and saddle points. The resulting sketch aims first at highlighting significant elementary cortical folds, second at representing the fold merging process during brain growth. The relevance of the framework is illustrated by the study of central sulcus sulcal roots from antenatal to adult age. Some results are proposed for ten different brains. Some preliminary results are also provided for superior temporal sulcus.

. Correlation matrices---symmetric positive semidefinite matrices with unit diagonal--- are important in statistics and in numerical linear algebra. For simulation and testing it is desirable to be able to generate random correlation matrices with specified eigenvalues (which must be nonnegative and sum to the dimension of the matrix). A popular algorithm of Bendel and Mickey takes a matrix having the specified eigenvalues and uses a finite sequence of Given rotations to introduce 1s on the diagonal. We give improved formulae for computing the rotations and prove that the resulting algorithm is numerically stable. We show by example that the formulae originally proposed, which are used in certain existing Fortran implementations, can lead to serious instability. We also show how to modify the algorithm to generate a rectangular matrix with columns of unit 2-norm. Such a matrix represents a correlation matrix in factored form, which can be preferable to representing the matrix itself, ...

ABSTRACT In high-dimensional data, one often seeks a few interesting low-dimensional projections which reveal important aspects of the data. Projection pursuit is a procedure for searching high-dimensional data for interesting low-dimensional projections via the optimization of a criterion function called the projection pursuit index. Very few projection pursuit indices incorporate class or group information in the calculation, and hence can be adequately applied to supervised classification problems. We introduce new indices derived from linear discriminant analysis that can be used for exploratory supervised classification.

Variation propagation in a multi-station manufacturing process (MMP) is described by the theory of ‘‘Stream of Variation.’ ’ Given that the measurements are obtained via certain sensor distribution scheme, the problem of whether the stream of variation of an MMP is diagnosable is of great interest to both academia and industry. We present a comprehensive study of the diagnosability of MMPs in this paper. It is based on the state space model and is parallel to the concept of observability in control theory. Analogous to the observability matrix and index, the diagnosability matrix and index are first defined and then derived for MMP systems. The result of diagnosability study is applied to the evaluation of sensor distribution strategy. It can also be used as the basis to develop an optimal sensor distribution algorithm. An example of a three-station assembly process with multifixture layouts is presented to illustrate the methodology. �DOI: 10.1115/1.1435645� 1

Abstract — In electromagnetic source analysis it is necessary to determine how many sources are required to describe the EEG or MEG adequately. Model selection procedures (MSP’s, or goodness of fit procedures) give an estimate of the required number of sources. Existing and new MSP’s are evaluated in different source and noise settings: two sources which are close or distant, and noise which is uncorrelated or correlated. The commonly used MSP residual variance is seen to be ineffective, that is it often selects too many sources. Alternatives like the adjusted Hotelling’s test, Bayes information criterion, and the Wald test on source amplitudes are seen to be effective. The adjusted Hotelling’s test is recommended if a conservative approach is taken, and MSP’s such as Bayes information criterion or the Wald test on source amplitudes are recommended if a more liberal approach is desirable. The MSP’s are applied to empirical data (visual evoked fields). I.

Abstract—This paper presents a methodology for optimal allocation of sensors in a multistation assembly process for the purpose of diagnosing in a timely manner variation sources that are responsible for product quality defects. A sensor system distributed in such a way can help manufacturers improve product quality while, at the same time, reducing process downtime. Traditional approaches in sensor optimization fall into two categories: multistation sensor allocation for the purpose of product inspection (rather than diagnosis); and allocation of sensors for the purpose of variation diagnosis but at a single measurement station. In our approach, sensing information from different measurement stations is integrated into a state-space model and the effectiveness of a distributed sensor system is quantified by a diagnosability index. This index is further studied in terms of variation transmissibility between stations as well as variation detectability at individual stations. Based on an understanding of the mechanism of variation propagation, we develop a backward-propagation strategy to determine the locations of measurement stations and the minimum number of sensors needed to achieve full diagnosability. An assembly example illustrates the methodology. Index Terms—Diagnosability, diagnosis of variation sources, multistation assembly process, sensor distribution.

Metabolic flux estimation — the problem of finding out the rates of reactions in metabolic pathways — is an important problem area in the study of metabolism. The most accurate technique for this task today is the use of isotopic tracer experiments, where a mixture of differently isotope labeled substrates is fed to a cell culture and the propagation of the labels is observed from the products and intermediate metabolites, where possible. We present a generic methodology for solving the fluxes of a metabolic network in a steady state. The method differs from most previous approaches by not making prior assumptions about the topology of the metabolic network. Also, only very mild assumptions are made about the available measurement data, for example, both positional enrichment and mass isotopomer data can be used.

We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementation of paraunitary system based on the decomposition of Hermitian unitary matrices. Within this framework, the linear-phase filterbank and pairwise mirror-image symmetry filterbank are revisited. Their structures are special cases of the proposed general structures. Compared with the existing structures, more efficient ones that only use approximately half the number of free parameters are derived. The proposed structures are complete and minimal. Although the factorization theory with or without constraints is discussed in the framework of-channel filterbanks, the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems.

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Relying on space-time linearly precoded orthogonal frequency-division multiple access (OFDMA) and exploiting both transmit and receive antenna diversity, we design herein multirate transceivers that guarantee deterministic symbol recovery with diversity gains regardless of the (possibly unknown) frequency-selective finite impulse response (FIR) channels and multiuser interference. Our approach is based on a three-level design of user codes: the top level (based on OFDMA) handles multiuser interference, the middle level (based on space-time block coding) results in space-time diversity gains, and the lower level (based on linear precoding) mitigates intersymbol interference (ISI). In a multiuser/multirate setting, with two transmit and a single receive antenna, our designs achieve guaranteed diversity gains, whereas the use of two receive antennas could potentially double the capacity of the system (in terms of maximum number of users or achievable transmission rates) under favorable conditions (such as no frequency offset). Simulations illustrate the merits of our approach.