Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Toward a molecular definition of long-term memory storage

The storage of long-term memory is associated with a cellular program of gene expression, altered protein synthesis, and the growth of new synaptic connections. Recent studies of a variety of memory processes, ranging in complexity from those produced by simple forms of implicit learning in invertebrates to those produced by more complex forms of explicit learning in mammals, suggest that part of the molecular switch required for consolidation of long-term memory is the activation of a cAMP-inducible cascade of genes and the recruitment of cAMP response element binding protein-related transcription factors. This conservation of steps in the mechanisms for learning-related synaptic plasticity suggests the possibility of a molecular biology of cognition.

The human AQP4 gene: definition of the locus encoding two water channel polypeptides in brain.

The aquaporin family of membrane water transport proteins are expressed in diverse tissues, and in brain the predominant water channel protein is AQP4. Here we report the isolation and characterization of the human AQP4 cDNAs and genomic DNA. Two cDNAs were isolated corresponding to the two initiating methionines (M1 in a 323-aa polypeptide and M23 in a 301-aa polypeptide) previously identified in rat [Jung, J.S., Bhat, R.V., Preston, G.M., Guggino, W.B. & Agre, P. (1994) Proc. Natl. Acad. Sci. USA 91, 13052-13056]. Similar to other aquaporins, the AQP4 gene is composed of four exons encoding 127, 55, 27, and 92 amino acids separated by introns of 0.8, 0.3, and 5.2 kb. Unlike other aquaporins, an alternative coding initiation sequence (designated exon 0) was located 2.7 kb upstream of exon 1. When spliced together, M1 and the subsequent 10 amino acids are encoded by exon 0; the next 11 amino acids and M23 are encoded by exon 1. Transcription initiation sites have been mapped in the proximal promoters of exons 0 and 1. RNase protection revealed distinct transcripts corresponding to M1 and M23 mRNAs, and AQP4 immunoblots of cerebellum demonstrated reactive polypeptides of 31 and 34 kDa. Using a P1 and a lambda EMBL subclone, the chromosomal site of the human AQP4 gene was mapped to chromosome 18 at the junction of q11.2 and q12.1 by fluorescence in situ hybridization. These studies may now permit molecular characterization of AQP4 during human development and in clinical disorders.

Minimal definition of the imprinting center and fixation of chromosome 15q11-q13 epigenotype by imprinting mutations.

Patients with disorders involving imprinted genes such as Angelman syndrome (AS) and Prader-Willi syndrome (PWS) can have a mutation in the imprinting mechanism. Previously, we identified an imprinting center (IC) within chromosome 15q11-ql3 and proposed that IC mutations block resetting of the imprint, fixing on that chromosome the parental imprint (epigenotype) on which the mutation arose. We now describe four new microdeletions of the IC, the smallest (6 kb) of which currently defines the minimal region sufficient to confer an AS imprinting mutation. The AS deletions all overlap this minimal region, centromeric to the PWS microdeletions, which include the first exon of the SNRPN gene. None of five genes or transcripts in the 1.0 Mb vicinity of the IC (ZNF127, SNRPN, PAR-5, IPW, and PAR-1), each normally expressed only from the paternal allele, was expressed in cells from PWS imprinting mutation patients. In contrast, AS imprinting mutation patients show biparental expression of SNRPN and IPW but must lack expression of the putative AS gene 250-1000 kb distal of the IC. These data strongly support a model in which the paternal chromosome of these PWS patients carries an ancestral maternal epigenotype, and the maternal chromosome of these AS patients carries an ancestral paternal epigenotype. The IC therefore functions to reset the maternal and paternal imprints throughout a 2-Mb imprinted domain within human chromosome 15q11-q13 during gametogenesis.

Definition of the HLA-A29 peptide ligand motif allows prediction of potential T-cell epitopes from the retinal soluble antigen, a candidate autoantigen in birdshot retinopathy.

The peptide-binding motif of HLA-A29, the predisposing allele for birdshot retinopathy, was determined after acid-elution of endogenous peptides from purified HLA-A29 molecules. Individual and pooled HPLC fractions were sequenced by Edman degradation. Major anchor residues could be defined as glutamate at the second position of the peptide and as tyrosine at the carboxyl terminus. In vitro binding of polyglycine synthetic peptides to purified HLA-A29 molecules also revealed the need for an auxiliary anchor residue at the third position, preferably phenylalanine. By using this motif, we synthesized six peptides from the retinal soluble antigen, a candidate autoantigen in autoimmune uveoretinitis. Their in vitro binding was tested on HLA-A29 and also on HLA-B44 and HLA-B61, two alleles sharing close peptide-binding motifs. Two peptides derived from the carboxyl-terminal sequence of the human retinal soluble antigen bound efficiently to HLA-A29. This study could contribute to the prediction of T-cell epitopes from retinal autoantigens implicated in birdshot retinopathy.

Physical and functional independency of p70 and p58 natural killer (NK) cell receptors for HLA class I: their role in the definition of different groups of alloreactive NK cell clones.

Natural killer (NK) cells express clonally distributed receptors for different groups of HLA class I alleles. The Z27 monoclonal antibody described in this study recognizes a p70 receptor specific for HLA-B alleles belonging to the Bw4 supertypic specificity. Single amino acid substitutions in the peptide-binding groove of HLA-B2705 molecules influenced the recognition by some, but not all, p7O/Z27+ clones. This suggests the existence of a limited polymorphism within the p7O family of receptors. The pattern of reactivity of monoclonal antibody Z27 revealed that Bw4-specific receptors may be expressed alone or in combination with different (GL183 and/or EB6) p58 molecules. Analysis of NK clones coexpressing p58 and p7O receptors allowed us to demonstrate that the two molecules represent physically and functionally independent receptors. The expression of p7O molecules either alone or in combination with EB6 molecules provided the molecular basis for understanding the cytolytic pattern of two previously defined groups of "alloreactive" NK cell clones ("group 3" and "group 5").

Definition of a metal-dependent/Li(+)-inhibited phosphomonoesterase protein family based upon a conserved three-dimensional core structure.

Inositol polyphosphate 1-phosphatase, inositol monophosphate phosphatase, and fructose 1,6-bisphosphatase share a sequence motif, Asp-Pro-(Ile or Leu)-Asp-(Gly or Ser)-(Thr or Ser), that has been shown by crystallographic and mutagenesis studies to bind metal ions and participate in catalysis. We compared the six alpha-carbon coordinates of this motif from the crystal structures of these three phosphatases and found that they are superimposable with rms deviations ranging from 0.27 to 0.60 A. Remarkably, when these proteins were aligned by this motif a common core structure emerged, defined by five alpha-helices and 11 beta-strands comprising 155 residues having rms deviations ranging from 1.48 to 2.66 A. We used the superimposed structures to align the sequences within the common core, and a distant relationship was observed suggesting a common ancestor. The common core was used to align the sequences of several other proteins that share significant similarity to inositol monophosphate phosphatase, including proteins encoded by fungal qa-X and qutG, bacterial suhB and cysQ (identical to amtA), and yeast met22 (identical to hal2). Evolutionary comparison of the core sequences indicate that five distinct branches exist within this family. These proteins share metal-dependent/Li(+)-sensitive phosphomonoesterase activity, and each predicted tree branch exhibits unique substrate specificity. Thus, these proteins define an ancient structurally conserved family involved in diverse metabolic pathways including inositol signaling, gluconeogenesis, sulfate assimilation, and possibly quinone metabolism. Furthermore, we suggest that this protein family identifies candidate enzymes to account for both the therapeutic and toxic actions of Li+ as it is used in patients treated for manic depressive disease.

3D plane-based egomotion for SLAM on semi-structured environment

Several works deal with 3D data in SLAM problem. Data come from a 3D laser sweeping unit or a stereo camera, both providing a huge amount of data. In this paper, we detail an efficient method to extract planar patches from 3D raw data. Then, we use these patches in an ICP-like method in order to address the SLAM problem. Using ICP with planes is not a trivial task. It needs some adaptation from the original ICP. Some promising results are shown for outdoor environment.

Vapor-liquid equilibria using the Gibbs energy and the common tangent plane criterion

Phase thermodynamics is often perceived as a difficult subject that many students never become fully comfortable with. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based on the common tangent plane criterion (the Gibbs stability test), is presented in this paper. From a T-composition phase diagram for the mixture, the temperature is set at different values: above, intermediate to, and below the boiling temperatures of the pure components, to intersect different regions of the system. Students prepare an Excel spreadsheet where the Gibbs energy of mixing of the vapor and liquid mixtures are calculated and represented over the whole range of compositions and then, apply the Gibbs stability test to ascertain the aggregation state of the system and to calculate the VL phase equilibrium compositions. Finally, Matlab is used to generate the 3D Gibbs energy of mixing surfaces for both phases over the whole range of temperatures which facilitates the geometrical interpretation of the vapor-liquid equilibrium.

Pitfalls on computing liquid-liquid phase equilibria using the k-value method

Poster presented in the 11th Mediterranean Congress of Chemical Engineering, Barcelona, October 21-24, 2008.

Method for targetless tracking subpixel in-plane movements

We present a targetless motion tracking method for detecting planar movements with subpixel accuracy. This method is based on the computation and tracking of the intersection of two nonparallel straight-line segments in the image of a moving object in a scene. The method is simple and easy to implement because no complex structures have to be detected. It has been tested and validated using a lab experiment consisting of a vibrating object that was recorded with a high-speed camera working at 1000 fps. We managed to track displacements with an accuracy of hundredths of pixel or even of thousandths of pixel in the case of tracking harmonic vibrations. The method is widely applicable because it can be used for distance measuring amplitude and frequency of vibrations with a vision system.

Characterization of the interfaces between Au(hkl) single crystal basal plane electrodes and [Emmim][Tf2N] ionic liquid

The interface between Au(hkl) basal planes and the ionic liquid 1-Ethyl-2,3-dimethyl imidazolium bis(trifluoromethyl)sulfonil imide was investigated by using both cyclic voltammetry and laser-induced temperature jump. Cyclic voltammetry showed characteristic features, revealing surface sensitive processes at the interfaces Au(hkl)/[Emmim][Tf2N]. From laser-induced heating the potential of maximum entropy (pme) is determined. Pme is close to the potential of zero charge (pzc) and, therefore, the technique provides relevant interfacial information. The following order for the pme values has been found: Au(111) > Au(100) > Au(110). This order correlates well with work function data and values of pzc in aqueous solutions.

A definition of primitive art / Phillip H. Lewis, Curator, Primitive Art.

v.36:no.10(1961)