On the nonlinear statistics of range image patches

In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford

Free α-Oxiranyl Amino Acids

Analogues of natural amino acids, in which the α-proton is replaced by an unsubstituted epoxide ring, are potential mechanism-based inhibitors for pyridoxal phosphate dependent enzymes.1 Yet, free α-oxiranyl amino acids have remained elusive until now. The synthesis of an α-(phenyl-substituted)oxiranyl amino ester has been reported. However, the accessibility and stability of the corresponding free, zwitterionic α-oxiranyl amino acid remained an open question.

METHOD FOR THE SYNTHESIS OF α-OXRANYL AMINO ACIDS

The present invention is related to a novel class of decar-boxylase enzyme inhibitors consisting of α-oxiranyl amino acids and derivatives thereof and a method of synthesizing Such compounds

A mapping approach to synchronization in the "Zajfman trap": stability conditions and the synchronization mechanism

We present a two particle model to explain the mechanism that stabilizes a bunch of positively charged ions in an "ion trap resonator" [Pedersen etal, Phys. Rev. Lett. 87 (2001) 055001]. The model decomposes the motion of the two ions into two mappings for the free motion in different parts of the trap and one for a compressing momentum kick. The ions' interaction is modelled by a time delay, which then changes the balance between adjacent momentum kicks. Through these mappings we identify the microscopic process that is responsible for synchronization and give the conditions for that regime.Comment: 12 pages, 9 figures; submitted to Phys Rev

The Nonlinear Statistics of High-Contrast Patches in Natural Images

Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely “sparse” with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases.Mathematic

Synthesis of Higher α-Chlorovinyl and α-Bromovinyl Amino Acids: The Amino Protecting Group Determines the Reaction Course

N-Trifluoroacetyl α-vinyl amino esters are smoothly converted to the corresponding α-chlorovinyl or α-bromovinyl amino esters through the agency of phenyselenyl chloride or phenylselenyl bromide, respectively, followed by oxidation and pyrolysis. Exclusively the (E)-extemal halovinyl isomer and the internal halovinyl isomer are observed. The amino protecting group is a critical determinant of the reaction course (alkene addition vs. 5-exo-trig-like cyclization)

α-VINYLLYSINE AND α-VINYLARGININE ARE TIME-DEPENDENT INHIBITORS OF THEIR COGNATE DECARBOXYLASES

(±)-α-Vinyllysine and (±)-α-vinylarginine display time-dependent inhibition of L-lysine decarboxylase from B. cadaveris, and L-arginine decarboxylase from E. coli, respectively. A complete Kitz-Wilson analysis has been performed using a modification of the Palcic continuous UV assay for decarboxylase activity

Changing the Support of a Spatial Covariate: A Simulation Study

Researchers are increasingly able to capture spatially referenced data on both a response and a covariate more frequently and in more detail. A combination of geostatisical models and analysis of covariance methods may be used to analyze such data. However, very basic questions regarding the effects of using a covariate whose support differs from that of the response variable must be addressed to utilize these methods most efficiently. In this experiment, a simulation study was conducted to assess the following: (i) the gain in efficiency when geostatistical models are used, (ii) the gain in efficiency when analysis of covariance methods are used, and (iii) the effects of including a covariate whose support differs from that of the response variable in the analysis. This study suggests that analyses which both account for spatial structure and exploit information from a covariate are most powerful. Also, the results indicate that the support of the covariate should be as close as possible to the support of the response variable to obtain the most accurate experimental results