Combinatorial data analysis: Confirmatory comparisons between sets of matrices

The task of assessing the similarity of pattern between the entries of two square matrices has been discussed extensively over the last decade, as a unifying strategy for approaching a variety of seemingly disparate statistical problems. As typically defined, the comparison depends on a measure of matrix correspondence, usually a normalized cross-product measure of some form, that is evaluated for relative size by the use of a reference distribution constructed through an equally likely permutation hypothesis defined at the level of the objects corresponding to the rows and columns of the two matrices. The extreme generality provided by this very simple framework subsumes a variety of different statistical problems, ranging from the study of spatial autocorrelation for variables observed over a set of geographic locations, to the topics of analysis of variance, the measurement of rank correlation, and confirmation techniques concerned with various conjectures of combinatorial structure that might be posited for an empirically determined measure of relationship between pairs of a given set of objects. The comparison strategies extant always assume that both matrices are fixed, and in those cases where one of the matrices codifies a given theoretical structure to be evaluated according to a second, this assumption can lead to substantial arbitrariness in how matrix similarity might be indexed, and thus, in how the comparison is implemented. As developed in this paper, exactly the same principles appropriate for use in the fixed comparison context can be extended to include matrices constructed through optimally weighted linear combinations of other sets of matrices. This generalization provides one mechanism for developing comparison strategies that allow assessment against very broad classes of matrices, which in turn serve to represent very general conjectures of possible combinatorial structure. This paper reviews some of these extensions in detail, with a particular emphasis on categorical and ordered categorical variables and whether they may reflect an empirically generated measure of object relationship.     

Gram‐Scale Enantioselective Formal Synthesis of Morphine through an ortho–para Oxidative Phenolic Coupling Strategy

A gram‐scale catalytic enantioselective formal synthesis of morphine is described. The key steps of the synthesis involve an ortho–para oxidative phenolic coupling and a highly diastereoselective “desymmetrization” of the resulting cyclohexadienone that generates three of the four morphinan ring junction stereocenters in one step. The stereochemistry is controlled from a single carbinol center installed through catalytic enantioselective hydrogenation. These transformations enabled the preparation of large quantities of key intermediates and could support a practical and scalable synthesis of morphine and related derivatives.     

Light on light: A response to Grøn

Einstein's second postulate (light-speed constancy) is modified in the following manner:(1) as to motion of light emitters, no modification is made;(2) as to motion of light absorbers, if the absorber moves with velocityv with respect to the observer, that observer will attribute to light the velocity (c+v). It is shown, with reference to the original Einstein train example, that such a modification of the second postulate restores to kinematics a concept of distant simultaneity. Thus is indicated the complicated (acausal) behavior that must be attributed to light in order that the simple behavior earlier attributed ⁽¹⁾ to matter (nonoccurrence of the Lorentz contraction) may be consistent with all known facts. A reply is made to Grøn's critique ⁽²⁾ of the earlier paper on metric standards. It is concluded that further experimental data are needed to decide the simple-light-complicated-matter versus complicated-light-simple-matter issue.     

Laser ablation of energetic polymer solutions: effect of viscosity and fluence on the splashing behavior

Laser plasma thrusters are a new kind of propulsion system for small satellites, and work with the thrust created by the laser ablation of a target. Liquid polymer solutions are very promising fuels for such systems, provided that no splashing of the target occurs, because ejection of droplets strongly decreases the performances of the system. We have investigated the nanosecond infrared laser ablation of glycidyl azide polymer solutions containing carbon nanoparticles as absorber. Shadowgraphy imaging revealed two cases, namely splashing regime and solid-like behavior. The transition between both regimes depends on the viscosity of the solution and on the laser fluence, and is explained by the recoil force acting on the target. Appropriate conditions to avoid splashing were identified, showing that this liquid polymer solution is a suitable fuel for laser plasma thrusters.     

Acoustic energy harvesting using an electromechanical Helmholtz resonator

This paper presents the development of an acoustic energy harvester using an electromechanical Helmholtz resonator (EMHR). The EMHR consists of an orifice, cavity, and a piezoelectric diaphragm. Acoustic energy is converted to mechanical energy when sound incident on the orifice generates an oscillatory pressure in the cavity, which in turns causes the vibration of the diaphragm. The conversion of acoustic energy to electrical energy is achieved via piezoelectric transduction in the diaphragm of the EMHR. Moreover, the diaphragm is coupled with energy reclamation circuitry to increase the efficiency of the energy conversion. Lumped element modeling of the EMHR is used to provide physical insight into the coupled energy domain dynamics governing the energy reclamation process. The feasibility of acoustic energy reclamation using an EMHR is demonstrated in a plane wave tube for two power converter topologies. The first is comprised of only a rectifier, and the second uses a rectifier connected to a flyback converter to improve load matching. Experimental results indicate that approximately 30 mW of output power is harvested for an incident sound pressure level of 160 dB with a flyback converter. Such power level is sufficient to power a variety of low power electronic devices.     

High throughput screening of library compounds against an oligonucleotide substructure of an RNA target

Approximately 300,000 compounds from selected libraries were screened against a subdomain of a hepatitis C viral (HCV) RNA using a high throughput flow injection mass spectrometry (FIA-MS) method with automated data storage and analysis. Samples contained 2 microM RNA target and 10 microM of each of up to ten ligands. Preliminary studies to optimize operational parameters used the binding of aminoglycosides to the A44 subdomain of bacterial RNA. Binding (confirmed by titration) and sensitivity were maximized within the constraints of the library and throughput. The mobile phase of 5 mM ammonium acetate in 50% isopropanol maintained the noncovalent complexes and provided good detection by electrospray mass spectrometry. Additionally, this composition maximized general solubility of the various classes of compounds including the oligonucleotide and organic library molecules. Cation adduction was insignificant in this screen although some solute and target dependent acetate adduction was observed. The ion trap mass spectrometer provided sufficient mass resolution to identify complexes of RNA with known components of the library. Converted mass spectral data (netCDF) were subjected to two types of statistical evaluation based on binding. The first algorithm identified noncovalent complexes that correlated with the molecular weights of the injected compounds. The second yielded the largest peak in the noncovalent complex region of the spectrum; this spectrum may or may not correlate with expected well components. Sixty-three compounds were confirmed to bind by more stringent secondary testing. Titrations, which were carried out with selected binding compounds, yielded a range of dissociation constants. Biological activity was observed for eleven confirmed binders.     

Laser-driven vehicles – from inner-space to outer-space

Laser-supported propulsion of a micro-airplane with a water-covered ablator is demonstrated. The repetitive use of an overlay structure is experimentally demonstrated with a specially designed water supply. Various transparent overlays are investigated by the CIP-based hydrodynamic code and by experiments using a pendulum and using a semi-conductor load cell. A momentum-coupling efficiency of ∼10⁴ N s/MJ is achieved by water–exotic-target experiments, in agreement with the simulation code, which predicts a maximum efficiency of ∼10⁵ N s/MJ. The concept of laser-supported propulsion can also be used for driving a Mach 5 airplane in the stratosphere, a micro-ship inside the human body, and a robot in a nuclear power reactor accident, during which large numbers of neutrons make electronic devices useless. Received: 7 October 2002 / Accepted: 20 January 2003 / Published online: 28 May 2003 RID="*" ID="*"Corresponding author. Fax: +81-3/5734-2165, E-mail: yabe@mech.titech.ac.jp