Generic tropical initial ideals of Cohen-Macaulay algebras

We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra R over an algebraically closed field k. Building on work of Römer and Schmitz, we give a formula for each initial ideal, and we express the associated quasivaluations in terms of certain I-adic filtrations. As a corollary, we show that in the case that R is a domain, every initial ideal coming from the codimension 1 skeleton of the tropical variety is prime, so “generic presentations of Cohen-Macaulay domains are well-poised in codimension 1.”     

Multivalent binding of small guest molecules and proteins to molecular printboards inside microchannels

Beta-Cyclodextrin (beta-CD) monolayers have been immobilized in microchannels. The host-guest interactions on the beta-CD monolayers inside the channels were comparable to the interactions on beta-CD monolayers on planar surfaces, and a divalent fluorescent guest attached with a comparable binding strength. Proteins were attached to these monolayers inside microchannels in a selective manner by employing a strategy that uses streptavidin and orthogonal linker molecules. The design of the chip, which involved a large channel that splits into four smaller channels, allowed the channels to be addressed separately and led to the selective immobilization of antibodies. Experiments with labeled antibodies showed the selective immobilization of these antibodies in the separate channels.     

Aerial Vehicle Search-Path Optimization: A Novel Method for Emergency Operations

This paper presents a novel search-path optimization method for moving target search by an aerial vehicle, applicable to realistically sized search areas. For such missions, long endurance vehicles are needed, which are usually fixed-winged. The proposed method accounts for flight kinematics of fixed-wing and rotary-wing aerial vehicles. It additionally accounts for movements of the target, considerably increasing complexity of search-path optimization, compared to a static target. The objective is to maximize the probability to detect a conditionally deterministic moving target within a given time period. We propose a first K-step-lookahead planning method that takes flight kinematic constraints into account and in which the target and platform state space are heterogeneous. It consists of a binary integer linear program that yields a physically feasible search-path, while maximizing the probability of detection. It is based on the Max-K-Coverage problem, as it selects K waypoints while maximizing the probability that a target is within the field of view of a platform at one of these waypoints. This K-step-lookahead planning method is embedded in an iterative framework, where the probability of overlooking a target is fed back to the controller after observations are made. Simulations show the applicability and effectiveness of this method.     

Experimental plant for simultaneous production of 14N and 15N by 15N/14N exchange in NO,NO2–HNO3 system under pressure

An experimental study on ¹⁴N and ¹⁵N simultaneous separation using the chemical exchange in NO, NO₂–HNO₃ system under pressure is presented. The influence of the pressure and of the interstage 10 M HNO₃ flow rate on the separation of ¹⁴N and ¹⁵N was measured on a packed column with product and waste refluxers. At steady state and 1.8 atm (absolute), the isotopic concentration at the bottom of the separation column was 0.563 at% ¹⁵N, and in the top of the column was 0.159 at% ¹⁵N. The height equivalent to a theoretical plate and interstage 10 M HNO₃ flow rate values, obtained in these experimental conditions, allows the separation of ¹⁴N highly depleted of ¹⁵N and of ¹⁵N at 99 at% ¹⁵N concentration.     

First Long-Distance SRN1 on a propargylic chloride

We report here the first example of a Long-Distance S_RN1 (LD-S_RN1) reaction on a propargylic chloride. The reaction of 1-(3-chloroprop-1-ynyl)-4-nitrobenzene (1) with nitronate anions led to both the formation of the C-alkylation product through an LD-S_RN1 mechanism and the ethylenic compound resulting from nitrous acid elimination on the C-alkylation product 2. In contrast with previous work on LD-S_RN1 reactivity, no O-alkylation product was observed. Only one original product 4 was isolated under phase transfer conditions, resulting from a nucleophilic attack by 2-nitropropane anion on the electrophilic alkyne. This LD-S_RN1 reactivity did not extend to sulfinate anions; the reaction of 1 with sulfinate anions yielded original ethylenic disulfone compounds which were formed via an ionic process.     

An Interacting Particle Model and a Pieri-Type Formula for the Orthogonal Group

We introduce a new interacting particle model with blocking and pushing interactions. Particles evolve on ?₊ jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q∈(0,1). We show that the model involves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases—q=0 and q=1—lead, respectively, to the random tiling model studied in Borodin and Kuan (Commun. Pure Appl. Math. 67:831–894, 2010) and the random matrix model considered in forthcoming paper of Defosseux (Electr. Commun. Probab., 2012).     

Temporal predictions based on a gradual change in tempo

Previous studies investigating sensitivity to step changes in tempo and prediction of tone onset time have generally utilized isochronous sequences. This study investigates subjects' ability to detect deviations from a gradual change in the tempo of a tone sequence (experiment 1) and their judgment of the perceptually optimal timing of this tone (experiment 2). In experiment 1, inter-onset-intervals within pairs of eight-tone sequences followed a geometric progression to create a gradual tempo change. In one sequence, the final tone was presented either earlier or later than specified by the progression. Subjects performed well at detecting deviations that exaggerated the tempo progression but poorly when it was counteracted. Experiment 2 used similar pairs except that the final tone was always presented earlier in one sequence than the other. Final interval length was adaptively adjusted to subjects' judgments; it was adjudged in best agreement with the progression when its length was roughly half way between the mathematically correct value and the length of the penultimate interval. The data support "multiple-look" and entrainment models of tempo sensitivity and suggest that temporal prediction is based less on the tempo contour of a whole sequence than on the duration of the preceding interval.     

Simultaneous time- and wavelength-resolved fluorescence spectroscopy for near real-time tissue diagnosis

A novel fiber-optic-based method for simultaneous time- and wavelength-resolved fluorescence spectroscopy for the rapid diagnosis of diseased tissue is demonstrated. By combining multiple bandpass and dichroic filters (405/40, 460/50, and 550/50) with different lengths of optical fiber (1, 10, and 19 m) acting as an optical delay this system enables the near real-time acquisition and characterization of time-resolved fluorescence spectra using a single detector and excitation input. The recording of multiple fluorescence response pulses at selected wavelengths can be completed in hundreds of nanoseconds, which provides the capability of a real-time characterization of biological systems.     

The non-linear least squares method in non-isothermal kinetics

The non-isothermal least squares method for the evaluation of the kinetics parameters was generalized to non-isothermal kinetics of heterogeneous reactions.