Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes

It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample to be sparse. Its running time is bounded by c(d)n ², where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper. This work was done while S.Y. Oudot was a post-doctoral fellow at Stanford University. His email there is no longer valid.     

Ambient noise cross correlation in free space: theoretical approach

It has been experimentally demonstrated that the Green's function between two points could be recovered using the cross-correlation function of the ambient noise measured at these two points. This paper investigates the theory behind this result in the simple case of a homogeneous medium with attenuation.     

The saturation scale and its x-dependence from Λ polarization studies

The transverse polarization of forward Λ   hyperons produced in high-energy p–A$p\text{–}A$ collisions is expected to display an extremum at a transverse momentum around the saturation scale. This was first observed within the context of the McLerran–Venugopalan model which has an x  -independent saturation scale. The extremum arises due to the kt$k_t$-odd nature of the polarization-dependent fragmentation function, which probes approximately the derivative of the dipole scattering amplitude. The amplitude changes most strongly around the saturation scale, resulting in a peak in the polarization. We find that the observation also extends to the more realistic case in which the saturation scale Qs$Q_s$ is x-dependent. Since a range of x   and therefore Qs$Q_s$ values is probed at a given transverse momentum and rapidity, this result is a priori not expected. Moreover, the measurement of Λ   polarization over a range of xF$x_F$ values actually provides a direct probe of the x-dependence of the saturation scale. This novel feature is demonstrated for typical LHC kinematics and for several phenomenological models of the dipole scattering amplitude. We show that although the measurement will be challenging, it may be feasible at LHC. The situation at RHIC is not favorable, because the peak will likely be at too low transverse momentum of the Λ to be a trustworthy measure of the saturation scale.     

BDD-based heuristics for binary optimization

In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems.     

Enhancing signal-to-noise ratio and resolution in low-field NMR relaxation measurements using post-acquisition digital filters

The traditional way to enhance signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) signals is to increase the number of scans. However, this procedure increases the measuring time that can be prohibitive for some applications. Therefore, we have tested the use of several post-acquisition digital filters to enhance SNR up to one order of magnitude in time domain NMR (TD-NMR) relaxation measurements. The procedures were studied using continuous wave free precession (CWFP-T₁) signals, acquired with very low flip angles that contain six times more noise than the Carr–Purcell–Meiboom–Gill (CPMG) signal of the same sample and experimental time. Linear (LI) and logarithmic (LO) data compression, low-pass infinity impulse response (LP), Savitzky–Golay (SG), and wavelet transform (WA) post-acquisition filters enhanced the SNR of the CWFP-T₁ signals by at least six times. The best filters were LO, SG, and WA that have high enhancement in SNR without significant distortions in the ILT relaxation distribution data. Therefore, it was demonstrated that these post-acquisition digital filters could be a useful way to denoise CWFP-T₁, as well as CPMG noisy signals, and consequently reducing the experimental time. It was also demonstrated that filtered CWFP-T₁ method has the potential to be a rapid and nondestructive method to measure fat content in beef and certainly in other meat samples.     

Open‐Pore Two‐Dimensional MFI Zeolite Nanosheets for the Fabrication of Hydrocarbon‐Isomer‐Selective Membranes on Porous Polymer Supports

Two‐dimensional zeolite nanosheets that do not contain any organic structure‐directing agents were prepared from a multilamellar MFI (ML‐MFI) zeolite. ML‐MFI was first exfoliated by melt compounding and then detemplated by treatment with a mixture of H₂SO₄ and H₂O₂ (piranha solution). The obtained OSDA‐free MFI nanosheets disperse well in water and can be used for coating applications. Deposits made on porous polybenzimidazole (PBI) supports by simple filtration of these suspensions exhibit an n‐butane/isobutane selectivity of 5.4, with an n‐butane permeance of 3.5×10^?7 mol m^?2 s^?1 Pa^?1 (ca. 1000 GPU).     

Improvement and simplification of synthesis of 3-aryloxy-1,2-epoxypropanes using solvent-free conditions and microwave irradiations. Relation with medium effects and reaction mechanism

Some 3-aryloxy-1,2-epoxypropanes, interesting as potential synthons in β-adrenergic receptor antagonists preparation, were obtained in excellent yields (65-96% within 2-17 min) by microwave activation (monomode system) using solid-liquid solvent-free phase transfer catalysis (PTC). The best results for the O-alkylation of some phenols with epichlorohydrin were obtained using TBAB and NaOH/K₂CO₃ (1:4 mol/mol) as phase transfer catalyst and more acceptable basic system, respectively. These new procedure is compared with classical methods. Significant specific microwave effect (non-purely thermal) was evidenced in all cases. They were discussed in terms of reaction medium and mechanism, taking into account the variations in polarity of the systems.     

Water substitution on iron centers: from 0D to 1D sandwich type polyoxotungstates

Four novel polyoxotungstates have been synthesized by reaction of the sandwich type compound [Fe (III) 4(H 2O) 10(B-beta-SbW 9O 33) 2] (6-) (noted Fe 4(H 2O) 10Sb 2W 18) with ethylenediamine (en) and/or oxalate (ox) ligands under various conditions. The one-dimensional (1D) compound [enH 2] 3[Fe (III) 4(H 2O) 8(SbW 9O 33) 2].20H 2O ( 1) is isolated at 130 degrees C and results from the elimination of two water molecules and the condensation of the polyoxotungstate precursor. The reaction of Fe 4(H 2O) 10Sb 2W 18 with oxalate ligands affords the molecular complex Na 14[Fe (III) 4(ox) 4(H 2O) 2(SbW 9O 33) 2].60H 2O ( 2) where two organic ligands substitute four water molecules, while the same reaction in the presence of en molecules at 130 degrees C leads to the formation of the functionalized 1D chain [enH 2] 7[Fe (III) 4(ox) 4(SbW 9O 33) 2].14H 2O ( 3) with protonated ethylenediamine counterions. Finally, at 160 degrees C a rearrangement of the Fe 4(H 2O) 10Sb 2W 18 polyoxotungstate is observed, and the sandwich type compound [enH 2] 5[Fe (II) 2Fe (II) 2(enH) 2(Fe (III)W 9O 34) 2].24H 2O ( 4) crystallizes. In 4, the heteroelement is a Fe (III) ion, and the water molecules on the two outer Fe (II) centers are bound to pendant monoprotonated en ligands. The four compounds have been characterized by IR spectroscopy, thermogravimetric analysis, and single crystal X-ray diffraction. A detailed study of the magnetic properties of the mixed-valent hexanuclear iron complex in 4 shows evidence of an S = 5 ground-state because of spin frustration effects. A quantification of the electronic parameters characterizing the ground state ( D = +1.12 cm (-1), E/ D = 0.15) confirms that polyoxotungstate ligands induce large magnetic anisotropy.     

Analysis on heat stress-induced hyperphosphorylation of stathmin at serine 37 in Jurkat cells by means of two-dimensional gel electrophoresis and tandem mass spectrometry

Two-dimensional gel electrophoresis (2-DE) and tandem mass spectrometry were successfully used for determination of a phosphorylation site of stathmin induced by heat stress to Jurkat cells of a human T lymphoblastic cell line. The cells were incubated for 30 min at 41 degrees C up to 45 degrees C in a serum free 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) buffered culture medium. The intracellular soluble proteins were separated by 2-DE, and some of the proteins increased their abundance by heat stress. Those proteins were identified to be calmodulin, protein kinase C substrate, thymosin beta-4 and F-actin capping protein beta-subunit by peptide mass fingerprinting (PMF) with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS). On the contrary, protein phosphatase 2C gamma-isoform, nucleophosmin, translationally controlled tumor protein, Rho GDP-dissociation inhibitor-1, eukaryotic translation initiation factors 5A and 3A subunit 2, ubiquitin-like protein SMT 3B and chloride intracellular channel protein-1 were decreased their abundance. A protein spot of M(r) 18,000 and pI 5.9 was markedly increased at temperatures higher than 43 degrees C at which the cells were led to apoptosis. The spot was identified to be stathmin of a signal relay protein which has a function of sequestering microtubule. MALDI-quadrupole ion trap (QIT)-TOF-MS/MS and immunoblotting with a monoclonal antibody specific for a phosphorylation site of stathmin showed that the spot was a phosphorylated stathmin at serine 37 (Ser 37). The phosphorylation was suppressed by treatment of cells with olomoucine of an inhibitor specific for cyclin dependent kinase (Cdk-1). These results strongly suggest that heat stress activates Cdk-1 which phosphorylates Ser 37 on the stathmin molecule. The phosphorylation may cause the functional loss of stathmin for dynamic microtubule assembly and leads Jurkat cells to cell cycle arrest and apoptosis.     

Liquid densities of THF and excess volumes for the mixture with water in a wide temperature and pressure range

In this paper densities for THF (tetrahydrofuran) and THF + water mixtures measured with the help of the Anton Paar DMA HPM vibrating tube densimeter are reported. The pure component densities of tetrahydrofuran measured in the temperature range from 278 to 437 K and pressures up to 130 MPa were correlated with the TRIDEN-System. Additionally densities of the binary mixture tetrahydrofuran + water were measured for 6 different concentrations in a temperature range from 288 to 338 K and up to 130 MPa. Excess volumes (vE)$(v^E)$ of the mixture were determined using the own correlation of the tetrahydrofuran densities and the equation of state (EoS) for water by Wagner and Pruß. Redlich–Kister polynomials were used to fit the vE-data$v^E\text{-data}$. Additionally in this work it was checked if the vibrating tube densimeter allows the determination of the miscibility gap for the system THF–water as a function of temperature and pressure.