Online Independent Set Beyond the Worst-Case: Secretaries, Prophets, and Periods

We investigate online algorithms for maximum (weight) independent set on graph classes with bounded inductive independence number like, e.g., interval and disk graphs with applications to, e.g., task scheduling and spectrum allocation. In the online setting, it is assumed that nodes of an unknown graph arrive one by one over time. An online algorithm has to decide whether an arriving node should be included into the independent set. Unfortunately, this natural and practically relevant online problem cannot be studied in a meaningful way within a classical competitive analysis as the competitive ratio on worst-case input sequences is lower bounded by $\Omega(n)$. As a worst-case analysis is pointless, we study online independent set in a stochastic analysis. Instead of focussing on a particular stochastic input model, we present a generic sampling approach that enables us to devise online algorithms achieving performance guarantees for a variety of input models. In particular, our analysis covers stochastic input models like the secretary model, in which an adversarial graph is presented in random order, and the prophet-inequality model, in which a randomly generated graph is presented in adversarial order. Our sampling approach bridges thus between stochastic input models of quite different nature. In addition, we show that our approach can be applied to a practically motivated admission control setting. Our sampling approach yields an online algorithm for maximum independent set with competitive ratio $O(\rho^2)$ with respect to all of the mentioned stochastic input models. for graph classes with inductive independence number $\rho$. The approach can be extended towards maximum-weight independent set by losing only a factor of $O(\log n)$ in the competitive ratio with $n$ denoting the (expected) number of nodes

A Compact Linear Programming Relaxation for Binary Sub-modular MRF

We propose a novel compact linear programming (LP) relaxation for binary sub-modular MRF in the context of object segmentation. Our model is obtained by linearizing an $l_1^+$-norm derived from the quadratic programming (QP) form of the MRF energy. The resultant LP model contains significantly fewer variables and constraints compared to the conventional LP relaxation of the MRF energy. In addition, unlike QP which can produce ambiguous labels, our model can be viewed as a quasi-total-variation minimization problem, and it can therefore preserve the discontinuities in the labels. We further establish a relaxation bound between our LP model and the conventional LP model. In the experiments, we demonstrate our method for the task of interactive object segmentation. Our LP model outperforms QP when converting the continuous labels to binary labels using different threshold values on the entire Oxford interactive segmentation dataset. The computational complexity of our LP is of the same order as that of the QP, and it is significantly lower than the conventional LP relaxation

Using microorganisms for cleaning oil-contaminated concrete

Revealed that the distribution of spots on the surface of the concrete depends on its density and structure, and the penetration of oil into the concrete occurs through micro- and nano-pores and cracks of the further spread of spots along the pathways. It was found that the use of hydrocarbon-oxidizing microorganisms strains as Micrococcus luteus IS16, M. varians IS41, micromycetes: Aspergillus sp., Penicillium sp., Alternaria sp., thiobacteria Acidithiobacillus ferrooxidans Ach1, A. ferrooxidans Ach2 promising for biological treatment of oil-contaminated concrete. Create optimal conditions for maintaining the activity of microorganisms: 55,0 ± 15,0% moisture, nutrients, temperature 38,0 ± 2,00C, trace elements, optimize the biodegradation of petroleum hydrocarbons

Infrared spectroscopy of small-molecule endofullerenes

Hydrogen is one of the few molecules which has been incarcerated in the molecular cage of C$_{60}$ and forms endohedral supramolecular complex H$_2$@C$_{60}$. In this confinement hydrogen acquires new properties. Its translational motion becomes quantized and is correlated with its rotations. We applied infrared spectroscopy to study the dynamics of hydrogen isotopologs H$_2$, D$_2$ and HD incarcerated in C$_{60}$. The translational and rotational modes appear as side bands to the hydrogen vibrational mode in the mid infrared part of the absorption spectrum. Because of the large mass difference of hydrogen and C$_{60}$ and the high symmetry of C$_{60}$ the problem is identical to a problem of a vibrating rotor moving in a three-dimensional spherical potential. The translational motion within the C$_{60}$ cavity breaks the inversion symmetry and induces optical activity of H$_2$. We derive potential, rotational, vibrational and dipole moment parameters from the analysis of the infrared absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H$_2$@C$_{60}$. The same parameters were used to predict H$_2$ energies inside C$_{70}$[Xu et al., J. Chem. Phys., {\bf 130}, 224306 (2009)]. We compare the predicted energies and the low temperature infrared absorption spectra of H$_2$@C$_{70}$.Comment: Updated author lis

Precise measurements of UV atomic lines: Hyperfine structure and isotope shifts in the 398.8 nm line of Yb

We demonstrate a technique for frequency measurements of UV transitions with sub-MHz precision. The frequency is measured using a ring-cavity resonator whose length is calibrated against a reference laser locked to the $D_2$ line of $^{87}$Rb. We have used this to measure the 398.8 nm ${^1S}_0 \leftrightarrow {^1P}_1$ line of atomic Yb. We report isotope shifts of all the seven stable isotopes, including the rarest isotope $^{168}$Yb. We have been able to resolve the overlapping $^{173}$Yb($F = 3/2$) and $^{172}$Yb transitions for the first time. We also obtain high-precision measurements of excited-state hyperfine structure in the odd isotopes, $^{171}$Yb and $^{173}$Yb. The measurements resolve several discrepancies among earlier measurements.Comment: 7 pages, 6 figure

Singular del Pezzo surfaces that are equivariant compactifications

We determine which singular del Pezzo surfaces are equivariant compactifications of G_a^2, to assist with proofs of Manin's conjecture for such surfaces. Additionally, we give an example of a singular quartic del Pezzo surface that is an equivariant compactification of a semidirect product of G_a and G_m.Comment: 14 pages, main result extended to non-closed ground field

Mechanisms underlying clinical efficacy of Angiotensin II type 2 receptor (AT(2)R) antagonist EMA401 in neuropathic pain: clinical tissue and in vitro studies

BACKGROUND: The clinical efficacy of the Angiotensin II (AngII) receptor AT(2)R antagonist EMA401, a novel peripherally-restricted analgesic, was reported recently in post-herpetic neuralgia. While previous studies have shown that AT(2)R is expressed by nociceptors in human DRG (hDRG), and that EMA401 inhibits capsaicin responses in cultured hDRG neurons, the expression and levels of its endogenous ligands AngII and AngIII in clinical neuropathic pain tissues, and their signalling pathways, require investigation. We have immunostained AngII, AT(2)R and the capsaicin receptor TRPV1 in control post-mortem and avulsion injured hDRG, control and injured human nerves, and in cultured hDRG neurons. AngII, AngIII, and Ang-(1-7) levels were quantified by ELISA. The in vitro effects of AngII, AT(2)R agonist C21, and Nerve growth factor (NGF) were measured on neurite lengths; AngII, NGF and EMA401 effects on expression of p38 and p42/44 MAPK were measured using quantitative immunofluorescence, and on capsaicin responses using calcium imaging. RESULTS: AngII immunostaining was observed in approximately 75% of small/medium diameter neurons in control (n = 5) and avulsion injured (n = 8) hDRG, but not large neurons i.e. similar to TRPV1. AngII was co-localised with AT(2)R and TRPV1 in hDRG and in vitro. AngII staining by image analysis showed no significant difference between control (n = 12) and injured (n = 13) human nerves. AngII levels by ELISA were also similar in control human nerves (4.09 ± 0.36 pmol/g, n = 31), injured nerves (3.99 ± 0.79 pmol/g, n = 7), and painful neuromas (3.43 ± 0.73 pmol/g, n = 12); AngIII and Ang-(1-7) levels were undetectable (<0.03 and 0.05 pmol/g respectively). Neurite lengths were significantly increased in the presence of NGF, AngII and C21 in cultured DRG neurons. AngII and, as expected, NGF significantly increased signal intensity of p38 and p42/44 MAPK, which was reversed by EMA401. AngII mediated sensitization of capsaicin responses was not observed in the presence of MAP kinase inhibitor PD98059, and the kinase inhibitor staurosporine. CONCLUSION: The major AT(2)R ligand in human peripheral nerves is AngII, and its levels are maintained in injured nerves. EMA401 may act on paracrine/autocrine mechanisms at peripheral nerve terminals, or intracrine mechanisms, to reduce neuropathic pain signalling in AngII/NGF/TRPV1-convergent pathways

Nociceptin/Orphanin FQ receptor expression in clinical pain disorders and functional effects in cultured neurons

The Nociceptin/Orphanin FQ peptide receptor (NOP), activated by its endogenous peptide ligand Nociceptin/Orphanin FQ (N/OFQ), exerts several effects including modulation of pain signalling. We have examined, for the first time, the tissue distribution of the NOP receptor in clinical visceral and somatic pain disorders by immunohistochemistry, and assessed functional effects of NOP and [micro] opioid receptor activation in cultured human and rat dorsal root ganglion (DRG) neurons. Quantification of NOP-positive nerve fibres within the bladder sub-urothelium revealed a remarkable several-fold increase in Detrusor Overactivity (p<0.0001) and Painful Bladder Syndrome patient specimens (p=0.0014), compared to controls. In post-mortem control human DRGs, 75-80% of small/medium neurons (<=50 [micro]m diameter) in the lumbar (somatic) and sacral (visceral) DRG were positive for NOP, and fewer large neurons; avulsion-injured cervical human DRG neurons showed similar numbers. NOP-immunoreactivity was significantly decreased in injured peripheral nerves (p=0.0004), and also in painful neuromas (p=0.025). Calcium imaging studies in cultured rat DRG neurons demonstrated dose-dependent inhibition of capsaicin responses in the presence of N/OFQ, with an IC50 of 8.6 pM. In cultured human DRG neurons, 32% inhibition of capsaicin responses was observed in the presence of 1 pM N/OFQ (p<0.001). The maximum inhibition of capsaicin responses was greater with N/OFQ than [mu]-opioid receptor agonist DAMGO. Our findings highlight the potential of NOP agonists, particularly in urinary bladder overactivity and pain syndromes. The regulation of NOP expression in visceral and somatic sensory neurons by target-derived neurotrophic factors deserves further study, and the efficacy of NOP selective agonists in clinical trials

Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations

Two-dimensional Bloch electrons in a uniform magnetic field exhibit complex energy spectrum. When static electric and magnetic modulations with a checkerboard pattern are superimposed on the uniform magnetic field, more structures and symmetries of the spectra are found, due to the additional adjustable parameters from the modulations. We give a comprehensive report on these new symmetries. We have also found an electric-modulation induced energy gap, whose magnitude is independent of the strength of either the uniform or the modulated magnetic field. This study is applicable to experimentally accessible systems and is related to the investigations on frustrated antiferromagnetism.Comment: 8 pages, 6 figures (reduced in sizes), submitted to Phys. Rev.

Theoretical and Experimental Studies of Schottky Diodes That Use Aligned Arrays of Single Walled Carbon Nanotubes

We present theoretical and experimental studies of Schottky diodes that use aligned arrays of single walled carbon nanotubes. A simple physical model, taking into account the basic physics of current rectification, can adequately describe the single-tube and array devices. We show that for as grown array diodes, the rectification ratio, defined by the maximum-to-minimum-current-ratio, is low due to the presence of m-SWNT shunts. These tubes can be eliminated in a single voltage sweep resulting in a high rectification array device. Further analysis also shows that the channel resistance, and not the intrinsic nanotube diode properties, limits the rectification in devices with channel length up to ten micrometer.Comment: Nano Research, 2010, accepte