Semidefinite and linear programming integrality gaps for scheduling identical machines

Sherali and Adams (SIAM J Discrete Math 3:411–430, 1990) and Lovász and Schrijver (SIAM J Optim 1:166–190, 1991) developed systematic procedures to construct the hierarchies of relaxations known as lift-and-project methods. They have been proven to be a strong tool for developing approximation algorithms, matching the best relaxations known for problems like Max-Cut and Sparsest-Cut. In this work we provide lower bounds for these hierarchies when applied over the configuration LP for the problem of scheduling identical machines to minimize the makespan. First we show that the configuration LP has an integrality gap of at least 1024/1023 by providing a family of instances with 15 different job sizes. Then we show that for any integer n there is an instance with n jobs in this family such that after \(\varOmega (n)\) rounds of the Sherali–Adams (\(\text {SA}\)) or the Lovász–Schrijver (\(\text {LS}_+\)) hierarchy the integrality gap remains at least 1024/1023.     

France: genetics education for non-genetics health care providers

OBJECTIVE: This paper explores the treatment of medical genetics in undergraduate medical education, specialists' training and continuing medical education (CME) for general practitioners, specialists, nurses and midwives. METHODS: We conducted a qualitative survey of websites, published or unpublished documents, telephone interviews and mailed questionnaires. RESULTS: Genetics is a medical specialty in France, and the small number of university professors in genetics are in charge of the genetic component of medical training of all future practitioners. The study was complicated by the ongoing waves of reforms in the French health and educational systems and by the autonomy of the faculties. Specialist training and CME in genetics is heterogeneous and not organised as a priority. CONCLUSIONS: Specialist education and CME in genetics of non-geneticist health care providers needs to be adapted to the fast ongoing developments of this field of knowledge.     

Longitudinal smoothness of the holonomy groupoid

Iakovos Androulidakis and Georges Skandalis have defined a holonomy groupoid for any singular foliation. This groupoid, whose topology is usually quite bad, is the starting point for the study of longitudinal pseudodifferential calculus on such foliation and its associated index theory. These studies can be highly simplified under the assumption of the holonomy groupoid being longitudinally smooth. In this note, we rephrase the period bounding lemma that asserts that a vector field on a compact manifold admits a strictly positive lower bound for its periodic orbits in order to prove that the holonomy groupoid is always longitudinally smooth.     

One-pot enol silane formation-Mukaiyama aldol reactions: Crossed aldehyde-aldehyde coupling,thioester substrates,and reactions in ester solvents

Trimethylsilyl trifluoromethanesulfonate (TMSOTf) and a trialkylamine base promote both in situ enol silane/silyl ketene acetal formation and Mukaiyama aldol addition reactions between a variety of reaction partners in a single reaction flask. Isolation of the required enol silane or silyl ketene acetal is not necessary. For example, crossed aldol reactions between α-disubstituted aldehydes and non-enolizable aldehydes yield β-hydroxy aldehydes in good yield. In a related reaction, the common laboratory solvent ethyl acetate functions as both an enolate precursor and a green reaction solvent. When thioesters are employed as enolate precursors, high yields for additions to non-enolizable aldehydes are routinely observed.     

CTP synthetase activity assay by liquid chromatography tandem mass spectrometry in the multiple reaction monitoring mode

Cytidine 5′‐triphosphate synthetase (CTPS) is known to be a central enzyme in the de novo synthesis of CTP. We have recently demonstrated that a deficiency in CTPS1 is associated with an impaired capacity of activated lymphocytes to proliferate leading to a combined immunodeficiency disease. In order to better document its role in immunomodulation, we developed a method for measuring CTPS activity in human lymphocytes. Using liquid chromatography‐mass spectrometry, we quantified CTPS activity by measuring CTP in cell lysates. A stable isotope analog of CTP served as internal standard. We characterized the kinetic parameters V_max and K_m of CTPS and verified that an inhibition of the enzyme activity was induced after 3‐deazauridine (3DAU) treatment, a known inhibitor of CTPS. We then determined CTPS activity in healthy volunteers, in a family whose child displayed a homozygous mutation in CTPS1 gene and in patients who had developed or not a chronic lung allograft dysfunction (CLAD) after lung transplantation. Linearity of the CTP determination was observed up to 451 μmol/L, with accuracy in the 15% tolerance range. Michaelis‐Menten kinetics for lysates of resting cells were K_m=280±310 μmol/L for UTP, V_max=83±20 pmol/min and, for lysates of activated PBMCs, K_m=230±280 μmol/L for UTP, V_max=379±90 pmol/min. Treatment by 3DAU and homozygous mutation in CTPS1 gene abolished the induction of CTPS activity associated with cell stimulation, and CTPS activity was significantly reduced in the patients who developed CLAD. We conclude that this test is suitable to reveal the involvement of CTPS alteration in immunodeficiency.     

In‐situ Electrochemical X‐ray Diffraction: A Rigorous Method to Navigate within Phase Diagrams Reveals β‐Fe1+xSe as Superconductor for All x

We report the precise postsynthetic control of the composition of β‐Fe_1+xSe by electrochemistry with simultaneous tracking of the associated structural changes via in situ synchrotron X‐ray diffraction. We access the full phase width of 0.01<x<0.04 and identify the superconducting state below 8 K, which in contrast to earlier reports is independent of the composition. However, in a second set of in situ X‐ray diffraction experiments, we demonstrate that β‐Fe_1+xSe forms a new phase in the presence of oxygen above a 100 °C which has the same anti‐PbO type structure but is not superconducting down to 1.8 K. The latter process can be reversed electrochemically to reinstate the superconducting state. These observations exploit the exquisite control afforded by electrochemistry in contrast with classical approaches of chemical synthesis.     

Out-of-equilibrium microrheology inside living cells

Both forced and spontaneous motions of magnetic microbeads engulfed by Dictyostelium cells have served as experimental probes of intracellular dynamics. The complex shear modulus G*(omega), determined from active oscillatory measurements, has a power-law dynamics and increases with the probe size, reflecting intracellular structural complexity. The combined use of passive microrheology allows one to derive the power spectrum of active forces acting on intracellular phagosomes and to test the validity of the fluctuation-dissipation theorem inside living cells.     

Cross-scale effects in solar-wind turbulence

The understanding of the small-scale termination of the turbulent energy cascade in collisionless plasmas is nowadays one of the outstanding problems in space physics. In the absence of collisional viscosity, the dynamics at small scales is presumably kinetic in nature; the identification of the physical mechanism which replaces energy dissipation and establishes the link between macroscopic and microscopic scales would open a new scenario in the study of turbulent heating in space plasmas. We present a numerical analysis of kinetic effects along the turbulent energy cascade in solar-wind plasmas which provides an effective unified interpretation of a wide set of spacecraft observations and shows that, simultaneously with an increase in the ion perpendicular temperature, strong bursts of electrostatic activity in the form of ion-acoustic turbulence are produced together with accelerated beams in the ion distribution function.     

Exploring the feasibility of simultaneous electroencephalography/functional magnetic resonance imaging at 7 T

The increased blood oxygenation level-dependent contrast available at high field makes the implementation of combined EEG/fMRI experiments at 7 T highly worthwhile from the point of view of fMRI data quality, but the higher field poses greater technical challenges for achieving good quality EEG data. A study of the feasibility of recording EEG signals from human subjects at 7 T using a commercially available, MR-compatible EEG system has therefore been carried out. This involved systematic measurement of the sources of noise in EEG recordings made in the 7 T scanner and measurement of RF heating effects on a gel phantom in the presence of a 32-electrode EEG cap. Having found no significant safety concerns and identified a set-up (involving switching off the magnet's cryo-cooler pumps and mounting the EEG amplifier on a cantilever) that limited scanner-induced noise, combined EEG/fMRI experiments employing visual stimulation were then successfully carried out on two human subjects. With the use of beamformer-based analysis of the EEG data, driven responses and alpha-band, event-related desynchronisation were identified in both subjects.