On a problem of Erdős and Lovász: Random lines in a projective plane

Letn(k) be the least size of an intersecting family ofk-sets with cover numberk, and let _k denote any projective plane of orderk–1.Theorem There is a constant A such that ifH is a random set ofm Aklogk lines from _k then P_r(H<)0(k).Corollary If there exists a _k thenn(k)=O(klogk). These statements were conjectured by P. Erds and L. Lovász in 1973.Supported in part by NSF-DMS87-83558 and AFOSR grants 89-0066, 89-0512 and 90-0008     

A General Deterministic Treatment of Derivatives in Particle Methods

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using “one-sided” integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.     

On lattices with M:obius function ±1, 0

We provide simple arguments of a geometric nature to explain why the Möbius functions of certain lattices take only the values –1, 0, 1.Supported in part by NSF Grant MCS83-01867 and by a Sloan Research Fellowship.     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Thermal stability and reaction properties of passivated Al/CuO nano-thermite

Thermal stability and reaction properties of Al-CuO system, a mixture of 50-200 nm aluminum nanoparticles passivated by nitrocellulose and 12 nm copper (II) oxide, were investigated with microstructure characterization, differential thermal analysis (DTA), and thermogravimetric analysis (TGA). Transmission electron microscopy observation confirmed that the passivation coating successfully hinders the oxidization. TGA revealed that the passivation shell does not influence the ignition temperature of the thermite reaction. Reaction chemistry of the nano-thermite was elucidated by heating the composite both in inert ambient and vacuum. It was found that the thermite reaction composes of three continuing steps: At 570 °C, Al is oxidized into Al₂O₃ by reacting with CuO, which forms Cu₂O and produces a significant amount of heat. Subsequently two endothermic reactions occur. Starting at 800 °C, alumina reacts with Cu₂O and forms CuAlO₂. Above this temperature CuAlO₂ will decompose and eventually produce alumina, Cu, and O₂ at 1000 °C. Since the nano-thermite reaction pathway differs greatly from bulk thermite reactions, these results are important to develop a nano-thermite platform that can be used for a novel low cost, low temperature, and copper based microjoining and advance IC packaging.     

Monitoring the brain metabolites of children with acute encephalopathy caused by the H1N1 virus responsible for the 2009 influenza pandemic: a quantitative in vivo H MR spectroscopy study

Background and Purpose

Influenza viral infection, which results in central nervous system dysfunction, is a major cause of acute encephalopathy (AE). The purpose of this study was to investigate the changes in the concentrations of brain metabolites in children with AE using single-voxel magnetic resonance spectroscopy (MRS) and to provide diagnostic information about the relationship between the symptoms of AE and metabolite concentrations.

Materials and Methods

The subjects were 10 children (mean age: 6.2 years; range: 1–13) with AE caused by the novel influenza A virus responsible for the 2009 influenza pandemic. The serial MRS data (TE/TR=30/5000 ms, 3 T) acquired from the basal ganglia (BG) and centrum semiovale (CS) of each patient were categorized into three periods: (1) initial neurological symptom presentation and the start of treatment (n= 10), (2) short-term follow-up (n= 9) and (3) long-term follow-up (n= 3). As controls, the magnetic resonance (MR) spectra of eight age-matched children were also investigated.

Results

In both regions, the concentrations of the major metabolites (N-acetylaspartate, creatine, choline, myo-inositol, glutamate/glutamine complex and glutamate) only showed minor fluctuations between the three periods. On the other hand, higher levels of taurine (Tau) were observed in the BG during the second period (P=.005), and increased levels of glucose were observed in the CS during the first (P=.005) and second (P=.036) periods.

Conclusions

Serial monitoring of brain metabolite changes was carried out with a clinical MR system. The concentrations of major metabolites only displayed very minor fluctuations in response to mild H1N1-related AE. However, a higher Tau concentration was found to be associated with neurological symptoms. Further studies are required to improve our understanding of the detailed activity of Tau in AE.     

A first-principles study of surface and subsurface H on and in Ni(1 1 1): diffusional properties and coverage-dependent behavior

Periodic, self-consistent, density functional theory (GGA-PW91) calculations are performed for both surface and subsurface atomic hydrogen on and in Ni(1 1 1). At a low coverage (θ=0.25 ML), the binding energies (BEs) of a hydrogen atom in surface fcc, subsurface octahedral (first layer), and subsurface octahedral (second layer) sites are −2.89, −2.18, and −2.11 eV, respectively. The activation energy barriers for hydrogen diffusion from the surface to the first subsurface layer and from the first to the second subsurface layer are estimated to be 0.88 and 0.52 eV, respectively. In the entire coverage range studied, hydrogen occupies surface fcc and hcp sites and subsurface octahedral sites. In addition, the magnitude of the BE per hydrogen atom and the magnetization of the nickel slabs both decrease as hydrogen coverage increases. Vibrational frequencies of hydrogen at various surface and subsurface sites are calculated and are in reasonable agreement with experimental data. A phase stability calculation with a 2 × 2 surface unit cell shows that a p(2 × 2)-2H overlayer structure (θ=0.5 ML) and a p(1 × 1)-1H structure (θ=1.0 ML) are stable at low hydrogen pressures, in agreement with numerous experimental results. A very large increase in pressure is required to populate subsurface sites. After such an increase occurs, the first subsurface layer is filled completely.     

Broken symmetries and pattern formation in two-frequency forced faraday waves

We exploit the approximate (broken) symmetries of time translation, time reversal, and Hamiltonian structure to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Using explicit parameter symmetries we determine, for the case of two-frequency forcing, how the strength of observed three-wave interactions depends on the frequency ratio and on the relative phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.     

Continuous‐scan capability at SSRL and applications to X‐ray diffraction

Typical X‐ray diffraction measurements are made by moving a detector to discrete positions in space and then measuring the signal at each stationary position. This step‐scanning method can be time‐consuming, and may induce vibrations in the measurement system when the motors are accelerated and decelerated at each position. Furthermore, diffraction information between the data points may be missed unless a fine step‐scanning is used, which further increases the total measurement time. To utilize beam time efficiently, the motor acceleration and deceleration time should be minimized, and the signal‐to‐noise ratio should be maximized. To accomplish this, an integrated continuous‐scan system was developed at the Stanford Synchrotron Radiation Lightsource (SSRL). The continuous‐scan system uses an in‐house integrated motor controller system and counter/timer electronics. SPEC software is used to control both the hardware and data acquisition systems. The time efficiency and repeatability of the continuous‐scan system were tested using X‐ray diffraction from a ZnO powder and compared with the step‐scan technique. Advantages and limitations of the continuous‐scan system and a demonstration of variable‐velocity continuous scan are discussed.