Cosmological surrealism: More than “eternal reality” is needed

Inflationary cosmology makes the universe eternal and provides for recurrent universe creation, ad infinitum — making it also plausible to assume that our Big Bang was also preceeded by others, etc.. However, GR tells us that in the parent universe's reference frame, the newborn universe's expansion will never start. Our picture of reality in spacetime has to be enlarged.Wolfson Distinguished Chair in Theoretical Physics.Also on leave from the University of Texas, Center for Particle Physics, Austin, Texas.     

Reflections on Schur-Cohn matrices and Jury-Marden tables and classification of related unit circle zero location criteria

We use the so-calledreflection coefficients (RCs) to examine, review, and classify the Schur-Cohn and Marden-Jury (SCMJ) class of tests for determining the zero location of a discrete-time system polynomial with respect to the unit circle. These parameters are taken as a platform to propose a partition of the SCMJ class into four useful types of schemes. The four types differ in the sequence of polynomials (the table) they associate with the tested polynomials by scaling factors: (A) a sequence of monic polynomials, (B) a sequence of least arithmetic operations, (C) a sequence that produces the principal minors of the Schur-Cohn matrix, and (D) a sequence that avoids division arithmetic. A direct derivation of a zero location rule in terms of the RCs is first provided and then used to track a proper zero location rule in terms of the leading coefficients of the polynomials of the B, C, and D scheme prototypes. We review many of the published stability tests in the SCMJ class and show that each can be sorted into one of these four types. This process is instrumental in extending some of the tests from stability conditions to zero location, from real to complex polynomial, in providing a proof of tests stated without a proof, or in correcting some inaccuracies. Another interesting outcome of the current approach is that a byproduct of developing a zero location rule for the Type C test is one more proof for the relation between the zero location of a polynomial and the inertia of its Schur-Cohn matrix.This research was supported by Grant No. 88-425 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.     

Evidence for new bands in the 3nu1 and 4nu1 regions of propyne

Vibrationally mediated photodissociation and room-temperature photoacoustic (PA) spectroscopy have been used for obtaining action (monitoring the yield of H photofragments) and absorption spectra of the second (3nu(1)) and third (4nu(1)) C-H acetylenic stretches overtone regions in propyne. The band contours appearing in these regions seem mostly regular even though they are perturbed, as expressed by the origin shifts in different K components, splitting of the K structure, and splitting due to resonances between neighboring states. Symmetric rotor simulations of the band contours of the PA and action spectra allowed extraction of the molecular parameters and rough estimates for the homogeneous broadening arising from energy flow to the bath vibrational states. We particularly benefited from the reduced congestion in the jet-cooled action spectra and their simulations, which enabled observation of yet unknown features in the vicinity of the 3nu(1) and 4nu(1) states. Particularly, the emergence of the new state in the 3nu(1) region was confirmed by the action spectra monitored at several differing jet temperatures, suggesting that it is a dark state in IR vibrational excitation that becomes brighter in UV excitation to the upper electronic state. The monitored and Gaussian-fitted Doppler profiles point to the release of H photofragments with low average translational energies, attributed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.     

Determining the vibrational pattern via overtone cold spectra: C-H methyl stretches of propyne

Vibrationally mediated photodissociation and photoacoustic (PA) spectroscopy were employed for studying the intramolecular dynamics of propyne initially excited to the first through fourth overtone of methyl C-H stretching modes. Room-temperature PA and jet-cooled action spectra, monitoring the absorption of the parent and the yield of the ensuing H photofragments, respectively, were obtained. The PA spectra exhibit mainly broad features, while the action spectra, due to inhomogeneous structure reduction, expose multiple peaks of recognizable shapes in the differing overtone manifolds. Symmetric rotor simulations of the band contours of the action spectra allowed retrieving of band origins and linewidths. The linewidths of the bands in each manifold enabled estimates for energy redistribution times out of the corresponding states to the bath states, the times ranging from 18+/-6 ps for two quanta of C-H excitation to subpicosecond for five quanta. The data were also analyzed in terms of a normal-mode model and a joint local-/normal-mode model. These models enabled determination of harmonic frequencies, anharmonicities, and interaction parameters reproducing the observed data in all monitored regions and provided spectral assignments. The measured Doppler profiles were well fitted by Gaussians with widths suggesting low average translational energies for the released H photofragments. These low energies and their similarities to those for dissociation of propyne isotopomers preexcited to acetylenic C-H stretches were ascribed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.     

Finding the needles in the haystack: efficient intelligence processing

As a result of communication technologies, the main intelligence challenge has shifted from collecting data to efficiently processing it so that relevant, and only relevant, information is passed on to intelligence analysts. We consider intelligence data intercepted on a social communication network. The social network includes both adversaries (eg terrorists) and benign participants. We propose a methodology for efficiently searching for relevant messages among the intercepted communications. Besides addressing a real and urgent problem that has attracted little attention in the open literature thus far, the main contributions of this paper are two-fold. First, we develop a novel knowledge accumulation model for intelligence processors, which addresses both the nodes of the social network (the participants) and its edges (the communications). Second, we propose efficient prioritization algorithms that utilize the processor’s accumulated knowledge. Our approach is based on methods from graphical models, social networks, random fields, Bayesian learning, and exploration/exploitation algorithms.     

Four random permutations conjugated by an adversary generate Sn with high probability

We prove a conjecture dating back to a 1978 paper of D.R. Musser [11], namely that four random permutations in the symmetric group S_n generate a transitive subgroup with probability for some independent of n, even when an adversary is allowed to conjugate each of the four by a possibly different element of . In other words, the cycle types already guarantee generation of a transitive subgroup; by a well known argument, this implies generation of A_n or except for probability as . The analysis is closely related to the following random set model. A random set is generated by including each independently with probability . The sumset is formed. Then at most four independent copies of are needed before their mutual intersection is no longer infinite. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 409–428, 2016     

Cutoff on all Ramanujan graphs

We show that on every Ramanujan graph \({G}\), the simple random walk exhibits cutoff: when \({G}\) has \({n}\) vertices and degree \({d}\), the total-variation distance of the walk from the uniform distribution at time \({t=\frac{d}{d-2} \log_{d-1} n + s\sqrt{\log n}}\) is asymptotically \({{\mathbb{P}}(Z > c \, s)}\) where \({Z}\) is a standard normal variable and \({c=c(d)}\) is an explicit constant. Furthermore, for all \({1 \leq p \leq \infty}\), \({d}\)-regular Ramanujan graphs minimize the asymptotic \({L^p}\)-mixing time for SRW among all \({d}\)-regular graphs. Our proof also shows that, for every vertex \({x}\) in \({G}\) as above, its distance from \({n-o(n)}\) of the vertices is asymptotically \({\log_{d-1} n}\).     

Frictional properties of surfactant-coated rod-shaped nanoparticles in dry and humid dodecane

We have investigated the effects of humidity (water content or activity from 0 to approximately 0.98) on the frictional properties of surfactant-coated ZnS nanoparticles of various shapes, specifically, nanorods and nanowires, dispersed in an organic solvent (dodecane). The friction coefficients were found to be sensitive to even trace amounts of water, increasing logarithmically with time after the systems were exposed to humid air, doubling after 2-4 h of exposure time to air of relative humidity approximately 98%. We also show that increasing the humidity caused noticeable effects on the interactions of the nanoparticles, increasing their adhesion and aggregation through capillary forces. These effects should be considered in the design of organic solvents containing nanoparticles with physisorbed surfactants, for example, lube oils with nanoparticles additives, particularly those exposed to atmospheric conditions.     

Adhesion and stable low friction provided by a subnanometer-thick monolayer of a natural polysaccharide

Using a surface forces apparatus, we have investigated the adhesive and lubrication forces of mica surfaces separated by a molecularly thin, subnanometer film of a high-molecular-weight (2.3 MDa) anionic polysaccharide from the algae Porphyridium sp. adsorbed from aqueous solution. The adhesion and friction forces of the confined biopolymer were monitored as a function of time, shearing distance, and driving velocity under a large range of compressive loads (pressures). Although the thickness of the dilute polysaccharide was <1 nm, the friction was low (coefficient of friction = 0.015), and no wear was ever observed even at a pressure of 110 atm over 3 decades of velocity, so long as the shearing distances were less than twice the contact diameter. Atomic force microscopy in solution shows that the biopolymer is able to adsorb to the mica surface but remains mobile and easily dragged upon shearing. The adhesion (adsorption) of this polysaccharide even to negatively charged surfaces, its stable low friction, its robustness (high-load carrying capacity and good wear protection), and the weak (logarithmic) dependence of the friction force on the sliding velocity make this class of polyelectrolytes excellent candidates for use in water-based lubricant fluids and as potential additives to synovial fluid in joints and other biolubricating fluids. The physical reasons for the remarkable tribological properties of the ultrathin polysaccharide monolayer are discussed and appear to be quite different from those of other polyelectrolytes and proteins that act as thick "polymer brush" layers.     

Interfacial characterization of chemical solution‐deposited thin films of PbSe on GaAs(100)

The microstructure and composition of the interfacial layer between chemically deposited PbSe and GaAs substrates were studied using high‐resolution transmission electron microscopy (HRTEM), Auger electron spectroscopy (AES), x‐ray photoelectron spectroscopy (XPS) and energy‐filtered TEM. The thickness of the interfacial layer varied significantly from direct contact of the film with the substrate to 5 nm in the thickest regions. The results established the presence of a discontinuous, amorphous intermediate layer of Ga₂O₃ at the PbSe/GaAs interface. Copyright © 2008 John Wiley & Sons, Ltd.