Log Eta Research Articles

Lower bounds on the state complexity of population protocols

Population protocols are a model of computation in which an arbitrary number of indistinguishable finite-state agents interact in pairs. The goal of the agents is to decide by stable consensus whether their initial global configuration satisfies a given property, specified as a predicate on the set of configurations. The state complexity of a predicate is the number of states of a smallest protocol that computes it. Previous work by Blondin et al. has shown that the counting predicates x ge eta have state complexity mathcal {O}(log eta ) for leaderless protocols and mathcal {O}(log log eta ) for protocols with leaders. We obtain the first non-trivial lower bounds: the state complexity of x ge eta is Omega (log log eta ) for leaderless protocols, and the inverse of a non-elementary function for protocols with leaders.

Uniform Machine Scheduling with Predictions

The revival in learning theory has provided us with improved capabilities for accurate predictions. This work contributes to an emerging research agenda of online scheduling with predictions by studying the makespan minimization in uniformly related machine non-clairvoyant scheduling with job size predictions. Our task is to design online algorithms that effectively use predictions and have performance guarantees with varying prediction quality. We first propose a simple algorithm-independent prediction error measurement to quantify prediction quality. To effectively use the predicted job sizes, we design an offline improved 2-relaxed decision procedure approximating the optimal schedule. With this decision procedure, we propose an online O(min{log eta, log m})-competitive algorithm that assumes a known prediction error. Finally, we extend this algorithm to construct a robust O(min{log eta, log m})-competitive algorithm that does not assume a known error. Both algorithms require only moderate predictions to improve the well-known Omega(log m) lower bound, showing the potential of using predictions in managing uncertainty.

Heat capacity, entropy, configurational entropy, and viscosity of magnesium silicate glasses and liquids

In this work, five Mg-silicate glasses with compositions between MgSiO_3 and Mg_2SiO_4 were synthesized by aerodynamic levitation combined with laser melting. Low-temperature heat capacity (C_p) was measured (by relaxation calorimetry in the range 2–310 K) for all of them, with the resulting vibrational entropies at T = 298.15 K: sample MG50 with composition Mg_{0.996}SiO_{2.996} and entropy 72.88 J mol^{-1} K^{-1}; MG54 Mg_{1.174}SiO_{3.174} 78.54; MG58 Mg_{1.364}SiO_{3.364} 85.05; MG62 Mg_{1.611}SiO_{3.611} 91.40; and MG67 Mg_{1.907}SiO_{3.907} 102.75. Heat capacity of the glasses is higher than that of the corresponding crystal mixtures below 200 K but plunges below the C_{p,mathrm{crystal}} at higher temperatures. High-temperature C_p was measured (by differential scanning calorimetry in the range 300–970 K) for MG50 and MG67 up to approx 1000 K. Using our C_p data, selected data for entropies of fusion, C_p of crystals, and fictive temperatures, the configurational entropy (S_mathrm{conf}) at glass transition temperature (T_mathrm{g}) were calculated. For the near-forsterite glass MG67, the S_mathrm{conf} is 1.9 J mol^{-1} K^{-1} at T_mathrm{g} = 1040 K. As this small value is a difference of several large numbers, its uncertainty is relatively high; we consider a conservative estimate of 15 J mol^{-1} K^{-1}. Using the expression log eta = A + B/[T S_mathrm{conf}(T)], the available experimental viscosities (eta ) and the temperature-dependent configurational entropy from our work, we refined the parameters A = -2.34 and B = 76,500 for this equation, with S_mathrm{conf} (T) = 1.90+(83.7 ln (T/1040)). The configurational entropy for the enstatitic MG50 glass is 16.8 J mol^{-1} K^{-1} at T_mathrm{g} = 1063 K. The presented data can be combined with enthalpies of formation and thermophysical properties of Mg-silicate glasses for models that could elucidate geological and geophysical observations in the crust and mantle of the Earth.

Viscoelastic properties of phonosurgical biomaterials at phonatory frequencies

The purpose of this study was to examine the functional biomechanical properties of several injectable biomaterials currently or potentially used for vocal fold augmentation. Rheometric investigation of phonosurgical materials in vitro. Linear viscoelastic shear properties of 3% bovine collagen (atelocollagen), micronized AlloDerm (Cymetra; LifeCell Corp., Branchburg, NJ), calcium hydroxylapatite (CaHA) (Radiesse; BioForm Medical, San Mateo, CA), and 2.4% cross-linked hyaluronic acid (HA) gel (Juvéderm; Allergan, Inc., Irvine, CA) were quantified as functions of frequency covering the phonatory range, and compared to those of the human vocal fold cover. Measurements of elastic shear modulus (G') and dynamic viscosity (eta') were made at up to 250 Hz with a controlled-strain simple-shear rheometer. Linear least-squares regression was conducted to curve-fit log G' and log eta' versus log frequency, and statistical analysis was performed with one-way analysis of variance. Radiesse and Cymetra were found to be the stiffest and the most viscous materials, followed by Juvéderm and atelocollagen. There were significant differences in the magnitudes of G' and eta' among the phonosurgical materials and the normal human vocal fold cover (p < .001), whereas there was no significant difference in the frequency dependence of G' and eta' among the materials. Post hoc Tukey tests revealed significant differences (p < .05) in pairwise comparisons of the magnitudes of G' and eta' among all materials and the vocal fold cover. These findings suggested that although these biomaterials may be injected lateral to the lamina propria for the treatment of glottic insufficiency, none of them are rheologically optimal for the functional reconstruction of the vocal fold lamina propria.

The inflection point in the pressure dependence of viscosity under high pressure: A comprehensive study of the temperature and pressure dependence of the viscosity of propylene carbonate

The pressure dependence of the prototypical glass-former propylene carbonate has been investigated over a broad range of temperature and pressure that were inaccessible in previous investigations using dielectric spectroscopy. We find that the viscosity measurements validate the scaling relation, eta(T,V)=J(TV gamma), with a scaling parameter gamma close to that found from dielectric relaxation measurements. In the pressure dependence of the viscosity, we observe an inflection point in the log eta versus P response, similar to that found previously for other materials. However, this inflection has never been observed in dielectric relaxation measurements. Using the scaling property above, it is possible to determine the behavior of the dielectric relaxation time in this otherwise inaccessible experimental range and compare it with the viscosity measurements. We find that the behaviors of eta and tau are very similar, and a very good agreement between the function phi P calculated for these two quantities is found. Starting from the validity of the scaling properties, we show that the inflection point in the pressure dependence of the viscosity can be attributed to the convolution of the pressure dependences of the compressibility kappa T and the apparent activation energy at constant volume EV.

High-pressure and -temperature viscosity measurements of methanol and 4:1 methanol:ethanol solution

Viscosity (eta) measurements using rolling sphere viscometry in a resistance-heated diamond-anvil pressure cell yield activation energies of 18-98 kJmol over a pressure range of 1.1-6.1 GPa for methanol and 26-78 kJmol over a pressure range of 2.9-5.4 GPa for a 4:1 methanol:ethanol solution. Nonlinear models of log eta (free-volume and power-law models) yield statistically better fits than the Arrhenius model at room temperature and extrapolate to lower glass-transition (10(12) Pa s) pressures. Glass-transition pressures for the free-volume model change little over the temperature range studied (298-338 K), whereas the power-law values converge to those of the Arrhenius model at temperatures above 320 K.

Spatial Dependence of a Differential Shading Artifact in Images from Coil Arrays with Reactive Cross-talk at 1.5 T

Reactive cross-talk causes leakage of the reception signal between neighboring coils of a receiver array. We present here experimental and computer-simulated NMR images (based upon a simple theory) to show, for an array of two coils, that the leakage (or secondary) signal is combined phase sensitively with the primary signal in each coil, to produce (in certain geometries) a differential shading artifact, manifest as a divot of missing intensity in the image derived from one (and only one) of the two coils. The asymmetry of this effect arises from the sense of the nuclear precession, and the afflicted coil may be swapped with its mate by reversing the direction of the static magnetic field. The artifact appears most clearly in transaxial images and is shown to be forbidden in certain types of saggital images. In a simplified theory for an array of two meshes (i.e., with only two degrees of freedom) the severity of the artifact depends upon the normalized coefficient of coupling (denoted eta and related to the cross-talk in decibels, psi, by psi=-20 log eta.) While the presence of input trap circuits in a typical array doubles the degrees of freedom and complicates both the circuit theory and the circuit measurements, the cross-talk is nonetheless shown to be given by an expression of the form psi=-20 log eta', where the new primed parameter eta' embodies the impedance-matching capacitance and the resistance of the scanner's preamplifiers, as well as the mutual reactance responsible for the cross-talk. The values of cross-talk inferred from the computer simulations of the image artifact are somewhat higher (by an estimated 3 to 6 dB) than those obtained by bench top measurements; but, given that the simulations unmistakably reproduce the unique and highly characteristic visual appearance of the artifact, the proposed model for its formation is claimed to be essentially correct. Finally, it is suggested that the artifact could be corrected by means of the filtered, edge-completed, reception profile described by Wald and co-workers (Wald et al., Magn. Reson. Med. 34, 433 (1995)).

Extreme area-time tradeoffs in VLSI

Consideration is given to the layout of bounded fan-in and fan-out prefix computation graphs in VLSI, and it is shown that the area requirements of such graphs exhibit this interesting property. A small constant factor reduction in time of computation from 2 log eta to log eta increases the area required to embed an eta node prefix computation graph significantly from O( eta log eta ) to Omega ( eta /sup 2/). The area requirements are also given. This behavior is an example of an extreme area-time tradeoff in VLSI. Since prefix computation also models the carry computation in a carry look-ahead adder, the same behavior is observed in the area requirements of a near-minimum computation time carry look-ahead adder. The authors also present circuits which meet the derived lower bounds for all values of T between log eta and 2 log eta .< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Plasma and erythrocyte lipids in two families with heterozygous hypobetalipoproteinemia

Erythrocyte morphology, kinematic viscosity, and membrane lipid composition have not been well documented in heterozygous hypobetalipoproteinemia (HBL). In our study of nine subjects with HBL from two kindreds, three presented with schistocytes (3-6%) while two of them also showed acanthocytosis (25-35%) on their peripheral blood films. The other affected family members had a normal RBC morphology despite a decreased kinematic viscosity of RBC suspension at 37 degrees C (log eta = 0.20 +/- 0.02 vs. log eta = 0.26 +/- 0.02) in all nine subjects; erythrocyte osmotic fragility however was normal. Although some subjects showed acanthocytosis total cholesterol (0.63 +/- 0.05 mol x 10(-6)/mg membrane protein) and sphingomyelin/lecithin ratio (0.905 +/- 0.042) of RBC membranes were normal while plasma from the subject with schistocytosis had a significantly decreased sphingomyelin/lecithin ratio in plasma (17.2 +/- 2.4 vs. 29.1 +/- 3.3) suggesting that sphingomyelin and lecithin are not freely exchangeable between plasma and the outer surface of RBC membranes.

Rheological properties of middle ear effusions from children with otitis media with effusion.

Freshly harvested middle ear effusions (MEE) were collected from children with otitis media with effusion. Both elasticity (G') and viscosity (eta') of the MEE were determined by an oscillating sphere magnetic rheometer and compared with transportability of the MEE on mucus-depleted frog palates. A maximum value of transport was obtained at G' of about 20 dyne/cm2 (at 1 Hz), and below this value there was a significant positive correlation between the transport rate and log G'. Above 20 dyne/cm2, the negative correlation between the transport rate and log G' was significant. This shows there is a sharp increase in transport with increase in G' up to 20 dyne/cm2, and at the higher value of G' there is a slow decrease in transport with increasing G'. A similar significant correlation between the transport rate and log eta' was observed.

Rheological Properties of Middle Ear Effusion and their Role on Mucociliary Clearance

The viscoelastic properties of freshly harvested middle ear effusion (MEE) from children were determined by an oscillating sphere magnetic rheometer and compared with transportability of MEE on mucus-depleted frog palate. The elastic modulus (G') at 1 Hz of MEE from 43 untreated ear was ranged from 1.9 to 1,790 dyn/cm2 and the mean value was 28.4 dyn/cm2. The dynamic viscosity (eta') at 1 Hz of the same samples was ranged from 0.2 to 146 poise with the mean value of 3.4 poise. A maximum value of transport was obtained at G' of about 20 dyn/cm2, and below this value there was a significant positive correlation between the transport rate and log G'. Above 20 dyn/cm2, the negative correlation between the transport rate and log G' was significant. A similar significant correlation between the transport rate and log eta' was observed.

LOCAN: A general FORTRAN program for latency-operating characteristic (LOC) analysis

A FORTRAN program to compute latency-operating characteristics (LOCs) is presented. Latency and accuracy scores from within-subject designs having equal cell frequencies and containing no missing data are appropriate. Output includes both latency measures (mean and median reaction times) and accuracy mea­ sures (d', d 12 • log odds. and log eta) for each latency band. The user determines the number of latency levels into which the data are partitioned. Input, output, and program subroutines are discussed.