Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions

For countably infinite IFSs on ℝ2 consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower box-counting dimension. Moreover, we identify a family of countably infinite IFSs for which the Hausdorff and affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed L\"uroth expansions

Modeling the iron oxides and oxyhydroxides for the prediction of environmentally sensitive phase transformations

Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ/mol, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density functional theory calculations with plane-wave and locally-confined-atomic-orbital basis sets, which are implemented in VASP and SIESTA packages, respectively. We have selected hematite, maghemite, goethite, lepidocrocite, and magnetite as model systems from a total of 13 known iron oxides and oxyhydroxides; and use same convergence criteria and almost equivalent settings in order to make consistent comparisons. Our results show both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set most appropriate, and combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principlesComment: 46 pages - Accepted for publication in PRB (19 journal pages), January 201

Ascaroside Expression in Caenorhabditis elegans Is Strongly Dependent on Diet and Developmental Stage

Background: The ascarosides form a family of small molecules that have been isolated from cultures of the nematode Caenorhabditis elegans. They are often referred to as “dauer pheromones” because most of them induce formation of long-lived and highly stress resistant dauer larvae. More recent studies have shown that ascarosides serve additional functions as social signals and mating pheromones. Thus, ascarosides have multiple functions. Until now, it has been generally assumed that ascarosides are constitutively expressed during nematode development. Methodology/Principal Findings: Cultures of C. elegans were developmentally synchronized on controlled diets. Ascarosides released into the media, as well as stored internally, were quantified by LC/MS. We found that ascaroside biosynthesis and release were strongly dependent on developmental stage and diet. The male attracting pheromone was verified to be a blend of at least four ascarosides, and peak production of the two most potent mating pheromone components, ascr#3 and asc#8 immediately preceded or coincided with the temporal window for mating. The concentration of ascr#2 increased under starvation conditions and peaked during dauer formation, strongly supporting ascr#2 as the main population density signal (dauer pheromone). After dauer formation, ascaroside production largely ceased and dauer larvae did not release any ascarosides. These findings show that both total ascaroside production and the relative proportions of individual ascarosides strongly correlate with these compounds' stage-specific biological functions. Conclusions/Significance: Ascaroside expression changes with development and environmental conditions. This is consistent with multiple functions of these signaling molecules. Knowledge of such differential regulation will make it possible to associate ascaroside production to gene expression profiles (transcript, protein or enzyme activity) and help to determine genetic pathways that control ascaroside biosynthesis. In conjunction with findings from previous studies, our results show that the pheromone system of C. elegans mimics that of insects in many ways, suggesting that pheromone signaling in C. elegans may exhibit functional homology also at the sensory level. In addition, our results provide a strong foundation for future behavioral modeling studies

Simultaneous Absolute Timing of the Crab Pulsar at Radio and Optical Wavelengths

The Crab pulsar emits across a large part of the electromagnetic spectrum. Determining the time delay between the emission at different wavelengths will allow to better constrain the site and mechanism of the emission. We have simultaneously observed the Crab Pulsar in the optical with S-Cam, an instrument based on Superconducting Tunneling Junctions (STJs) with $\mu$s time resolution and at 2 GHz using the Nan\c{c}ay radio telescope with an instrument doing coherent dedispersion and able to record giant pulses data. We have studied the delay between the radio and optical pulse using simultaneously obtained data therefore reducing possible uncertainties present in previous observations. We determined the arrival times of the (mean) optical and radio pulse and compared them using the tempo2 software package. We present the most accurate value for the optical-radio lag of 255 $\pm$ 21 $\mu$s and suggest the likelihood of a spectral dependence to the excess optical emission asociated with giant radio pulses.Comment: 8 pages; accepted for publication in Astronomy and Astrophysic

Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

Circular dichroism and bilayer splitting in the normal state of underdoped (Pb,Bi)2_2Sr2_2(Cax_xY1−x_{1-x})Cu2_2O8+δ_{8+\delta} and overdoped (Pb,Bi)2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

We report an ARPES investigation of the circular dichroism in the first Brillouin zone (BZ) of under- and overdoped Pb-Bi2212 samples. We show that the dichroism has opposite signs for bonding and antibonding components of the bilayer-split CuO-band and is antisymmetric with respect to reflections in both mirror planes parallel to the c-axis. Using this property of the energy and momentum intensity distributions we prove the existence of the bilayer splitting in the normal state of the underdoped compound and compare its value with the splitting in overdoped sample. In agreement with previous studies the magnitude of the interlayer coupling does not depend significantly on doping. We also discuss possible origins of the observed dichroism.Comment: 4 RevTex pages, 4 EPS figure

Chemical kinetics and photochemical data for use in stratospheric modeling. Evaluation number 6

Evaluated sets of rate constants and photochemical cross sections are presented. The primary application of the data is in the modeling of stratospheric processes, with particular emphasis on the ozone layer and its possible perturbation by anthropogenic and natural phenomena

Evidence for Interlayer Collapse of Nontronite on Mars from Laboratory Visible and Near-IR Reflective Spectra

Dioctahedral smectites (e.g., nontronite and montmorillionite) are interpreted to occupy the optical surface of Mars at a number of locations on the basis of spectral features derived from interlayer H2O and MOH (M=Fe(3+)2, Fe(3+)Al, Al2, etc.) as observed by orbiting MRO-CRISM and MEx-OMEGA hyperspectral imaging spectrometers. At wavelengths shorter than approximately 2.7 micrometers, the strongest bands from interlayer H2O occur at approximately 1.4 and 1.9 micrometers from 2v1 and v1+v2, respectively, where v1 and v2 are the fundamental stretching and bending vibrations of the H2O molecule. Smectite MOH vibrations occur near 1.4 micrometers (stretching overtone) and in the region between 2.1 and 2.7 micrometers (stretching + bending combination). Because interlayer H2O can exchange with the martian environment, a number of studies have examined the strength of the interlayer H2O spectral features under Mars-like environmental conditions. The relationship between spectral properties and the underlying crystal structure of the smectites was not determined, and the extent of interlayer H2O removal was not established. We report combined visible and near-IR (VNIR), Mossbauer (MB), and powder X-ray diffraction (XRD) data for samples of the Fe-bearing smectite nontronite where the interlayer was collapsed by complete removal of interlayer H2O

Colligative properties of solutions: I. Fixed concentrations

Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing point depression. The limit of infinitesimal concentrations is described in a subsequent paper.Comment: 28 pages, 1 fig; see also math-ph/0407035 (both to appear in JSP