A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents

We consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer science, mathematics, and economics. Although, the elegant Selfridge-Conway envy-free protocol for three agents has been known since 1960, it has been a major open problem for the last fifty years to obtain a bounded envy-free protocol for more than three agents. We propose a discrete and bounded envy-free protocol for four agents

Low-Temperature Dephasing in Disordered Conductors: the Effect of ``1/f'' Fluctuations

Electronic quantum effects in disordered conductors are controlled by the dephasing rate of conduction electrons. This rate is expected to vanish with the temperature. We consider the very intriguing recently reported apparent saturation of this dephasing rate in several systems at very low temperatures. We show that the ``standard model'' of a conductor with static defects can {\em not} have such an effect. However, allowing some dynamics of the defects may produce it.Comment: 6page

Field Theory And Second Renormalization Group For Multifractals In Percolation

The field-theory for multifractals in percolation is reformulated in such a way that multifractal exponents clearly appear as eigenvalues of a second renormalization group. The first renormalization group describes geometrical properties of percolation clusters, while the second-one describes electrical properties, including noise cumulants. In this context, multifractal exponents are associated with symmetry-breaking fields in replica space. This provides an explanation for their observability. It is suggested that multifractal exponents are ''dominant'' instead of ''relevant'' since there exists an arbitrary scale factor which can change their sign from positive to negative without changing the Physics of the problem.Comment: RevTex, 10 page

Variability in bioreactivity linked to changes in size and zeta potential of diesel exhaust particles in human immune cells

Acting as fuel combustion catalysts to increase fuel economy, cerium dioxide (ceria, CeO(2)) nanoparticles have been used in Europe as diesel fuel additives (Envirox™). We attempted to examine the effects of particles emitted from a diesel engine burning either diesel (diesel exhaust particles, DEP) or diesel doped with various concentrations of CeO(2) (DEP-Env) on innate immune responses in THP-1 and primary human peripheral blood mononuclear cells (PBMC). Batches of DEP and DEP-Env were obtained on three separate occasions using identical collection and extraction protocols with the aim of determining the reproducibility of particles generated at different times. However, we observed significant differences in size and surface charge (zeta potential) of the DEP and DEP-Env across the three batches. We also observed that exposure of THP-1 cells and PBMC to identical concentrations of DEP and DEP-Env from the three batches resulted in statistically significant differences in bioreactivity as determined by IL-1β, TNF-α, IL-6, IFN-γ, and IL-12p40 mRNA (by qRT-PCR) and protein expression (by ELISPOT assays). Importantly, bioreactivity was noted in very tight ranges of DEP size (60 to 120 nm) and zeta potential (−37 to −41 mV). Thus, these physical properties of DEP and DEP-Env were found to be the primary determinants of the bioreactivity measured in this study. Our findings also point to the potential risk of over- or under- estimation of expected bioreactivity effects (and by inference of public health risks) from bulk DEP use without taking into account potential batch-to-batch variations in physical (and possibly chemical) properties

The Intrinsic Quantum Excitations of Low Temperature Glasses

Several puzzling regularities concerning the low temperature excitations of glasses are quantitatively explained by quantizing domain wall motions of the random first order glass transition theory. The density of excitations agrees with experiment and scales with the size of a dynamically coherent region at $T_g$, being about 200 molecules. The phonon coupling depends on the Lindemann ratio for vitrification yielding the observed universal relation $l/\lambda \simeq 150$ between phonon wavelength $\lambda$ and mean free path $l$. Multilevel behavior is predicted to occur in the temperature range of the thermal conductivity plateau.Comment: 4 pages, submitted to PR

Nanometer Scale Dielectric Fluctuations at the Glass Transition

Using non-contact scanning probe microscopy (SPM) techniques, dielectric properties were studied on 50 nanometer length scales in poly-vinyl-acetate (PVAc) films in the vicinity of the glass transition. Low frequency (1/f) noise observed in the measurements, was shown to arise from thermal fluctuations of the electric polarization. Anomalous variations observed in the noise spectrum provide direct evidence for cooperative nano-regions with heterogeneous kinetics. The cooperative length scale was determined. Heterogeneity was long-lived only well below the glass transition for faster than average processes.Comment: 4 pages, 4 embedded PS figures, RevTeX - To appear in Phys. Rev. Let

Structure of the Dead Sea Pull-Apart Basin From Gravity Analyses

Analyses and modeling of gravity data in the Dead Sea pull-apart basin reveal the geometry of the basin and constrain models for its evolution. The basin is located within a valley which defines the Dead Sea transform plate boundary between Africa and Arabia. Three hundred kilometers of continuous marine gravity data, collected in a lake occupying the northern part of the basin, were integrated with land gravity data from Israel and Jordan to provide coverage to 30 km either side of the basin. Free-air and variable-density Bouguer anomaly maps, a horizontal first derivative map of the Bouguer anomaly, and gravity models of profiles across and along the basin were used with existing geological and geophysical information to infer the structure of the basin. The basin is a long (132 km), narrow (7-10 km), and deep (≤10 km) full graben which is bounded by subvertical faults along its long sides. The Bouguer anomaly along the axis of the basin decreases gradually from both the northern and southern ends, suggesting that the basin sags toward the center and is not bounded by faults at its narrow ends. The surface expression of the basin is wider at its center (≤16 km) and covers the entire width of the transform valley due to the presence of shallower blocks that dip toward the basin. These blocks are interpreted to represent the widening of the basin by a passive collapse of the valley floor as the full graben deepened. The collapse was probably facilitated by movement along the normal faults that bound the transform valley. We present a model in which the geometry of the Dead Sea basin (i.e., full graben with relative along-axis symmetry) may be controlled by stretching of the entire (brittle and ductile) crust along its long axis. There is no evidence for the participation of the upper mantle in the deformation of the basin, and the Moho is not significantly elevated. The basin is probably close to being isostatically uncompensated, and thermal effects related to stretching are expected to be minimal. The amount of crustal stretching calculated from this model is 21 km and the stretching factor is 1.19. If the rate of crustal stretching is similar to the rate of relative plate motion (6 mm/yr), the basin should be ~3.5 m.y. old, in accord with geological evidence

European Society of Endodontology position statement: Management of deep caries and the exposed pulp

This position statement on the management of deep caries and the exposed pulp represents the consensus of an expert committee, convened by the European Society of Endodontology (ESE). Preserving the pulp in a healthy state with sustained vitality, preventing apical periodontitis and developing minimally invasive biologically based therapies are key themes within contemporary clinical endodontics. The aim of this statement was to summarize current best evidence on the diagnosis and classification of deep caries and caries‐induced pulpal disease, as well as indicating appropriate clinical management strategies for avoiding and treating pulp exposure in permanent teeth with deep or extremely deep caries. In presenting these findings, areas of controversy, low‐quality evidence and uncertainties are highlighted, prior to recommendations for each area of interest. A recently published review article provides more detailed information and was the basis for this position statement (Bjørndal et al. 2019, International Endodontic Journal, doi:10.1111/iej.13128). The intention of this position statement is to provide the practitioner with relevant clinical guidance in this rapidly developing area. An update will be provided within 5 years as further evidence emerges