Frequency of occurrence of numbers in the World Wide Web

The distribution of numbers in human documents is determined by a variety of diverse natural and human factors, whose relative significance can be evaluated by studying the numbers' frequency of occurrence. Although it has been studied since the 1880's, this subject remains poorly understood. Here, we obtain the detailed statistics of numbers in the World Wide Web, finding that their distribution is a heavy-tailed dependence which splits in a set of power-law ones. In particular, we find that the frequency of numbers associated to western calendar years shows an uneven behavior: 2004 represents a `singular critical' point, appearing with a strikingly high frequency; as we move away from it, the decreasing frequency allows us to compare the amounts of existing information on the past and on the future. Moreover, while powers of ten occur extremely often, allowing us to obtain statistics up to the huge 10^127, `non-round' numbers occur in a much more limited range, the variations of their frequencies being dramatically different from standard statistical fluctuations. These findings provide a view of the array of numbers used by humans as a highly non-equilibrium and inhomogeneous system, and shed a new light on an issue that, once fully investigated, could lead to a better understanding of many sociological and psychological phenomena.Comment: 5 pages, 4 figure

The effect of three topical agents on posterior subcapsular cataract progression in royal college of surgeon (r.c.s.) rats

Three substances are currently reported to possess cataract retardation properties: Scenecio Maritema, N-N dimethylglycine, and Conjunctivisan A. To test their potential in retarding cataract progression, Royal College of Surgeon (R.C.S.) rats were selected as the experimental model. This strain of rats develops posterior subcapsular cataracts secondarily to an inherited retinal degeneration. At birth, the rats were divided into four groups. The ten rats in each group received twice daily topical instillation of saline, Scenecio Maritema, N-N dimethylglycine, or Conjunctivisan A for eight weeks. Analysis of serial slit lamp evaluations showed a significant delay in cataract progression in the rats receiving any of the three agents compared to : the saline control. This suggests that there might be an alternative to surgery in cataract treatment

Evidence for Adiabatic Magnetization of cold Dy_N Clusters

Magnetic properties of Dy_N clusters in a molecular beam generated with a liquid helium cooled nozzle are investigated by Stern-Gerlach experiments. The cluster magnetizations \mu_z are measured as a function of magnetic field (B = 0 - 1.6T) and cluster size (16 < N < 56). The most important observation is the saturation of the magnetization \mu_z(B) at large field strengths. The magnetization approaches saturation following the power law |\mu_z-\mu_0| proportional to 1/\sqrt{B}, where \mu_0 denotes the magnetic moment. This gives evidence for adiabatic magnetization.Comment: 4 pages, 3 figure

Vector lattice model for stresses in granular materials

A vector lattice model for stresses in granular materials is proposed. A two dimensional pile built by pouring from a point is constructed numerically according to this model. Remarkably, the pile violates the Mohr Coulomb stability criterion for granular matter, probably because of the inherent anisotropy of such poured piles. The numerical results are also compared to the earlier continuum FPA model and the (scalar) lattice $q$-model

Guidelines on the use of Structure from Motion Photogrammetry in Geomorphic Research

As a topographic modelling technique, structure-from-motion (SfM) photogrammetry combines the utility of digital photogrammetry with a flexibility and ease of use derived from multi-view computer vision methods. In conjunction with the rapidly increasing availability of imagery, particularly from unmanned aerial vehicles, SfM photogrammetry represents a powerful tool for geomorphological research. However, to fully realize this potential, its application must be carefully underpinned by photogrammetric considerations, surveys should be reported in sufficient detail to be repeatable (if practical) and results appropriately assessed to understand fully the potential errors involved. To deliver these goals, robust survey and reporting must be supported through (i) using appropriate survey design, (ii) applying suitable statistics to identify systematic error (bias) and to estimate precision within results, and (iii) propagating uncertainty estimates into the final data products

Guidelines on the use of Structure from Motion Photogrammetry in Geomorphic Research

As a topographic modelling technique, structure-from-motion (SfM) photogrammetry combines the utility of digital photogrammetry with a flexibility and ease of use derived from multi-view computer vision methods. In conjunction with the rapidly increasing availability of imagery, particularly from unmanned aerial vehicles, SfM photogrammetry represents a powerful tool for geomorphological research. However, to fully realize this potential, its application must be carefully underpinned by photogrammetric considerations, surveys should be reported in sufficient detail to be repeatable (if practical) and results appropriately assessed to understand fully the potential errors involved. To deliver these goals, robust survey and reporting must be supported through (i) using appropriate survey design, (ii) applying suitable statistics to identify systematic error (bias) and to estimate precision within results, and (iii) propagating uncertainty estimates into the final data products

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

Diffusion of particles moving with constant speed

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A Fokker-Planck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement $$ along with an approximate expression for the marginal probability distribution function $P(x,t)$ are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time ($8t^*$) only after which the diffusion approximation becomes valid. This factor of eight is a well known experimental fact. A persistence exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions by studying the survival probability of the particle in a semi-infinite medium. The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E

Use of high cost care among Veterans with comorbid mental illness and Alzheimer's Disease and related dementias

Introduction/Objective Alzheimer's Disease and Other Related Dementias (AD/ADRD) leads to frequent emergency department (ED) and inpatient use. Mental health symptoms among persons with AD/ADRD increases cognitive and functional disabilities and could contribute to these high rates of intensive health care use. The objective of this paper is to assess the relationship of mental illness on 12-month patterns in hospitalization and ED use among Veterans aged 65 and over with a new AD/ADRD diagnosis. Methods We used an existing dataset of administrative electronic health record data of Veterans with AD/ADRD from the US Veterans Health Administration linked with Medicare claims data from 2011-2015. We use multivariable logistic regression to examine the association between no pre-existing mental illness, pre-existing mental illness (e.g., major depressive disorder, generalized anxiety disorder, or post-traumatic stress disorder), and pre-existing severe mental illness-or SMI-(e.g., bipolar disorder, major depressive disorder with psychosis, or schizophrenia) and 12- month ED and hospitalization use and readmissions among Veterans who had an initial hospitalization visit. We estimated predicted probabilities, differential effect, and associated 95% confidence intervals. Results In our sample, 1.4% had SMI and 11% had non-SMI mental illness. The unadjusted percentage with inpatient and ED use was higher among Veterans with SMI (34% and 26%, respectively) and Veterans with non-SMI mental illness (20%, 16%) compared with Veterans without pre-existing mental illness (12%, 9%). Compared to individuals with no pre-existing mental illness, having a pre-existing mental illness (1.27 percentage points, 95% CI: 0.76, 1.78) and a pre-existing SMI (7.17 percentage points, 95% CI: 5.66, 8.69) were both associated with an increased likelihood of ED use. The same pattern was observed for any inpatient use (mental illness 2.18, 95% CI: 1.59, 2.77; SMI 9.91, 95% CI: 8.21, 11.61). Only preexisting SMI was associated higher hospitalization readmission. Discussion Pre-existing mental illness increases use of high cost, intensive health care and this association is higher of more severe mental health conditions. We also show that pre-existing mental illness exerts a unique influence, above and beyond other comorbidities, such as diabetes, on ED and inpatient visits. More needs to be done to increase recognition of the unique risks of this combination of health conditions and encourage strategies to address them. Developing, testing, and implementing comprehensive strategies that address the intersection of ADRD and mental illness is promising approach that requires more focused attention

Josephson dynamics for coupled polariton modes under the atom-field interaction in the cavity

We consider a new approach to the problem of Bose-Einstein condensation (BEC) of polaritons for atom-field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons.Comment: 10 pages, 6 postscript figures, uses svjour.cl