On the structure of subsets of an orderable group with some small doubling properties

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and is non-abelian

The Lagrange and Markov spectra from the dynamical point of view

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl

Interactions between Use of and Insurance for Specialty Ambulatory Mental Health Services

Abstract Background: There is continuing interest in the effects of coinsurance rates on the use of ambulatory mental health services. Persons who expect to use mental health services may choose coverage with more generous mental health benefits, as such treatment may be expected to be a recurring activity. However, it may also be the case that if the expected need for such services is somehow reflected in lower perceived human capital in the labor market, then persons who have a higher probability of use may face a less generous set of health insurance options. These behaviors imply some simultaneity in the determinants of the coinsurance rate facing an individual and their mental health use. Aim of the study: To explore the joint determination of the use of and coinsurance for ambulatory mental health services, using non-experimental data for a nationally representative sample of the non-institutionalized who had employer-based health insurance in the United States. Methods: I estimate an instrument for the ambulatory mental health coinsurance rate. I then estimate two models of the demand for ambulatory mental health care as a function of the coinsurance rate for this type of care and other factors, one using the actual coinsurance rate and the other using the estimated instrument for the coinsurance rate. Results: In the instrumental equation, an index of the mental distress of the key worker most likely to be the policy-holder has no statistically significant effect on the worker's coinsurance rate. However, a similar measure for other members of the worker's family has a positive and statistically significant effect on the worker's coinsurance rate. In the demand equations, neither the actual coinsurance rate nor its instrument has a statistically significant coefficient. Discussion: Having another family member who may need mental health care results in some effort to seek a health plan with a higher coinsurance rate for such services. While the mental health index for the key worker would motivate the same type of seeking behavior, a higher level for this index for the key worker might also be correlated with a lower level of perceived human capital in a prospective employer's eyes, and this might result in a more restricted set of plan options for mental health care in the labor market. The absence of statistical significant for the coefficients of the actual coinsurance rate and its instrument also provides some limited but suggestive evidence of employer-side selection effects

Processing Bi-Pb-Sr-Ca-Cu-O superconductors from amorphous state

The bismuth based high T sub c superconductors can be processed via an amorphous Bi-Pb-Sr-Ca-Cu oxide. The amorphous oxides were prepared by melting the constituent powders in an alumina crucible at 1200 C in air followed by pouring the liquid onto an aluminum plate, and rapidly pressing with a second plate. In the amorphous state, no crystalline phase was identified in the powder x ray diffraction pattern of the quenched materials. After heat treatment at high temperature the amorphous materials crystallized into a glass ceramic containing a large fraction of the Bi2Sr2Ca2Cu3O(x) phase T sub c = 110 K. The processing method, crystallization, and results of dc electrical resistivity and ac magnetic susceptibility measurements are discussed

The comprehensive cohort model in a pilot trial in orthopaedic trauma

Background: The primary aim of this study was to provide an estimate of effect size for the functional outcome of operative versus non-operative treatment for patients with an acute rupture of the Achilles tendon using accelerated rehabilitation for both groups of patients. The secondary aim was to assess the use of a comprehensive cohort research design (i.e. a parallel patient-preference group alongside a randomised group) in improving the accuracy of this estimate within an orthopaedic trauma setting. Methods: Pragmatic randomised controlled trial and comprehensive cohort study within a level 1 trauma centre. Twenty randomised participants (10 operative and 10 non-operative) and 29 preference participants (3 operative and 26 non-operative). The ge range was 22-72 years and 37 of the 52 patients were men. All participants had an acute rupture of their Achilles tendon and no other injuries. All of the patients in the operative group had a simple end-to-end repair of the tendon with no augmentation. Both groups then followed the same eight-week immediate weight-bearing rehabilitation programme using an off-the-shelf orthotic. The disability rating index (DRI; primary outcome), EQ-5D, Achilles Total Rupture Score and complications were assessed ed at two weeks, six weeks, three months, six months and nine months after initial injury. Results: At nine months, there was no significant difference in DRI between patients randomised to operative or non-operative management. There was no difference in DRI between the randomised group and the parallel patient preference group. The use of a comprehensive cohort of patients did not provide useful additional information as to the treatment effect size because the majority of patients chose non-operative management. Conclusions: Recruitment to clinical trials that compare operative and non-operative interventions is notoriously difficult; especially within the trauma setting. Including a parallel patient preference group to create a comprehensive cohort of patients has been suggested as a way of increasing the power of such trials. In our study, the comprehensive cohort model doubled the number of patients involved in the study. However, a strong preference for non-operative treatment meant that the increased number of patients did not significantly increase the ability of the trial to detect a difference between the two interventions

On orientational relief of inter-molecular potential and the structure of domain walls in fullerite C60

A simple planar model for an orientational ordering of threefold molecules on a triangular lattice modelling a close-packed (111) plane of fullerite is considered. The system has 3-sublattice ordered ground state which includes 3 different molecular orientations. There exist 6 kinds of orientational domains, which are related with a permutation or a mirror symmetry. Interdomain walls are found to be rather narrow. The model molecules have two-well orientational potential profiles, which are slightly effected by a presence of a straight domain wall. The reason is a stronger correlation between neighbour molecules in triangular lattice versus previously considered square lattice A considerable reduction (up to one order) of orientational interwell potential barrier is found in the core regions of essentially two-dimentional potential defects, such as a three-domain boundary or a kink in the domain wall. For ultimately uncorrelated nearest neighbours the height of the interwell barrier can be reduced even by a factor of 100.Comment: 11 pages, 13 figures, LaTeX, to appear in Low Temperature Physic

GLOBAL REFINEMENT OF TERRESTRIAL LASER SCANNER DATA REGISTRATION USING WEIGHTED SENSOR POSES

Terrestrial laser scanner (TLS) sensor captures highly dense and accurate point clouds quite useful for indoor and outdoor mapping, navigation, 3D reconstruction, surveillance, industrial projects, infrastructure management, and others. In this paper, we present a global registration method that weights the sensor poses for refinement of TLS data registration. Our global refinement method assumes that the variance-covariance matrix that describes the uncertainty of sensor poses is available to refine the registration errors. The effectiveness of the proposed method is demonstrated with TLS dataset obtained into outdoor environment. Our results show that the weighting the sensor poses obtained in registration task improves the positional accuracy of TLS sensor

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Third order dielectric susceptibility in a model quantum paraelectric

In the context of perovskite quantum paraelectrics, we study the effects of a quadrupolar interaction $J_q$, in addition to the standard dipolar one $J_d$. We concentrate here on the nonlinear dielectric response $\chi_{P}^{(3)}$, as the main response function sensitive to quadrupolar (in our case antiquadrupolar) interactions. We employ a 3D quantum four-state lattice model and mean-field theory. The results show that inclusion of quadrupolar coupling of moderate strength ($J_q \sim {{1}\over{4}} J_d$) is clearly accompanied by a double change of sign of $\chi_{P}^{(3)}$ from negative to positive, near the quantum temperature $T_Q$ where the quantum paraelectric behaviour sets in. We fit our $\chi_{P}^{(3)}$ to recent experimental data for SrTiO$_3$, where the sign change is identified close to $T_Q \sim 37 K$.Comment: 22 page