Finding largest small polygons with GloptiPoly

A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices $n$. Many instances are already solved in the literature, namely for all odd $n$, and for $n=4, 6$ and 8. Thus, for even $n\geq 10$, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite programming approach to the generalized problem of moments and implemented in the public-domain Matlab package GloptiPoly, can successfully find largest small polygons for $n=10$ and $n=12$. Therefore this significantly improves existing results in the domain. When coupled with accurate convex conic solvers, GloptiPoly can provide numerical guarantees of global optimality, as well as rigorous guarantees relying on interval arithmetic

The Multi-Site Study: An Innovative Research Methodology

The Multi-Site Study is a qualitative research approach that we designed to gain an in-depth knowledge of an organizational phenomenon that had barely been researched: strategic scanning. It combines several approaches to case study research, borrowing from the positivist tradition, the interpretative approach and the qualitative research corpus. It involves the observation and analysis of several sites using namely cross-case comparisons and explanation building techniques to analyze data. The following report primarily explains the thought process that led to the research decision, a description of the process itself is then presented, followed by an illustration and discussion of the results obtained and finally, a note of reflection on the entire experience

A Comparison Of Hip And Knee Joint Kinematics Between Two Alpine Ski Ergometers

This study was conducted to determine if hip and knee joint kinematics differed between conditions as subjects "skied" on two alpine ski ergometers. Eleven male recreational skiers, ages 18-23, participated in the study. During the random test, sagittal plane motions of the hip and knee joints were videotaped as subjects skied on each ski ergometer at a slow speed (92 turns/minute) and a fast speed (102 turns/minute). Each subject was vid.eotaped at 30 frames per second during the last thirty seconds of a two minute exercise bout. Three turns were randomly selected and digitized on the Ariel Performance Analysis System (APAS). Relative angular displacements of the left hip and knee were measured and compared. Hip and knee flexion were significantly different between the two ergometers at the fast speed. A comparison of the fast and slow trials revealed that subjects were able to achieve more knee flexion at the fast speed on one ergometer. However, on the other ergometer, the degree of knee flexion was greater at the slow speed. How closely the two ski ergometers simulate actual downhill skiing is unknown and warrants further investigation

Dry-Spun Silk Produces Native-Like Fibroin Solutions

Silk's outstanding mechanical properties and energy efficient solidification mechanisms provide inspiration for biomaterial self-assembly as well as offering a diverse platform of materials suitable for many biotechnology applications. Experiments now reveal that the mulberry silkworm Bombyx mori secretes its silk in a practically "unspun" state that retains much of the solvent water and exhibits a surprisingly low degree of molecular order (β-sheet crystallinity) compared to the state found in a fully formed and matured fiber. These new observations challenge the general understanding of silk spinning and in particular the role of the spinning duct for structure development. Building on this discovery we report that silk spun in low humidity appears to arrest a molecular annealing process crucial for β-sheet formation. This, in turn, has significant positive implications, enabling the production of a high fidelity reconstituted silk fibroin with properties akin to the gold standard of unspun native silk

A new insight into the coupler curves of the RCCC four-bar linkage

The final publication is available at link.springer.comBased on the condition for four points to lie on the unit sphere, derived using Distance Geometry, a new mathematical formulation for the coupler curves of the RCCC linkage is presented. The relevance of this formulation is not only its simplicity, but the elegant way in which we can obtain the derivative of any variable with respect to any other, and the simple way in which intervals of monotonicity can be detected. All these results are compactly expressed in terms of Gramians and, as a consequence, they have a direct geometric meaning contrarily to what happens with previous approaches based on kinematic loop equations.Peer ReviewedPostprint (author's final draft

Fouling layers on heat exchangers with temperature dependent viscosity

This report descibes a mathematical model for the fluid motion and the heat transfer in a heat exchanger which gradually becomes clogged by particle deposition on the walls. A lubrication model is derived and then averaged

Perceptions of Community Involvement in the Peruvian Mental Health Reform Process Among Clinicians and Policy-Makers: A Qualitative Study

Background: The global burden of mental health conditions has led to the implementation of new models of care for persons with mental illness. Recent mental health reforms in Peru include the implementation of a community mental health model (CMHM) that, among its core objectives, aims to provide care in the community through specialized facilities, the community mental health centers (CMHCs). Community involvement is a key component of this model. This study aims to describe perceptions of community engagement activities in the current model of care in three CMHCs and identify barriers and potential solutions to implementation.Methods: A qualitative research study using in-depth semi-structured interviews with clinicians from three CMHCs and with policy-makers involved in the implementation of the mental health reforms was conducted in two regions of Peru. The interviews, conducted in Spanish, were digitally recorded with consent, transcribed and analyzed using principles of grounded theory applying a framework approach. Community engagement activities are described at different stages of patient care.Results: Twenty-five full-time employees (17 women, 8 men) were interviewed, of which 21 were clinicians (diverse health professions) from CMHCs, and 4 were policy-makers. Interviews elucidated community engagement activities currently being utilized including: (1) employing community mental health workers (CMHWs); (2) home visits; (3) psychosocial clubs; (4) mental health workshops and campaigns; and (5) peer support groups. Inadequate infrastructure and financial resources, lack of knowledge about the CMHM, poorly defined catchment areas, stigma, and inadequate productivity approach were identified as barriers to program implementation. Solutions suggested by participants included increasing knowledge and awareness about mental health and the new model, implementation of peer-training, and improving productivity evaluation and research initiatives.Conclusion: Community engagement activities are being conducted in Peru as part of a new model of care. However, their structure, frequency, and content are perceived by clinicians and policy-makers as highly variable due to a lack of consistent training and resources across CMHCs. Barriers to implementation should be quickly addressed and potential solutions executed, so that scale-up best optimizes the utilization of resources in the implementation process