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

On the perimeters of simple polygons contained in a plane convex body

A simple n-gon is a polygon with n edges such that each vertex belongs to exactly two edges and every other point belongs to at most one edge. Brass, Moser and Pach asked the following question: For n > 3 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet, Hansen and Messine answered this question, and showed that the supremum is the perimeter of an isosceles triangle inscribed in the disk, with an edge of multiplicity n-2. L\'angi generalized their result for polygons contained in a hyperbolic disk. In this note we find the supremum of the perimeters of simple n-gons contained in an arbitrary plane convex body in the Euclidean or in the hyperbolic plane.Comment: 7 pages, 7 figure

On the perimeters of simple polygons contained in a disk

A simple $n$-gon is a polygon with $n$ edges with each vertex belonging to exactly two edges and every other point belonging to at most one edge. Brass asked the following question: For $n \geq 5$ odd, what is the maximum perimeter of a simple $n$-gon contained in a Euclidean unit disk? In 2009, Audet, Hansen and Messine answered this question, and showed that the optimal configuration is an isosceles triangle with a multiple edge, inscribed in the disk. In this note we give a shorter and simpler proof of their result, which we generalize also for hyperbolic disks, and for spherical disks of sufficiently small radii.Comment: 6 pages, 2 figure

Pooling problem: Alternate formulations and solution methods

Copyright @ 2004 INFORMSThe pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion. of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.This project was funded by Ultramar Canada and Luc Massé. The work of C. Audet was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 and by CRPC (Center for Research on Parallel Computation). The work of J. Brimberg was supported by NSERC grant #OGP205041. The work of P. Hansen was supported by FCAR(Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95ER1048, and NSERC grant #GP0105574

Recovering Legacy Geological Data into a Geospatial Database Product: An Example from Baja California Norte, México

This project develops a workflow for the extraction of legacy geological map data using a case study in the Baja California Norte, México by four workers over forty years. This project is unique from other digitization efforts worldwide because the data were already in an unregistered vector format, instead of a raster format. Thus, the methodology used in this project took advantage of this digital format by writing arcpy scripts for use inside of ArcMap, and using database feature manipulation software, in order to streamline the data extraction process, with the goal being to develop methods for dealing with other similar legacy geological datasets. The project was conditionally successful, with the developed arcpy script extracting strike and dip direction information from the structural geological data, with only minimal manual review required. Additionally, implementation of the FME Workbench software allowed text information describing Dip and Plunge to be extracted and combined with its companion direction and position data; however, project limitations only allowed for a method that required extensive manual review after the automated process. Transferability of the developed workflow is limited by requiring access to FME workbench software in addition to ArcGIS, but as that part of the workflow requires substantial manual work, it could perhaps be replaced by completely manual methods. Additionally, the arcpy scripts might not work properly if used on tightly clustered data, or data constructed differently than the Baja California data. Copies of the arcpy script, FME workflows, and maps can be found on https://drive.google.com/open?id=1yWlCXTGTtm1qSN1uWHy6BaP1ZcIWXyco

Alien Registration- Audet, Mrs. Exerila C. (Brownville, Piscataquis County)

https://digitalmaine.com/alien_docs/10198/thumbnail.jp

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

Chronic Delivery of a Thrombospondin-1 Mimetic Decreases Skeletal Muscle Capillarity in Mice

Angiogenesis is an essential process for normal skeletal muscle function. There is a growing body of evidence suggesting that thrombospondin-1 (TSP-1), a potent antiangiogenic protein in tumorigenesis, is an important regulator of both physiological and pathological skeletal muscle angiogenesis. We tested the hypothesis that chronic exposure to a TSP-1 mimetic (ABT-510), which targets the CD36 TSP-1 receptor, would decrease skeletal muscle capillarity as well as alter the balance between positive and negative angiogenic proteins under basal conditions. Osmotic minipumps with either ABT-510 or vehicle (5% dextrose) were implanted subcutaneously in the subscapular region of C57/BL6 mice for 14 days. When compared to the vehicle treated mice, the ABT-510 group had a 20% decrease in capillarity in the superficial region of the gastrocnemius (GA), 11% decrease in the plantaris (PLT), and a 35% decrease in the soleus (SOL). ABT-510 also decreased muscle protein expression of vascular endothelial growth factor (VEGF) in both the GA (−140%) and SOL (−62%); however there was no change in VEGF in the PLT. Serum VEGF was not altered in ABT-510 treated animals. Endogenous TSP-1 protein expression in all muscles remained unaltered. Tunnel staining revealed no difference in muscle apoptosis between ABT-510 and vehicle treated groups. These data provide evidence that the anti-angiogenic effects of TSP-1 are mediated, at least in part, via the CD36 receptor. It also suggests that under physiologic conditions the TSP-1/CD36 axis plays a role in regulating basal skeletal muscle microvessel density