Aurora Stronger

For my Integrate Clinical Experience class, we were asked to complete journal entries based on our experiences, podcasts, and/or APTA modules. This was one of my entries about a podcast on allyship in the field of physical therapy that can also be applied to any medical field. The podcast can be found at http://podcast.healthywealthysmart.com/pod-cast/ episode 499. This entry is about my personal experience during the peaceful protests and riot that ensued after the unjust murder of George Floyd. Dr. Adrienne McAuley suggested I submit this work to Akesis to share my experience and my personal beliefs change after I decided to educate myself about BLM and the correlation of my experiences to the podcast

Real algebraic geometry for matrices over commutative rings

We define and study preorderings and orderings on rings of the form $M_n(R)$ where $R$ is a commutative unital ring. We extend the Artin-Lang theorem and Krivine-Stengle Stellens\"atze (both abstract and geometric) from $R$ to $M_n(R)$. While the orderings of $M_n(R)$ are in one-to-one correspondence with the orderings of $R$, this is not true for preorderings. Therefore, our theory is not Morita equivalent to the classical real algebraic geometry

Sampling of Glacial Snow for Pesticide Analysis on the High Plateau Glacier of Mount Logan

Recently there have been a number of attempts to determine the presence of pollutants in remote areas of the world. The snow of glaciers is a particularly interesting subject for such work, since it contains a record of past years as well as the present. ... Such pollutants are transported by the atmosphere, and it is especially interesting to know if they are present in precipitation that forms at high altitude. As part of the Ice Field Ranges Research Project (IRRP) of 1970, we undertook the study of another common pollutant, the pesticide DDT. Here we report on our attempt to develop techniques for taking snow samples at high altitude in locations where work had to be done under adverse conditions, and with simple equipment. Samples were taken at an elevation of 5,364 metres on Mount Logan, Yukon Territory, Canada. ... The work was performed at temperatures below -20°C, and often in high winds. At this elevation the effects of hypoxia are quite marked .... when unpacked in the field, quantities of an oily material were found on the [new SIPRE snow] auger. It was not practical to achieve a thorough cleaning under field conditions, but as much of the material as possible was removed by using Coleman Fuel - a highly refined non-leaded gasoline designed for camp stoves. Provision of suitable sample containers was an important aspect of the preparations. Two-gallon wide-mouth Nalgene jugs were used on the glacier. The mouth was large enough so that the snow core could slide into the jug directly from the auger without intermediate handling. As long as the samples remained frozen, they could be stored in plastic. However, since liquid water slowly leaches material from the jugs, the samples were transferred to glass jars as soon as they melted. ... A special effort was made in the precleaning of both jars and jugs because of the low levels of pesticide expected. ... Precautions were taken to avoid contamination during sample collection. The first few samples were discarded in the hope of removing any residual contamination from the auger. During the sampling process the auger was never touched by bare hands or gloves. The only surface which came into contact with the samples before their arrival at the laboratory were the auger and the precleaned jugs and jars. At the end of the work, one sample was deliberately mishandled as a control. It subsequently showed no contamination from either polychlorinated biphenyls (PCBs) or DDT. Nineteen samples were taken at depths of from 1 to 15 metres. The DDT analysis was carried out ... using a gas chromatographic technique .... DDT was not detected in any of the samples. In seven of the samples the lower limit of detectibility for DDT was 5 nanograms per liter. Due to interference, apparently from PCBs, 10 to 50 ng/l of DDT could have been present in the remaining samples and not have been detected by this method. It is suggestive that the samples showing no PCB contamination were the last ones taken. It is likely that the PCB contamination came from the oily material originally on the auger, and that the remnant of this was removed during the early part of the drilling. On the basis of these results it seems that sampling of glacial snow for trace organic pollutants is feasible, even when samples must be taken under unfavourable conditions with primitive techniques. It is of paramount importance to preclean every surface that will come into contact with the sample, both sampling tools, and sample containers. ..

Why Are Unemployment Insurance Claims So Low?

In this paper, we examine the reasons why unemployment insurance (UI) claims have declined so dramatically over the past three decades. The fall in the UI claims rate is concerning because it suggests a reduced countercyclical effectiveness of the UI program. Additionally, weekly initial UI claims are regarded as an important leading indicator of aggregate economic activity, so their meaning has changed. We use a Oaxaca (1973) decomposition approach to identify the main factors for the decline in claims. The procedure suggests what the level of claims would have been later in the period, had values of variables or parameters of the system been at levels observed earlier in the period. Our analysis of state-year data over the past three decades suggests that the decline in UI claims stems from changes in the industrial and occupational mix of employment interacting with changes in UI program features set by individual states. Employment declines in manufacturing and increases in the health-care and education workforce, along with lower potential UI duration and lower wage replacement rates, contribute to the decline in claims. This decline could be offset by federal rules for states to improve benefit access, replacement rates, and durations. Such changes could improve the relevance of UI to the labor market and help restore UI as meaningful social insurance against job loss and as an automatic stabilizer of the macroeconomy

Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear algebra or semidefinite programming relaxations of many kinds of feasibility or optimization questions. We are particularly interested in problems arising in combinatorial optimization.Comment: 28 pages, survey pape

Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples

On the Generation of Positivstellensatz Witnesses in Degenerate Cases

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some linear equality (Positivstellensatz). This produces a witness for the desired property, from which it is reasonably easy to obtain a formal proof of the property suitable for a proof assistant such as Coq. The problem of finding a witness reduces to a feasibility problem in semidefinite programming, for which there exist numerical solvers. Unfortunately, this problem is in general not strictly feasible, meaning the solution can be a convex set with empty interior, in which case the numerical optimization method fails. Previously published methods thus assumed strict feasibility; we propose a workaround for this difficulty. We implemented our method and illustrate its use with examples, including extractions of proofs to Coq.Comment: To appear in ITP 201