On separating a fixed point from zero by invariants

Assume a fixed point v in V^G can be separated from zero by a homogeneous invariant f ∈ k[V]^G of degree p^r d where p > 0 is the characteristic of the ground field k and p, d are coprime. We show that then v can also be separated from zero by an invariant of degree p^r , which we obtain explicitly from f . It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power

Fourier series approximations and low pass filtering: facilitating learning of digital signal processing for biomechanics students

pre-printFiltering raw biomechanical data to remove noise is a key first step that must be performed prior to further biomechanical analysis. Raw biomechanical data are usually filtered to remove noise above a specified cutoff frequency, a process known as "low pass filtering". The concept of frequency content within a signal may be difficult for students to grasp, and authors of biomechanics textbooks often use Fourier series approximations to introduce this concept. To facilitate student learning, we have created an Excel spreadsheet that allows students to observe several orders of Fourier series approximations to a representative set of biomechanical data. In this paper, we provide a short tutorial on Fourier series approximations and instructions for using the Excel spreadsheet. The Fourier series coefficients are determined iteratively with a first-principles approach of minimizing the sum of squared error between the original data and the approximation using the Solver function in Excel. The user can reset these coefficients and run Solver to observe the iterative process. This first-principles approach may be helpful in a broad range of applications because it allows users to perform non-linear regression within an Excel spreadsheet. The Excel spreadsheet also includes a fourth-order zero-lag Butterworth low pass filter with adjustable cutoff frequency so that the effects of filtering can be observed and compared with the Fourier series approximations. We believe this tutorial and Excel spreadsheet will be helpful to those teaching and learning digital signal processing in biomechanics

JOINT-SPECIFIC POWER PRODUCTION DURING SUBMAXIMAL AND MAXIMAL CYCLING

Cycle ergometry is commonly used to quantify muscular work and power, and to elicit perturbations to metabolic homeostasis for a broad range of physiological investigations. Separate authors have reported that knee extension dominates power production during submaximal cycling (SUBcyc; Ericson, 1988) and hip extension is the dominate action during maximal cycling (MAXcyc, Martin & Brown, 2009). Changes in joint-specific powers across broad ranges of net cycling powers within one group of cyclists have not been reported. Our purpose was to determine the extent to which ankle, knee, and hip joint actions produced power across a range of net cycling powers. Based on previous reports we hypothesized that relative contributions of knee extension power would decrease and relative knee flexion and hip extension powers would increase as net cycling power increase

Motion of a Solitonic Vortex in the BEC-BCS Crossover

We observe a long-lived solitary wave in a superfluid Fermi gas of $^6$Li atoms after phase-imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known equation of state in the BEC-BCS crossover

Antiparasitic and Antiproliferative Effects of Indoleamine 2,3-dioxygenase Enzyme Expression in Human Fibroblasts.

Studies were carried out to evaluate the proposed role of indoleamine 2,3-dioxygenase (INDO) induction in the antimicrobial and antiproliferative effects of gamma interferon (IFN-gamma) in human fibroblasts. The INDO cDNA coding region was cloned in the pMEP4 expression vector, containing the metallothionein (MTII) promoter in the sense (+ve) or the antisense (-ve) orientation. Human fibroblasts (GM637) stably transfected with the sense construct expressed INDO activity after treatment with CdCl2 or ZnSO4, but cells transfected with the antisense construct did not. The growth of Chlamydia psittaci was strongly inhibited in INDO +ve cells but not in INDO -ve cells after treatment with Cd2+ or Zn2+. The inhibition correlated with the level of INDO activity induced and could be reversed by the addition of excess tryptophan to the medium. The growth of Toxoplasma gondii was also strongly inhibited in INDO +ve cells but not in INDO -ve cells after treatment with Cd2+. Expression of Cd(2+)-induced INDO activity also inhibited thymidine incorporation and led to cytotoxicity in INDO +ve cells but not in INDO -ve cells. Thus, the induction of INDO activity by IFN-gamma may be an important factor in the antimicrobial and antiproliferative effects of IFN-gamma in human fibroblasts

The Cohen-Macaulay property of separating invariants of finite groups

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although separating algebras are often better behaved than the ring of invariants, we show that many of the criteria which imply that the ring of invariants is non Cohen-Macaulay actually imply that no graded separating algebra is Cohen-Macaulay. For example, we show that, over a field of positive characteristic p, given sufficiently many copies of a faithful modular representation, no graded separating algebra is Cohen-Macaulay. Furthermore, we show that, for a p-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireflections. Furthermore, we show that, for a $p$-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireflections. Additionally, we give an example which shows that Cohen-Macaulay separating algebras can occur when the ring of invariants is not Cohen-Macaulay.Comment: We removed the conjecture which appeared in previous versions: we give a counter-example. We fixed the proof of Lemma 2.2 (previously Remark 2.2). 16 page

The Building Blocks of Interoperability. A Multisite Analysis of Patient Demographic Attributes Available for Matching.

BackgroundPatient matching is a key barrier to achieving interoperability. Patient demographic elements must be consistently collected over time and region to be valuable elements for patient matching.ObjectivesWe sought to determine what patient demographic attributes are collected at multiple institutions in the United States and see how their availability changes over time and across clinical sites.MethodsWe compiled a list of 36 demographic elements that stakeholders previously identified as essential patient demographic attributes that should be collected for the purpose of linking patient records. We studied a convenience sample of 9 health care systems from geographically distinct sites around the country. We identified changes in the availability of individual patient demographic attributes over time and across clinical sites.ResultsSeveral attributes were consistently available over the study period (2005-2014) including last name (99.96%), first name (99.95%), date of birth (98.82%), gender/sex (99.73%), postal code (94.71%), and full street address (94.65%). Other attributes changed significantly from 2005-2014: Social security number (SSN) availability declined from 83.3% to 50.44% (p<0.0001). Email address availability increased from 8.94% up to 54% availability (p<0.0001). Work phone number increased from 20.61% to 52.33% (p<0.0001).ConclusionsOverall, first name, last name, date of birth, gender/sex and address were widely collected across institutional sites and over time. Availability of emerging attributes such as email and phone numbers are increasing while SSN use is declining. Understanding the relative availability of patient attributes can inform strategies for optimal matching in healthcare

Reconstructing Seesaws

We explore some aspects of "reconstructing" the heavy singlet sector of supersymmetric type I seesaw models, for two, three or four singlets. We work in the limit where one light neutrino is massless. In an ideal world, where selected coefficients of the TeV-scale effective Lagrangian could be measured with arbitrary accuracy, the two-singlet case can be reconstructed, two three or more singlets can be differentiated, and an inverse seesaw with four singlets can be reconstructed. In a more realistic world, we estimate \ell_\a \to \ell_\b \gamma expectations with a "Minimal-Flavour-Violation-like" ansatz, which gives a relation between ratios of the three branching ratios. The two singlet model predicts a discrete set of ratios.Comment: 14 page