Representations of the Weyl group and Wigner functions for SU(3)

Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl group is represented as the symmetric group of permutations of the particle coordinates of these space. Wigner functions for SU(3) are expressed as products of SU(2) Wigner functions and matrix elements of Weyl transformations. The constructions make explicit use of dual reductive pairs which are shown to be particularly relevant to problems in optics and quantum interferometry.Comment: : RevTex file, 11 pages with 2 figure

Unitary transformations for testing Bell inequalities

It is shown that optical experimental tests of Bell inequality violations can be described by SU(1,1) transformations of the vacuum state, followed by photon coincidence detections. The set of all possible tests are described by various SU(1,1) subgroups of Sp(8,$\Bbb R$). In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post--selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.Comment: 3 figure

Lost and found: the radial quantum number of Laguerre-Gauss modes

We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.Comment: Some minor typos fixed

BIOMECHANICAL STUDY ON CADAVER KNEE FOR THE EVALUATION OF CRUCIATE KNEE LIGAMENT RECONSTRUCTIONS

INTRODUCTION: Ruptures of the anterior and posterior cruciate knee ligament (ACL and PCL), alone or combined, are some of the most frequent joint injuries, especially in sports. The long-term unsatisfactory results and lack of systematic evaluation of surgical reconstructions have led us to undergo an evaluation on cadaver knees. MATERIAL AND METHOD: A preliminary study was performed on one cadaver knee. The femur was fixed on a holder and magnetic sensors “BirdsTM” were attached to the tibia and the femur, which tracked the knee’s movement. A threedimensional knee analyzer GENI(1) was used to calculate kinematic parameters (tibial internal and external rotation and ab/adduction), as well as ligament combined deformation (elongation / bending / torsion) during knee flexion. This experiment was performed on an intact knee and a knee where the PCL has been cut and reconstructed using a synthetic Trevia ligament. Finally the knee was dissected to produce a combined postero-lateral instability and reconstructed with and without postero-lateral corner reconstruction. The effect of different reconstruction methods on kinematics and ligament deformation were compared. RESULTS AND DISCUSSION: Kinematic parameters changed significantly when PCl and postero-lateral corner were dissected. The reconstruction of the PCL alone, using an “Over-the-Bottom” method described by Krudwig(2), shifted the curves back to the initial situation and decreased the variability of the movement. Ligament deformation was 3 mm elongation, 50o femoral flexion and 90o torsion. These values are in accordance with material properties and should lead to good long-term biofunctionnality. CONCLUSION: This study proposes an in vitro protocol for a better understanding of the clinical success or failure of different procedures. Preliminary results showed that the system and the protocol setup are sensitive to changes in kinematics following posterior cruciate ligament dissection and reconstruction. Experiments are performed at this time on several cadaver knees, in order to compare different reconstruction methods. REFERENCES: Sati, M. et al. (1997). Computer Assisted Knee Surgery: Diagnostics and Planning of Knee Surgery. Computer Aided Surgery 2, 108-123. Krudwig, W. (1997). In L'H. Yahia (Ed.), Ligaments and Ligamentoplasties. Heidelberg: Springer Verlag

Exposure to Oil and Hypoxia Results In Alterations of Immune Transcriptional Patterns In Developing Sheepshead Minnows (\u3ci\u3eCyprinodon variegatus\u3c/i\u3e)

The area and timing of the Deepwater Horizon oil spill highlight the need to study oil and hypoxia exposure in early life stage fishes. Though critical to health, little research has targeted the effect of oil and hypoxia exposure on developing immune systems. To this end, we exposed sheepshead minnows (Cyprinodon variegatus) at three early life stages: embryonic; post-hatch; and post-larval, to a high energy water accommodated fraction (HEWAF) of oil, hypoxia, or both for 48 hours. We performed RNAseq to understand how exposures alter expression of immune transcripts and pathways. Under control conditions, the embryonic to post-hatch comparison (first transition) had a greater number of significantly regulated immune pathways than the second transition (post-hatch to post-larval). The addition of oil had little effect in the first transition, however, hypoxia elicited changes in cellular and humoral immune responses. In the second transition, oil exposure significantly altered many immune pathways (43), and while hypoxia altered few pathways, it did induce a unique signature of generally suppressing immune pathways. These data suggest that timing of exposure to oil and/or hypoxia matters, and underscores the need to further investigate the impacts of multiple stressors on immune system development in early life stage fishes

Changes in physical education teachers’ beliefs regarding motivational strategies: A quasi-experimental study

Abstract Physical education teachers use motivational strategies that can (positively or negatively) affect their students’ level of motivation and engagement. Indeed, according to their experiences and beliefs, some teachers may focus on strategies that thwart, rather than support, students’ psychological needs (autonomy, competence, and relatedness). Effective professional development represents an excellent opportunity to help teachers use research-supported motivational strategies. Therefore, this study aimed to discover if attendance at a 2-day training course could positively affect PE teachers’ beliefs regarding empowering motivational strategies. Specifically, 11 PE teachers (experimental group = 6 [attending the training]; control group = 5 [no training]) from primary school (n = 6) and secondary school (n = 5) expressed their beliefs (effectiveness, feasibility, and normality) regarding 31 empowering motivational strategies proposed during training at the beginning (October) and the end (April) of the school year. Results of the Wilcoxon signed-rank test for related samples indicated no significant differences for the belief regarding effectiveness in either group. However, some positive significant changes (p ≤ .05) occurred in the experimental group for two motivational strategies supporting students’ need for autonomy and one supporting their need for competence. Given the small sample, positive trends (p ≤ .10) are also considered results of interest. In conclusion, the training appears likely to impact teachers’ beliefs. However, future professional development should provide additional feedback and follow-up time with teachers during experimentation with students to allow teachers to refine their understanding and use of the motivational strategies proposed

SU(N)-symmetric quasi-probability distribution functions

We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-functions. We then show the fundamental properties of these functions and discuss their usefulness for analyzing N-dimensional pure and mixed quantum states.Comment: 16 pages, 2 figures. Updated text to reflect referee comment

A complementarity-based approach to phase in finite-dimensional quantum systems

We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of this class consists of diagonal operators that represent amplitudes (or inversions). By the finite Fourier transform, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss the examples of qubits and qutrits, and show how these results generalize previous approaches.Comment: 6 pages, no figure