Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?

We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$, containing a square, into its factors. Illustrative low dimensional examples are the quartit ($q=4$) and two-qubit ($q=2^2$) systems, the octit ($q=8$), qubit/quartit ($q=2\times 4$) and three-qubit ($q=2^3$) systems, and so on. In the single qudit case, e.g. $q=4,8,12,...$, one defines a bijection between the $\sigma (q)$ maximal commuting sets [with $\sigma[q)$ the sum of divisors of $q$] of Pauli observables and the maximal submodules of the modular ring $\mathbb{Z}_q^2$, that arrange into the projective line $P_1(\mathbb{Z}_q)$ and a independent set of size $\sigma (q)-\psi(q)$ [with $\psi(q)$ the Dedekind psi function]. In the multiple qudit case, e.g. $q=2^2, 2^3, 3^2,...$, the Pauli graphs rely on symplectic polar spaces such as the generalized quadrangles GQ(2,2) (if $q=2^2$) and GQ(3,3) (if $q=3^2$). More precisely, in dimension $p^n$ ($p$ a prime) of the Hilbert space, the observables of the Pauli group (modulo the center) are seen as the elements of the $2n$-dimensional vector space over the field $\mathbb{F}_p$. In this space, one makes use of the commutator to define a symplectic polar space $W_{2n-1}(p)$ of cardinality $\sigma(p^{2n-1})$, that encodes the maximal commuting sets of the Pauli group by its totally isotropic subspaces. Building blocks of $W_{2n-1}(p)$ are punctured polar spaces (i.e. a observable and all maximum cliques passing to it are removed) of size given by the Dedekind psi function $\psi(p^{2n-1})$. For multiple qudit mixtures (e.g. qubit/quartit, qubit/octit and so on), one finds multiple copies of polar spaces, ponctured polar spaces, hypercube geometries and other intricate structures. Such structures play a role in the science of quantum information.Comment: 18 pages, version submiited to J. Phys. A: Math. Theo

Validation of equilibrium tools on the COMPASS tokamak

SOFT 2014 conference, submitted to Fusion Engineering and DesignInternational audienceVarious MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpreting and planning tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code [L.C. Appel et al., EPS 2006, P2.184], the free-boundary equilibrium code FREEBIE [J.-F. Artaud, S.H. Kim, EPS 2012, P4.023], and a rapid plasma boundary reconstruction code VacTH [B. Faugeras et al., PPCF 56, 114010 (2014)]. We demonstrate that FREEBIE can calculate the equilibrium and corresponding poloidal field (PF) coils currents consistently with EFIT++ reconstructions from experimental data. Both EFIT++ and VacTH can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. Hence, VacTH is suitable for real-time control. Optimum reconstruction parameters are estimated

Soil conservation and sustainable development goals(SDGs) achievement in Europe and central Asia: Which role for the European soil partnership?

Voluntary soil protection measures are not sufficient to achieve sustainable soil management at a global scale. Additionally, binding soil protection legislation at national and international levels has also proved to be insufficient for the effective protection of this almost non-renewable natural resource. The European Soil Partnership (ESP) and its sub-regional partnerships (Eurasian Sub-Regional Soil Partnership, Alpine Soil Partnership) were established in the context of FAO's Global Soil Partnership (GSP) with the mission to facilitate and contribute to the exchange of knowledge and technologies related to soils, to develop dialogue and to raise awareness for the need to establish a binding global agreement for sustainable soil management. The ESP has taken a role of an umbrella network covering countries in Europe and Central Asia. It aims to improve the dialogue in the whole region and has encouraged establishing goals that would promote sustainable soil management, taking into account various national and local approaches and priorities, as well as cultural specificities. The ESP first regional implementation plan for the 2017–2020 period was adopted and implemented along the five GSP pillars of action. Building on the experience of the last four years, this study demonstrates that establishing sub-regional and national partnerships is an additional step in a concrete sustainable soil management implementation process. It also suggests that a complementary approach between legal instruments and voluntary initiatives linked to the development of efficient communication and strong commitment is the key to success

Simulations of COMPASS vertical displacement events with a self-consistent model for halo currents including neutrals and sheath boundary conditions

The understanding of the halo current properties during disruptions is key to design and operate large scale tokamaks in view of the large thermal and electromagnetic loads that they entail. For the first time, we present a fully self-consistent model for halo current simulations including neutral particles and sheath boundary conditions. The model is used to simulate vertical displacement events (VDEs) occurring in the COMPASS tokamak. Recent COMPASS experiments have shown that the parallel halo current density at the plasma-wall interface is limited by the ion saturation current during VDE-induced disruptions. We show that usual magneto-hydrodynamic boundary conditions can lead to the violation of this physical limit and we implement this current density limitation through a boundary condition for the electrostatic potential. Sheath boundary conditions for the density, the heat flux, the parallel velocity and a realistic parameter choice (e.g. Spitzer's resistivity and Spitzer-Harm parallel thermal conductivity) extend present VDE simulations beyond the state of the art. Experimental measurements of the current density, temperature and heat flux profiles at the COMPASS divertor are compared with the results obtained from axisymmetric simulations. Since the ion saturation current density (Jsat) is shown to be essential to determine the halo current profile, parametric scans are performed to study its dependence on different quantities such as the plasma resistivity and the particle and heat diffusion coefficients. In this respect, the plasma resistivity in the halo region broadens significantly the Jsat profile, increasing the halo width at a similar total halo current

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

Toxoplasma and coxiella infection and psychiatric morbidity: A retrospective cohort analysis

BACKGROUND: It has been suggested that infection with Toxoplasma gondii is associated with slow reaction and poor concentration, whilst infection with Coxiella burnetii may lead to persistent symptoms of fatigue. METHODS: 425 farmers completed the Revised Clinical Interview Schedule (CIS-R) by computer between March and July 1999 to assess psychiatric morbidity. Samples of venous blood had been previously collected and seroprevalence of T. gondii and C. burnetii was assessed. RESULTS: 45% of the cohort were seropositive for T. gondii and 31% were positive for C. burnetii. Infection with either agent was not associated with symptoms reflecting clinically relevant levels of concentration difficulties, fatigue, depression, depressive ideas or overall psychiatric morbidity. CONCLUSIONS: We do not provide any evidence that infection with Toxoplasma gondii or Coxiella burnetii is associated with neuropsychiatric morbidity, in particular with symptoms of poor concentration or fatigue. However, this is a relatively healthy cohort with few individuals reporting neuropsychiatric morbidity and therefore the statistical power to test the study hypotheses is limited

Organizational Culture and Physician Satisfaction with Dimensions of Group Practice

To assess the extent to which the organizational culture of physician group practices is associated with individual physician satisfaction with the managerial and organizational capabilities of the groups. Study Design and Methods . Physician surveys from 1997 to 1998 assessing the culture of their medical groups and their satisfaction with six aspects of group practice. Organizational culture was conceptualized using the Competing Values framework, yielding four distinct cultural types. Physician-level data were aggregated to the group level to attain measures of organizational culture. Using hierarchical linear modeling, individual physician satisfaction with six dimensions of group practice was predicted using physician-level variables and group-level variables. Separate models for each of the four cultural types were estimated for each of the six satisfaction measures, yielding a total of 24 models. Sample Studied . Fifty-two medical groups affiliated with 12 integrated health systems from across the U.S., involving 1,593 physician respondents (38.3 percent response rate). Larger medical groups and multispecialty groups were over-represented compared with the U.S. as a whole. Principal Findings . Our models explain up to 31 percent of the variance in individual physician satisfaction with group practice, with individual organizational culture scales explaining up to 5 percent of the variance. Group-level predictors: group (i.e., participatory) culture was positively associated with satisfaction with staff and human resources, technological sophistication, and price competition. Hierarchical (i.e., bureaucratic) culture was negatively associated with satisfaction with managerial decision making, practice level competitiveness, price competition, and financial capabilities. Rational (i.e., task-oriented) culture was negatively associated with satisfaction with staff and human resources, and price competition. Developmental (i.e., risk-taking) culture was not significantly associated with any of the satisfaction measures. In some of the models, being a single-specialty group (compared with a primary care group) and a group having a higher percent of male physicians were positively associated with satisfaction with financial capabilities. Physician-level predictors: individual physicians' ratings of organizational culture were significantly related to many of the satisfaction measures. In general, older physicians were more satisfied than younger physicians with many of the satisfaction measures. Male physicians were less satisfied with data capabilities. Primary care physicians (versus specialists) were less satisfied with price competition. Conclusion . Some dimensions of physician organizational culture are significantly associated with various aspects of individual physician satisfaction with group practice.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/1/j.1475-6773.2006.00648.x.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/2/HESR+648+Appendix+A.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/3/HESR+648+Appendix+C.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/4/HESR+648+Appendix+B.pd