Phase-Space Metric for Non-Hamiltonian Systems

We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page

On FO2 quantifier alternation over words

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels

Daily Eastern News: March 03, 2017

https://thekeep.eiu.edu/den_2017_mar/1002/thumbnail.jp

Precision calculation of γd→π+nn\gamma d\to \pi^+ nn within chiral perturbation theory

The reaction $\gamma d\to \pi^+ nn$ is calculated up to order $\chi^{5/2}$ in chiral perturbation theory, where $\chi$ denotes the ratio of the pion to the nucleon mass. Special emphasis is put on the role of nucleon--recoil corrections that are the source of contributions with fractional power in $\chi$. Using the known near threshold production amplitude for $\gamma p\to \pi^+ n$ as the only input, the total cross section for $\gamma d\to \pi^+ nn$ is described very well. A conservative estimate suggests that the theoretical uncertainty for the transition operator amounts to 3 % for the computed amplitude near threshold.Comment: 28 page

The Change Laboratory in Higher Education:research-intervention using activity theory

In this chapter we discuss the Change Laboratory as an intervention-research methodology in higher education. We trace its theoretical origins in dialectical-materialism and activity theory, consider the recommendations made by its main proponents, and discuss its use in a range of higher education settings. We suggest that the Change Laboratory offers considerable potential for higher education research, though tensions between Change Laboratory design recommendations and typical higher education contexts require consideration

Water vapour at high redshift: Arecibo monitoring of the megamaser in MG J0414+0534

The study of water masers at cosmological distances would allow us to investigate the parsec-scale environment around powerful radio sources, to probe the physical conditions of the molecular gas in the inner parsecs of quasars, and to estimate their nuclear engine masses in the early universe. To derive this information, the nature of the maser source, jet or disk-maser, needs to be assessed through a detailed investigation of the observational characteristics of the line emission. We monitored the maser line in the lensed quasar MGJ0414+0534 at z = 2.64 with the 300-m Arecibo telescope for ~15 months to detect possible additional maser components and to measure a potential velocity drift of the lines. In addition, we follow the maser and continuum emissions to reveal significant variations in their flux density and to determine correlation or time-lag, if any, between them. The main maser line profile is complex and can be resolved into a number of broad features with line widths of 30-160 km/s. A new maser component was tentatively detected in October 2008 that is redshifted by 470 km/s w.r.t the systemic velocity of the quasar. The line width of the main maser feature increased by a factor of two between the Effelsberg and EVLA observations reported by Impellizzeri et al. (2008) and the first epoch of the Arecibo monitoring campaign. After correcting for the lens magnification, we find that the total H2O isotropic luminosity of the maser in MGJ0414+0534 is now ~30,000 Lsun, making this source the most luminous ever discovered.[Abridged]Comment: 8 pages, 6 figures, accepted for publication in A&

Role of medial prefrontal cortex and primary somatosensory cortex in self and other-directed vicarious social touch: a TMS study

Conflicting evidence points to the contribution of several key nodes of the 'social brain' to the processing of both discriminatory and affective qualities of interpersonal touch. Whether the primary somatosensory cortex (S1) and the medial prefrontal cortex (mPFC), two brain areas vital for tactile mirroring and affective mentalizing, play a functional role in shared representations of C-tactile (CT) targeted affective touch is still a matter of debate. Here, we used offline continuous theta-burst Transcranial Magnetic Stimulation (cTBS) to mPFC, S1 and Vertex (control) prior to participants providing ratings of vicarious touch pleasantness for self and others delivered across several body sites at CT-targeted velocities. We found that S1-cTBS led to a significant increase in touch ratings to the self, with this effect being positively associated to levels of interoceptive awareness. Conversely, mPFC-cTBS reduced pleasantness ratings for touch to another person. These effects were not specific for CT-optimal (slow) stroking velocities, but rather they applied to all types of social touch. Overall, our findings challenge the causal role of the S1 and mPFC in vicarious affective touch and suggest that self- vs. other-directed vicarious touch responses might crucially depend on the specific involvement of key social networks in gentle tactile interactions