Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

First observations of separated atmospheric nu_mu and bar{nu-mu} events in the MINOS detector

The complete 5.4 kton MINOS far detector has been taking data since the beginning of August 2003 at a depth of 2070 meters water-equivalent in the Soudan mine, Minnesota. This paper presents the first MINOS observations of nuµ and [overline nu ]µ charged-current atmospheric neutrino interactions based on an exposure of 418 days. The ratio of upward- to downward-going events in the data is compared to the Monte Carlo expectation in the absence of neutrino oscillations, giving Rup/downdata/Rup/downMC=0.62-0.14+0.19(stat.)±0.02(sys.). An extended maximum likelihood analysis of the observed L/E distributions excludes the null hypothesis of no neutrino oscillations at the 98% confidence level. Using the curvature of the observed muons in the 1.3 T MINOS magnetic field nuµ and [overline nu ]µ interactions are separated. The ratio of [overline nu ]µ to nuµ events in the data is compared to the Monte Carlo expectation assuming neutrinos and antineutrinos oscillate in the same manner, giving R[overline nu ][sub mu]/nu[sub mu]data/R[overline nu ][sub mu]/nu[sub mu]MC=0.96-0.27+0.38(stat.)±0.15(sys.), where the errors are the statistical and systematic uncertainties. Although the statistics are limited, this is the first direct observation of atmospheric neutrino interactions separately for nuµ and [overline nu ]µ

The role of pharmacists in developing countries: the current scenario in Pakistan

During the past few years, the pharmacy profession has expanded significantly in terms of professional services delivery and now has been recognized as an important profession in the multidisciplinary provision of health care. In contrast to the situation in developed countries, pharmacists in developing countries are still underutilized and their role as health care professionals is not deemed important by either the community or other health care providers. The aim of this paper is to highlight the role of pharmacists in developing countries, particularly in Pakistan. The paper draws on the literature related to the socioeconomic and health status of Pakistan's population, along with background on the pharmacy profession in the country in the context of the current directions of health care

Never Resting Brain: Simultaneous Representation of Two Alpha Related Processes in Humans

Brain activity is continuously modulated, even at “rest”. The alpha rhythm (8–12 Hz) has been known as the hallmark of the brain's idle-state. However, it is still debated if the alpha rhythm reflects synchronization in a distributed network or focal generator and whether it occurs spontaneously or is driven by a stimulus. This EEG/fMRI study aimed to explore the source of alpha modulations and their distribution in the resting brain. By serendipity, while computing the individually defined power modulations of the alpha-band, two simultaneously occurring components of these modulations were found. An ‘induced alpha’ that was correlated with the paradigm (eyes open/ eyes closed), and a ‘spontaneous alpha’ that was on-going and unrelated to the paradigm. These alpha components when used as regressors for BOLD activation revealed two segregated activation maps: the ‘induced map’ included left lateral temporal cortical regions and the hippocampus; the ‘spontaneous map’ included prefrontal cortical regions and the thalamus. Our combined fMRI/EEG approach allowed to computationally untangle two parallel patterns of alpha modulations and underpin their anatomical basis in the human brain. These findings suggest that the human alpha rhythm represents at least two simultaneously occurring processes which characterize the ‘resting brain’; one is related to expected change in sensory information, while the other is endogenous and independent of stimulus change

Brain classification reveals the right cerebellum as the best biomarker of dyslexia

Background Developmental dyslexia is a specific cognitive disorder in reading acquisition that has genetic and neurological origins. Despite histological evidence for brain differences in dyslexia, we recently demonstrated that in large cohort of subjects, no differences between control and dyslexic readers can be found at the macroscopic level (MRI voxel), because of large variances in brain local volumes. In the present study, we aimed at finding brain areas that most discriminate dyslexic from control normal readers despite the large variance across subjects. After segmenting brain grey matter, normalizing brain size and shape and modulating the voxels' content, normal readers' brains were used to build a 'typical' brain via bootstrapped confidence intervals. Each dyslexic reader's brain was then classified independently at each voxel as being within or outside the normal range. We used this simple strategy to build a brain map showing regional percentages of differences between groups. The significance of this map was then assessed using a randomization technique. Results The right cerebellar declive and the right lentiform nucleus were the two areas that significantly differed the most between groups with 100% of the dyslexic subjects (N = 38) falling outside of the control group (N = 39) 95% confidence interval boundaries. The clinical relevance of this result was assessed by inquiring cognitive brain-based differences among dyslexic brain subgroups in comparison to normal readers' performances. The strongest difference between dyslexic subgroups was observed between subjects with lower cerebellar declive (LCD) grey matter volumes than controls and subjects with higher cerebellar declive (HCD) grey matter volumes than controls. Dyslexic subjects with LCD volumes performed worse than subjects with HCD volumes in phonologically and lexicon related tasks. Furthermore, cerebellar and lentiform grey matter volumes interacted in dyslexic subjects, so that lower and higher lentiform grey matter volumes compared to controls differently modulated the phonological and lexical performances. Best performances (observed in controls) corresponded to an optimal value of grey matter and they dropped for higher or lower volumes. Conclusion These results provide evidence for the existence of various subtypes of dyslexia characterized by different brain phenotypes. In addition, behavioural analyses suggest that these brain phenotypes relate to different deficits of automatization of language-based processes such as grapheme/phoneme correspondence and/or rapid access to lexicon entries. article available here: http://www.biomedcentral.com/1471-2202/10/6

Active inference, sensory attenuation and illusions.

Active inference provides a simple and neurobiologically plausible account of how action and perception are coupled in producing (Bayes) optimal behaviour. This can be seen most easily as minimising prediction error: we can either change our predictions to explain sensory input through perception. Alternatively, we can actively change sensory input to fulfil our predictions. In active inference, this action is mediated by classical reflex arcs that minimise proprioceptive prediction error created by descending proprioceptive predictions. However, this creates a conflict between action and perception; in that, self-generated movements require predictions to override the sensory evidence that one is not actually moving. However, ignoring sensory evidence means that externally generated sensations will not be perceived. Conversely, attending to (proprioceptive and somatosensory) sensations enables the detection of externally generated events but precludes generation of actions. This conflict can be resolved by attenuating the precision of sensory evidence during movement or, equivalently, attending away from the consequences of self-made acts. We propose that this Bayes optimal withdrawal of precise sensory evidence during movement is the cause of psychophysical sensory attenuation. Furthermore, it explains the force-matching illusion and reproduces empirical results almost exactly. Finally, if attenuation is removed, the force-matching illusion disappears and false (delusional) inferences about agency emerge. This is important, given the negative correlation between sensory attenuation and delusional beliefs in normal subjects--and the reduction in the magnitude of the illusion in schizophrenia. Active inference therefore links the neuromodulatory optimisation of precision to sensory attenuation and illusory phenomena during the attribution of agency in normal subjects. It also provides a functional account of deficits in syndromes characterised by false inference and impaired movement--like schizophrenia and Parkinsonism--syndromes that implicate abnormal modulatory neurotransmission

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Observation of Two New Excited Ξb0 States Decaying to Λb0 K-π+

Two narrow resonant states are observed in the Λb0K-π+ mass spectrum using a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 6 fb-1. The minimal quark content of the Λb0K-π+ system indicates that these are excited Ξb0 baryons. The masses of the Ξb(6327)0 and Ξb(6333)0 states are m[Ξb(6327)0]=6327.28-0.21+0.23±0.12±0.24 and m[Ξb(6333)0]=6332.69-0.18+0.17±0.03±0.22 MeV, respectively, with a mass splitting of Δm=5.41-0.27+0.26±0.12 MeV, where the uncertainties are statistical, systematic, and due to the Λb0 mass measurement. The measured natural widths of these states are consistent with zero, with upper limits of Γ[Ξb(6327)0]<2.20(2.56) and Γ[Ξb(6333)0]<1.60(1.92) MeV at a 90% (95%) credibility level. The significance of the two-peak hypothesis is larger than nine (five) Gaussian standard deviations compared to the no-peak (one-peak) hypothesis. The masses, widths, and resonant structure of the new states are in good agreement with the expectations for a doublet of 1D Ξb0 resonances