A possible method for non-Hermitian and non-PTPT-symmetric Hamiltonian systems

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator $\eta_+$ represents the $\eta_+$-pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-$PT$-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator $\eta_+$ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-$PT$-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1 figure, clarifications made clearer; v4: 19 pages, the main context is completely rewritten; v5: 25 pages, title slightly changed, clarifications added, the final version to appear in PLOS ON

Perspective from a Younger Generation -- The Astro-Spectroscopy of Gisbert Winnewisser

Gisbert Winnewisser's astronomical career was practically coextensive with the whole development of molecular radio astronomy. Here I would like to pick out a few of his many contributions, which I, personally, find particularly interesting and put them in the context of newer results.Comment: 14 pages. (Co)authored by members of the MPIfR (Sub)millimeter Astronomy Group. To appear in the Proceedings of the 4th Cologne-Bonn-Zermatt-Symposium "The Dense Interstellar Medium in Galaxies" eds. S. Pfalzner, C. Kramer, C. Straubmeier, & A. Heithausen (Springer: Berlin

Intravascular lymphoma presenting as a specific pulmonary embolism and acute respiratory failure: a case report

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Noncommutative Particles in Curved Spaces

We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a noncommutative first-order action in D=10 curved spacetime and the covariant equations of motions were computed. This model, invariant under diffeomorphism, generalizes recent relativistic results.Comment: 1+15 pages. Latex. New comments and results adde

Noncommutative geometry inspired black holes in higher dimensions at the LHC

When embedding models of noncommutative geometry inspired black holes into the peridium of large extra dimensions, it is natural to relate the noncommutativity scale to the higher-dimensional Planck scale. If the Planck scale is of the order of a TeV, noncommutative geometry inspired black holes could become accessible to experiments. In this paper, we present a detailed phenomenological study of the production and decay of these black holes at the Large Hadron Collider (LHC). Noncommutative inspired black holes are relatively cold and can be well described by the microcanonical ensemble during their entire decay. One of the main consequences of the model is the existence of a black hole remnant. The mass of the black hole remnant increases with decreasing mass scale associated with noncommutative and decreasing number of dimensions. The experimental signatures could be quite different from previous studies of black holes and remnants at the LHC since the mass of the remnant could be well above the Planck scale. Although the black hole remnant can be very heavy, and perhaps even charged, it could result in very little activity in the central detectors of the LHC experiments, when compared to the usual anticipated black hole signatures. If this type of noncommutative inspired black hole can be produced and detected, it would result in an additional mass threshold above the Planck scale at which new physics occurs.Comment: 21 pages, 7 figure

A population of luminous accreting black holes with hidden mergers

Major galaxy mergers are thought to play an important part in fuelling the growth of supermassive black holes. However, observational support for this hypothesis is mixed, with some studies showing a correlation between merging galaxies and luminous quasars and others showing no such association. Recent observations have shown that a black hole is likely to become heavily obscured behind merger-driven gas and dust, even in the early stages of the merger, when the galaxies are well separated (5 to 40 kiloparsecs). Merger simulations further suggest that such obscuration and black-hole accretion peaks in the final merger stage, when the two galactic nuclei are closely separated (less than 3 kiloparsecs). Resolving this final stage requires a combination of high-spatial-resolution infrared imaging and high-sensitivity hard-X-ray observations to detect highly obscured sources. However, large numbers of obscured luminous accreting supermassive black holes have been recently detected nearby (distances below 250 megaparsecs) in X-ray observations. Here we report high-resolution infrared observations of hard-X-ray-selected black holes and the discovery of obscured nuclear mergers, the parent populations of supermassive-black-hole mergers. We find that obscured luminous black holes (bolometric luminosity higher than 2x10^44 ergs per second) show a significant (P<0.001) excess of late-stage nuclear mergers (17.6 per cent) compared to a sample of inactive galaxies with matching stellar masses and star formation rates (1.1 per cent), in agreement with theoretical predictions. Using hydrodynamic simulations, we confirm that the excess of nuclear mergers is indeed strongest for gas-rich major-merger hosts of obscured luminous black holes in this final stage.Comment: To appear in the 8 November 2018 issue of Nature. This is the authors' version of the wor

Alpha-band rhythms in visual task performance: phase-locking by rhythmic sensory stimulation

Oscillations are an important aspect of neuronal activity. Interestingly, oscillatory patterns are also observed in behaviour, such as in visual performance measures after the presentation of a brief sensory event in the visual or another modality. These oscillations in visual performance cycle at the typical frequencies of brain rhythms, suggesting that perception may be closely linked to brain oscillations. We here investigated this link for a prominent rhythm of the visual system (the alpha-rhythm, 8-12 Hz) by applying rhythmic visual stimulation at alpha-frequency (10.6 Hz), known to lead to a resonance response in visual areas, and testing its effects on subsequent visual target discrimination. Our data show that rhythmic visual stimulation at 10.6 Hz: 1) has specific behavioral consequences, relative to stimulation at control frequencies (3.9 Hz, 7.1 Hz, 14.2 Hz), and 2) leads to alpha-band oscillations in visual performance measures, that 3) correlate in precise frequency across individuals with resting alpha-rhythms recorded over parieto-occipital areas. The most parsimonious explanation for these three findings is entrainment (phase-locking) of ongoing perceptually relevant alpha-band brain oscillations by rhythmic sensory events. These findings are in line with occipital alpha-oscillations underlying periodicity in visual performance, and suggest that rhythmic stimulation at frequencies of intrinsic brain-rhythms can be used to reveal influences of these rhythms on task performance to study their functional roles

How functional programming mattered

In 1989 when functional programming was still considered a niche topic, Hughes wrote a visionary paper arguing convincingly ‘why functional programming matters’. More than two decades have passed. Has functional programming really mattered? Our answer is a resounding ‘Yes!’. Functional programming is now at the forefront of a new generation of programming technologies, and enjoying increasing popularity and influence. In this paper, we review the impact of functional programming, focusing on how it has changed the way we may construct programs, the way we may verify programs, and fundamentally the way we may think about programs

Learning and Long-Term Retention of Large-Scale Artificial Languages

Recovering discrete words from continuous speech is one of the first challenges facing language learners. Infants and adults can make use of the statistical structure of utterances to learn the forms of words from unsegmented input, suggesting that this ability may be useful for bootstrapping language-specific cues to segmentation. It is unknown, however, whether performance shown in small-scale laboratory demonstrations of “statistical learning” can scale up to allow learning of the lexicons of natural languages, which are orders of magnitude larger. Artificial language experiments with adults can be used to test whether the mechanisms of statistical learning are in principle scalable to larger lexicons. We report data from a large-scale learning experiment that demonstrates that adults can learn words from unsegmented input in much larger languages than previously documented and that they retain the words they learn for years. These results suggest that statistical word segmentation could be scalable to the challenges of lexical acquisition in natural language learning.National Science Foundation (U.S.) (NSF DDRIG #0746251