Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck remnants of black holes appearing in the assumption of the Generalized Uncertainty Relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the Holographic Principle. Because of this, a conjecture is made about the possibility for obtaining the Generalized Uncertainty Relations from the covariant entropy bound at high energies in the same way as R. Bousso has derived Heisenberg uncertainty principle for the flat space.Comment: 12 pages,no figures,some corrections,new reference

The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.Comment: 9 pages,Revte

#Bigbirds never die: Understanding social dynamics of emergent hashtag

We examine the growth, survival, and context of 256 novel hashtags during the 2012 U.S. presidential debates. Our analysis reveals the trajectories of hashtag use fall into two distinct classes: “winners” that emerge more quickly and are sustained for longer periods of time than other “also-rans” hashtags. We propose a “conversational vibrancy” framework to capture dynamics of hashtags based on their topicality, interactivity, diversity, and prominence. Statistical analyses of the growth and persistence of hashtags reveal novel relationships between features of this framework and the relative success of hashtags. Specifically, retweets always contribute to faster hashtag adoption, replies extend the life of “winners” while having no effect on “also-rans.” This is the first study on the lifecycle of hashtag adoption and use in response to purely exogenous shocks. We draw on theories of uses and gratification, organizational ecology, and language evolution to discuss these findings and their implications for understanding social influence and collective action in social media more generally

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure

Chow's theorem and universal holonomic quantum computation

A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, these conditions determine that the holonomy group of the two-qubit interaction model contains $SU(2) \times SU(2)$. In particular, a universal two-qubit logic gate is attainable for this model.Comment: 13 page

Quantum Mechanics at Planck's scale and Density Matrix

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies on the fact that here density matrix subjects to deformation whereas so far commutators have been deformed. The density matrix obtained by deformation of quantum-mechanical density one is named throughout this paper density pro-matrix. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows to describe dynamics. In particular, the explicit form of deformed Liouville's equation and the deformed Shr\"odinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that obtained results allow to deduce in a simple and natural way the Bekenstein-Hawking's formula for black hole entropy in semiclassical approximation.Comment: 18 pages,Latex,new reference

Ectopic A-lattice seams destabilize microtubules

Natural microtubules typically include one A-lattice seam within an otherwise helically symmetric B-lattice tube. It is currently unclear how A-lattice seams influence microtubule dynamic instability. Here we find that including extra A-lattice seams in GMPCPP microtubules, structural analogues of the GTP caps of dynamic microtubules, destabilizes them, enhancing their median shrinkage rate by >20-fold. Dynamic microtubules nucleated by seeds containing extra A-lattice seams have growth rates similar to microtubules nucleated by B-lattice seeds, yet have increased catastrophe frequencies at both ends. Furthermore, binding B-lattice GDP microtubules to a rigor kinesin surface stabilizes them against shrinkage, whereas microtubules with extra A-lattice seams are stabilized only slightly. Our data suggest that introducing extra A-lattice seams into dynamic microtubules destabilizes them by destabilizing their GTP caps. On this basis, we propose that the single A-lattice seam of natural B-lattice MTs may act as a trigger point, and potentially a regulation point, for catastrophe

The melanoma-specific graded prognostic assessment does not adequately discriminate prognosis in a modern population with brain metastases from malignant melanoma

The melanoma-specific graded prognostic assessment (msGPA) assigns patients with brain metastases from malignant melanoma to 1 of 4 prognostic groups. It was largely derived using clinical data from patients treated in the era that preceded the development of newer therapies such as BRAF, MEK and immune checkpoint inhibitors. Therefore, its current relevance to patients diagnosed with brain metastases from malignant melanoma is unclear. This study is an external validation of the msGPA in two temporally distinct British populations.Performance of the msGPA was assessed in Cohort I (1997-2008, n=231) and Cohort II (2008-2013, n=162) using Kaplan-Meier methods and Harrell's c-index of concordance. Cox regression was used to explore additional factors that may have prognostic relevance.The msGPA does not perform well as a prognostic score outside of the derivation cohort, with suboptimal statistical calibration and discrimination, particularly in those patients with an intermediate prognosis. Extra-cerebral metastases, leptomeningeal disease, age and potential use of novel targeted agents after brain metastases are diagnosed, should be incorporated into future prognostic models.An improved prognostic score is required to underpin high-quality randomised controlled trials in an area with a wide disparity in clinical care

On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure