Sources of quantum waves

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.Comment: 12 pages, 7 inlined figures; typos correcte

Percolation in the Harmonic Crystal and Voter Model in three dimensions

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential, $U=\frac{J}{2} \sum_{} (\phi(x) - \phi(y))^2$, $x,y \in \mathbb{Z}^3$, $J > 0$ and $\phi(x) \in \mathbb{R}$, a scalar height variable, and define occupation variables $\rho_h(x) =1,(0)$ for $\phi(x) > h (<h)$. The probability $p$ of a site being occupied, is then a function of $h$. In the voter model we consider the stationary measure, in which each site is either occupied or empty, with probability $p$. In both cases the truncated pair correlation of the occupation variables, $G(x-y)$, decays asymptotically like $|x-y|^{-1}$. Using some novel Monte Carlo simulation methods and finite size scaling we find accurate values of $p_c$ as well as the critical exponents for these systems. The latter are different from that of independent percolation in $d=3$, as expected from the work of Weinrib and Halperin [WH] for the percolation transition of systems with $G(r) \sim r^{-a}$ [A. Weinrib and B. Halperin, Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent $\nu$ is very close to the predicted value of 2 supporting the conjecture by WH that $\nu= \frac{2}{a}$ is exact.Comment: 8 figures. new version significantly different from the old one, includes new results, figures et

Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors

HISTOLOGICAL, IMMUNOHISTOCHEMICAL, ТЕМ AND SEM INVESTIGATIONS IN THE VALVE-CUSP FREE BORDER OF GREAT VARICOSE SAPHENOUS VEIN

The authors studied venous valve cusps from surgically removed great saphenous vein with essential lower limb varicosis from 20 patients without data about previous thrombophlebitis. Venous valves without varicose alterations were used as controls. The histological, immunohistochemical, ТЕМ and SEM techniques were applied. In morphologically complete valve cusps from non-varicose great saphenous vein, a small marginal thickening was observed by routine histology. The cells visualised in these thickenings showed positive reaction against anti-vimentin but negative reaction against anti—smooth muscle actin antibody. In varicose vein valve cusps a marginal thickening with considerably larger diameter was histologically observed. In the fibrin-like material which was disposed around these thickenings, proliferation of fibroblasts as well as collagen fibres' depositions were seen. The SEM study showed partial "rollings" of the free cusp border. In the marginal thickening, the cells showed negative reaction not only to anti—smooth muscle actin but they also lost the reaction to anti-vimentin monoclonal antibody. The process mentioned above advanced, it occupied a new part at the valve cusp and so the cusp shortened. According to our hypothesis, this was one of the ways of initiating and advancing incompetence in primary varicosis

Gene expression changes in a tumor xenograft by a pyrrole-imidazole polyamide

Gene regulation by DNA binding small molecules could have important therapeutic applications. This study reports the investigation of a DNA-binding pyrrole-imidazole polyamide targeted to bind the DNA sequence 5′-WGGWWW-3′ with reference to its potency in a subcutaneous xenograft tumor model. The molecule is capable of trafficking to the tumor site following subcutaneous injection and modulates transcription of select genes in vivo. An FITC-labeled analogue of this polyamide can be detected in tumor-derived cells by confocal microscopy. RNA deep sequencing (RNA-seq) of tumor tissue allowed the identification of further affected genes, a representative panel of which was interrogated by quantitative reverse transcription-PCR and correlated with cell culture expression levels

Antitumor activity of a pyrrole-imidazole polyamide

Many cancer therapeutics target DNA and exert cytotoxicity through the induction of DNA damage and inhibition of transcription. We report that a DNA minor groove binding hairpin pyrrole-imidazole (Py-Im) polyamide interferes with RNA polymerase II (RNAP2) activity in cell culture. Polyamide treatment activates p53 signaling in LNCaP prostate cancer cells without detectable DNA damage. Genome-wide mapping of RNAP2 binding shows reduction of occupancy, preferentially at transcription start sites, but occupancy at enhancer sites is unchanged. Polyamide treatment results in a time- and dose-dependent depletion of the RNAP2 large subunit RPB1 that is preventable with proteasome inhibition. This polyamide demonstrates antitumor activity in a prostate tumor xenograft model with limited host toxicity

Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

Quantum Tunneling in the Wigner Representation

Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various initial state preparations and local potential barriers. It is manifestly causal and includes time-lag effects and quantum spreading. Specific features of quantum dynamics which disappear in the standard semi-classical approximation are revealed. The propagator may be applied to calculation of the final momentum and coordinate distributions, for particles transmitted through or reflected from the potential barrier, as well as for elucidating the tunneling time problem.Comment: 18 pages, LATEX, no figure

Mitigation of off-target toxicity in CRISPR-Cas9 screens for essential non-coding elements.

Pooled CRISPR-Cas9 screens are a powerful method for functionally characterizing regulatory elements in the non-coding genome, but off-target effects in these experiments have not been systematically evaluated. Here, we investigate Cas9, dCas9, and CRISPRi/a off-target activity in screens for essential regulatory elements. The sgRNAs with the largest effects in genome-scale screens for essential CTCF loop anchors in K562 cells were not single guide RNAs (sgRNAs) that disrupted gene expression near the on-target CTCF anchor. Rather, these sgRNAs had high off-target activity that, while only weakly correlated with absolute off-target site number, could be predicted by the recently developed GuideScan specificity score. Screens conducted in parallel with CRISPRi/a, which do not induce double-stranded DNA breaks, revealed that a distinct set of off-targets also cause strong confounding fitness effects with these epigenome-editing tools. Promisingly, filtering of CRISPRi libraries using GuideScan specificity scores removed these confounded sgRNAs and enabled identification of essential regulatory elements