EPG-representations with small grid-size

In an EPG-representation of a graph $G$ each vertex is represented by a path in the rectangular grid, and $(v,w)$ is an edge in $G$ if and only if the paths representing $v$ an $w$ share a grid-edge. Requiring paths representing edges to be x-monotone or, even stronger, both x- and y-monotone gives rise to three natural variants of EPG-representations, one where edges have no monotonicity requirements and two with the aforementioned monotonicity requirements. The focus of this paper is understanding how small a grid can be achieved for such EPG-representations with respect to various graph parameters. We show that there are $m$-edge graphs that require a grid of area $\Omega(m)$ in any variant of EPG-representations. Similarly there are pathwidth-$k$ graphs that require height $\Omega(k)$ and area $\Omega(kn)$ in any variant of EPG-representations. We prove a matching upper bound of $O(kn)$ area for all pathwidth-$k$ graphs in the strongest model, the one where edges are required to be both x- and y-monotone. Thus in this strongest model, the result implies, for example, $O(n)$, $O(n \log n)$ and $O(n^{3/2})$ area bounds for bounded pathwidth graphs, bounded treewidth graphs and all classes of graphs that exclude a fixed minor, respectively. For the model with no restrictions on the monotonicity of the edges, stronger results can be achieved for some graph classes, for example an $O(n)$ area bound for bounded treewidth graphs and $O(n \log^2 n)$ bound for graphs of bounded genus.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Radiation of Charged Particles by Charged Black Hole

The probability of a charged particle production by the electric field of a charged black hole depends essentially on the particle energy. This probability is found in the nonrelativistic and ultrarelativistic limits. The range of values for the mass and charge of a black hole is indicated where the discussed mechanism of radiation is dominating over the Hawking one.Comment: 10 pages, latex, 4 ps-figure

Antioxidant and Antibacterial Activity of the Beverage Obtained by Fermentation of Sweetened Lemon Balm (Melissa offi cinalis L.) Tea with Symbiotic Consortium of Bacteria and Yeasts

Kombucha je napitak koji se tradicionalno dobiva fermentacijom zaslađenog crnog ili zelenog čaja (Camellia sinensis L.) s pomoću simbiotičke kulture bakterija i kvasaca (engl. SCOBY). U ovom je radu za pripremu napitka kombucha kao izvor dušika pri fermentaciji upotrijebljena melisa (Melissa officinalis L.). Tijekom sedmodnevne fermentacije mjereni su sljedeći parametri: pH-vrijednost, titracijska kiselost, udjeli ukupnih fenola i fenolnih spojeva, te sposobnost uklanjanja hidroksilnog (˙OH) i 1,1-difenil-2-pikrilhidrazilnog (DPPH) radikala da bi se utvrdila povezanost trajanja fermentacije s antioksidativnom i antibakterijskom aktivnošću fermentiranog napitka od melise. Određena je optimalna titracijska kiselost od 4 do 4,5 g/L, koju su potvrdili dugogodišnji konzumenti tog napitka. Ispitan je antibakterijski učinak napitaka povećane kiselosti od 8,12 g/L na jedanaest divljih bakterijskih sojeva. Rezultati pokazuju da se u proizvodnji fermentiranog napitka kombucha čaj (C. sinensis) može uspješno zamijeniti melisom. Udjel ukupnih fenola i sposobnost uklanjanja DPPH radikala bili su veći u podlozi s melisom nego u tradicionalnom napitku kombucha. Za biološku je aktivnost napitka kombucha s melisom najvjerojatnije zaslužna ružmarinska kiselina, glavni fenolni spoj u napitku. Vrijednosti EC50 pokazuju da napitak kombucha ima veću antioksidativnu vrijednost od čajnih infuzija C. sinensis L. i M. officinalis L., čemu vjerojatno pridonose metaboliti simbiotičke kulture bakterija i kvasaca. Kombucha s melisom optimalne i povećane titracijske kiselosti imala je izraženi antibakterijski učinak, ponajprije zbog prisustva octene kiseline, ali i zbog drugih sastojaka čaja te prisustva metabolita simbiotičke kulture.Kombucha is a fermented tea beverage which is traditionally prepared by fermenting sweetened black or green tea (Camellia sinensis L.) with symbiotic consortium of bacteria and yeasts (SCOBY). In this study, lemon balm (Melissa offi cinalis L.) was used as the only nitrogen source for kombucha fermentation. During the seven-day fermentation process, pH value, titratable acidity (TA), total phenolic content, phenolic compounds, and antioxidant activity against hydroxyl (˙OH) and 1,1-diphenyl-2-picrylhydrazil (DPPH) radicals were measured to detect the connection between the fermentation time and antioxidant and antibacterial activities of lemon balm kombucha. Antibacterial activity of fi nished beverages with optimum acidity (TA=4–4.5 g/L), the value which is confi rmed by long-time kombucha consumers, and enhanced acidity (TA=8.12 g/L) was tested against eleven wild bacterial strains. The results showed that lemon balm could be successfully used as an alternative to C. sinensis L. for kombucha fermentation. Total phenolic content and antioxidant activity against DPPH radicals of lemon balm fermentation broth were higher than those of traditional kombucha. Rosmarinic acid is the main phenolic compound of the lemon balm-based kombucha that probably provides biological activity of the beverage. Judging from the EC50 values, kombucha beverages exhibited higher antioxidant activities compared with C. sinensis L. and M. offi cinalis L. infusions, which can probably be ascribed to SCOBY metabolites. Lemon balm kombucha with both optimum and enhanced acidity showed antibacterial activity, which can be primarily ascribed to acetic acid, but also to some other tea components and SCOBY metabolites

The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation

Within the framework of the semiclassical approximation, we derive the Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD plasma. The probability of the plasmon-plasmon scattering at the leading order in the coupling constant is obtained. This probability is gauge-independent at least in the class of the covariant and temporal gauges. It is noted that the structure of the scattering kernel possesses important qualitative difference from the corresponding one in the Abelian plasma, in spite of the fact that we focused our study on the colorless soft excitations. It is shown that four-plasmon decay is suppressed by the power of $g$ relative to the process of nonlinear scattering of plasmons by thermal particles at the soft momentum scale. It is stated that the former process becomes important in going to the ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio

A Cosmological Theory without Singularities

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.Comment: 25 pages, 11 figures (available as hard copies from the authors), uses phyzzx, BROWN-HET-89

Classical model of elementary particle with Bertotti-Robinson core and extremal black holes

We discuss the question, whether the Reissner-Nordstr\"{o}m RN) metric can be glued to another solutions of Einstein-Maxwell equations in such a way that (i) the singularity at r=0 typical of the RN metric is removed (ii), matching is smooth. Such a construction could be viewed as a classical model of an elementary particle balanced by its own forces without support by an external agent. One choice is the Minkowski interior that goes back to the old Vilenkin and Fomin's idea who claimed that in this case the bare delta-like stresses at the horizon vanish if the RN metric is extremal. However, the relevant entity here is the integral of these stresses over the proper distance which is infinite in the extremal case. As a result of the competition of these two factors, the Lanczos tensor does not vanish and the extremal RN cannot be glued to the Minkowski metric smoothly, so the elementary-particle model as a ball empty inside fails. We examine the alternative possibility for the extremal RN metric - gluing to the Bertotti-Robinson (BR) metric. For a surface placed outside the horizon there always exist bare stresses but their amplitude goes to zero as the radius of the shell approaches that of the horizon. This limit realizes the Wheeler idea of "mass without mass" and "charge without charge". We generalize the model to the extremal Kerr-Newman metric glued to the rotating analog of the BR metric.Comment: 23 pages. Misprints correcte

3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels

Using the method of Green's functions within a Bethe-Salpeter framework characterized by a pairwise qq interaction with a Lorentz-covariant 3D support to its kernel, the 4D BS wave function for a system of 3 identical relativistic spinless quarks is reconstructed from the corresponding 3D form which satisfies a fully connected 3D BSE. This result is a 3-body generalization of a similar 2-body result found earlier under identical conditions of a 3D support to the corresponding qq-bar BS kernel under Covariant Instaneity (CIA for short). (The generalization from spinless to fermion quarks is straightforward). To set the CIA with 3D BS kernel support ansatz in the context of contemporary approaches to the qqq baryon problem, a model scalar 4D qqq BSE with pairwise contact interactions to simulate the NJL-Faddeev equations is worked out fully, and a comparison of both vertex functions shows that the CIA vertex reduces exactly to the NJL form in the limit of zero spatial range. This consistency check on the CIA vertex function is part of a fuller accounting for its mathematical structure whose physical motivation is traceable to the role of `spectroscopy' as an integral part of the dynamics.Comment: 20 pages, Latex, submitted via the account of K.-C. Yan

Vortices and chirality of magnetostatic modes in quasi-2D ferrite disk particles

In this paper we show that the vortex states can be created not only in magnetically soft "small" (with the dipolar and exchange energy competition) cylindrical dots, but also in magnetically saturated "big" (when the exchange is neglected) cylindrical dots. A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a ferrite disk with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. In this case the scalar (magnetostatic-potential) wave functions may have a phase singularity in a center of a dot. A non-zero azimuth component of the flow velocity demonstrates the vortex structure. The vortices are guaranteed by the chiral edge states of magnetic-dipolar modes in a quasi-2D ferrite disk

Optical monitoring of the z=4.40 quasar Q 2203+292

We report Cousins R-band monitoring of the high-redshift (z=4.40) radio quiet quasar Q 2203+292 from May 1999 to October 2007. The quasar shows maximum peak-to-peak light curve amplitude of ~0.3 mag during the time of our monitoring, and ~0.9 mag when combined with older literature data. The rms of a fit to the light curve with a constant is 0.08 mag and 0.2 mag, respectively. The detected changes are at ~3-sigma level. The quasar was in a stable state during the recent years and it might have undergone a brightening event in the past. The structure function analysis concluded that the object shows variability properties similar to those of the lower redshift quasars. We set a lower limit to the Q 2203+292 broad line region mass of 0.3-0.4 M_odot. Narrow-band imaging search for redshifted Ly_alpha from other emission line objects at the same redshift shows no emission line objects in the quasar vicinity.Comment: 9 pages, 8 figures, accepted for publication in MNRA

Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibriums measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.Comment: 19 pages, 7 figures, accepted author manuscript, to appear in J. Phys.: Cond. Mat