Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.Comment: 28 page

Regular black holes in an asymptotically de Sitter universe

A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis is put on the degenerate configurations (when at least two horizons coincide) and their near horizon geometry. It is explicitly demonstrated that approximating the metric potentials in the region between the horizons by simple functions and making use of a limiting procedure one obtains the solutions constructed from maximally symmetric subspaces with different absolute values of radii. Topologically they are $AdS_{2}\times S^{2}$ for the cold black hole, $dS_{2}\times S^{2}$ when the event and cosmological horizon coincide, and the Pleba\'nski- Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyze

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental appendi

Intersecting Solitons, Amoeba and Tropical Geometry

We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1} \times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortex charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C^\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin function. The general form of the Kahler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.Comment: 39 pages, 11 figure

Streptococcus mutans in the oral cavity as a risk factor for threatened miscarriage

Objectives: The aim of this study was to investigate the bacterial colonization of the oral and vaginal ecosystem in pregnant women during the first trimester of pregnancy. Material and methods: We analyzed 162 pregnant women, (99 women with threatened abortion and 63 women with healthy pregnancies). We collected oral and vaginal swabs, using PCR analysis to assess the presence of various bacteria (S. mutans, E. faecalis, E. coli, Lactobacillus acidophilus, Prevotella intermedia, Gardnerella vaginalis, S. agalactiae). Results: Results showed that the presence of Streptococcus mutans in the oral cavity was significantly more common in women with threatened abortion compared to those with healthy pregnancies (p = 0.046). The presence of Lactobacillus acidophilus in the vagina was significantly more common in women with healthy pregnancies (p = 0.041). Conclusions: Our study suggests that the presence of Streptococcus mutans in the oral cavity may be a risk factor for threatened abortion

Lack of consensus in social systems

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

COMBINING AIRBORNE OBLIQUE CAMERA AND LIDAR SENSORS: INVESTIGATION AND NEW PERSPECTIVES

Hybrid sensor solutions, that feature active laser and passive image sensors on the same platform, are rapidly entering the airborne market of topographic and urban mapping, offering new opportunities for an improved quality of geo-spatial products. In this perspective, a concurrent acquisition of LiDAR data and oblique imagery, seems to have all the potential to lead the airborne (urban) mapping sector a step forward. This contribution focuses on the first commercial example of such an integrated, all-in-one mapping solution, namely the Leica CityMapper hybrid sensor. By analysing two CityMapper datasets acquired over the city of Heilbronn (Germany) and Bordeaux (France), the paper investigates potential and challenges, w.r.t. (i) number and distribution of tie points between nadir and oblique images, (ii) strategy for image aerial triangulation (AT) and accuracy achievable w.r.t ground truth data, (iii) local noise level and completeness of dense image matching (DIM) point clouds w.r.t LiDAR data. Solutions for an integrated processing of the concurrently acquired ranging and imaging data are proposed, that open new opportunities for exploiting the real potential of both data sources