283 research outputs found
The interval ordering problem
For a given set of intervals on the real line, we consider the problem of
ordering the intervals with the goal of minimizing an objective function that
depends on the exposed interval pieces (that is, the pieces that are not
covered by earlier intervals in the ordering). This problem is motivated by an
application in molecular biology that concerns the determination of the
structure of the backbone of a protein.
We present polynomial-time algorithms for several natural special cases of
the problem that cover the situation where the interval boundaries are
agreeably ordered and the situation where the interval set is laminar. Also the
bottleneck variant of the problem is shown to be solvable in polynomial time.
Finally we prove that the general problem is NP-hard, and that the existence of
a constant-factor-approximation algorithm is unlikely
Effective modeling of high-energy laboratory-based x-ray phase contrast imaging utilizing absorption masks or gratings
Model refinements for the edge illumination x-ray phase contrast imaging method have been developed to improve simulation accuracy for high energy, polychromatic beams. High-energy x rays are desirable in imaging due to their penetrative power and, for biological samples, their lower dose deposition rate. Accurate models of such scenarios are required for designing appropriate imaging systems and to predict signal strength in complex settings such as clinical imaging or industrial quality assurance. When using optical components appropriate for high-energy x rays in a non-synchrotron setting, system performance was observed to deviate from that predicted by existing models. In this work, experimental data utilizing increasing thicknesses of a known filter material are used to illustrate the limitations of existing models and as validation for the new modeling features. Angular filtration of the cone beam was observed to be the most significant effect; however, specific features of the source and detector are also shown to affect system performance. We conclude by showing that a significantly improved agreement between experimental and simulated data is obtained with the refined model compared to previously existing ones
Formulation of the uncertainty relations in terms of the Renyi entropies
Quantum mechanical uncertainty relations for position and momentum are
expressed in the form of inequalities involving the Renyi entropies. The proof
of these inequalities requires the use of the exact expression for the
(p,q)-norm of the Fourier transformation derived by Babenko and Beckner.
Analogous uncertainty relations are derived for angle and angular momentum and
also for a pair of complementary observables in N-level systems. All these
uncertainty relations become more attractive when expressed in terms of the
symmetrized Renyi entropies
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a
function that is the reciprocal of another power series. In this note the
sharpness of this condition is explored and various examples in terms of the
Gaussian hypergeometric series are given. A criterion for the monotonicity of
the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page
Reducible means and reducible inequalities
It is well-known that if a real valued function acting on a convex set
satisfies the -variable Jensen inequality, for some natural number , then, for all , it fulfills the -variable Jensen
inequality as well. In other words, the arithmetic mean and the Jensen
inequality (as a convexity property) are both reducible. Motivated by this
phenomenon, we investigate this property concerning more general means and
convexity notions. We introduce a wide class of means which generalize the
well-known means for arbitrary linear spaces and enjoy a so-called reducibility
property. Finally, we give a sufficient condition for the reducibility of the
-convexity property of functions and also for H\"older--Minkowski type
inequalities
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production
Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagnetic autoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy of relativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metal target. The plasma synchrotron acts in a regime of a magnetic field pulse packet under constant level of microwave power. Experiments and numerical modeling of the process showed that such a regime allowed obtaining dense short lived relativistic electron bunches with average electron energy of 500 keV – 4.5 MeV. Parameters of the relativistic electron bunch (energy, density and volume) and dynamics of the electron bunches can be controlled by varying the parameters of the SGA process. Possibilities of x-ray intensity increase are also discussed
Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics
The atmospheric greenhouse effect, an idea that many authors trace back to
the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896),
and which is still supported in global climatology, essentially describes a
fictitious mechanism, in which a planetary atmosphere acts as a heat pump
driven by an environment that is radiatively interacting with but radiatively
equilibrated to the atmospheric system. According to the second law of
thermodynamics such a planetary machine can never exist. Nevertheless, in
almost all texts of global climatology and in a widespread secondary literature
it is taken for granted that such mechanism is real and stands on a firm
scientific foundation. In this paper the popular conjecture is analyzed and the
underlying physical principles are clarified. By showing that (a) there are no
common physical laws between the warming phenomenon in glass houses and the
fictitious atmospheric greenhouse effects, (b) there are no calculations to
determine an average surface temperature of a planet, (c) the frequently
mentioned difference of 33 degrees Celsius is a meaningless number calculated
wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the
assumption of a radiative balance is unphysical, (f) thermal conductivity and
friction must not be set to zero, the atmospheric greenhouse conjecture is
falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected
The highly rearranged mitochondrial genomes of the crabs Maja crispata and Maja squinado (Majidae) and gene order evolution in Brachyura
Abstract
We sequenced the mitochondrial genomes of the spider crabs Maja crispata and Maja squinado (Majidae, Brachyura). Both genomes contain the whole set of 37 genes characteristic of Bilaterian genomes, encoded on both \u3b1- and \u3b2-strands. Both species exhibit the same gene order, which is unique among known animal genomes. In particular, all the genes located on the \u3b2-strand form a single block. This gene order was analysed together with the other nine gene orders known for the Brachyura. Our study confirms that the most widespread gene order (BraGO) represents the plesiomorphic condition for Brachyura and was established at the onset of this clade. All other gene orders are the result of transformational pathways originating from BraGO. The different gene orders exhibit variable levels of genes rearrangements, which involve only tRNAs or all types of genes. Local homoplastic arrangements were identified, while complete gene orders remain unique and represent signatures that can have a diagnostic value. Brachyura appear to be a hot-spot of gene order diversity within the phylum Arthropoda. Our analysis, allowed to track, for the first time, the fully evolutionary pathways producing the Brachyuran gene orders. This goal was achieved by coupling sophisticated bioinformatic tools with phylogenetic analysis
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