The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market is not complete. A construction of a bounded contingent claim, which can not be replicated, is provided.
Quantitative methods for studying biodiversity have been traditionally rooted in the classical theory of finite frequency tables analysis. However, with the help of modern experimental tools, like high throughput sequencing, we now begin to unlock th
e outstanding diversity of genomic data in plants and animals reflective of the long evolutionary history of our planet. This molecular data often defies the classical frequency/contingency tables assumptions and seems to require sparse tables with very large number of categories and highly unbalanced cell counts, e.g., following heavy tailed distributions (for instance, power laws). Motivated by the molecular diversity studies, we propose here a frequency-based framework for biodiversity analysis in the asymptotic regime where the number of categories grows with sample size (an infinite contingency table). Our approach is rooted in information theory and based on the Gaussian limit results for the effective number of species (the Hill numbers) and the empirical Renyi entropy and divergence. We argue that when applied to molecular biodiversity analysis our methods can properly account for the complicated data frequency patterns on one hand and the practical sample size limitations on the other. We illustrate this principle with two specific RNA sequencing examples: a comparative study of T-cell receptor populations and a validation of some preselected molecular hepatocellular carcinoma (HCC) markers.
We present the results of an experimental study of the elastic enhancement factor W for a microwave rectangular cavity simulating a two-dimensional quantum billiard in a transient region between regular and chaotic dynamics. The cavity was coupled to
a vector network analyzer via two microwave antennas. The departure of the system from the integrable one due to presence of antennas acting as scatterers is characterised by the parameter of chaoticity k = 2.8. The experimental results for the rectangular cavity are compared with the ones obtained for a microwave rough cavity simulating a chaotic quantum billiard. The experimental results were obtained for the frequency range v = 16 - 18.5 GHz and moderate absorption strength y = 5.2 - 7.4. We show that the elastic enhancement factor for the rectangular cavity lies below the theoretical value W = 3 predicted for integrable systems and it is significantly higher than the one obtained for the rough cavity. The results obtained for the microwave rough cavity are smaller than the ones obtained within the framework of Random Matrix Theory and lie between them and the ones predicted within a recently introduced model of the two-channel coupling (V. Sokolov and O. Zhirov, arXiv:1411.6211v2[nucl-th], 12 Dec 2014).
Gamma-ray bursts (GRBs) are the most energetic phenomena in the Universe; believed to result from the collapse and subsequent explosion of massive stars. Even though it has profound consequences for our understanding of their nature and selection bia
ses, little is known about the dust properties of the galaxies hosting GRBs. We present analysis of the far-infrared properties of an unbiased sample of 20 textit{BeppoSAX} and textit{Swift} GRB host galaxies (at an average redshift of $z,=,3.1$) located in the {it Herschel} Astrophysical Terahertz Large Area Survey, the {it Herschel} Virgo Cluster Survey, the {it Herschel} Fornax Cluster Survey, the {it Herschel} Stripe 82 Survey and the {it Herschel} Multi-tiered Extragalactic Survey, totalling $880$ deg$^2$, or $sim 3$% of the sky in total. Our sample selection is serendipitous, based only on whether the X-ray position of a GRB lies within a large-scale {it Herschel} survey -- therefore our sample can be considered completely unbiased. Using deep data at wavelengths of 100,--,500$,mu$m, we tentatively detected 1 out of 20 GRB hosts located in these fields. We constrain their dust masses and star formation rates (SFRs), and discuss these in the context of recent measurements of submillimetre galaxies and ultraluminous infrared galaxies. The average far-infrared flux of our sample gives an upper limit on SFR of $<114,{rm M}odot,mbox{yr}^{-1}$. The detection rate of GRB hosts is consistent with that predicted assuming that GRBs trace the cosmic SFR density in an unbiased way, i.e. that the fraction of GRB hosts with $mbox{SFR}>500,{rm M}odot,mbox{yr}^{-1}$ is consistent with the contribution of such luminous galaxies to the cosmic star formation density.
Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetri
c matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials.
Pure states are very important in any theory since they represent states of maximal information about the system within the theory. Here, we show that no non-trivial (not local realistic) extremal states (boxes) of general no-signaling theories can b
e realized within quantum theory. We then explore three interesting consequences of this fact. Firstly, since the pure states are uncorrelated from the environment, the statement forms a no-go result against the most straightforward device-independent protocol for randomness or secure key generation against general no-signaling adversaries. It also leads to the interesting question whether all non-extremal boxes allow for non-local correlations with the adversary. Secondly, in addition to the fact that new information-theoretic principles (designed to pick out the set of quantum correlations from among all non signaling ones) can in consequence be tested on arbitrary non-local vertices to check their validity, it also allows the possibility of excluding from the quantum set any box of no-signaling correlations that can be distilled to a non-local vertex. Finally, it also forms a sufficient condition to identify non-local games with no quantum winning strategy, when one can show that the game has a single unique non-signaling winning strategy. We illustrate each of these consequences with the example of generalized Popescu-Rohrlich boxes.
Blazars are the established sources of an intense and variable non-thermal radiation extending from radio wavelengths up to HE and VHE gamma-rays. Understanding the spectral evolution of blazars in selected frequency ranges, as well as multi-frequenc
y correlations in various types of blazar sources, is of a primary importance for constraining the blazar physics. Here we present the results of a long-term optical monitoring of a sample of 30 blazars of the BL Lac type. We study the optical color-magnitude correlation patterns emerging in the analyzed sample, and compare the optical properties of the targets with the high-energy gamma-ray and high-frequency radio data. The optical observations were carried out in R and B filters using ATOM telescope. Each object was observed during at least 20 nights in the period 2007-2012. We find significant global color-magnitude correlations in 40 % of the sample. The sources which do not display any clear chromatism often do exhibit bluer-when-brighter (bwb) behavior but only in isolated shorter time intervals. We also discovered spectral state transitions at optical wavelengths in several sources. Finally, we find that the radio, optical, and gamma-ray luminosities of the sources obey almost linear correlations, which seem however induced, at least partly, by the redshift dependance, and may be also affected by non-simultaneousness of the analyzed dataset. We argue that the observed bwb behavior is intrinsic to the jet emission regions, at least for some of the analyzed blazars, rather than resulting from the contamination of the measured flux by the starlight of host galaxies. We also conclude that the significance of color-magnitude scalings does not correlate with the optical color, but instead seems to depend on the source luminosity, in a sense that these are the lowest-luminosity BL Lac objects which display the strongest correlations.
In this paper we consider the packing spectra for local dimension of Bernoulli measures supported on Bedford-McMullen carpets. We show that typically the packing dimension of the regular set is smaller than the packing dimension of the attractor. We
also consider a specific class of measures for which we are able to calculate the packing spectrum exactly and we show that the packing spectrum is discontinuous as a function on the space of Bernoulli measures.
We investigate which pure states of $n$ photons in $d$ modes can be transformed into each other via linear optics, without post-selection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states. Writing our
state as $f^dagger|Omegarangle$, with $f^dagger$ a homogeneous polynomial in the mode creation operators, we propose two sets of LU-invariants: (a) spectral invariants, which are the eigenvalues of the operator $ff^dagger$, and (b) moments, each given by the norm of the symmetric component of a tensor power of the initial state, which can be computed as vacuum expectation values of $f^k(f^dagger)^k$. We provide scheme for experimental measurement of the later, as related to the post-selection probability of creating state $f^{dagger k}|Omegarangle$ from $k$ copies of $f^{dagger}|Omegarangle$.
Until recently, dust emission has been detected in very few host galaxies of gamma-ray bursts (GRBHs). With Herschel, we have now observed 17 GRBHs up to redshift z~3 and detected seven of them at infrared (IR) wavelengths. This relatively high detec
tion rate (41%) may be due to the composition of our sample which at a median redshift of 1.1 is dominated by the hosts of dark GRBs. Although the numbers are small, statistics suggest that dark GRBs are more likely to be detected in the IR than their optically-bright counterparts. Combining our IR data with optical, near-infrared, and radio data from our own datasets and from the literature, we have constructed spectral energy distributions (SEDs) which span up to 6 orders of magnitude in wavelength. By fitting the SEDs, we have obtained stellar masses, dust masses, star-formation rate (SFR), and extinctions for our sample galaxies. We find that GRBHs are galaxies that tend to have a high specfic SFR (sSFR), and like other star-forming galaxies, their ratios of dust-to-stellar mass are well correlated with sSFR. We incorporate our Herschel sample into a larger compilation of GRBHs, and compare this combined sample to SFR-weighted median stellar masses of the widest, deepest galaxy survey to date. This is done in order to establish whether or not GRBs can be used as an unbiased tracer of cosmic comoving SFR density (SFRD) in the universe. In contrast with previous results, this comparison shows that GRBHs are medium-sized galaxies with relatively high sSFRs; stellar masses and sSFRs of GRBHs as a function of redshift are similar to what is expected for star-forming galaxy populations at similar redshifts. We conclude that there is no strong evidence that GRBs are biased tracers of SFRD; thus they should be able to reliably probe the SFRD to early epochs.
