Lyman-tomography of cosmic infrared background fluctuations with Euclid: probing emissions and baryonic acoustic oscillations at z>10

The Euclid space mission, designed to probe evolution of the Dark Energy, will map a large area of the sky at three adjacent near-IR filters, Y, J and H. This coverage will also enable mapping source-subtracted cosmic infrared background (CIB) fluctuations with unprecedented accuracy on sub-degree angular scales. Here we propose methodology, using the Lyman-break tomography applied to the Euclid-based CIB maps, to accurately isolate the history of CIB emissions as a function of redshift from 10 < z < 20, and to identify the baryonic acoustic oscillations (BAOs) at those epochs. To identify the BAO signature, we would assemble individual CIB maps over conservatively large contiguous areas of >~ 400 sq deg. The method can isolate the CIB spatial spectrum by z to sub-percent statistical accuracy. We illustrate this with a specific model of CIB production at high z normalized to reproduce the measured Spitzer-based CIB fluctuation. We show that even if the latter contain only a small component from high-z sources, the amplitude of that component can be accurately isolated with the methodology proposed here and the BAO signatures at z>~ 10 are recovered well from the CIB fluctuation spatial spectrum. Probing the BAO at those redshifts will be an important test of the underlying cosmological paradigm, and would narrow the overall uncertainties on the evolution of cosmological parameters, including the Dark Energy. Similar methodology is applicable to the planned WFIRST mission, where we show that a possible fourth near-IR channel at > 2 micron would be beneficial.Comment: comments welcom

Medical concepts related to individual risk are better explained with "plausibility" rather than "probability"

BACKGROUND: The concept of risk has pervaded medical literature in the last decades and has become a familiar topic, and the concept of probability, linked to binary logic approach, is commonly applied in epidemiology and clinical medicine. The application of probability theory to groups of individuals is quite straightforward but can pose communication challenges at individual level. Few articles by the way have tried to focus the concept of "risk" at the individual subject level rather than at population level. DISCUSSION: The author has reviewed the conceptual framework which has led to the use of probability theory in the medical field in a time when the principal causes of death were represented by acute disease often of infective origin. In the present scenario, in which chronic degenerative disease dominate and there are smooth transitions between health and disease the use of fuzzy logic rather than binary logic would be more appropriate. The use of fuzzy logic in which more than two possible truth-value assignments are allowed overcomes the trap of probability theory when dealing with uncertain outcomes, thereby making the meaning of a certain prognostic statement easier to understand by the patient. SUMMARY: At individual subject level the recourse to the term plausibility, related to fuzzy logic, would help the physician to communicate to the patient more efficiently in comparison with the term probability, related to binary logic. This would represent an evident advantage for the transfer of medical evidences to individual subjects

Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

Reconstructing emission from pre-reionization sources with cosmic infrared background fluctuation measurements by the JWST

We present new methodology to use cosmic infrared background (CIB) fluctuations to probe sources at 10<z<30 from a JWST/NIRCam configuration that will isolate known galaxies to 28 AB mag at 0.5--5 micron. At present significant mutually consistent source-subtracted CIB fluctuations have been identified in the Spitzer and Akari data at 2--5 micron, but we demonstrate internal inconsistencies at shorter wavelengths in the recent CIBER data. We evaluate CIB contributions from remaining galaxies and show that the bulk of the high-z sources will be in the confusion noise of the NIRCam beam, requiring CIB studies. The accurate measurement of the angular spectrum of the fluctuations and probing the dependence of its clustering component on the remaining shot noise power would discriminate between the various currently proposed models for their origin and probe the flux distribution of its sources. We show that the contribution to CIB fluctuations from remaining galaxies is large at visible wavelengths for the current instruments precluding probing the putative Lyman-break of the CIB fluctuations. We demonstrate that with the proposed JWST configuration such measurements will enable probing the Lyman break. We develop a Lyman-break tomography method to use the NIRCam wavelength coverage to identify or constrain, via the adjacent two-band subtraction, the history of emissions over 10<z<30 as the Universe comes out of the 'Dark Ages'. We apply the proposed tomography to the current Spitzer/IRAC measurements at 3.6 and 4.5 micron, to find that it already leads to interestingly low upper limit on emissions at z>30.Comment: ApJ, in press. Minor revisions/additions to match the version in proof

Generalized quantum tomographic maps

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of "thick" quantum tomography. Applications for quantum state measurements of photons and matter waves are discussed.Comment: 8 page

Classical Tensors and Quantum Entanglement II: Mixed States

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.Comment: 23 pages, 4 figure

Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.Comment: 7pages, LaTeX2

Null Phase Curves and Manifolds in Geometric Phase Theory

Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made up entirely of null phase curves, and so are equally important for geometric phase considerations. It is shown that the complete characterization of null phase manifolds involves both the Riemannian metric structure and the symplectic structure of ray space in equal measure, which thus brings together these two aspects in a natural manner.Comment: 10 pages, 1 figur

How artificial intelligence tools can be used to assess individual patient risk in cardiovascular disease: problems with the current methods

BACKGROUND: In recent years a number of algorithms for cardiovascular risk assessment has been proposed to the medical community. These algorithms consider a number of variables and express their results as the percentage risk of developing a major fatal or non-fatal cardiovascular event in the following 10 to 20 years DISCUSSION: The author has identified three major pitfalls of these algorithms, linked to the limitation of the classical statistical approach in dealing with this kind of non linear and complex information. The pitfalls are the inability to capture the disease complexity, the inability to capture process dynamics, and the wide confidence interval of individual risk assessment. Artificial Intelligence tools can provide potential advantage in trying to overcome these limitations. The theoretical background and some application examples related to artificial neural networks and fuzzy logic have been reviewed and discussed. SUMMARY: The use of predictive algorithms to assess individual absolute risk of cardiovascular future events is currently hampered by methodological and mathematical flaws. The use of newer approaches, such as fuzzy logic and artificial neural networks, linked to artificial intelligence, seems to better address both the challenge of increasing complexity resulting from a correlation between predisposing factors, data on the occurrence of cardiovascular events, and the prediction of future events on an individual level

Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant

A bistochastic matrix B of size N is called unistochastic if there exists a unitary U such that B_ij=|U_{ij}|^{2} for i,j=1,...,N. The set U_3 of all unistochastic matrices of order N=3 forms a proper subset of the Birkhoff polytope, which contains all bistochastic (doubly stochastic) matrices. We compute the volume of the set U_3 with respect to the flat (Lebesgue) measure and analytically evaluate the mean entropy of an unistochastic matrix of this order. We also analyze the Jarlskog invariant J, defined for any unitary matrix of order three, and derive its probability distribution for the ensemble of matrices distributed with respect to the Haar measure on U(3) and for the ensemble which generates the flat measure on the set of unistochastic matrices. For both measures the probability of finding |J| smaller than the value observed for the CKM matrix, which describes the violation of the CP parity, is shown to be small. Similar statistical reasoning may also be applied to the MNS matrix, which plays role in describing the neutrino oscillations. Some conjectures are made concerning analogous probability measures in the space of unitary matrices in higher dimensions.Comment: 33 pages, 6 figures version 2 - misprints corrected, explicit formulae for phases provide