The spectrum of the random environment and localization of noise

We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized.Comment: 18 pages, 1 figur

Prox-regularity of rank constraint sets and implications for algorithms

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank exactly equal to $s$. The normal cone formula appears to be new. This allows for easy application of prior results guaranteeing local linear convergence of the fundamental alternating projection algorithm between sets, one of which is a rank constraint set. We apply this to show local linear convergence of another fundamental algorithm, approximate steepest descent. Our results apply not only to linear systems with rank constraints, as has been treated extensively in the literature, but also nonconvex systems with rank constraints.Comment: 12 pages, 24 references. Revised manuscript to appear in the Journal of Mathematical Imaging and Visio

Entanglement transmission and generation under channel uncertainty: Universal quantum channel coding

We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels, so that they are forced to use quantum codes that are reliable for the whole set of channels. This is precisely the quantum analog of the compound channel coding problem. We determine the entanglement transmission and entanglement-generating capacities of compound quantum channels and show that they are equal. Moreover, we investigate two variants of that basic scenario, namely the cases of informed decoder or informed encoder, and derive corresponding capacity results.Comment: 45 pages, no figures. Section 6.2 rewritten due to an error in equation (72) of the old version. Added table of contents, added section 'Conclusions and further remarks'. Accepted for publication in 'Communications in Mathematical Physics

Gaussian quantum marginal problem

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.Comment: 18 pages, 1 figure, material added, references updated, except from figure identical with version to appear in Commun. Math. Phy

Isospin Fluctuations from a Thermally Equilibrated Hadron Gas

Partition functions, multiplicity distributions, and isospin fluctuations are calculated for canonical ensembles in which additive quantum numbers as well as total isospin are strictly conserved. When properly accounting for Bose-Einstein symmetrization, the multiplicity distributions of neutral pions in a pion gas are significantly broader as compared to the non-degenerate case. Inclusion of resonances compensates for this broadening effect. Recursion relations are derived which allow calculation of exact results with modest computer time.Comment: 10 pages, 5 figure

Thromboelastometry and Platelet Function during Acclimatization to High Altitude

Interaction between hypoxia and coagulation is important given the increased risk of thrombotic diseases in chronically hypoxic patients who reside at sea level and in residents at high altitude. Hypoxia alters the proteome of platelets favouring a prothrombotic phenotype, but studies of activation and consumption of specific coagulation factors in hypoxic humans have yielded conflicting results. We tested blood from 63 healthy lowland volunteers acclimatizing to high altitude (5,200 m) using thromboelastometry and assays of platelet function to examine the effects of hypoxia on haemostasis. Using data from two separate cohorts of patients following identical ascent profiles, we detected a significant delay in clot formation, but increased clot strength by day 7 at 5,200 m. The latter finding may be accounted for by the significant rise in platelet count and fibrinogen concentration that occurred during acclimatization. Platelet function assays revealed evidence of platelet hyper-reactivity, with shortened PFA-100 closure times and increased platelet aggregation in response to adenosine diphosphate. Post-expedition results were consistent with the normalization of coagulation following descent to sea level. These robust findings indicate that hypoxia increases platelet reactivity and, with the exception of the paradoxical delay in thromboelastometry clotting time, suggest a prothrombotic phenotype at altitude. Further work to elucidate the mechanism of platelet activation in hypoxia will be important and could impact upon the management of patients with acute or chronic hypoxic respiratory diseases who are at risk of thrombotic events. Erratum to: Thromboelastometry and platelet function during acclimatisation to high altitude (doi: 10.1160/TH17-02-0138) http://eprints.whiterose.ac.uk/129510/ In the Original Article by Rocke et al. “Thromboelastometry and platelet function during acclimatization to high altitude” (Thromb Haemost 2018; 118: 063-071) after publication of the article it has come to the corresponding author's attention that an author was inadvertently omitted from the manuscript. The author, Martin MacInnis, made a significant contribution to: 1. initiating the coagulation research that led to the manuscript, 2. designing the research protocol and performing the initial data analysis, 3. recruiting volunteers, writing applications for ethical approval and making other logistical arrangements that were necessary to complete the study. Martin MacInnis has read and approved the published version of the manuscript. Furthermore, a middle initial was added to the updated list (Shona E. Main) and misspelling of Elizabeth Horn's surname was corrected. The amended author list is as above. https://doi.org

Solving the Uncalibrated Photometric Stereo Problem using Total Variation

International audienceIn this paper we propose a new method to solve the problem of uncalibrated photometric stereo, making very weak assumptions on the properties of the scene to be reconstructed. Our goal is to solve the generalized bas-relief ambiguity (GBR) by performing a total variation regularization of both the estimated normal field and albedo. Unlike most of the previous attempts to solve this ambiguity, our approach does not rely on any prior information about the shape or the albedo, apart from its piecewise smoothness. We test our method on real images and obtain results comparable to the state-of-the-art algorithms

Statistical Multifragmentation in Central Au+Au Collisions at 35 MeV/u

Multifragment disintegrations, measured for central Au + Au collisions at E/A = 35 MeV, are analyzed with the Statistical Multifragmentation Model. Charge distributions, mean fragment energies, and two-fragment correlation functions are well reproduced by the statistical breakup of a large, diluted and thermalized system slightly above the multifragmentation threshold.Comment: Latex file, 8 pages + 4 postscript figures available upon request from [email protected]

Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial wave analysis

Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for $\gamma p\to p\pi^0$ and $\gamma p\to n\pi^+$ are given and compared to results from other analyses.Comment: 18 pages, 14 figure