Lower Bounds of Concurrence for Tripartite Quantum Systems

We derive an analytical lower bound for the concurrence of tripartite quantum mixed states. A functional relation is established relating concurrence and the generalized partial transpositions.Comment: 10 page

Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: $u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$ where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave solutions describing one dimensional propagation of waves

Scanning Tunnelling Spectroscopic Studies of Dirac Fermions in Graphene and Topological Insulators

We report novel properties derived from scanning tunnelling spectroscopic (STS) studies of Dirac fermions in graphene and the surface state (SS) of a strong topological insulator (STI), Bi_2Se_3. For mono-layer graphene grown on Cu by chemical vapour deposition (CVD), strain-induced scalar and gauge potentials are manifested by the charging effects and the tunnelling conductance peaks at quantized energies, respectively. Additionally, spontaneous time-reversal symmetry breaking is evidenced by the alternating anti-localization and localization spectra associated with the zero-mode of two sublattices while global time-reversal symmetry is preserved under the presence of pseudo-magnetic fields. For Bi_2Se_3 epitaxial films grown on Si(111) by molecular beam epitaxy (MBE), spatially localized unitary impurity resonances with sensitive dependence on the energy difference between the Fermi level and the Dirac point are observed for samples thicker than 6 quintuple layers (QL). These findings are characteristic of the SS of a STI and are direct manifestation of strong topological protection against impurities. For samples thinner than 6-QL, STS studies reveal the openup of an energy gap in the SS due to overlaps of wave functions between the surface and interface layers. Additionally, spin-preserving quasiparticle interference wave-vectors are observed, which are consistent with the Rashba-like spin-orbit splitting

Spin alignment of vector meson in e+e- annihilation at Z0 pole

We calculate the spin density matrix of the vector meson produced in e+e- annihilation at Z^0 pole. We show that the data imply a significant polarization for the antiquark which is created in the fragmentation process of the polarized initial quark and combines with the fragmenting quark to form the vector meson. The direction of polarization is opposite to that of the fragmenting quark and the magnitude is of the order of 0.5. A qualitative explanation of this result based on the LUND string fragmentation model is given.Comment: 15 pages, 2 fgiures; submitted to Phys. Rev.

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

Hyperon polarization in e^-p --> e^-HK with polarized electron beams

We apply the picture proposed in a recent Letter for transverse hyperon polarization in unpolarized hadron-hadron collisions to the exclusive process e^-p --> e^-HK such as e^-p-->e^-\Lambda K^+, e^-p --> e^-\Sigma^+ K^0, or e^-p--> e^-\Sigma^0 K^+, or the similar process e^-p\to e^-n\pi^+ with longitudinally polarized electron beams. We present the predictions for the longitudinal polarizations of the hyperons or neutron in these reactions, which can be used as further tests of the picture.Comment: 15 pages, 2 figures. submitted to Phys. Rev.

Intraabdominal Intravascular Papillary Endothelial Hyperplasia (Masson's Tumor): A Rare and Novel Cause of Gastrointestinal Bleeding

Intravascular papillary endothelial hyperplasia (IPEH), or Masson's tumor, a rare benign vascular lesion, occurs mainly in the head, neck, and hands in the human population. Aberrant tumor locations have been rarely reported. We present a case of a patient with chronic abdominal pain and melena of variable severity due to a Masson's tumor, with no apparent Masson's tumor-associated comorbidities, along with a comprehensive review of the literature. Using PubMed, a search engine provided by the U.S. National Library of Medicine and the National Institutes of Health, we searched for all reports of Masson's tumor limited within the abdominal cavity. Furthermore, keywords such as ‘intravascular papillary endothelial hyperplasia’, ‘renal’, ‘gastrointestinal’, ‘hepatic’ and ‘intraabdominal’ were used to facilitate the search. We thus found fourteen cases of intraabdominal Masson's tumors published. Six (42.9%) of these were located in the renal vein, 4 (28.6%) were reported in the gastrointestinal tract, 1 (7.1%) in the adrenal gland, 1 (7.1%) in the liver, and 1 (7.1%) instance with multiple lesion sites including the renal hilum and retroperitoneum. Among these patients, 9 (64.3%) were female and 5 (35.7%) male, with a mean age of 38.9 years (7–69). IPEH is a reactive process, having three subtypes, all involving the proliferation of epithelial cells around a thrombus in the setting of venous stasis. In its pure form, the organized thrombus is solely localized within the vascular lumen. Mixed-form IPEH is formed in preexisting vascular lesions (such as arteriovenous malformation, hemangioma, pyogenic granuloma, etc.). The rarest form is the extravascular variety, which arises in hematomas often from recent trauma to the area. In its pure form, IPEH has a zero recurrence rate when an R0 resection is performed; all mixed and extravascular forms show the highest recurrence rates. The exact histogenesis of these epithelial cells remains a mystery and multiple theories have been offered. Although difficult to distinguish from malignant angiosarcomas solely on presentation and radiologic work-up, Masson's tumors occur more frequently in women, demonstrate no local invasion, do not metastasize, are commonly located intravascularly, and are associated with a significantly more favorable prognosis than angiosarcomas. Only four Masson's tumors have been reported in the gastrointestinal tract, two of these cases were related to microvascular thrombosis secondary to paroxysmal nocturnal hemoglobinuria and two were formed secondary to arteriovenous malformations. Our case lacked solitary evidence of either of these comorbidities. An incidental finding of an enlarged ovary, which was removed during our exploratory laparoscopy, plus strong demographic statistics that suggest women have an increased prevalence of this lesion may help support a hormonal theory of pathogenesis

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure

Finite-dimensional integrable systems associated with Davey-Stewartson I equation

For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained and their functional independence is proved. Therefore, the Hamiltonian systems are completely integrable in Liouville sense. A periodic solution of the Davey-Stewartson I equation is obtained by solving these classical Hamiltonian systems as an example.Comment: 18 pages, LaTe