Data taking strategy for the phase study in ψ′→K+K−\psi^{\prime} \to K^+K^-

The study of the relative phase between strong and electromagnetic amplitudes is of great importance for understanding the dynamics of charmonium decays. The information of the phase can be obtained model-independently by fitting the scan data of some special decay channels, one of which is $\psi^{\prime} \to K^{+}K^{-}$. To find out the optimal data taking strategy for a scan experiment in the measurement of the phase in $\psi^{\prime} \to K^{+} K^{-}$, the minimization process is analyzed from a theoretical point of view. The result indicates that for one parameter fit, only one data taking point in the vicinity of a resonance peak is sufficient to acquire the optimal precision. Numerical results are obtained by fitting simulated scan data. Besides the results related to the relative phase between strong and electromagnetic amplitudes, the method is extended to analyze the fits of other resonant parameters, such as the mass and the total decay width of $\psi^{\prime}$.Comment: 13 pages, 7 figure

Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination

We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case that the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison to the minimum failure probability.Comment: Replaced by final version, accepted for publication in Phys. Rev. A. Revtex4, 6 pages, 3 figure

Stoner gap in the superconducting ferromagnet UGe2

We report the temperature ($T$) dependence of ferromagnetic Bragg peak intensities and dc magnetization of the superconducting ferromagnet UGe2 under pressure ($P$). We have found that the low-$T$ behavior of the uniform magnetization can be explained by a conventional Stoner model. A functional analysis of the data produces the following results: The ferromagnetic state below a critical pressure can be understood as the perfectly polarized state, in which heavy quasiparticles occupy only majority spin bands. A Stoner gap $\Delta(P)$ decreases monotonically with increasing pressure and increases linearly with magnetic field. We show that the present analysis based on the Stoner model is justified by a consistency check, i.e., comparison of density of states at the Fermi energy deduced from the analysis with observed electronic specific heat coeffieients. We also argue the influence of the ferromagnetism on the superconductivity.Comment: 5 pages, 4 figures. to be published in Phys. Rev.

Optimal quantum detectors for unambiguous detection of mixed states

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.Comment: Submitted to Phys. Rev.

Minimum-error discrimination between symmetric mixed quantum states

We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and nonnegative in the basis of the eigenstates of the symmetry operator.Comment: 10 page

Machine Learning and Portfolio Optimization

The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution towards one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-CVaR problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a QCQP, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both Sample Average Approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right hand sides of the PBR constraints, we develop new, performance-based k-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1 and L2 regularizations and the equally-weighted portfolio. We find that PBR dominates all other benchmarks for two out of three of Fama-French data sets

Unambiguous quantum state filtering

In this paper, we consider the generalized measurement where one particular quantum signal is unambiguously extracted from a set of non-commutative quantum signals and the other signals are filtered out. Simple expressions for the maximum detection probability and its POVM are derived. We applyl such unambiguous quantum state filtering to evaluation of the sensing of decoherence channels. The bounds of the precision limit for a given quantum state of probes and possible device implementations are discussed.Comment: 7 pages, 5 figure

NASSAM: a server to search for and annotate tertiary interactions and motifs in three-dimensional structures of complex RNA molecules

Similarities in the 3D patterns of RNA base interactions or arrangements can provide insights into their functions and roles in stabilization of the RNA 3D structure. Nucleic Acids Search for Substructures and Motifs (NASSAM) is a graph theoretical program that can search for 3D patterns of base arrangements by representing the bases as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graph's nodes while the edges are the inter-pseudo-atomic distances. The input files for NASSAM are PDB formatted 3D coordinates. This web server can be used to identify matches of base arrangement patterns in a query structure to annotated patterns that have been reported in the literature or that have possible functional and structural stabilization implications. The NASSAM program is freely accessible without any login requirement at http://mfrlab.org/grafss/nassam/