The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization

Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success probability, measurement, POVM elements, Helstrom family of ensembles, convex optimization, conjugate states PACS Nos: 03.67.Hk, 03.65.TaComment: 15 page

Cross-Document Pattern Matching

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem

Slowly Rotating General Relativistic Superfluid Neutron Stars with Relativistic Entrainment

Neutron stars that are cold enough should have two or more superfluids/supercondutors in their inner crusts and cores. The implication of superfluidity/superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect, i.e. the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modelling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic $\sigma$ - $\omega$ mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit.Comment: 30 pages, 10 figures, uses ReVTeX

Multiple mitochondrial introgression events and heteroplasmy in trypanosoma cruzi revealed by Maxicircle MLST and next generation sequencing

Background Mitochondrial DNA is a valuable taxonomic marker due to its relatively fast rate of evolution. In Trypanosoma cruzi, the causative agent of Chagas disease, the mitochondrial genome has a unique structural organization consisting of 20–50 maxicircles (∼20 kb) and thousands of minicircles (0.5–10 kb). T. cruzi is an early diverging protist displaying remarkable genetic heterogeneity and is recognized as a complex of six discrete typing units (DTUs). The majority of infected humans are asymptomatic for life while 30–35% develop potentially fatal cardiac and/or digestive syndromes. However, the relationship between specific clinical outcomes and T. cruzi genotype remains elusive. The availability of whole genome sequences has driven advances in high resolution genotyping techniques and re-invigorated interest in exploring the diversity present within the various DTUs. Methodology/Principal Findings To describe intra-DTU diversity, we developed a highly resolutive maxicircle multilocus sequence typing (mtMLST) scheme based on ten gene fragments. A panel of 32 TcI isolates was genotyped using the mtMLST scheme, GPI, mini-exon and 25 microsatellite loci. Comparison of nuclear and mitochondrial data revealed clearly incongruent phylogenetic histories among different geographical populations as well as major DTUs. In parallel, we exploited read depth data, generated by Illumina sequencing of the maxicircle genome from the TcI reference strain Sylvio X10/1, to provide the first evidence of mitochondrial heteroplasmy (heterogeneous mitochondrial genomes in an individual cell) in T. cruzi. Conclusions/Significance mtMLST provides a powerful approach to genotyping at the sub-DTU level. This strategy will facilitate attempts to resolve phenotypic variation in T. cruzi and to address epidemiologically important hypotheses in conjunction with intensive spatio-temporal sampling. The observations of both general and specific incidences of nuclear-mitochondrial phylogenetic incongruence indicate that genetic recombination is geographically widespread and continues to influence the natural population structure of TcI, a conclusion which challenges the traditional paradigm of clonality in T. cruzi

Genuine Three-Body Bose-Einstein Correlations and Percolation of Strings

Recent data show a large difference of the genuine three-body Bose-Einstein correlations in S-Pb collisions and in Pb-Pb central collisions being close to zero in the first case and to one in the second one. These results, unexpected from conventional approaches, are naturally explained by the percolation of colour strings produced in the collisions and subsequent incoherent fragmentation of the formed clusters.Comment: 8 pages, 2 figures, ReVTe

Gravitational waves from rapidly rotating neutron stars

Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed as an interesting source of gravitational waves. In this chapter we present estimates of the gravitational wave emission for various scenarios, given the (electromagnetically) observed characteristics of these systems. First of all we focus on the r-mode instability and show that a 'minimal' neutron star model (which does not incorporate exotica in the core, dynamically important magnetic fields or superfluid degrees of freedom), is not consistent with observations. We then present estimates of both thermally induced and magnetically sustained mountains in the crust. In general magnetic mountains are likely to be detectable only if the buried magnetic field of the star is of the order of $B\approx 10^{12}$ G. In the thermal mountain case we find that gravitational wave emission from persistent systems may be detected by ground based interferometers. Finally we re-asses the idea that gravitational wave emission may be balancing the accretion torque in these systems, and show that in most cases the disc/magnetosphere interaction can account for the observed spin periods.Comment: To appear in 'Gravitational Waves Astrophysics: 3rd Session of the Sant Cugat Forum on Astrophysics, 2014', Editor: Carlos F. Sopuert

The Influence of the effect of solute on the thermodynamic driving force on grain refinement of Al alloys

Grain refinement is known to be strongly affected by the solute in cast alloys. Addition of some solute can reduce grain size considerably while others have a limited effect. This is usually attributed to the constitutional supercooling which is quantified by the growth restriction factor, Q. However, one factor that has not been considered is whether different solutes have differing effects on the thermodynamic driving force for solidification. This paper reveals that addition of solute reduces the driving force for solidification for a given undercooling, and that for a particular Q value, it is reduced more substantially when adding eutectic-forming solutes than peritectic-forming elements. Therefore, compared with the eutectic-forming solutes, addition of peritectic-forming solutes into Al alloys not only possesses a higher initial nucleation rate resulted from the larger thermodynamic driving force for solidification, but also promotes nucleation within the constitutionally supercooled zone during growth. As subsequent nucleation can occur at smaller constitutional supercoolings for peritectic-forming elements, a smaller grain size is thus produced. The very small constitutional supercooling required to trigger subsequent nucleation in alloys containing Ti is considered as a major contributor to its extraordinary grain refining efficiency in cast Al alloys even without the deliberate addition of inoculants.The Australian Research Council (ARC DP10955737)