Revisiting the Equivalence Problem for Finite Multitape Automata

The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability yields a co_NP upper bound, but apparently not much more is known about the complexity of the problem. In this paper we give an alternative proof of decidability, which follows the basic strategy of Harju and Karhumaki but replaces their use of group theory with results on matrix algebras. From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape automata. The algorithm involves only matrix exponentiation and runs in polynomial time for each fixed number of tapes. If the two input automata are inequivalent then the algorithm outputs a word on which they differ

Measurements with a noninvasive detector and dephasing mechanism

We study dynamics of the measurement process in quantum dot systems, where a particular state out of coherent superposition is observed. The ballistic point-contact placed near one of the dots is taken as a noninvasive detector. We demonstrate that the measurement process is fully described by the Bloch-type equations applied to the whole system. These equations clearly reproduce the collapse of the density-matrix into the statistical mixture in the course of the measurement process. The corresponding dephasing width is uniquely defined. We show that the continuous observation of one of the states in a coherent superposition may accelerate decay from this state -- in contradiction with rapidly repeated observations, which slow down the transitions between quantum states (the quantum Zeno effect).Comment: The difference between continuous and rapidly repeated observations is elaborated. To appear in Phys. Rev.

Trust me; I know what I am doing

One core assumption of standard economic theory is that an individual’s preferences are stable, irrespective of the method used to elicit them. This assumption may be violated if preference reversals are observed when comparing different methods to elicit people’s preferences. People may then prefer A over B using one method while preferring B over A using another. Such preference reversals pose a significant problem for theoretical and applied research. We used a sample of medical and economics students to investigate preference reversals in the health and financial domain when choosing patients/clients. We explored whether preference reversals are associated with domain-relevant training and tested whether using guided ‘choice list’ elicitation reduces reversals. Our findings suggest that preference reversals were more likely to occur for medical students, within the health domain, and for open-ended valuation questions. Familiarity with a domain reduced the likelihood of preference reversals in that domain. Although preference reversals occur less frequently within specialist domains, they remain a significant theoretical and practical problem. The use of clearer valuation procedures offers a promising approach to reduce preference reversals

Output spectrum of a detector measuring quantum oscillations

We consider a two-level quantum system (qubit) which is continuously measured by a detector and calculate the spectral density of the detector output. In the weakly coupled case the spectrum exhibits a moderate peak at the frequency of quantum oscillations and a Lorentzian-shape increase of the detector noise at low frequency. With increasing coupling the spectrum transforms into a single Lorentzian corresponding to random jumps between two states. We prove that the Bayesian formalism for the selective evolution of the density matrix gives the same spectrum as the conventional master equation approach, despite the significant difference in interpretation. The effects of the detector nonideality and the finite-temperature environment are also discussed.Comment: 8 pages, 6 figure

Warm stellar matter with deconfinement: application to compact stars

We investigate the properties of mixed stars formed by hadronic and quark matter in $\beta$-equilibrium described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. We use the non- linear Walecka model for the hadron matter and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The phase transition to a deconfined quark phase is investigated. In particular, we study the dependence of the onset of a mixed phase and a pure quark phase on the hyperon couplings, quark model and properties of the hadronic model. We calculate the strangeness fraction with baryonic density for the different EOS. With the NJL model the strangeness content in the mixed phase decreases. The calculations were performed for T=0 and for finite temperatures in order to describe neutron and proto-neutron stars. The star properties are discussed. Both the Bag model and the NJL model predict a mixed phase in the interior of the star. Maximum allowed masses for proto-neutron stars are larger for the NJL model ($\sim 1.9$ M$_{\bigodot}$) than for the Bag model ($\sim 1.6$ M$_{\bigodot}$).Comment: RevTeX,14 figures, accepted to publication in Physical Review

A class of Schrodinger operators with decaying oscillatory potentials

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.Comment: 18 page

Selective quantum evolution of a qubit state due to continuous measurement

We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We discuss the Bayesian formalism for such ``selective'' evolution of an individual qubit and apply it to several solid-state setups. In particular, we show how to suppress the qubit decoherence using continuous measurement and the feedback loop.Comment: 15 pages (including 9 figures

CABARET in the ocean gyres

Author Posting. © The Author(s), 2009. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Ocean Modelling 30 (2009): 155-168, doi:10.1016/j.ocemod.2009.06.009.A new high-resolution Eulerian numerical method is proposed for modelling quasigeostrophic ocean dynamics in eddying regimes. The method is based on a novel, second-order non-dissipative and lowdispersive conservative advection scheme called CABARET. The properties of the new method are compared with those of several high-resolution Eulerian methods for linear advection and gas dynamics. Then, the CABARET method is applied to the classical model of the double-gyre ocean circulation and its performance is contrasted against that of the common vorticity-preserving Arakawa method. In turbulent regimes, the new method permits credible numerical simulations on much coarser computational grids.Supports from the Royal Society of London and from the Mary Sears Visitor Grant are acknowledged by SK with gratitude. The work of VG was supported by the Russian Foundation for Basic Research (RFBR), grant 06-01-00819a. Funding for PB was provided by the NSF grant 0725796

Determination of Population Structure of Wheat Core Collection for Association Mapping

The microsatellites, as one of the most robust markers for identification of wheat varieties, were used for assessment of genetic diversity and population structure to promote effective use of genetic resources. In this study, the set of 284 wheat varieties were genotyped using 30 microsatellite markers. The chosen SSR markers were located among almost all linkage groups and covered all three genomes. The genotypes used originate from 24 different breeding centers worldwide and are included in an extensive core collection of the Institute of Field and Vegetable Crops in Novi Sad, Serbia. The total number of detected alleles was 349 at all analyzed loci. The average number of detected allelic variant per locus was 11.5. The mean value of polymorphic information content was 0.68. According to the probability of data obtained by program Structure, the results have shown presence of 6 subpopulations within the studied set of genotypes. The population structure positively correlated to some extent with geographic origin. The available pedigree data were included for additional explanation of population structure. The results of this study should provide valuable information for future association studies using the diverse wheat breeding material