Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic Matrices

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list seven axioms that we might want such a theory to satisfy, and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we construct a new hidden-variable theory that is both robust to small perturbations and indifferent to the identity operation, by exploiting an unexpected connection between unitary matrices and network flows. We also analyze previous hidden-variable theories of Dieks and Schrodinger in terms of our axioms. In a companion paper, we will show that actually sampling the history of a hidden variable under reasonable axioms is at least as hard as solving the Graph Isomorphism problem; and indeed is probably intractable even for quantum computers.Comment: 19 pages, 1 figure. Together with a companion paper to appear, subsumes the earlier paper "Quantum Computing and Dynamical Quantum Models" (quant-ph/0205059

Differential Hox expression in murine embryonic stem cell models of normal and malignant hematopoiesis

The Hox family are master transcriptional regulators of developmental processes, including hematopoiesis. The Hox regulators, caudal homeobox factors (Cdx1-4), and Meis1, along with several individual Hox proteins, are implicated in stem cell expansion during embryonic development, with gene dosage playing a significant role in the overall function of the integrated Hox network. To investigate the role of this network in normal and aberrant, early hematopoiesis, we employed an in vitro embryonic stem cell differentiation system, which recapitulates mouse developmental hematopoiesis. Expression profiles of Hox, Pbx1, and Meis1 genes were quantified at distinct stages during the hematopoietic differentiation process and compared with the effects of expressing the leukemic oncogene Tel/PDGFR;2. During normal differentiation the Hoxa cluster, Pbx1 and Meis1 predominated, with a marked reduction in the majority of Hox genes (27/39) and Meis1 occurring during hematopoietic commitment. Only the posterior Hoxa cluster genes (a9, a10, a11, and a13) maintained or increased expression at the hematopoietic colony stage. Cdx4, Meis1, and a subset of Hox genes, including a7 and a9, were differentially expressed after short-term oncogenic (Tel/PDGFR;2) induction. Whereas Hoxa4-10, b1, b2, b4, and b9 were upregulated during oncogenic driven myelomonocytic differentiation. Heterodimers between Hoxa7/Hoxa9, Meis1, and Pbx have previously been implicated in regulating target genes involved in hematopoietic stem cell (HSC) expansion and leukemic progression. These results provide direct evidence that transcriptional flux through the Hox network occurs at very early stages during hematopoietic differentiation and validates embryonic stem cell models for gaining insights into the genetic regulation of normal and malignant hematopoiesis

Jump-like unravelings for non-Markovian open quantum systems

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $\Omega$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, $\omega_0$, and the two side bands have frequencies $\omega_0\pm\Omega$. In the large $\Omega$ limit we observed that the jump-like behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However the length of time for which the Markovian-like behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure

PKS2250-41: a case study for triggering

We present the results of a multiwavelength study of the z = 0.31 radio source PKS2250-41. Integral field unit and long-slit spectroscopy obtained using VIMOS and FORS1 on the VLT, and archival HST optical imaging observations are used to study the morphology, kinematics and ionisation state of the extended emission line region (EELR) surrounding this source, and also a companion galaxy at a similar redshift. Near-infrared imaging observations obtained using the NTT are used to analyse the underlying galaxy morphologies. The EELR displays a complex variety of different gas kinematics and ionization states, consistent with a mixture of radio source shocks and AGN photoionization. The radio galaxy is likely to lie within a group environment, and is plausibly undergoing interactions with one or more other objects. The disk-like galaxy to the northeast of the radio source lies at a similar redshift to the radio galaxy itself, and has its major axis position angle aligned with the filamentary continuum and line emission extending outwards from the radio galaxy. This filamentary structure is most plausibly interpreted as a tidal structure associated with an interaction involving the radio source host galaxy and the aligned companion galaxy to the north-east; this encounter may have potentially triggered the current epoch of radio source activity. Overall, PKS2250-41 displays some of the best evidence that radio source activity can be triggered in this manner. [abridged]Comment: 16 pages, 13 figures (some colour). Accepted for publication in MNRAS. Abstract abridge

Separable Dual Space Gaussian Pseudo-potentials

We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numerical calculations using plane waves as basis set. At most 7 coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudo-potential to a wave-function can be done in an efficient way on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudo-potentials by extensive atomic and molecular test calculations.Comment: 16 pages, 4 postscript figure

Elliptic Solitons and Groebner Bases

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gr\"obner bases method and others. New integrable potentials and corresponding solutions of the Sawada-Kotera, Kaup-Kupershmidt, Boussinesq equations and others are found.Comment: 18 pages, no figures, LaTeX'2

An Exploratory Study into the Factors Impeding Ethical Consumption

Although consumers are increasingly engaged with ethical factors when forming opinions about products and making purchase decisions, recent studies have highlighted significant differences between consumers’ intentions to consume ethically, and their actual purchase behaviour. This article contributes to an understanding of this “ethical purchasing gap” through a review of existing literature, and the inductive analysis of focus group discussions. A model is suggested which includes exogenous variables such as moral maturity and age which have been well covered in the literature, together with further impeding factors identified from the focus group discussions. For some consumers, inertia in purchasing behaviour was such that the decision-making process was devoid of ethical considerations. Several manifested their ethical views through post-purchase dissonance and retrospective feelings of guilt. Others displayed a reluctance to consume ethically due to personal constraints, a perceived negative impact on image or quality, or an outright negation of responsibility. Those who expressed a desire to consume ethically often seemed deterred by cynicism, which caused them to question the impact they, as an individual, could achieve. These findings enhance the understanding of ethical consumption decisions and provide a platform for future research in this area

Correlated sampling in quantum Monte Carlo: a route to forces

In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate numerical forces and potential energy surfaces in diffusion Monte Carlo. It employs a novel coordinate transformation, earlier used in variational Monte Carlo, to greatly reduce the statistical error. Results are presented for first-row diatomic molecules.Comment: 5 pages, 2 postscript figure

Interviewing suspects: examining the association between skills, questioning, evidence disclosure, and interview outcomes

The interviewing of suspects is an important element in the investigation of crime. However, studies concerning actual performance of investigators when undertaking such interviews remain sparse. Nevertheless, in England and Wales, since the introduction of a prescribed framework over 20 years ago, field studies have generally shown an improvement in interviewing performance, notwithstanding ongoing concerns largely relating to the more demanding aspects (such as building/maintaining rapport, intermittent summarising and the logical development of topics). Using a sample of 70 real-life interviews, the present study examined questioning and various evidence disclosure strategies (which have also been found demanding), examining their relationships between interview skills and interview outcomes. It was found that when evidence was disclosed gradually (but revealed later), interviews were generally both more skilled and involved the gaining of comprehensive accounts, whereas when evidence was disclosed either early or very late, interviews were found to be both less skilled and less likely to involve this outcome. These findings contribute towards an increased research base for the prescribed framework