An extension of Chaitin's halting probability \Omega to a measurement operator in an infinite dimensional quantum system

This paper proposes an extension of Chaitin's halting probability \Omega to a measurement operator in an infinite dimensional quantum system. Chaitin's \Omega is defined as the probability that the universal self-delimiting Turing machine U halts, and plays a central role in the development of algorithmic information theory. In the theory, there are two equivalent ways to define the program-size complexity H(s) of a given finite binary string s. In the standard way, H(s) is defined as the length of the shortest input string for U to output s. In the other way, the so-called universal probability m is introduced first, and then H(s) is defined as -log_2 m(s) without reference to the concept of program-size. Mathematically, the statistics of outcomes in a quantum measurement are described by a positive operator-valued measure (POVM) in the most general setting. Based on the theory of computability structures on a Banach space developed by Pour-El and Richards, we extend the universal probability to an analogue of POVM in an infinite dimensional quantum system, called a universal semi-POVM. We also give another characterization of Chaitin's \Omega numbers by universal probabilities. Then, based on this characterization, we propose to define an extension of \Omega as a sum of the POVM elements of a universal semi-POVM. The validity of this definition is discussed. In what follows, we introduce an operator version \hat{H}(s) of H(s) in a Hilbert space of infinite dimension using a universal semi-POVM, and study its properties.Comment: 24 pages, LaTeX2e, no figures, accepted for publication in Mathematical Logic Quarterly: The title was slightly changed and a section on an operator-valued algorithmic information theory was adde

Radiocarbon Ecology of the Land Snail Helix Melanostoma in Northeastern Libya

Terrestrial gastropods are problematical for radiocarbon (14C) measurement because they tend to incorporate carbon from ancient sources as a result of their dietary behavior. The 14C ecology of the pulmonate land snail, Helix melanostoma in Cyrenaica, northeastern Libya, was investigated as part of a wider study on the potential of using terrestrial mollusk shell for 14C dating of archaeological deposits. H. melanostoma was selected out of the species available in the region as it has the most predictable 14C ecology and also had a ubiquitous presence within the local archaeology. The ecological observations indicate that H. melanostoma has a very homogenous 14C ecology with consistent variations in F14C across sample sites controlled by availability of dietary vegetation. The majority of dated specimens from nonurbanized sample locations have only a small old carbon effect, weighted mean of 476±48 14C yr, with between ~1% and 9% of dietary F14C from non-organic carbonate sources. Observed instabilities in the 14C ecology can all be attributed to the results of intense human activity not present before the Roman Period. Therefore, H. melanostoma and species with similar ecological behavior are suitable for 14C dating of archaeological and geological deposits with the use of a suitable offset

Anaerobic Metazoans: No longer an oxymoron

The sediments of a deep-sea hypersaline and sulfidic Mediterranean basin have yielded an unexpected discovery, the first multicellular animals living entirely without oxygen. Reported by Danovaro et al. in BMC Biology, these three new species of Loricifera add a new and remarkable dimension to anoxic ecosystems previously thought to support only unicellular life

Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig

Application of ¹⁴C analyses to source apportionment of carbonaceous PM_2.5 in the UK

Determination of the radiocarbon (<sup>14</sup>C) content of airborne particulate matter yields insight into the proportion of the carbonaceous material derived from fossil and contemporary carbon sources. Daily samples of PM<sub>2.5</sub> were collected by high-volume sampler at an urban background site in Birmingham, UK, and the fraction of <sup>14</sup>C in both the total carbon, and in the organic and elemental carbon fractions, determined by two-stage combustion to CO<sub>2</sub>, graphitisation and quantification by accelerator mass spectrometry. OC and EC content was also determined by Sunset Analyzer. The mean fraction contemporary TC in the PM<sub>2.5</sub> samples was 0.50 (range 0.27–0.66, n = 26). There was no seasonality to the data, but there was a positive trend between fraction contemporary TC and magnitude of SOC/TC ratio and for the high values of these two parameters to be associated with air-mass back trajectories arriving in Birmingham from over land. Using a five-compartment mass balance model on fraction contemporary carbon in OC and EC, the following average source apportionment for the TC in these PM<sub>2.5</sub> samples was derived: 27% fossil EC; 20% fossil OC; 2% biomass EC; 10% biomass OC; and 41% biogenic OC. The latter category will comprise, in addition to BVOC-derived SOC, other non-combustion contemporary carbon sources such as biological particles, vegetative detritus, humic material and tyre wear. The proportion of total PM<sub>2.5</sub> at this location estimated to derive from BVOC-derived secondary organic aerosol was 9–29%. The findings from this work are consistent with those from elsewhere in Europe and support the conclusion of a significant and ubiquitous contribution from non-fossil biogenic sources to the carbon in terrestrial aerosol

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Molecular identification of adenoviruses associated with respiratory infection in Egypt from 2003 to 2010.

BACKGROUND: Human adenoviruses of species B, C, and E (HAdV-B, -C, -E) are frequent causative agents of acute respiratory infections worldwide. As part of a surveillance program aimed at identifying the etiology of influenza-like illness (ILI) in Egypt, we characterized 105 adenovirus isolates from clinical samples collected between 2003 and 2010. METHODS: Identification of the isolates as HAdV was accomplished by an immunofluorescence assay (IFA) and confirmed by a set of species and type specific polymerase chain reactions (PCR). RESULTS: Of the 105 isolates, 42% were identified as belonging to HAdV-B, 60% as HAdV-C, and 1% as HAdV-E. We identified a total of six co-infections by PCR, of which five were HAdV-B/HAdV-C co-infections, and one was a co-infection of two HAdV-C types: HAdV-5/HAdV-6. Molecular typing by PCR enabled the identification of eight genotypes of human adenoviruses; HAdV-3 (n = 22), HAdV-7 (n = 14), HAdV-11 (n = 8), HAdV-1 (n = 22), HAdV-2 (20), HAdV-5 (n = 15), HAdV-6 (n = 3) and HAdV-4 (n = 1). The most abundant species in the characterized collection of isolates was HAdV-C, which is concordant with existing data for worldwide epidemiology of HAdV respiratory infections. CONCLUSIONS: We identified three species, HAdV-B, -C and -E, among patients with ILI over the course of 7 years in Egypt, with at least eight diverse types circulating

Engagement and Action for Health: The Contribution of Leaders’ Collaborative Skills to Partnership Success

A multi-site evaluation (survey) of five Kellogg-funded Community Partnerships (CPs) in South Africa was undertaken to explore the relationship between leadership skills and a range of 30 operational, functional and organisational factors deemed critical to successful CPs. The CPs were collaborative academic-health service-community efforts aimed at health professions education reforms. The level of agreement to eleven dichotomous (‘Yes/No’) leadership skills items was used to compute two measures of members’ appreciation of their CPs’ leadership. The associations between these measures and 30 CPs factors were explored, and the partnership factors that leadership skills explained were assessed after controlling. Respondents who perceived the leadership of their CPs favourably had more positive ratings across 30 other partnership factors than those who rated leadership skills less favourably, and were more likely to report a positive cost/ benefit ratio. In addition, respondents who viewed their CPs’ leadership positively also rated the operational understanding, the communication mechanisms, as well as the rules and procedures of the CPs more favourably. Leadership skills explained between 20% and 7% of the variance of 10 partnership factors. The influence of leaders’ skills in effective health-focussed partnerships is much broader than previously conceptualised

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior