Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators and the implications of restricting the contour of integration. Typos correcte

A self-interaction corrected pseudopotential scheme for magnetic and strongly-correlated systems

Local-spin-density functional calculations may be affected by severe errors when applied to the study of magnetic and strongly-correlated materials. Some of these faults can be traced back to the presence of the spurious self-interaction in the density functional. Since the application of a fully self-consistent self-interaction correction is highly demanding even for moderately large systems, we pursue a strategy of approximating the self-interaction corrected potential with a non-local, pseudopotential-like projector, first generated within the isolated atom and then updated during the self-consistent cycle in the crystal. This scheme, whose implementation is totally uncomplicated and particularly suited for the pseudopotental formalism, dramatically improves the LSDA results for a variety of compounds with a minimal increase of computing cost.Comment: 18 pages, 14 figure

Local optical spectroscopy of semiconductor nanostructures in the linear regime

We present a theoretical approach to calculate the local absorption spectrum of excitons confined in a semiconductor nanostructure. Using the density-matrix formalism, we derive a microscopic expression for the nonlocal susceptibility, both in the linear and nonlinear regimes, which includes a three-dimensional description of electronic quantum states and their Coulomb interaction. The knowledge of the nonlocal susceptibility allows us to calculate a properly defined local absorbed power, which depends on the electromagnetic field distribution. We report on explicit calculations of the local linear response of excitons confined in single and coupled T-shaped quantum wires with realistic geometry and composition. We show that significant interference effects in the interacting electron-hole wave function induce new features in the space-resolved optical spectra, particularly in coupled nanostructures. When the spatial extension of the electromagnetic field is comparable to the exciton Bohr radius, Coulomb effects on the local spectra must be taken into account for a correct assignment of the observed features

Large-Scale Neighbor-Joining with NINJA

Abstract Neighbor-joining is a well-established hierarchical clustering algorithm for inferring phylogenies. It begins with observed distances between pairs of sequences, and clustering order depends on a metric related to those distances. The canonical algorithm requires O(n3) time and O(n2) space for n sequences, which precludes application to very large sequence families, e.g. those containing 100,000 sequences. Datasets of this size are available today, and such phylogenies will play an increasingly important role in comparative genomics studies. Recent algorithmic advances have greatly sped up neighbor-joining for inputs of thousands of sequences, but are limited to fewer than 13,000 sequences on a system with 4GB RAM. In this paper, I describe an algorithm that speeds up neighbor-joining by dramatically reducing the number of distance values that are viewed in each iteration of the clustering procedure, while still computing a correct neighbor-joining tree. This algorithm can scale to inputs larger than 100,000 sequences because of external-memory-efficient data structures. A free implementation may by obtained fro

Size Doesn't Matter: Towards a More Inclusive Philosophy of Biology

notes: As the primary author, O’Malley drafted the paper, and gathered and analysed data (scientific papers and talks). Conceptual analysis was conducted by both authors.publication-status: Publishedtypes: ArticlePhilosophers of biology, along with everyone else, generally perceive life to fall into two broad categories, the microbes and macrobes, and then pay most of their attention to the latter. ‘Macrobe’ is the word we propose for larger life forms, and we use it as part of an argument for microbial equality. We suggest that taking more notice of microbes – the dominant life form on the planet, both now and throughout evolutionary history – will transform some of the philosophy of biology’s standard ideas on ontology, evolution, taxonomy and biodiversity. We set out a number of recent developments in microbiology – including biofilm formation, chemotaxis, quorum sensing and gene transfer – that highlight microbial capacities for cooperation and communication and break down conventional thinking that microbes are solely or primarily single-celled organisms. These insights also bring new perspectives to the levels of selection debate, as well as to discussions of the evolution and nature of multicellularity, and to neo-Darwinian understandings of evolutionary mechanisms. We show how these revisions lead to further complications for microbial classification and the philosophies of systematics and biodiversity. Incorporating microbial insights into the philosophy of biology will challenge many of its assumptions, but also give greater scope and depth to its investigations

Civil society and global governance : the possibilities for global citizenship

In this article we reassert the role of governance as well as of civil society in the analysis of citizenship. We argue that to analyse global civil society and global citizenship it is necessary to focus on global governance. Just as states may facilitate or obstruct the emergence and development of national civil society, so too global governance institutions may facilitate or obstruct an emerging global civil society. Our key contention is that civil society at the global level thrives through its interaction with strong facilitating institutions of global governance. We start with a discussion of civil society and citizenship within the nation-state, and from there develop a model of global civil society and citizenship. Through analysing the impacts of various modes of global governance, we identify strategically appropriate forms of political and social engagement that best advance the prospects for global citizenship. <br /

Measurement of the View the tt production cross-section using eμ events with b-tagged jets in pp collisions at √s = 13 TeV with the ATLAS detector

This paper describes a measurement of the inclusive top quark pair production cross-section (σtt¯) with a data sample of 3.2 fb−1 of proton–proton collisions at a centre-of-mass energy of √s = 13 TeV, collected in 2015 by the ATLAS detector at the LHC. This measurement uses events with an opposite-charge electron–muon pair in the final state. Jets containing b-quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b-tagged jets are counted and used to determine simultaneously σtt¯ and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be: σtt¯ = 818 ± 8 (stat) ± 27 (syst) ± 19 (lumi) ± 12 (beam) pb, where the four uncertainties arise from data statistics, experimental and theoretical systematic effects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. A fiducial measurement corresponding to the experimental acceptance of the leptons is also presented

Search for TeV-scale gravity signatures in high-mass final states with leptons and jets with the ATLAS detector at sqrt [ s ] = 13TeV

A search for physics beyond the Standard Model, in final states with at least one high transverse momentum charged lepton (electron or muon) and two additional high transverse momentum leptons or jets, is performed using 3.2 fb−1 of proton–proton collision data recorded by the ATLAS detector at the Large Hadron Collider in 2015 at √s = 13 TeV. The upper end of the distribution of the scalar sum of the transverse momenta of leptons and jets is sensitive to the production of high-mass objects. No excess of events beyond Standard Model predictions is observed. Exclusion limits are set for models of microscopic black holes with two to six extra dimensions

Search for dark matter produced in association with a hadronically decaying vector boson in pp collisions at sqrt (s) = 13 TeV with the ATLAS detector

A search is presented for dark matter produced in association with a hadronically decaying W or Z boson using 3.2 fb−1 of pp collisions at View the MathML sources=13 TeV recorded by the ATLAS detector at the Large Hadron Collider. Events with a hadronic jet compatible with a W or Z boson and with large missing transverse momentum are analysed. The data are consistent with the Standard Model predictions and are interpreted in terms of both an effective field theory and a simplified model containing dark matter