The Interacting Branching Process as a Simple Model of Innovation

We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/\tau at each generation. In contrast to mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For \tau = \infty, surviving processes exhibit a bottleneck before exploding super-exponentially - a growth consistent with a law of accelerating returns. This behavior persists for finite \tau. We analyze, in detail, the asymptotic behavior as p \to 0.Comment: 4 pages, 4 figure

What is the Discrete Gauge Symmetry of the MSSM?

We systematically study the extension of the Supersymmetric Standard Model (SSM) by an anomaly-free discrete gauge symmetry Z_N. We extend the work of Ibanez and Ross with N=2,3 to arbitrary values of N. As new fundamental symmetries, we find four Z_6, nine Z_9 and nine Z_18. We then place three phenomenological demands upon the low-energy effective SSM: (i) the presence of the mu-term in the superpotential, (ii) baryon-number conservation upto dimension-five operators, and (iii) the presence of the see-saw neutrino mass term LHLH. We are then left with only two anomaly-free discrete gauge symmetries: baryon-triality, B_3, and a new Z_6, which we call proton-hexality, P_6. Unlike B_3, P_6 prohibits the dimension-four lepton-number violating operators. This we propose as the discrete gauge symmetry of the Minimal SSM, instead of R-parity.Comment: Typo in item 2 below Eq.(6.9) corrected (wrong factor of "3"); 27 pages, 5 table

The phylogeny and classification of the Diseae (Orchidoideae:orchidaceae).

The subtribal classification of the Diseae (Orchidoideae) is reviewed in light of the available morphological, leaf anatomical, and palynological data. These data are critically assessed, and the more prominent features are illustrated. The data are analyzed cladistically, and the robustness of the various components of the most parsimonious tree is assessed by a bootstrap analysis. Based on the cladistic analysis and the bootstrap analysis, a new classification is proposed for the Diseae. The results of the bootstrap analysis are used to establish the nodes at which formal taxa should be recognized. This classification recognizes five monophyletic subtribes: the Satyriinae, Disinae, Brownleeinae (a new subtribe), Huttonaeinae, and Coryciinae. It is suggested that Brownleea, the only genus of the Brownleeinae, may be of hybrid origin, as it shares the autapomorphies of the Disinae and Coryciinae. Huttonaea is shown to be more closely related to the Diseae than to the Orchideae, and is consequently included as a subtribe of the Diseae. The new classification is formally presented, and a key to the genera is provided

Webs of Lagrangian Tori in Projective Symplectic Manifolds

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.Comment: 18 pages, minor latex problem fixe

Digital chronofiles of life experience

Technology has brought us to the point where we are able to digitally sample life experience in rich multimedia detail, often referred to as lifelogging. In this paper we explore the potential of lifelogging for the digitisation and archiving of life experience into a longitudinal media archive for an individual. We motivate the historical archive potential for rich digital memories, enabling individuals’ digital footprints to con- tribute to societal memories, and propose a data framework to gather and organise the lifetime of the subject

Quantum memory effects on the dynamics of electrons in small gold clusters

Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a 'memory term', i.e. attempts to describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn exchange-correlation (XC) kernel we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical Jellium 'gold clusters'. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the Jellium model. Two-dimensional pump-probe spectroscopy is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail. Finally, we examine memory effects on high harmonic generation, finding memory narrows emission lines

Users, Economics, Technology: Unavoidable Interdynamics

This paper briefly presents some conclusions of a brainstorming session on the way technology is evolving in ICT. Technology advances have overcome society ability to answer, both in economic and in human aspects. The current design paradigms, of agnostic technology development, need to be reconsidered, and the user needs to be repositioned at the center of future developments

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

Das Zerstörungspotenzial von Big Data und Künstlicher Intelligenz für die Demokratie

Der Ansatz, Massendaten („Big Data“) mit den heutigen mächtigen, nach wie vor exponentiell wachsenden Computerkapazitäten und dazu passenden Methoden zu erfassen, zu speichern, zu durchforsten, zu kombinieren und auszuwerten, hat auch für die Künstliche Intelligenz (KI) neue Impulse und Möglichkeiten geschaffen. Diese rücken einerseits alte KI-Träume näher in den Bereich des Realen, können aber andererseits ein großes zerstörerisches Potenzial entfalten. Damit gehen neue Bedrohungen einher, unter anderem für die Datenintegrität, Persönlichkeitsrechte und Privatheit, für die Unabhängigkeit von Wissen und Information sowie für den gesellschaftlichen Zusammenhalt. Neue Medien wie Facebook oder Twitter, übermächtige IT-Konzerne wie Google oder Amazon sowie die fortschreitende Digitalisierung alltäglicher Vorgänge und Gegenstände („Internet der Dinge“) spielen dabei eine entscheidende Mittlerrolle

Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for QED. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations