On an easy transition from operator dynamics to generating functionals by Clifford algebras

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture relying on geometry does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to corresponding generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerable short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a non-linear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]

Overcoming Psychologism. Twardowski on Actions and Products

This paper is about the topic of psychologism in the work of Kazimierz Twardowski and my aim is to revisit this important issue in light of recent publications from, and on Twardowski’s works. I will first examine the genesis of psychologism in the young Twardowski’s work; secondly, I will examine Twardowski’s picture theory of meaning and Husserl’s criticism in Logical Investigations; the third part is about Twardowski’s recognition and criticism of his psychologism in his lectures on the psychology of thinking; the fourth and fifth parts provide an overview of Twardowski’s paper “Actions and Products” while the sixth part addresses the psychologism issue in the last part of this paper through the delineation of psychology and the humanities. I shall conclude this study with a brief assessment of Twardowski’s solution to psychologism

Nanoscale periodicity in stripe-forming systems at high temperature: Au/W(110)

We observe using low-energy electron microscopy the self-assembly of monolayer-thick stripes of Au on W(110) near the transition temperature between stripes and the non-patterned (homogeneous) phase. We demonstrate that the amplitude of this Au stripe phase decreases with increasing temperature and vanishes at the order-disorder transition (ODT). The wavelength varies much more slowly with temperature and coverage than theories of stress-domain patterns with sharp phase boundaries would predict, and maintains a finite value of about 100 nm at the ODT. We argue that such nanometer-scale stripes should often appear near the ODT.Comment: 5 page

Integrating rich user feedback into intelligent user interfaces

The potential for machine learning systems to improve via a mutually beneficial exchange of information with users has yet to be explored in much detail. Previously, we found that users were willing to provide a generous amount of rich feedback to machine learning systems, and that the types of some of this rich feedback seem promising for assimilation by machine learning algorithms. Following up on those findings, we ran an experiment to assess the viability of incorporating real-time keyword-based feedback in initial training phases when data is limited. We found that rich feedback improved accuracy but an initial unstable period often caused large fluctuations in classifier behavior. Participants were able to give feedback by relying heavily on system communication in order to respond to changes. The results show that in order to benefit from the user’s knowledge, machine learning systems must be able to absorb keyword-based rich feedback in a graceful manner and provide clear explanations of their predictions

ABC-SysBio-approximate Bayesian computation in Python with GPU support.

Motivation: The growing field of systems biology has driven demand for flexible tools to model and simulate biological systems. Two established problems in the modeling of biological processes are model selection and the estimation of associated parameters. A number of statistical approaches, both frequentist and Bayesian, have been proposed to answer these questions. Results: Here we present a Python package, ABC-SysBio, that implements parameter inference and model selection for dynamical systems in an approximate Bayesian computation (ABC) framework. ABC-SysBio combines three algorithms: ABC rejection sampler, ABC SMC for parameter inference and ABC SMC for model selection. It is designed to work with models written in Systems Biology Markup Language (SBML). Deterministic and stochastic models can be analyzed in ABC-SysBio

Finite temperature dynamics of the Anderson model

The recently introduced local moment approach (LMA) is extended to encompass single-particle dynamics and transport properties of the Anderson impurity model at finite-temperature, T. While applicable to arbitrary interaction strengths, primary emphasis is given to the strongly correlated Kondo regime (characterized by the T=0 Kondo scale $\omega_{\rm K}$). In particular the resultant universal scaling behaviour of the single-particle spectrum D(\omega; T) \equiv F(\frac{\w}{\omega_{\rm K}}; \frac{T}{\omega_{\rm K}}) within the LMA is obtained in closed form; leading to an analytical description of the thermal destruction of the Kondo resonance on all energy scales. Transport properties follow directly from a knowledge of $D(\omega; T)$. The $T / \omega_{\rm K}$-dependence of the resulting resistivity $\rho(T)$, which is found to agree rather well with numerical renormalization group calculations, is shown to be asymptotically exact at high temperatures; to concur well with the Hamann approximation for the s-d model down to $T/\omega_{\rm K} \sim 1$, and to cross over smoothly to the Fermi liquid form $\rho (T) - \rho (0) \propto -(T/\omega_{\rm K})^2$ in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models

Physics of the Be(101̅0) Surface Core Level Spectrum

Photoelectron diffraction has been utilized to confirm the theoretical prediction that the surface core level shifts observed for Be(101̅0) have been improperly assigned. The original assignment based upon the relative intensity of the shifted components was intuitively obvious: the peak with the largest shift of −0.7eV with respect to the bulk was associated with the surface plane, the next peak shifted by −0.5eV stems from the second layer, and the third peak at −0.22eV from the third and fourth layers. First-principles theory and our experimental data show that the largest shift is associated with the second plane, not the first plane

Atomistic modelling of large-scale metal film growth fronts

We present simulations of metallization morphologies under ionized sputter deposition conditions, obtained by a new theoretical approach. By means of molecular dynamics simulations using a carefully designed interaction potential, we analyze the surface adsorption, reflection, and etching reactions taking place during Al physical vapor deposition, and calculate their relative probability. These probabilities are then employed in a feature-scale cellular-automaton simulator, which produces calculated film morphologies in excellent agreement with scanning-electron-microscopy data on ionized sputter deposition.Comment: RevTeX 4 pages, 2 figure

ABC-SysBio—approximate Bayesian computation in Python with GPU support

Motivation: The growing field of systems biology has driven demand for flexible tools to model and simulate biological systems. Two established problems in the modeling of biological processes are model selection and the estimation of associated parameters. A number of statistical approaches, both frequentist and Bayesian, have been proposed to answer these questions