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]

Mixed Symmetry Solutions of Generalized Three-Particle Bargmann-Wigner Equations in the Strong-Coupling Limit

Starting from a nonlinear isospinor-spinor field equation, generalized three-particle Bargmann-Wigner equations are derived. In the strong-coupling limit, a special class of spin 1/2 bound-states are calculated. These solutions which are antisymmetric with respect to all indices, have mixed symmetries in isospin-superspin space and in spin orbit space. As a consequence of this mixed symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these solution manifolds are interpreted as the three generations of leptons and quarks. This interpretation will be justified in a forthcoming paper.Comment: 17 page

The use of provenance in information retrieval

The volume of electronic information that users accumulate is steadily rising. A recent study [2] found that there were on average 32,000 pieces of information (e-mails, web pages, documents, etc.) for each user. The problem of organizin

Surface circulation in the Great Lakes as observed by LANDSAT-1 August 1972 - December 1973: Southern Lake Michigan

The surface current circulation patterns of southern Lake Michigan were charted for all cardinal and subcardinal wind directions, employing LANDSAT-1 observations of the distribution of natural tracing material borne in the surface waters. These colorants consist chiefly of river discharges composed of suspended sediments, pollutants, and algae; extensive chemical precipitations proved valuable for areas farther from shore. Comparison of the satellite-derived surface current charts with previous theoretical and empirical studies shows good agreement

Theology and Jurisprudence

Our era is one in which the law plays a far more important role than at any other time in history, for the law has insinuated itself into the control of almost every facet of man\u27s life. If it was true over a century ago, as Chief Justice Marshall said, that the judicial department comes home in its effects to every man\u27s fireside; it passes on his property, his reputation, his life, his all, \u27 it is even more true today as the law has continued to proliferate its influence over an ever-widening range of human conduct. But it is precisely because the law has become such a dominant factor in life that profound questions about its nature have arisen for which the everyday conceptions of law do not provide us with adequate answers. The dramatic events of recent history which have focused attention again upon the question of law, particularly the rise of totalitarianism, reveal not only the decisive effect of the regime of law upon human life and destiny but also the impotence of contemporary legal theory to cope with the lawlessness of law. Even in calmer days, Holmes argued that theory is the most important part of the dogma of the law,\u27 a view grimly corroborated by one of the great legal minds of modern times, Gustav Radbruch, who, looking back upon the debacle of his country wrote that the inherited conception of law, the legal positivism that ruled unchallenged among German legal scholars for decades and taught that law is law --this view was helpless when confronted with lawlessness in a statutory form

Control mechanisms for stochastic biochemical systems via computation of reachable sets.

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters

Finite-temperature hole dynamics in the t-J model: Exact results for high dimensions

We discuss the dynamics of a single hole in the t-J model at finite temperature, in the limit of large spatial dimensions. The problem is shown to yield a simple and physically transparent solution, that exemplifies the continuous thermal evolution of the underlying string picture from the T=0 string-pinned limit through to the paramagnetic phase.Comment: 6 pages, including 2 figure

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

A NEW APPROACH TO ANALYSING CERVICAL SPINAL MOTION

INTRODUCTION Several investigations on the problem of cervical spine motion describe the difficulties of measuring the movement exactly. Those models have to deal with the difficulties to fixate something at the human head and to track the range of motion in degrees concerning the three directions of movement, flexiodextension, lateral bending and rotation. The only objective method of measuring cervical spine movement and CO/C 1 or C 1lC2 displacements is the functional computer tomogram as described by Dvorak et. al. (1989). The aim of our survey has been to differ between the "normal" and pathologic cervical spine (after whip leash injuries, disc diseases or spondylarthrosis in sport) concerning with the range of movement and angular velocity. l b o Groups of 15 probants have been tested by a new computer-controlled setup. By using a three-dimensional motion-analysis-system special rigid-body software has been developed to calculate the cervical spine motion in all three coordinate directions (Truesdell & Noll, 1965). The first time it is possible to get results about the movement and their time-derivations. These angles and the angular velocities were traced for 15 normal individuals and 15 persons suffering with cervical spine problems. The setup for the tested patients was not more then a small frame like sunglasses which gives us an exact information about the movement in space. This information gives accurate data to calculate the amount of motion concerning the patients personal orientation in space and can be additionally used to compute the coupled motions to the probants reference coordinate system. We found significant differences in the range of motion between normal individuals as reference group and patients with cervical spine problems in all defined directions. CONCLUSIONS One conclusion, was that there were possibilities to measure those differences in cervical spine motion by the presented biomechanical measurement-setup very easily. The setup furthermore is capable of getting exact results about rang of motion, coupled motion end their time-derivations very fast and without any x-ray exposition for the patient. This possibilities and the good results are very important to judge problems after "whip lash injuries" and other cervical spine diseases in sport. REFERENCES Dvorak, A. et. al. (1989): Functional evaluation of the spinal cord by magnetic imaging in patients with rheumatoid arthritis and instability of upper cervical spine, Spine 14 (10); 1057- 1064. Truesdell, C.; W. No11 (1965): The nonlinear field theories of mechanics - Kinematics, in: Handbuch der Physik, von: S. Fliigge, Springer, New York

Transition state characteristics during cell differentiation

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington’s epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes—change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions