Projective Systems of Imprimitivity and Applications for the Galilei Group in 1+2 and 1+3 Dimensions

The study of the projective unitary irreducible representations of the Galilei group (in 1+3 and 1+2 dimensions) is usually done using firstly some group extensions techniques (in this way one is reduced to the study of true unitary representations) and then Mackey induction procedure. In this paper we reobtain these results using a different approach based on the notion of projective systems of imprimitivity due also to Mackey. This extension of the usual Mackey procedure is presented rather extensively and illustrated by detailed computations concerning the classification of the projective unitary irreducible representations.     

Mackey Theorem and Two-Electron Wave Function of a Multi-Centre System

The two-electron wave function in a system of many equivalent atoms is investigated group-theoretically. It is shown that the classification of different types of two-electron (two-hole) localizations can be made by the double-coset decomposition of the symmetry group with respect to the local subgroup, and that the group appearing in the Mackey theorem can be used for the additional classification of states. The Mackey theorem on symmetrized squares and the generalized Frobenius reciprocity theorem are applied to the construction of two-electron states in octahedral symmetry. Received October 23, 1995; revised June 21, 1996; accepted for publication July 1, 1996     

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.     

Josephson junctions and dark energy

In a recent paper Beck and Mackey [C. Beck, M.C. Mackey, astro-ph/0603397] argue that the argument we gave in our paper [Ph. Jetzer, N. Straumann, Phys. Lett. B 606 (2005) 77, astro-ph/0411034] to disprove their claim that dark energy can be discovered in the Lab through noise measurements of Josephson junctions is incorrect. In particular, they emphasize that the measured noise spectrum in Josephson junctions is a consequence of the fluctuation dissipation theorem, while our argument was based on equilibrium statistical mechanics. In this note we show that the fluctuation dissipation relation does not depend upon any shift of vacuum (zero-point) energies, and therefore, as already concluded in our previous paper, dark energy has nothing to do with the proposed measurements.     

Gravitational force between two electrons in superconductors

The attractive gravitational force between two electrons in superconductors is deduced from the Eddington–Dirac large number relation, together with Beck and Mackey electromagnetic model of vacuum energy in superconductors. This force is estimated to be weaker than the gravitational attraction between two electrons in the vacuum.     

Mdm2生成速率调控的p53-Mdm2振子的全局动力学和稳定性

肿瘤抑制蛋白p53的动力学在一定程度上可以决定DNA损伤后的细胞命运.p53的动力学行为与p53信号通路中p53-Mdm2振子模块密切相关.然而,p53的负调控子Mdm2的生成速率的增加使其在一些癌细胞中过表达.因此探讨Mdm2生成速率对p53动力学的影响有重要意义.同时,PDCD5作为p53的激活子也调控p53的表达.因此,本文针对PDCD5调控的p53-Mdm2振子模型,通过分岔分析获得了Mdm2生成速率所调控的p53的单稳态、振荡以及单稳态与振荡共存的动力学行为,且稳定性通过能量面进行了分析.此外,噪声强度对p53动力学的稳定性有重要的影响.因此,针对p53的振荡行为,探讨了噪声强度对势垒高度和周期的影响.本文所获得的结果对理解DNA损伤后的p53信号通路调控起到一定的指导作用.     

On the problem of the metastable region at morphological instability

The study deals with numerical analysis of the morphological stability of a growing round particle with respect to harmonic perturbations of an arbitrary amplitude. Various growth regimes (from diffusion to kinetic-limited) are considered. It is found that the critical size of the particle stability decreases as the perturbation amplitude increases and tends to the value, which was determined analytically elsewhere using the maximum entropy production principle. This result is a crucial argument in support of the hypothesis that the entropy production can be used for analysis of a nonequilibrium phase transitions similarly to thermodynamic potentials in the case of equilibrium phase transitions.     

On the simultaneous verifiability of yes-no measurements

The relation of simultaneous verifiability (compatibility) of yes-no measurements, introduced by G. W. Mackey for the purposes of quantum axiomatics, is investigated. The meaning of this important relation is clarified here by showing its position among all the so-called weak compatibilities defined axiomatically in the logic of propositions.     

Geometric dequantization and the correspondence problem

On the way to settle a conjecture proposed by Mackey, we first present in detail a complete solution to the correspondence problem for systems whose configuration space isR ⁿ . We then indicate how this can be considered as a first step in the elaboration of a geometric dequantization program which would extend the results to more general manifolds.     

Electromagnetic dark energy and gravitoelectrodynamics of superconductors

It is shown that Beck and Mackey electromagnetic model of dark energy in superconductors can account for the non-classical inertial properties of superconductors, which have been conjectured by the author to explain the Cooper pair’s mass excess reported by Cabrera and Tate. A new fundamental scale of nature (the Planck-Einstein scale) for gravitation in low temperature condensed matter is proposed to host the gravitoelectrodynamic properties of superconductors.     

Topological origin of global attractors in gene regulatory networks

Fixed-point attractors with global stability manifest themselves in a number of gene regulatory networks. This property indicates the stability of regulatory networks against small state perturbations and is closely related to other complex dynamics. In this paper, we aim to reveal the core modules in regulatory networks that determine their global attractors and the relationship between these core modules and other motifs. This work has been done via three steps. Firstly, inspired by the signal transmission in the regulation process, we extract the model of chain-like network from regulation networks. We propose a module of “ideal transmission chain(ITC)”, which is proved sufficient and necessary(under certain condition) to form a global fixed-point in the context of chain-like network. Secondly, by examining two well-studied regulatory networks(i.e., the cell-cycle regulatory networks of Budding yeast and Fission yeast), we identify the ideal modules in true regulation networks and demonstrate that the modules have a superior contribution to network stability(quantified by the relative size of the biggest attraction basin). Thirdly, in these two regulation networks, we find that the double negative feedback loops, which are the key motifs of forming bistability in regulation, are connected to these core modules with high network stability. These results have shed new light on the connection between the topological feature and the dynamic property of regulatory networks.     

Projective unitary antiunitary representations of locally compact groups

We give here a systematic presentation of the theory of projective representations when antiunitary operators are present. In particular the imprimitivity theorem of Mackey is proved in this situation and all the unitary antiunitary representations of the extended Poincaré group are derived.     

Quantum mechanics of the quaternionic Hilbert spaces based upon the imprimitivity theorem

We survey the realization of quantum mechanics in quaternionic Hilbert spaces following the methods of Mackey, who examined the complex and real cases exploiting the imprimitivity theorem. We show that there exists a unique unitary skew-adjoint operator which commutes with all the observables. This operator not only plays the role of the imaginary unit in the complex case, but allows a complexification of the Hilbert space by the choice of any quaternionic imaginary unit. Difficulties in the definition of time reversal, however, arise because of the properties of the quaternionic field. The introduction of an extra imaginary unit, commuting with the others, is suggested in order to implement time reversal properly. In the Appendix we give the proof of the imprimitivity theorem, in the quaternionic case, that we use in the paper.     

Taming instabilities in power grid networks by decentralized control

Renewables will soon dominate energy production in our electric power system. And yet, how to integrate renewable energy into the grid and the market is still a subject of major debate. Decentral Smart Grid Control (DSGC) was recently proposed as a robust and decentralized approach to balance supply and demand and to guarantee a grid operation that is both economically and dynamically feasible. Here, we analyze the impact of network topology by assessing the stability of essential network motifs using both linear stability analysis and basin volume for delay systems. Our results indicate that if frequency measurements are averaged over sufficiently large time intervals, DSGC enhances the stability of extended power grid systems. We further investigate whether DSGC supports centralized and/or decentralized power production and find it to be applicable to both. However, our results on cycle-like systems suggest that DSGC favors systems with decentralized production. Here, lower line capacities and lower averaging times are required compared to those with centralized production.     

Probability measures on operator algebras

The problem of linearity of probability measures on hyperfinite factors is studied in Part I. Part II contains the extension of Vital-Hahn-Saks, Egoroff and Lusic theorems for probability measures on von Neumann algebras. These problems have immediate connections with properties of physical states on observable algebras in the sense of Mackey.     

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.     

Product Cocycles and the Approximate Transitivity

Some criteria of the approximate transitivity in the terms of Mackey actions and product cocycles are proved. The Mackey action constructed by an amenable type II or III transformation group G and a 1-cocycle × , where is the Radon–Nikodym cocycle while is an arbitrary 1-cocycle with values in a locally compact separable group A, is approximately transitive (AT) if and only if the pair (G,(, )) is weakly equivalent to a product odometer supplied with a product cocycle. Besides, in the case when the given AT action from the very beginning was a range of a type II action and a nontransient cocycle, then this cocycle turns out to be cohomologous to a -product cocycle. An example is constructed that shows that it is necessary to consider the double Mackey actions since they can not be reduced to the single ones.     

Ultrasonic resonance regulated near-field scanning optical microscope and laser induced near-field optical-force interaction

We have developed a novel sample-tip regulation for a near-field optical microscope: an ultrasonic resonance regulation method. The regulation range is from 0 to 50 nm. It shows not only stability, simplicity in construction, but also versatility in vacuum, magnetic field, and low temperature environments. The main advantage of this technique is that it is a non-optical detecting scheme, which is very important for near-field spectroscopy. Such construction can also be used as a force microscope to study the topography of insulating samples. The laser light induced force interaction in the near-field range has been observed for the first time, showing that aided by laser radiation, the shear force between sample and tip can be changed depending on the type of sample. This can be interpreted as the light induced optical tip-sample interaction of light pressure effect. The van der Waals dispersion energy and the optical binding energy induced by laser beam between dielectric tip and samples play important role. The effect confirms a theoretical prediction. This new technique and phenomenon will add new aspects to near-field optics.     

Characterizations of Categories of Commutative C*-Subalgebras

We aim to characterize the category of injective *-homomorphisms between commutative C*-subalgebras of a given C*-algebra A. We reduce this problem to finding a weakly terminal commutative subalgebra of A, and solve the latter for various C*-algebras, including all commutative ones and all type I von Neumann algebras. This addresses a natural generalization of the Mackey–Piron programme: which lattices are those of closed subspaces of Hilbert space? We also discuss the way this categorified generalization differs from the original question.