Deformations of Gabor Frames

The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one-parameter family of frames, which we call a deformation of the original. For example, beginning with the usual tight frame F of Gabor wavelets generated by a compactly supported window g(t) and parameterized by a regular lattice in the time-frequency plane, one obtains a family of frames F_\theta generated by the non-compactly supported windows g_\theta=W(theta)g, parameterized by rotated versions of the original lattice. This gives a method for constructing tight frames of Gabor wavelets for which neither the window nor its Fourier transform have compact support. When \theta=\pi/2, we obtain the well-known Gabor frame generated by a window with compactly supported Fourier transform. The family F_\theta therefore interpolates these two familiar examples.Comment: 8 pages in Plain Te

Stochastic Pulse Switching in a Degenerate Resonant Optical Medium

Using the idealized integrable Maxwell-Bloch model, we describe random optical-pulse polarization switching along an active optical medium in the Lambda-configuration with disordered occupation numbers of its lower energy sub-level pair. The description combines complete integrability and stochastic dynamics. For the single-soliton pulse, we derive the statistics of the electric-field polarization ellipse at a given point along the medium in closed form. If the average initial population difference of the two lower sub-levels vanishes, we show that the pulse polarization will switch intermittently between the two circular polarizations as it travels along the medium. If this difference does not vanish, the pulse will eventually forever remain in the circular polarization determined by which sub-level is more occupied on average. We also derive the exact expressions for the statistics of the polarization-switching dynamics, such as the probability distribution of the distance between two consecutive switches and the percentage of the distance along the medium the pulse spends in the elliptical polarization of a given orientation in the case of vanishing average initial population difference. We find that the latter distribution is given in terms of the well-known arcsine law

Cys-Ph-TAHA: a lanthanide binding tag for RDC and PCS enhanced protein NMR

Here we present Cys-Ph-TAHA, a new nonadentate lanthanide tag for the paramagnetic labelling of proteins. The tag can be easily synthesized and is stereochemically homogenous over a wide range of temperatures, yielding NMR spectra with a single set of peaks. Bound to ubiquitin, it induced large residual dipolar couplings and pseudocontact shifts that could be measured easily and agreed very well with the protein structure. We show that Cys-Ph-TAHA can be used to label large proteins that are biochemically challenging such as the Lac repressor in a 90 kDa ternary complex with DNA and inducer

A Dynamic Input-Output Model with Renewable Resources

Absztrakt. A dolgozat a dinamikus input-output modell egy általánosítását tárgyalja. A sztenderd dinamikus Leontief-modellt terjesztjük ki arra az esetre, amikor a megújuló erőforrások egyenleteit is a modellhez csatoljuk. A megújuló erőforrások készletei növekednek a regenerációs rátával, amit csökkent a felhasználás üteme. Ebben a dolgozatban az új modell irányíthatóságát vizsgáljuk, a fogyasztási rátát tekintve irányítási változónak. Az egyensúlyi arányos pályát vizsgálva arra keresünk választ, hogy milyen növekedési ütemet képes elérni a gazdaság anélkül, hogy kimerítené a megújuló erőforrásokat. A megoldásban az irányításelmélet és a klasszikus lineáris algebra eredményeit használjuk fel. ----- Abstract. The paper studies a generalisation of the dynamic Leontief input-output model. The standard dynamic Leontief model will be extended with the balance equation of renewable resources. The renewable stocks will increase regenerating and decrease exploiting primary natural resources. In this study the controllability of this extended model is examined by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate the exhaustion of renewable resources in dependence on the balanced growth rate and on the rate of natural regeneration. In doing so, classic results from control theory and on eigenvalue problems in linear algebra are applied

Primjena genetskog programiranja u CAE neuronskih mreža za prognozu izdržljivosti kod savijanja ZnTiCu traka

Genetic programming (GP) and CAE NN analysis have been applied for the prediction of bending capability of rolled ZnTiCu alloy sheet. Investigation revealed that an analysis with CAE NN is faster than GP but less accurate for lower amount of data. Both methods enable good assessment of separate influencing parameters in the complex system.Metode genetskog programiranja (GP) i CAE NN bile su upotrebljene za studij utjecaja izdržljivosti savijanja tankih ploča slitine ZnTiCu. Istraživanje je pokazalo da je CAE NN metoda brža od GP metode a istovremeno je manje precizna pri manjoj bazi podataka. Obje primenjene metode dobro vrednuju utjecaj parcijalnih komponenata kompleksnog sistema

Genetic programming and cae neural networks approach for prediction of the bending capability of ZnTiCu sheets

Genetic programming (GP) and CAE NN analysis have been applied for the prediction of bending capability of rolled ZnTiCu alloy sheet. Investigation revealed that an analysis with CAE NN is faster than GP but less accurate for lower amount of data. Both methods enable good assessment of separate influencing parameters in the complex system

Views and experiences of persons with chronic diseases about strategies that aim to integrate and re-integrate them into work: A systematic review of qualitative studies

The effectiveness of strategies targeting professional integration and reintegration strongly depends on the experiences of participants. The aim of this systematic literature review is to synthesize European qualitative studies exploring views and experiences of persons with chronic conditions regarding strategies for integration and reintegration into work. The systematic search was conducted in Medline, PsycINFO, CDR-HTA, CDR-DARE and Cochrane Systematic Reviews. Overall, 24 studies published in English between January 2011 and April 2016 were included. Most studies were carried out in Nordic countries or in the UK, and most participants were persons with either mental or musculoskeletal disorders. Ten themes emerged: individual and holistic approach, clarity of strategy and processes, timing of rehabilitation processes, experience with professionals, at the workplace and with peer groups, changes in the understanding of health and work, active involvement in the process, competencies development and motivating aspects of work. Findings highlight, among others, the need to actively involve participants in the return to work process and to provide timely and clearly structured processes and interventions. This review provides stakeholders key information to develop, plan, implement and evaluate interventions to integrate and re-integrate persons with chronic conditions into work in Europe. © 2018 by the authors. Licensee MDPI, Basel, Switzerland