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Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions  [PDF]
Frederic von Wegner
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.513198
Abstract: A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent 1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.
Dynamic BOLD functional connectivity in humans and its electrophysiological correlates
Enzo Tagliazucchi,Frederic von Wegner,Helmut Laufs
Frontiers in Human Neuroscience , 2012, DOI: 10.3389/fnhum.2012.00339
Abstract: Neural oscillations subserve many human perceptual and cognitive operations. Accordingly, brain functional connectivity is not static in time, but fluctuates dynamically following the synchronization and desynchronization of neural populations. This dynamic functional connectivity has recently been demonstrated in spontaneous fluctuations of the Blood Oxygen Level-Dependent (BOLD) signal, measured with functional Magnetic Resonance Imaging (fMRI). We analyzed temporal fluctuations in BOLD connectivity and their electrophysiological correlates, by means of long (≈50 min) joint electroencephalographic (EEG) and fMRI recordings obtained from two populations: 15 awake subjects and 13 subjects undergoing vigilance transitions. We identified positive and negative correlations between EEG spectral power (extracted from electrodes covering different scalp regions) and fMRI BOLD connectivity in a network of 90 cortical and subcortical regions (with millimeter spatial resolution). In particular, increased alpha (8–12 Hz) and beta (15–30 Hz) power were related to decreased functional connectivity, whereas gamma (30–60 Hz) power correlated positively with BOLD connectivity between specific brain regions. These patterns were altered for subjects undergoing vigilance changes, with slower oscillations being correlated with functional connectivity increases. Dynamic BOLD functional connectivity was reflected in the fluctuations of graph theoretical indices of network structure, with changes in frontal and central alpha power correlating with average path length. Our results strongly suggest that fluctuations of BOLD functional connectivity have a neurophysiological origin. Positive correlations with gamma can be interpreted as facilitating increased BOLD connectivity needed to integrate brain regions for cognitive performance. Negative correlations with alpha suggest a temporary functional weakening of local and long-range connectivity, associated with an idling state.
Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics
Nicolas Wieder,Rainer H. A. Fink,Frederic von Wegner
Journal of Biomedicine and Biotechnology , 2011, DOI: 10.1155/2011/572492
Abstract: In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.
L-Type Ca2+ Channel Function Is Linked to Dystrophin Expression in Mammalian Muscle
Oliver Friedrich, Frederic von Wegner, Jeffrey S. Chamberlain, Rainer H. A. Fink, Petra Rohrbach
PLOS ONE , 2008, DOI: 10.1371/journal.pone.0001762
Abstract: Background In dystrophic mdx skeletal muscle, aberrant Ca2+ homeostasis and fibre degeneration are found. The absence of dystrophin in models of Duchenne muscular dystrophy (DMD) has been connected to altered ion channel properties e.g. impaired L-type Ca2+ currents. In regenerating mdx muscle, ‘revertant’ fibres restore dystrophin expression. Their functionality involving DHPR-Ca2+-channels is elusive. Methods and Results We developed a novel ‘in-situ’ confocal immuno-fluorescence and imaging technique that allows, for the first time, quantitative subcellular dystrophin-DHPR colocalization in individual, non-fixed, muscle fibres. Tubular DHPR signals alternated with second harmonic generation signals originating from myosin. Dystrophin-DHPR colocalization was substantial in wt fibres, but diminished in most mdx fibres. Mini-dystrophin (MinD) expressing fibres successfully restored colocalization. Interestingly, in some aged mdx fibres, colocalization was similar to wt fibres. Most mdx fibres showed very weak membrane dystrophin staining and were classified ‘mdx-like’. Some mdx fibres, however, had strong ‘wt-like’ dystrophin signals and were identified as ‘revertants’. Split mdx fibres were mostly ‘mdx-like’ and are not generally ‘revertants’. Correlations between membrane dystrophin and DHPR colocalization suggest a restored putative link in ‘revertants’. Using the two-micro-electrode-voltage clamp technique, Ca2+-current amplitudes (imax) showed very similar behaviours: reduced amplitudes in most aged mdx fibres (as seen exclusively in young mdx mice) and a few mdx fibres, most likely ‘revertants’, with amplitudes similar to wt or MinD fibres. Ca2+ current activation curves were similar in ‘wt-like’ and ‘mdx-like’ aged mdx fibres and are not the cause for the differences in current amplitudes. imax amplitudes were fully restored in MinD fibres. Conclusions We present evidence for a direct/indirect DHPR-dystrophin interaction present in wt, MinD and ‘revertant’ mdx fibres but absent in remaining mdx fibres. Our imaging technique reliably detects single isolated ‘revertant’ fibres that could be used for subsequent physiological experiments to study mechanisms and therapy concepts in DMD.
Electrophysiological correlates of non-stationary BOLD functional connectivity fluctuations
Enzo Tagliazucchi,Frederic von Wegner,Astrid Morzelewski,Verena Brodbeck,Helmut Laufs
Quantitative Biology , 2012,
Abstract: Spontaneous fluctuations of the BOLD (Blood Oxygen Level-Dependent) signal, measured with fMRI (functional Magnetic Resonance Imaging), display a rich and neurobiologically relevant functional connectivity structure. This structure is usually revealed using time averaging methods, which prevent the detection of functional connectivity changes over time. In this work we studied the electrophysiological correlates of dynamical BOLD functional connectivity fluctuations, by means of long (approx. 50 min) joint electroencephalographic (EEG) and fMRI recordings. We identified widespread positive and negative correlations between EEG spectral power and fMRI BOLD connectivity fluctuations in a network of 90 cortical and subcortical regions. In particular, increased alpha (8-12 Hz) and beta (15-30 Hz) power were related to decreased functional connectivity, whereas gamma (30-60 Hz) power correlated positively with BOLD connectivity between specific brain regions. Furthermore, these patterns were altered for subjects undergoing vigilance changes, with an involvement of the slow delta (0.4 - 4 Hz) band in localized positive correlations. Finally, graph theoretical indices of network structure also exhibited sharp changes over time, with average path length correlating positively with alpha power extracted from central and frontal electrodes. Our results strongly suggest that non-stationary BOLD functional connectivity has a neurophysiological origin. Positive correlations of BOLD connectivity with gamma can be interpreted as increased average binding over relatively long periods of time, possibly due to spontaneous cognition occurring during rest. Negative correlations with alpha suggest functional inhibition of local and long-range connectivity, associated with an idling state of the brain.
Fixation method does not affect restoration of rotation center in hip replacements: A single-site retrospective study
Alexander Wegner, Max Daniel Kauther, Stefan Landgraeber, Marius von Knoch
Journal of Orthopaedic Surgery and Research , 2012, DOI: 10.1186/1749-799x-7-25
Abstract: We retrospectively compared pre- and post-operative positions of the hip rotation center in 25 and 68 patients who underwent artificial hip replacements in our department in 2007 using cemented or cementless cup fixation, respectively, with digital radiographic image analysis.The mean horizontal and vertical distances between the rotation center and the acetabular teardrop were compared in radiographic images taken pre- and post-operatively. The mean horizontal difference was ?2.63 mm (range: -11.00 mm to 10.46 mm, standard deviation 4.23 mm) for patients who underwent cementless fixation, and ?2.84 mm (range: -10.87 to 5.30 mm, standard deviation 4.59 mm) for patients who underwent cemented fixation. The mean vertical difference was 0.60 mm (range: -20.15 mm to 10.00 mm, standard deviation 3.93 mm) and 0.41 mm (range: -9.26 mm to 6.54 mm, standard deviation 3.58 mm) for the cementless and cemented fixation groups, respectively. The two fixation techniques had no significant difference on the position of the hip rotation center in the 93 patients in this study.The hip rotation center was similarly restored using either the cemented or cementless fixation techniques in this patient cohort, indicating that the fixation technique itself does not interfere with the position of the center of rotation. To completely answer this question further studies with more patients are needed.
Differences in Trabecular Bone of Leptin-Deficient ob/ob Mice in Response to Biomechanical Loading
Hansjoerg Heep, Christian Wedemeyer, Alexander Wegner, Sebastian Hofmeister, Marius von Knoch
International Journal of Biological Sciences , 2008,
Abstract: Objective: It is known that bone mineral density (BMD) and the strength of bone is predicted by body mass. Fat mass is a significant predictor of bone mineral density which correlates with body weight. This suggests that body fat regulates bone metabolism first by means of hormonal factors and second that the effects of muscle and loading are signaling factors in mechanotransduction. Leptin, a peptide hormone produced predominantly by white fat cells, is one of these hormonal factors. The aim of this study was to investigate and measure by micro-CT the different effects of weight-bearing on trabecular bone formation in mice without the stimulation of leptin. Results: Animals with an ad-libitum-diet (Group A) were found to increase body weight significantly at the age of six weeks in comparison with lean mice (Group B). From this point on, the difference increased constantly. At the age of twenty weeks the obese mice were almost twice as heavy as the lean mice. Significant statistical differences are shown between the two groups for body weight and bone mineral density. Examination of trabecular bone (BV/TV, trabecular number (Tb.N.), trabecular thickness (Tb.Th.)) revealed that the only statistically significant difference between the two groups was the Tb.N. for the proximal femur. High weight-bearing insignificantly improved all trabecular bone parameters in the obese mice. Compared with the control-diet Group B, the BV/TV and Tb.N. were slightly higher in the controlled-diet Group A, but not the Tb.Th.. However, correlation was found between Tb.N. and BMD on the one hand and body weight on the other hand. Conclusion: biomechanical loading led to decreased bone mineral density by a decrease in the number of trabeculae. Trabecular thickness was not increased by biomechanical loading in growing mice. Decreased body weight in leptin-deficient mice protects against bone loss. This finding is consistent with the principle of light-weight construction of bone. Differences in cortical and trabecular bone will be examined in later studies. It is not possible to conclude that these results also apply to human beings.
The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material  [PDF]
Tadeusz WEGNER, Dariusz KURPISZ
Advances in Materials Physics and Chemistry (AMPC) , 2012, DOI: 10.4236/ampc.2012.24B015
Abstract: In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.
Reading and Accounts
Frederic Will
Kritike : an Online Journal of Philosophy , 2009,
Abstract:
Temporal Foundations in the Construction of History: Two Essays
Frederic Will
Cosmos and History : the Journal of Natural and Social Philosophy , 2009,
Abstract: The two essays included here are parts of a longer study of temporality, and the genesis of the “religious.” The first part, “Multiple Nows,” depicts a universe in which a present to past relation is establishable from any and every point in consciousness. The resulting perspective differs from that offered by the linear timeline of chronological history. Remembering where I put my glasses is an historicizing act, as fully as is remembering when the Battle of Zama was fought or who won there. On this alternate view of temporality the genesis of the historical perspective is the historicizing subject. The second essay, “The History of a House,” places the observer before an historical structure, then asks where the historicity in the structure is. We discover that the historicity is put there by the observer/subject. This discovery resembles our earlier discovery that historicity is generated by an infinite sequence of nows. The two essays converge on a description of historical cognition as subject-generated.
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