Stochastic algorithms Dotaz Zobrazit nápovědu
Cryo Electron Tomography (cryoET) plays an essential role in Structural Biology, as it is the only technique that allows to study the structure of large macromolecular complexes in their close to native environment in situ. The reconstruction methods currently in use, such as Weighted Back Projection (WBP) or Simultaneous Iterative Reconstruction Technique (SIRT), deliver noisy and low-contrast reconstructions, which complicates the application of high-resolution protocols, such as Subtomogram Averaging (SA). We propose a Progressive Stochastic Reconstruction Technique (PSRT) - a novel iterative approach to tomographic reconstruction in cryoET based on Monte Carlo random walks guided by Metropolis-Hastings sampling strategy. We design a progressive reconstruction scheme to suit the conditions present in cryoET and apply it successfully to reconstructions of macromolecular complexes from both synthetic and experimental datasets. We show how to integrate PSRT into SA, where it provides an elegant solution to the region-of-interest problem and delivers high-contrast reconstructions that significantly improve template-based localization without any loss of high-resolution structural information. Furthermore, the locality of SA is exploited to design an importance sampling scheme which significantly speeds up the otherwise slow Monte Carlo approach. Finally, we design a new memory efficient solution for the specimen-level interior problem of cryoET, removing all associated artifacts.
- MeSH
- algoritmy MeSH
- elektronová kryomikroskopie metody MeSH
- makromolekulární látky chemie MeSH
- metoda Monte Carlo MeSH
- počítačové zpracování obrazu metody MeSH
- reprodukovatelnost výsledků MeSH
- ribozomy chemie MeSH
- stochastické procesy * MeSH
- tomografie elektronová metody MeSH
- zobrazování trojrozměrné metody MeSH
- Publikační typ
- časopisecké články MeSH
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
- MeSH
- algoritmy MeSH
- diagnóza počítačová metody MeSH
- duktální karcinom prsu MeSH
- fraktály MeSH
- hodnocení rizik metody MeSH
- lidé MeSH
- nádory prsu diagnóza patologie MeSH
- patologie metody MeSH
- počítačová simulace MeSH
- stochastické procesy MeSH
- Check Tag
- lidé MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- srovnávací studie MeSH
The Canonical Distribution and Stochastic Differential Equations -- 7. Numerical Methods for Stochastic Molecular Dynamics -- 8.
Interdisciplinary Applied Mathematics, ISSN 0939-6047 39
1st edition XXII, 443 stran : ilustrace ; 24 cm
This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications. Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method
- MeSH
- matematika MeSH
- simulace molekulární dynamiky MeSH
- Publikační typ
- monografie MeSH
- Konspekt
- Matematika
- NLK Obory
- přírodní vědy
It is automatically assumed that the accuracy with which a stimulus can be decoded is entirely determined by the properties of the neuronal system. We challenge this perspective by showing that the identification of pure tone intensities in an auditory nerve fiber depends on both the stochastic response model and the arbitrarily chosen stimulus units. We expose an apparently paradoxical situation in which it is impossible to decide whether loud or quiet tones are encoded more precisely. Our conclusion reaches beyond the topic of auditory neuroscience, however, as we show that the choice of stimulus scale is an integral part of the neural coding problem and not just a matter of convenience.
- MeSH
- akustická stimulace metody MeSH
- algoritmy * MeSH
- lidé MeSH
- modely neurologické * MeSH
- nervová vlákna fyziologie MeSH
- nervové vedení fyziologie MeSH
- nervus cochlearis fyziologie MeSH
- počítačová simulace využití MeSH
- stochastické procesy MeSH
- vnímání hlasitosti fyziologie MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
The common procedure for reconstructing growth and fertility rates from skeletal samples involves regressing a growth or fertility rate on the age-at-death ratio, an indicator that captures the proportion of children and juveniles in a skeletal sample. Current methods derive formulae for predicting growth and fertility rates in skeletal samples from modern reference populations with many deaths, although recent levels of mortality are not good proxies for prehistoric populations, and stochastic error may considerably affect the age distributions of deaths in small skeletal samples. This study addresses these issues and proposes a novel algorithm allowing a customized prediction formula to be produced for each target skeletal sample, which increases the accuracy of growth and fertility rate estimation. Every prediction equation is derived from a unique reference set of simulated skeletal samples that match the target skeletal sample in size and assumed mortality level of the population that the target skeletal sample represents. The mortality regimes of reference populations are based on model life tables in which life expectancy can be flexibly set between 18 and 80 years. Regression models provide a reliable prediction; the models explain 83-95% of total variance. Due to stochastic variation, the prediction error is large when the estimate is based on a small number of skeletons but decreases substantially with increasing sample size. The applicability of our approach is demonstrated by a comparison with baseline estimates, defined here as predictions based on the widely used Bocquet-Appel (2002, doi: 10.1086/342429) equation.
- MeSH
- celosvětové zdraví MeSH
- dítě MeSH
- fertilita MeSH
- lidé MeSH
- mortalita MeSH
- naděje dožití * MeSH
- porodnost * MeSH
- tabulky života MeSH
- věkové rozložení MeSH
- Check Tag
- dítě MeSH
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Several models (concentration detectors and a flux detector) for coding of odor intensity in olfactory sensory neurons are investigated. Behavior of the system is described by different stochastic processes of binding the odorant molecules to the receptors and their activation. Characteristics how well the odorant concentration can be estimated from the knowledge of response, the number of activated neurons, are studied. The approach is based on the Fisher information and analogous measures. These measures of optimality are computed and applied to locate the odorant concentration which is most suitable for coding. The results are compared with the classical deterministic approach which judges the optimal odorant concentration via steepness of the input-output function.
