fractal dimensions Dotaz Zobrazit nápovědu
Fraktální charakter mocninného rozdělení velikostí částic umožňuje využití fraktální dimenzek hodnocení výsledků granulometrické analýzy.Podmínky sedimentační analýzy mastku ve vodnémprostředí byly optimalizovány přísadou neionogenního tenzidu a deflokulačního elektrolytu. Analýzarozptylu prokázala vhodnost minimálně 0,2 g/l polysorbátu 80 ke smáčení mastku. Při hodnocenífarmaceutické granulometrie je vhodné obvykle uváděný měrný povrch doplnit fraktální dimenzí,která přispívá především k obecnější interpretaci variability rozměru částic.
The fractal character of exponential particle size distribution makes it possible to use fractaldimension for the evaluation of the results of granulometric analysis. The conditions of sedimentationanalysis of talc in aqueous solution were optimized by adding nonionogenic tenside anddeflocculation electrolyte. Dispersion analysis demonstrated the suitability of minimally 0,2 g/l ofpolysorbate 80 for talc soaking. In the evaluation of pharmaceutical granulometry, it is advisable tosupplement the usually reported specific surface area with fractal dimension, which primarilycontributes to a more general interpretation of variability of particle size.
Pro kinetiku uvolňování prvního řádu je charakteristická lineární závislost rychlosti uvolňování nauvolněném množství léčiva, přičemž trojnásobek absolutní hodnoty exponentu mocninné funkcevyjadřuje reakční fraktální dimenzi DR. Uvolňování skopolaminiumbromidu z hydroxypropylmethylcelulózovéhohydrogelu bylo nejprve vyjádřeno kinetikou prvního řádu s odhadem DR v rozmezí2,98–3,00. Využití mocninné rovnice s exponentem uvolňování n umožňuje předpoklad o mechanizmuuvolňování. V rozmezí n=0,505–0,550 je odhadnuta DR = 2,46–2,94. V této oblasti převládáuvolňování mechanizmem Fickovy difuze. Pro vztah mezi oběma veličinami obecně platí DR=(3/n)– 3, což umožňuje využití poznatků z experimentálního ovlivnění exponentou uvolňování přisledování vztahu mezi reakční fraktální dimenzí a mechanizmem uvolňování skopolaminiumbromiduz hydrogelu. Zvětšení exponentu uvolňování výrazně snižuje odpovídající hodnoty reakčnífraktální dimenze.
First-order release kinetics is characterized by a linear dependence of the release rate on thereleased amount of the active ingredient, the triple of the absolute value of the exponent of theexponential function expressing the reactive fractal dimension DR. Scopolamine bromide releasefrom hydroxypropylmethylcellulose hydrogel was first expressed by first-order kinetics with anestimated DR ranging from 2.98–3.00. The employment of an exponential equation with theexponent of release n renders it possible to make an assumption about the mechanism of release.Within a range of n=0.505–0.550, estimated DR=2.46–2.94. In this region, release by means of themechanism of Fick’s diffusion prevails.DR=(3/n) – 3 generally holds true for the relationship betweenboth variables, which makes it possible to use the knowledge gained in the experimental influencingof the exponent of release in the examination of the relationship between the reactive fractaldimension and the mechanism of release of scopolamine bromide from hydrogel. An increase in theexponent of release markedly decreases the corresponding values of reactive fractal dimension.
Je sledováno využití fraktální dimenze k vyjádření tvaru náhodných shluků primárních částic čtyřpráškových látek pro farmaceutické zásypy. Hodnoty v rozmezí 1,14 až 1,24 jsou srovnány s výsledky rovnovážného gravitačního třídění v rozmezí 15 až 45 mm. Kolísání fraktální dimenze je ovlivněnohodnotami měrného povrchu zjištěného z parametrů RRSistribuce vzdušného třídění. Fraktálnídimenze rozšiřuje morfologické charakteristiky práškových látek. Pro potřeby farmaceutické technologie je však třeba lépe specifikovat podmínky jejího zjišťování především při volbě vhodnéhorozmezí hodnotícího rozměru („walk“) vzhledem k největšímu rozměru hodnocených shluků částicpráškových látek.
The paper examines the use of the fractal dimension for the expression of the shape of randomaggregates of primary particles of four powders for pharmaceutical dusting powders. The valueswithin a range from 1.14 to 1.24 are compared with the results of the equilibrium gravitationalclassification within a range from 15 to 45 mm. Vacillation of the fractal dimension is influenced bythe values of the specific surface determined from the parameters of the RRS-distribution ofelutriation. The fractal dimension extends the morphological characteristics of powders. For theneeds of pharmaceutical technology it is, however, necessary to specify better the conditions of itsdetermination, above all in the selection of a suitable range of the dimension of evaluation („walk“)with regard to the largest dimension of the aggregates of powders.
Fraktální dimenze částic práškových pomocných látek vyjadřuje členitost jejich povrchu, která můžeovlivnit jak sypnou hmotnost, tak jejich rychlost sypání otvorem násypky. U velikostních frakcí0,20–0,25 mm šesti práškových pomocných látek byly zjištěny jejich lineární fraktální dimenzev rozmezí 1,031 až 1,109 a odpovídající rychlosti sypání kruhovými otvory násypky o průměru 6; 8;10 a 12 mm.Byla prokázána významnásouvislostmezi objemově vyjádřenou rychlostí sypání (cm3/s)a fraktální dimenzí, která po zvětšení o jednotku charakterizuje povrch částic. S rostoucí fraktálnídimenzí se zvětšuje porozita volně nasypané vrstvy práškových pomocných látek a současně i objemověvyjádřená rychlost jejich sypání. Pro obvykle uváděnou hmotnostní rychlost sypání (g/s) nenítakové ovlivnění významné.
Fractal dimension of the particles of powdered auxiliary substances expresses the raggedness oftheir surface, which can influence both the bulk density and their flow rate through the opening ofthe powder funnel. In the size fractions of 0.20–0.25 mmof six powdered auxiliary substances, theirlinear fractal dimensions within a range of 1.031 to 1.109 and the corresponding flow rates throughthe circular openings of the powder funnel of diameters of 6; 8; 10, and 12 mm were found.A significant correlation has been demonstrated between the flow rate expressed in volume (cm3/s)and the fractal dimension, which after an increase by one unit characterizes the surface of theparticles.With increasing fractal dimension, the porosity of freely poured layer of powdered auxiliarysubstances is increased and simultaneously also their flow rate expressed in volume.For the usuallyreported flow rate expressed in weight (g/s), such influence is not significant.
Objective: The most important part of signal processing for classification is feature extraction as a mapping from original input electroencephalographic (EEG) data space to new features space with the biggest class separability value. Features are not only the most important, but also the most difficult task from the classification process as they define input data and classification quality. An ideal set of features would make the classification problem trivial. This article presents novel methods of feature extraction processing and automatic epilepsy seizure classification combining machine learning methods with genetic evolution algorithms. Methods: Classification is performed on EEG data that represent electric brain activity. At first, the signal is preprocessed with digital filtration and adaptive segmentation using fractal dimensions as the only segmentation measure. In the next step, a novel method using genetic programming (GP) combined with support vector machine (SVM) confusion matrix as fitness function weight is used to extract feature vectors compressed into lower dimension space and classify the final result into ictal or interictal epochs. Results: The final application of GP-SVM method improves the discriminatory performance of a classifier by reducing feature dimensionality at the same time. Members of the GP tree structure represent the features themselves and their number is automatically decided by the compression function introduced in this paper. This novel method improves the overall performance of the SVM classification by dramatically reducing the size of input feature vector. Conclusion: According to results, the accuracy of this algorithm is very high and comparable, or even superior to other automatic detection algorithms. In combination with the great efficiency, this algorithm can be used in real-time epilepsy detection applications. From the results of the algorithm's classification, we can observe high sensitivity, specificity results, except for the Generalized Tonic Clonic Seizure (GTCS). As the next step, the optimization of the compression stage and final SVM evaluation stage is in place. More data need to be obtained on GTCS to improve the overall classification score for GTCS.
- Publikační typ
- časopisecké články MeSH
Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool).
The microvascular pattern in the histological section, i.e. the point-pattern composed of capillaries perpendicular to the plane of section, contains information about the three-dimensional structure of the capillary network. Histological processing is followed by the shrinkage of tissue of uncertain magnitude. In order to obtain relevant information, the scale-independent analysis is necessary. We used an approach based on the Minkowski cover of measured set. The true fractal dimension of the point pattern is obviously of zero, but the artificial result of the algorithm can be related to the complexity of shape. We fitted the log-log plot by the modified rounded ramp function and the slope of the oblique part was used as the fractal based descriptor. We demonstrated on histological samples of the heart that this fractal-based parameter has the property of scale and rotation invariance.
The microvascular pattern in the histological section, i.e. the point-pattern composed of capillaries perpendicular to the plane of section, contains information about the three-dimensional structure of the capillary network. Histological processing is followed by the shrinkage of tissue of uncertain magnitude. In order to obtain relevant information, the scale-independent analysis is necessary. We used an approach based on the Minkowski cover of measured set. The true fractal dimension of the point pattern is obviously of zero, but the artificial result of the algorithm can be related to the complexity of shape. We fitted the log-log plot by the modified rounded ramp function and the slope of the oblique part was used as the fractal based descriptor. We demonstrated on histological samples of the heart that this fractal-based parameter has the property of scale and rotation invariance.
- MeSH
- fraktály MeSH
- histologické techniky * MeSH
- interpretace obrazu počítačem * MeSH
- lidé MeSH
- rozpoznávání automatizované MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- práce podpořená grantem MeSH
One of the most recent non-invasive technologies to examine the gastrointestinal tract is wireless capsule endoscopy (WCE). As there are thousands of endoscopic images in an 8-15 h long video, an evaluator has to pay constant attention for a relatively long time (60-120 min). Therefore the possibility of the presence of pathological findings in a few images (displayed for evaluation for a few seconds only) brings a significant risk of missing the pathology with all negative consequences for the patient. Hence, manually reviewing a video to identify abnormal images is not only a tedious and time consuming task that overwhelms human attention but also is error prone. In this paper, a method is proposed for the automatic detection of abnormal WCE images. The differential box counting method is used for the extraction of fractal dimension (FD) of WCE images and the random forest based ensemble classifier is used for the identification of abnormal frames. The FD is a well-known technique for extraction of features related to texture, smoothness, and roughness. In this paper, FDs are extracted from pixel-blocks of WCE images and are fed to the classifier for identification of images with abnormalities. To determine a suitable pixel block size for FD feature extraction, various sizes of blocks are considered and are fed into six frequently used classifiers separately, and the block size of 7×7 giving the best performance is empirically determined. Further, the selection of the random forest ensemble classifier is also done using the same empirical study. Performance of the proposed method is evaluated on two datasets containing WCE frames. Results demonstrate that the proposed method outperforms some of the state-of-the-art methods with AUC of 85% and 99% on Dataset-I and Dataset-II respectively.
- MeSH
- fraktály MeSH
- gastrointestinální trakt MeSH
- kapslová endoskopie * MeSH
- lidé MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Sypnost práškových pomocných látek je přímo ovlivněna jejich velikostí a tvarem, ačkoliv granulometrické ovlivnění tokového a smykového chování partikulárních materiálů není studováno příliš často. V práci byl sledován vliv velikosti částic čtyř velikostních frakcí sorbitolu pro přímé lisování v rozmezí 0,080–0,400 mm na rychlost sypání otvorem kónické násypky a na kohezi a tokovou funkci. Částice byly granulometricky charakterizovány pomocí optické mikroskopie; pro pravidelné částice sorbitolu byla určena lineární fraktální dimenze 1,066. Ve studovaném rozmezí velikosti částic byla detekována nelineární závislost mezi střední velikostí částic a hmotnostní rychlostí sypání Q10 (g/s) smaximem pro frakci 0,245mm. Pomocí Jenikeho smykové cely byly výborné tokové vlastnosti této frakce ověřeny díky nejvyšší hodnotě tokové funkce anejnižší kohezi. Výsledky potvrzují důležitost správného výběru velikosti částic pomocné látky kdosažení nejlepších tokových vlastností materiálu.
Flowability of powder excipients is directly influenced by their size and shape although the granulometric influence of the flow and shear behaviour of particulate matter is not studied frequently. In this work, the influence of particle size on the mass flow rate through the orifice of a conical hopper, and the cohesion and flow function was studied for four free-flowable size fractions of sorbitol for direct compression in the range of 0.080–0.400 mm. The particles were granulometricaly characterized using an optical microscopy; a boundary fractal dimension of 1.066 was estimated for regular sorbitol particles. In the particle size range studied, a non-linear relationship between the mean particle size and the mass flow rate Q10 (g/s) was detected having amaximum at the 0.245mm fraction. The best flow properties of this fraction were verified with aJenike shear tester due to the highest value of flow function and the lowest value of the cohesion. The results of this work show the importance of the right choice of the excipient particle size to achieve the best flow behaviour of particulate material.
- Klíčová slova
- sypkost, smykový přístroj Jenike,
- MeSH
- fraktály MeSH
- lidé MeSH
- prášky, zásypy, pudry MeSH
- příprava léků MeSH
- sorbitol * MeSH
- velikost částic MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- práce podpořená grantem MeSH
Measures from the theory of nonlinear dynamics were applied on complex fractionated atrial electrograms (CFAEs) in order to characterize their physiological dynamic behavior. The results were obtained considering 113 short term atrial electrograms (A-EGMs) which were annotated by three experts into four classes of fractionation according to A-EGMs signal regularity. The following measures were applied on A-EGM signals: General Correlation Dimension, Approximate Entropy, Detrended Fluctuation Analysis, Lempel-Ziv Complexity, and Katz-Sevcik, Variance and Box Counting Fractal Dimension. Assessment of disorganization was evaluated by a Kruskal Wallis statistical test. Except Detrended Fluctuation Analysis and Variance Fractal Dimension, the CFAE disorganization was found statistically significant even for low significant level alpha = 0.001. Moreover, the increasing complexity of A-EGM signals was reflected by higher values of General Correlation Dimension of order 1 and Approximate Entropy.
