Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems.

• MeSH
• algoritmy MeSH
• interpretace statistických dat MeSH
• matematika * MeSH
• nelineární dynamika MeSH
• neuronové sítě * MeSH
• počasí MeSH
• počítačová simulace MeSH
• strojové učení MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

It has been known for discrete-time recurrent neural networks (NNs) that binary-state models using the Heaviside activation function (with Boolean outputs 0 or 1) are equivalent to finite automata (level 3 in the Chomsky hierarchy), while analog-state NNs with rational weights, employing the saturated-linear function (with real-number outputs in the interval [0,1]), are Turing complete (Chomsky level 0) even for three analog units. However, it is as yet unknown whether there exist subrecursive (i.e. sub-Turing) NN models which occur on Chomsky levels 1 or 2. In this paper, we provide such a model which is a binary-state NN extended with one extra analog unit (1ANN). We achieve a syntactic characterization of languages that are accepted online by 1ANNs in terms of so-called cut languages which are combined in a certain way by usual operations. We employ this characterization for proving that languages accepted by 1ANNs with rational weights are context-sensitive (Chomsky level 1) and we present explicit examples of such languages that are not context-free (i.e. are above Chomsky level 2). In addition, we formulate a sufficient condition when a 1ANN recognizes a regular language (Chomsky level 3) in terms of quasi-periodicity of parameters derived from its real weights, which is satisfied e.g. for rational weights provided that the inverse of the real self-loop weight of the analog unit is a Pisot number.

• MeSH
• jazyk (prostředek komunikace) * MeSH
• neuronové sítě * MeSH
• teoretické modely * MeSH
• Publikační typ
• časopisecké články MeSH

Integral transforms with kernels corresponding to computational units are exploited to derive estimates of network complexity. The estimates are obtained by combining tools from nonlinear approximation theory and functional analysis together with representations of functions in the form of infinite neural networks. The results are applied to perceptron networks.

• MeSH
• nelineární dynamika MeSH
• neuronové sítě * MeSH
• výpočetní biologie metody   MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

• MeSH
• chování MeSH
• molekulární biologie MeSH
• nemoci nervového systému MeSH
• nervový systém MeSH
• neurochemie MeSH
• neurofyziologie MeSH
• neurony MeSH
• neurovědy MeSH
• Publikační typ
• monografie MeSH

• Konspekt
• Fyziologie člověka a srovnávací fyziologie
• NLK Obory
• neurovědy
• biologie

Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle, this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases, this is not an option since the bivariate distributions needed may not be reliably estimated or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples.

• MeSH
• entropie MeSH
• informační systémy * MeSH
• korelace dat MeSH
• neuronové sítě MeSH
• teoretické modely MeSH
• Publikační typ
• práce podpořená grantem MeSH

• MeSH
• neurofyziologie MeSH
• oči - fyziologické jevy MeSH
• zrak fyziologie   MeSH
• Publikační typ
• kongresy MeSH

• Konspekt
• Lékařské vědy. Lékařství
• NLK Obory
• fyziologie
• neurovědy
• oftalmologie

Polysaccharides are long carbohydrate molecules of monosaccharide units joined together by glycosidic bonds. These biological polymers have emerged as promising materials for tissue engineering due to their biocompatibility, mostly good availability and tailorable properties. This complex group of biomolecules can be classified using several criteria, such as chemical composition (homo- and heteropolysaccharides), structure (linear and branched), function in the organism (structural, storage and secreted polysaccharides), or source (animals, plants, microorganisms). Polysaccharides most widely used in tissue engineering include starch, cellulose, chitosan, pectins, alginate, agar, dextran, pullulan, gellan, xanthan and glycosaminoglycans. Polysaccharides have been applied for engineering and regeneration of practically all tissues, though mostly at the experimental level. Polysaccharides have been tested for engineering of blood vessels, myocardium, heart valves, bone, articular and tracheal cartilage, intervertebral discs, menisci, skin, liver, skeletal muscle, neural tissue, urinary bladder, and also for encapsulation and delivery of pancreatic islets and ovarian follicles. For these purposes, polysaccharides have been applied in various forms, such as injectable hydrogels or porous and fibrous scaffolds, and often in combination with other natural or synthetic polymers or inorganic nanoparticles. The immune response evoked by polysaccharides is usually mild, and can be reduced by purifying the material or by choosing appropriate crosslinking agents.

• MeSH
• biokompatibilní materiály chemická syntéza   MeSH
• buněčné kultury přístrojové vybavení   metody   MeSH
• celulosa chemie   MeSH
• cévní protézy MeSH
• cévy cytologie   růst a vývoj   MeSH
• endoteliální buňky cytologie   fyziologie   MeSH
• kultivované buňky MeSH
• lidé MeSH
• protézy - design MeSH
• řízená tkáňová regenerace přístrojové vybavení   MeSH
• tkáňové inženýrství přístrojové vybavení   metody   MeSH
• tkáňové podpůrné struktury * MeSH
• zvířata MeSH
• Check Tag
• lidé MeSH
• zvířata MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH
• přehledy MeSH

• MeSH
• biomedicínské inženýrství MeSH
• Publikační typ
• abstrakty MeSH
• kongresy MeSH
• sborníky MeSH

• Konspekt
• Lékařské vědy. Lékařství
• NLK Obory
• biomedicínské inženýrství

• MeSH
• lékařská informatika metody   trendy   MeSH
• mezinárodní spolupráce MeSH
• využití lékařské informatiky MeSH
• Publikační typ
• abstrakty MeSH
• kongresy MeSH
• sborníky MeSH
• Geografické názvy
• Rumunsko MeSH

• Konspekt
• Lékařské vědy. Lékařství
• NLK Obory
• lékařská informatika

• MeSH
• biologie buňky MeSH
• molekulární biologie MeSH
• Publikační typ
• monografie MeSH

• Konspekt
• Biochemie. Molekulární biologie. Biofyzika
• NLK Obory
• biologie
• cytologie, klinická cytologie