Generating polynomial
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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.
- Klíčová slova
- Differential polynomial neural network, General partial differential equation composition, Multi-variable function approximation, Sum derivative term substitution,
- 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
This paper brings analysis of the multiple-valued memory system (MVMS) composed by a pair of the resonant tunneling diodes (RTD). Ampere-voltage characteristic (AVC) of both diodes is approximated in operational voltage range as common in practice: by polynomial scalar function. Mathematical model of MVMS represents autonomous deterministic dynamical system with three degrees of freedom and smooth vector field. Based on the very recent results achieved for piecewise-linear MVMS numerical values of the parameters are calculated such that funnel and double spiral chaotic attractor is observed. Existence of such types of strange attractors is proved both numerically by using concept of the largest Lyapunov exponents (LLE) and experimentally by computer-aided simulation of designed lumped circuit using only commercially available active elements.
- Klíčová slova
- Lyapunov exponents, chaos, multiple-valued, static memory, strange attractors,
- Publikační typ
- časopisecké články MeSH
Circular RNAs play a crucial role in cell development and serve as biomarkers in many diseases. Nevertheless, the function of many circular RNAs remains unknown. This function can be inferred from sponging and silencing interactions with micro RNAs and messenger RNAs. We recently proposed a network-based circRNA functional annotation tool, circGPA. However, validation data for RNA interactions are often sparse and predicted interactions contain many false positives. To address this issue, we propose an extended algorithm named circGPAcorr, which uses expression data to weight the interactions, resulting in more precise functional annotation. To assess the significance of the results, the p-value is calculated using reduction to circGPA, a generating-polynomial-based method. We show that the problem is #P-hard, and thus computationally difficult. The circGPAcorr algorithm is tested on publicly available myelodysplastic syndromes expression data, providing gene ontology annotations that align with the literature on myelodysplastic syndromes. At the same time, we demonstrate its performance in the circRNA-disease annotation task.
- Klíčová slova
- CircRNA, Functional annotation, Gene expression, Generating polynomial,
- Publikační typ
- časopisecké články MeSH
Numerous physiological processes are cyclical, but sampling these processes densely enough to perform frequency decomposition and subsequent analyses can be challenging. Mathematical approaches for decomposition and reconstruction of sparsely and irregularly sampled signals are well established but have been under-utilized in physiological applications. We developed a basis pursuit denoising with polynomial detrending (BPWP) model that recovers oscillations and trends from sparse and irregularly sampled timeseries. We validated this model on a unique dataset of long-term inter-ictal epileptiform discharge (IED) rates from human hippocampus recorded with a novel investigational device with continuous local field potential sensing. IED rates have well established circadian and multiday cycles related to sleep, wakefulness, and seizure clusters. Given sparse and irregular samples of IED rates from multi-month intracranial EEG recordings from ambulatory humans, we used BPWP to compute narrowband spectral power and polynomial trend coefficients and identify IED rate cycles in three subjects. In select cases, we propose that random and irregular sampling may be leveraged for frequency decomposition of physiological signals. Trial Registration: NCT03946618.
- MeSH
- algoritmy MeSH
- elektroencefalografie metody MeSH
- elektrokortikografie metody MeSH
- epilepsie * patofyziologie diagnóza MeSH
- hipokampus patofyziologie fyziologie MeSH
- lidé MeSH
- modely neurologické MeSH
- počítačové zpracování signálu MeSH
- výpočetní biologie metody MeSH
- záchvaty patofyziologie diagnóza MeSH
- Check Tag
- lidé MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Research Support, N.I.H., Extramural MeSH
- Research Support, U.S. Gov't, Non-P.H.S. MeSH
BACKGROUND: Pregnenolone sulfate (PregS) is known as a steroid conjugate positively modulating N-methyl-D-aspartate receptors on neuronal membranes. These receptors are responsible for permeability of calcium channels and activation of neuronal function. Neuroactivating effect of PregS is also exerted via non-competitive negative modulation of GABA(A) receptors regulating the chloride influx. Recently, a penetrability of blood-brain barrier for PregS was found in rat, but some experiments in agreement with this finding were reported even earlier. It is known that circulating levels of PregS in human are relatively high depending primarily on age and adrenal activity. METHODS: Concerning the neuromodulating effect of PregS, we recently evaluated age relationships of PregS in both sexes using polynomial regression models known to bring about the problems of multicollinearity, i.e., strong correlations among independent variables. Several criteria for the selection of suitable bias are demonstrated. Biased estimators based on the generalized principal component regression (GPCR) method avoiding multicollinearity problems are described. RESULTS: Significant differences were found between men and women in the course of the age dependence of PregS. In women, a significant maximum was found around the 30th year followed by a rapid decline, while the maximum in men was achieved almost 10 years earlier and changes were minor up to the 60th year. The investigation of gender differences and age dependencies in PregS could be of interest given its well-known neurostimulating effect, relatively high serum concentration, and the probable partial permeability of the blood-brain barrier for the steroid conjugate. CONCLUSIONS: GPCR in combination with the MEP (mean quadric error of prediction) criterion is extremely useful and appealing for constructing biased models. It can also be used for achieving such estimates with regard to keeping the model course corresponding to the data trend, especially in polynomial type regression models.
- MeSH
- dítě MeSH
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- lineární modely MeSH
- mladiství MeSH
- pohlavní dimorfismus * MeSH
- předškolní dítě MeSH
- pregnenolon krev MeSH
- senioři MeSH
- stárnutí krev MeSH
- zdraví * MeSH
- Check Tag
- dítě MeSH
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- mladiství MeSH
- mužské pohlaví MeSH
- předškolní dítě MeSH
- senioři MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Názvy látek
- pregnenolon MeSH
- pregnenolone sulfate MeSH Prohlížeč
This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion.
- Klíčová slova
- Lypunov exponent, admittance parameters, bipolar transistor, chaos, entropy, non-unilateral two-port, strange attractors,
- Publikační typ
- časopisecké články MeSH
The paper presents an example of a sectional analysis of drug consumption in a large in-patient health-service facility which is to be used as a foundation for making decisions about the measures to decrease the costs of drugs. Consumption of industrially produced pharmaceutical preparations at a selected facility for a period of four months was analyzed. The authors evaluated possible substitution of administered important preparations by cheaper equivalents and by means of model analysis they calculated expected savings when using the cheapest available mass-produced pharmaceutical preparations. In the preparations under study, possible savings of costs in the extent of 2.2% of the spent sum were found. On the basis of the results of the analysis, the hospital formulary authors consider the positive list with a quality system of objective monitoring of drug consumption to be the most suitable way of introduction of more rational prescription of industrially produced drugs in an in-patient facility.
- MeSH
- generika * ekonomika MeSH
- nemocniční lékárny * ekonomika MeSH
- statistické modely MeSH
- úspory nákladů MeSH
- Publikační typ
- anglický abstrakt MeSH
- časopisecké články MeSH
- Geografické názvy
- Česká republika MeSH
- Názvy látek
- generika * MeSH
The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition.
- MeSH
- algoritmy MeSH
- nejistota * MeSH
- teoretické modely * MeSH
- Publikační typ
- časopisecké články MeSH
Sixteen types of the discrete multivariate transforms, induced by the multivariate antisymmetric and symmetric sine functions, are explicitly developed. Provided by the discrete transforms, inherent interpolation methods are formulated. The four generated classes of the corresponding orthogonal polynomials generalize the formation of the Chebyshev polynomials of the second and fourth kinds. Continuous orthogonality relations of the polynomials together with the inherent weight functions are deduced. Sixteen cubature rules, including the four Gaussian, are produced by the related discrete transforms. For the three-dimensional case, interpolation tests, unitary transform matrices and recursive algorithms for calculation of the polynomials are presented.
- Klíčová slova
- cubature formulas, discrete multivariate sine transforms, orthogonal polynomials,
- Publikační typ
- časopisecké články MeSH
We survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classification include the architecture of the network (feedforward versus recurrent), time model (discrete versus continuous), state type (binary versus analog), weight constraints (symmetric versus asymmetric), network size (finite nets versus infinite families), and computation type (deterministic versus probabilistic), among others. The underlying results concerning the computational power and complexity issues of perceptron, radial basis function, winner-take-all, and spiking neural networks are briefly surveyed, with pointers to the relevant literature. In our survey, we focus mainly on the digital computation whose inputs and outputs are binary in nature, although their values are quite often encoded as analog neuron states. We omit the important learning issues.
