Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

Steady state genuine multipartite entanglement in harmonic oscillator ensembles with a common environment

Steady state entanglement in ensembles of harmonic oscillators with a common squeezed reservoir is studied. Under certain conditions the ensemble features genuine multipartite entanglement in the steady state. Several analytic results regarding the bipartite and multipartite entanglement properties of the system are derived. We also discuss a possible experimental implementation which may exhibit steady state genuine multipartite entanglement.

Classification of echolocation calls from 14 species of bat by Support Vector Machines and Ensembles of Neural Networks

Calls from 14 species of bat were classified to genus and species using discriminant function analysis (DFA), support vector machines (SVM) and ensembles of neural networks (ENN). Both SVMs and ENNs outperformed DFA for every species while ENNs (mean identification rate – 97%) consistently outperformed SVMs (mean identification rate – 87%). Correct classification rates produced by the ENNs varied from 91% to 100%; calls from six species were correctly identified with 100% accuracy. Calls from the five species of Myotis, a genus whose species are considered difficult to distinguish acoustically, had correct identification rates that varied from 91 – 100%. Five parameters were most important for classifying calls correctly while seven others contributed little to classification performance.

Some comparison on whole-proteome phylogeny of large dsDNA viruses based on dynamical language approach and feature frequency profiles method

There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. Among them, CVTree method, feature frequency profiles method and dynamical language approach were used to investigate the whole-proteome phylogeny of large dsDNA viruses. Using the data set of large dsDNA viruses from Gao and Qi (BMC Evol. Biol. 2007), the phylogenetic results based on the CVTree method and the dynamical language approach were compared in Yu et al. (BMC Evol. Biol. 2010). In this paper, we first apply dynamical language approach to the data set of large dsDNA viruses from Wu et al. (Proc. Natl. Acad. Sci. USA 2009) and compare our phylogenetic results with those based on the feature frequency profiles method. Then we construct the whole-proteome phylogeny of the larger dataset combining the above two data sets. According to the report of The International Committee on the Taxonomy of Viruses (ICTV), the trees from our analyses are in good agreement to the latest classification of large dsDNA viruses.

Intermittent Dynamics, Stochastic Resonance and Dynamical Heterogeneity in Supercooled Liquid Water

Here we find through computer simulations and theoretical analysis that the low temperature thermodynamic anomalies of liquid water arises from the intermittent fluctuation between its high density and low density forms, consisting largely of 5-coordinated and 4-coordinated water molecules, respectively. The fluctuations exhibit strong dynamic heterogeneity (defined by the four point time correlation function), accompanied by a divergence like growth of the dynamic correlation length, of the type encountered in fragile supercooled liquids. The intermittency has been explained by invoking a two state model often employed to understand stochastic resonance, with the relevant periodic perturbation provided here by the fluctuation of the total volume of the system.

Dynamical Transition of Water in the Grooves of DNA Duplex at Low Temperature

At low temperature (below its freezing/melting temperature), liquid water under confinement is known to exhibit anomalous dynamical features. Here we study structure and dynamics of water in the grooves of a long DNA duplex using molecular dynamics simulations with TIP5P potential at low temperature. We find signatures of a dynamical transition in both translational and orientational dynamics of water molecules in both the major and the minor grooves of a DNA duplex. The transition occurs at a slightly higher temperature (TGL ≈ 255 K) than the temperature at which the bulk water is found to undergo a dynamical transition, which for the TIP5P potential is at 247 K. Groove water, however, exhibits markedly different temperature dependence of its properties from the bulk. Entropy calculations reveal that the minor groove water is ordered even at room temperature, and the transition at T ≈ 255 K can be characterized as a strong-to-strong dynamical transition. Confinement of water in the grooves of DNA favors the formation of a low density four-coordinated state (as a consequence of enthalpy−entropy balance) that makes the liquid−liquid transition stronger. The low temperature water is characterized by pronounced tetrahedral order, as manifested in the sharp rise near 109° in the O−O−O angle distribution. We find that the Adams−Gibbs relation between configurational entropy and translational diffusion holds quite well when the two quantities are plotted together in a master plot for different region of aqueous DNA duplex (bulk, major, and minor grooves) at different temperatures. The activation energy for the transfer of water molecules between different regions of DNA is found to be weakly dependent on temperature.

Unusual dynamical arrest in polymer grafted nanoparticles

We present results of temperature dependent measurements of dynamics of polymer grafted nanoparticles with high grafting density with star polymerlike morphology. We observed for the low grafting density and hence low functionality sample, a dynamically arrested state with lowering of temperature, similar to what was conjectured earlier. However the high grafting density sample shows liquidlike relaxation at all measured temperatures. Possible origin of dynamical arrest in the two grafting density sample is discussed.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Sademääräsimulaatiot ENSEMBLES-hankkeen alueellisissa ilmastomalleissa

Alueellisten ilmastomallien vaakasuuntainen erottelukyky on globaaleja malleja huomattavasti tarkempi, minkä vuoksi niillä on useita käyttökohteita ilmastonmuutoksen vaikutusten arvioinnissa. Tässä Pro Gradu – työssä tutkittiin alueellisten ilmastomallien tuottamia sademääräsimulaatioita sekä sadehavaintoaineistoja Euroopassa. Aineistona käytettiin ENSEMBLES-hankkeen tarjoamia 10 alueellista ilmastosimulaatiota, kahta hilamuotoista havaintoaineistoa sekä Ilmatieteen laitoksen sadeasemahavaintoja. Aineisto oli päiväkohtaista. Vuositasolla ilmastomallit ovat pääsääntöisesti sademäärää yliennustavia, mutta harha vaihtelee alueiden ja vuodenaikojen kesken. Osa tästä harhasta selittyy kuitenkin sillä, että havaintoaineistoihin sisältyy tyypillisesti sademäärän mittaustapahtumasta aiheutuva virhe. Alueellisten simulaatioiden harha pyritään minimoimaan kun halutaan kvantifioida tulevaisuuden sademääriä ilmastomallitulosten avulla. Tutkimuksessa sovellettiin tähän tarkoitettua empiiristä korjausmenetelmää tapauskohtaisella testialueella Suomessa. Korjausmenetelmä huomioi sadetapahtumien harhan niiden intensiteetin mukaan, jolloin se periaatteessa soveltuu paremmin myös rankkasateiden korjaamiseen. Korjausmenetelmässä harhan riippuvuus sadetapahtuman intensiteetistä oletetaan skenaariojaksolla samaksi kuin vertailujaksolla. Edellytyksenä korjausmenetelmän käytölle on se, että sadetapahtumien intensiteettijakauma simulaatioaineistoissa on kohtuullisen lähellä havaittua jakaumaa. Korjausmenetelmä parantaa sademäärän vuodenaikaiskeskiarvoja tarkastelualueella vertailujaksolla, vuoden kokonaissadekertymän harhan suuruus aineiston keskiarvossa on vain 7 mm. Koska sadetapahtumien intensiteettijakauma muuttuu simulaatioissa vertailu- ja skenaariojaksojen välillä, korjausmenetelmä vaikuttaa kuitenkin sademäärän muutoksen suuruuteen. Lisäksi menetelmän vaikutus sademäärän muutokseen jakautuu epätasaisesti sadetapahtuman intensiteetistä riippuen: menetelmä pienentää rankkasateiden kertymien muutosta, mutta kasvattaa sitä tavallisten sadetapahtumien osalta. Rankkasadetapahtumien erilliskäsittely korjausmenetelmässä aiheuttaa sen, että korjatusta sadetapahtumien intensiteettijakaumasta tulee epäjatkuva riippumatta siitä, mikä tarkastelujakso on kyseessä. Tässä työssä käytetty korjausmenetelmä ei ole ainoa laatuaan, perinteisesti mallitulosten korjaamiseen on käytetty vakiokertoimiin perustuvaa menetelmää kaikille sadetapahtumille. Korjausmenetelmien testaaminen on monien sovellusten kannalta tärkeää, mutta parhaan menetelmän löytäminen ei ole yksiselitteisen helppoa. Globaaleihin malleihin verrattuna alueellisten ilmastomallien ja korjausmenetelmien käyttö aiheuttavat molemmat ylimääräisen epävarmuuslähteen ilmastosimulaatioihin.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems