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Bellman Prize in Mathematical Biosciences | 1983

Evolution of Body Size: An Optimization Model

Mariusz Ziółko; Jan Kozłowski

The growth of individuals is often described by bioenergetic equations which partition assimilated energy into maintenance, growth, reproduction, and so on. Such energy flows vary with body size. The bioenergetic equations in this paper, under the assumptions that organisms will adopt behavior that channels a maximum amount of energy into the production of surviving progeny, produce a model optimizing growth and reproduction. Using the Weierstrass theorem, we show that a solution of the optimization problem exists. The problem is further solved analytically using the Pontryagin maximum principle. The main conclusion of the paper is that in a given environment an optimal body size exists, one which maximizes the energy channeled to the production of progeny. This body size depends on the mortality rate, the maximum life span, and the derivative of the growth equation with respect to body size. The biological results predicted from the model are compared with ecological data for zooplankton and vertebrate species, which support the conclusions obtained.


Functional Ecology | 1989

Optimal Allocation of Energy to Growth of the Alimentary Tract in Birds

Marek Konarzewski; Jan Kozłowski; Mariusz Ziółko

One hypothesis concerning the growth rates of birds is that weight (size) of alimentary tract limits the availability of energy to growing chicks. To test this, the optimal allocation of energy to the growth of the alimentary tract compared to the rest of the body is considered, under the assumption that the duration of postnatal development in birds is to be minimized. The model starts from bioenergetic equations, and the optimal solution is found by means of the Pontryagin Maximum Principle, assuming that growth is constrained by physiological limitations and not by availability of food. Depending on the initial and final proportion of the alimentary tract to body weight, the predicted optimal relationship between body weight and alimentary tract weight can be described by a single straight line, or twoor three-segmented straight lines. Predictions from the model are compared with data on the growth of a small altricial species the tree sparrow (Passer montanus Linnaeus) and support is found for the model. Key-words: Digestive tract, dynamic optimization, energy allocation, growth rate maximization, nestlings


Theoretical Population Biology | 1988

Gradual Transition from Vegetative to Reproductive Growth Is Optimal When the Maximum Rate of Reproductive Growth Is Limited

Jan Kozłowski; Mariusz Ziółko

Abstract The optimization of energy allocation to growth and reproduction, constrained by the maximum possible growth rate of developing fruits or embryos, is considered for an annual life style. Such a limitation may result from the small size of reproductive organs in the initial stages of development, which precludes absorbing all the surplus energy that the maternal individual can assimilate. When temporary storage of energy is impossible or too costly, a gradual switch from vegetative to reproductive growth will be optimal. An algorithm is provided to determine the age at which energy allocation to reproduction should start, and the age at which vegetative growth should cease altogether. In the case of a gradual switch, the seed yield is only slightly lower then it would have been if an instantaneous switch-over had been possible.


language and technology conference | 2009

Triphone Statistics for Polish Language

Bartosz Ziółko; Jakub Gałka; Suresh Manandhar; Richard C. Wilson; Mariusz Ziółko

The Polish text corpus was analysed to find information about phoneme statistics. We were especially interested in triphones as they are commonly used in many speech processing applications like HTK speech recogniser. An attempt to create the full list of triphones for Polish language is presented. A vast amount of phonetically transcribed text was analysed to obtain the frequency of triphone occurrences. A distibution of frequency of triphones occuring and other phenomena are presented. The standard phonetic alphabet for Polish and methods of providing phonetic transcriptions are described.


mediterranean electrotechnical conference | 2008

Wavelets in speech segmentation

J. Galka; Mariusz Ziółko

A new event-driven method of speech signals segmentation is presented. The wavelet discrete transform was used for spectral analysis and to create a segmentation procedure. Innovative event detector is the core of the process. Efficiency of the algorithm is tested against the hand annotated speech corpus.


international conference on audio, language and image processing | 2008

Application of HTK to the Polish language

Bartosz Ziółko; Suresh Manandhar; Richard C. Wilson; Mariusz Ziółko; Jakub Gałka

A speech recognition system based on HTK for Polish is presented. It was trained on 365 utterances, all spoken by 26 males. The features of Polish with respect to speech recognition are described. Some aspects of speech recognition differ in comparison to English. Errors in recognition were analysed in details in an attempt to find reasons and scenarios of wrong recognitions.


IEEE Transactions on Automatic Control | 1995

Some optimization models of growth in biology

Mariusz Ziółko; Jan Kozłowski

The presented models are applications of classical optimal control methods in biology. The growth of plants and animals are described by nonlinear ordinary differential equations. Biologically justified limitations provide additional inequality constraints on the control functions and the state variable. The solutions of the optimization models are control functions which either maximize the amounts of energy allocated to reproduction or minimize the age of achieving adult body size. >


language and technology conference | 2009

Time durations of phonemes in polish language for speech and speaker recognition

Bartosz Ziółko; Mariusz Ziółko

Statistical phonetic data for Polish were collected. Phonemes are of different lengths, varying from 30 ms to 200 ms. Average phoneme durations are presented. A corpus of spoken Polish was used to collect statistic values of real language and evaluated to be applied in an automatic speech recognition and speaker identification systems. These natural phenomena could be used in phonemes parametrisation and modelling. An additional source of information for a case of speech segmentation was obtained. The collected data are presented in the paper (average values for all available male speakers and for some chosen ones), along with comments on the corpus and the used method. The obtained data were compared with the expected values according to phonetic literature.


international conference on digital signal processing | 2006

Lossless Jpeg-Base Compression of Transmultiplexed Images

Przemyslaw Sypka; Mariusz Ziółko; Bartosz Ziółko

A transmultiplexer assigned to combine images into one image to be sent through a single communication channel is presented. The considered system can be equipped with integer-to-integer filters to enable the lossless compression. The efficiency of lossless JPEG compression applied to transmultiplexed signals has been verified


IEEE Transactions on Automatic Control | 1990

Application of Lyapunov functionals to studying stability of linear hyperbolic systems

Mariusz Ziółko

The Lyapunov functional method is used to prove the stability conditions for Cauchy problems and initial-boundary value problems if the system is described by a set of linear first-order partial differential equations of the hyperbolic type. The application of the Lyapunov functional method to stability of linear hyperbolic systems with more than two equations leads to the search for functionals with diagonal matrices. The question of whether or not there exists a positive diagonal matrix G such that D/sup T/G+GD, >

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Bartosz Ziółko

AGH University of Science and Technology

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Jakub Gałka

AGH University of Science and Technology

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Magdalena Igras

AGH University of Science and Technology

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Przemyslaw Sypka

AGH University of Science and Technology

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Stanisław Kacprzak

AGH University of Science and Technology

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Dawid Skurzok

AGH University of Science and Technology

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Mariusz Mąsior

AGH University of Science and Technology

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