Nestrukturirani modeli mliječno-kiselog vrenja

To describe a microbial process, two kinds of models can be developed, structured and unstructured models. Contrary to structured models, which take into account some basic aspects of cell structure, their function and composition, no physiological characterization of cells is considered in unstructured models, which only consider total cellular concentration. However, in spite of their simplicity, unstructured models have proven to accurately describe lactic acid fermentation in a wide range of experimental conditions and media. A partial link between cell growth and production, namely the Luedeking and Piret model, is mostly considered by the authors. Culture pH is the main parameter to be considered for model development. Acidic pH leads to inhibitory concentrations of undissociated lactic acid, the main inhibitory component, which causes cessation of growth and then production. On the other hand, pH control at optimal value for LAB growth allows to overcome product inhibition (by the total lactic acid produced or its undissociated part); hence nutritional limitations have to be considered for model development. Nitrogen is mainly involved in cessation of growth, owing to the fastidious nutritional requirements of LAB, while lactic acid production ceased when carbon was exhausted from the medium. The lack of substrate inhibition when usual concentrations of carbon substrate are used should be noted.Da bi se opisao mikrobni proces, upotijebljeni su strukturirani i nestrukturirani modeli. Strukturirani modeli uzimaju u obzir strukturu, funkciju i raspored stanica, a nestrukturirani ne uzimaju fiziološka svojstva, već samo ukupnu koncentraciju stanica. Ipak, usprkos njihovoj jednostavnosti, nestrukturirani modeli precizno opisuju mliječno-kiselo vrenje u različitim eksperimentalnim uvjetima i na raznim podlogama. Autori najčešće koriste Luedekingov i Piretov model, koji opisuje djelomičnu vezu između rasta stanica i proizvodnje mliječne kiseline. U razvoju ovoga modela najčešće je pH-vrijednost glavni parametar. Pri niskoj pH-vrijednosti nastaju inhibicijske koncentracije nedisocirane mliječne kiseline, što zaustavlja rast mliječno-kiselih bakterija, a time i proizvodnju mliječne kiseline. Taj se inhibicijski učinak može prevladati održavanjem optimalne pH-vrijednosti, ali pritom treba uzeti u obzir utjecaj hranjivih tvari na rast mliječno-kiselih bakterija. Nedostatak dušika je najčešći uzrok inhibicije mliječno-kiselih bakterija, jer im je prijeko potreban za rast, dok nakon iscrpljivanja ugljika iz podloge prestaje proizvodnja mliječne kiseline, što se može izbjeći korištenjem odgovarajućih koncentracija ugljika

Multicountry and Regional Macroeconometric Models

Multicountry models were developed in the previous century to serve the analyses and projections of the world economy and/or its regions (for instance Latin America). They distinguish the largest countries and the rest of the world (ROW) composed of particular countries. Hence, their structure is based on the specifications of equations for individual countries using full statistical information available at the countries level. The regional macroeconomic models are built for either administrative or geographical units distinguished within large countries (USA, China, Russia). Their structure should be in principle similar to those of the national economy. However, the statistical information of the regional economies is typically uncomplete: no sufficient information is available on exports and imports of the region, migrations and financial flows. Appropriate approximations are necessary. As in majority of countries the prices and wages movements are in general unified over the country, the variables representing the national level excerpt an impact on the regional variables. The regional impact on the national variables is rather unusual. The paper shows the skeleton model applied in the multicountry models and the skeleton of the macroeconomic regional model. The specific properties of the regional model are discussed and the possibilities of its extensions analysed.Modele gospodarki światowej lub jej części (regionów) zostały zbudowane w ubiegłym stuleciu, służąc celom analizy rozwoju i prognozowaniu gospodarki całego świata lub wyróżnionych regionów (np. Ameryki Łacińskiej). Modele te zwykle wyróżniały największe, uprzemysłowione kraje świata oraz sumarycznie pozostałe kraje (ROW). Stąd ich struktura została oparta na specyfikacjach równań typowych dla poszczególnych krajów, wykorzystując pełnię statystycznych informacji gromadzonych dla każdego kraju. Makroekonometryczne modele regionalne są budowane albo dla wyróżnionych jednostek administracyjnych albo geograficznych w obrębie na ogół dużych krajów (USA, Chiny, Rosja, etc.). Ich struktura winna być zbliżona do struktury modeli danych krajów. Jednakże, dane statystyczne dotyczące regionów są na ogół niekompletne: brak jest danych o eksporcie i imporcie regionu, migracjach ludności, przepływach finansowych etc.. Wymaga to odpowiednich aproksymacji. Ponieważ w wielu krajach dynamika cen i plac przebiega w sposób podobny w skali kraju - wprowadza się do modeli regionalnych zmienne dotyczące całego kraju. Z drugiej strony oddziaływanie zwrotne występuje na ogół rzadko w tych modelach. W referacie przedstawiono typowe struktury makroekonometrycznych modeli występujących w modelach gospodarki światowej oraz struktury modeli charakterystyczne dla modeli regionalnych. Specyficzne własności modeli regionalnych są przedmiotem odrębnej dyskusji a także możliwości rozbudowy tych modeli są analizowane

SWARCH modeli

Zbog velikog utjecaja šokova na procjenu ARCH familije modela bila potrebna nova specifikacija koja dozvoljava promjene u režimu generirajućeg procesa. Cai [3] i Hamilton i Susmel [17], nezavisno predlažu SWARCH model, koji je dizajniran da obuhvati promjene režima u volatilnosti pomoću neopažene varijable stanja koja prati Markovljev lanac prvog reda sa diskretnim skupom stanja. U ovom radu, prezentirani su SWARCH modeli, s fokusom na SWARCH model razvijen od strane Hamiltona i Susmela [17], za koji je dan i prikaz procjene parametara i značajki modela te na temelju kojeg je i napravljen primjer upotrebe modela, naveden u ovom radu. Ukratko su opisani E-SWARCH model te multivarijantni SWARCH model, kao glavna proširenja osnovnog modela. Glavni zaključak je da model primjereno modelira pojave tijekom kojih dolazi do promjena u volatilnosti, bitno reducirajući ustrajnost utjecaja šokova i time dodatno naglašava potrebu za modelom uvjetne varijance koji dozvoljava stohastička prebacivanja. Također, model dopušta datiranje i time identifikaciju glavnih epizoda i događaja u pozadini visoko volatilnih perioda na financijskim tržištima.Because of the large influence of shocks on the estimation of ARCH family of models, a new specification was needed, which will allow changes in the regime of the generating process. Cai [3] and Hamilton and Susmel [17], independently suggested SWARCH model, which was designed to capture regime switches in volatility with unobserved state variable that follows first order, discrete state Markov chain. In this paper, SWARCH models are presented, focusing on SWARCH model developed by Hamilton and Susmel [17], for which is given the parameter estimation procedure and features of the model, and on which basis was made an example of usage of the model, referred to in this paper. Also, there are brief descriptions of the E-SWARCH model and multivariate SWARCH model, as major extensions of the basic model. The main conclusion is that the model adequately models phenomenona in which occurred the change in volatility, significantly reducing the persistence of shocks and thus further emphasizes the need for a model of conditional variance that allows the stochastic switching. Also, the model allows for time dating and identification of key episodes and events in the background of highly volatile periods in financial markets

A simple model for low variability in neural spike trains

Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, which can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters, but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like Linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity this model has the potential to explain low variability in other areas

MATHEMATICAL SIMULATION FOR ASSESSMENT OF THE SMALL BUSINESS EFFICIENCY: REGIONAL ASPECTS

Mathematical simulation of economic systems and processes are considered. The description of macroeconomic models for assets formation, consumer behaviour, production activity of an enterprise, and market balance is given. The line balance model of diversified economic system is examined

Molecular Dynamics Simulations of Detonation Instability

After making modifications to the Reactive Empirical Bond Order potential for Molecular Dynamics (MD) of Brenner et al. in order to make the model behave in a more conventional manner, we discover that the new model exhibits detonation instability, a first for MD. The instability is analyzed in terms of the accepted theory.Comment: 7 pages, 6 figures. Submitted to Phys. Rev. E Minor edits. Removed parenthetical statement about P^\nu from conclusion

Multimodel inference to quantify the relative importance of abiotic factors in the population dynamics of marine zooplankton

The effect of multiple stressors on marine ecosystems remains poorly understood and most of the knowledge available is related to phytoplankton. To partly address this knowledge gap, we tested if combining multimodel inference with generalized additive modelling could quantify the relative contribution of environmental variables on the population dynamics of a zooplankton species in the Belgian part of the North Sea. Hence, we have quantified the relative contribution of oceanographic variables (e.g. water temperature, salinity, nutrient concentrations, and chlorophyll a concentrations) and anthropogenic chemicals (i.e. polychlorinated biphenyls) to the density of Acartia clausi. We found that models with water temperature and chlorophyll a concentration explained ca. 73% of the population density of the marine copepod. Multimodel inference in combination with regression-based models are a generic way to disentangle and quantify multiple stressor-induced changes in marine ecosystems. Future-oriented simulations of copepod densities suggested increased copepod densities under predicted environmental changes

Modeling of the Labour Force Redistribution in Investment Projects with Account of their Delay

The mathematical model of the labour force redistribution in investment projects is presented in the article. The redistribution mode of funds, labour force in particular, according to the equal risk approach applied to the loss of some assets due to delay in all the investment projects is provided in the model. The sample of the developed model for three investment projects with the specified labour force volumes and their defined unit costs at the particular moment is given