On convergence of transforms based on parabolic scaling

This thesis studies properties of transforms based on parabolic scaling, like Curvelet-, Contourlet-, Shearlet- and Hart-Smith-transform. Essentially, two di erent questions are considered: How these transforms can characterize H older regularity and how non-linear approximation of a piecewise smooth function converges. In study of Hölder regularities, several theorems that relate regularity of a function f : R2 → R to decay properties of its transform are presented. Of particular interest is the case where a function has lower regularity along some line segment than elsewhere. Theorems that give estimates for direction and location of this line, and regularity of the function are presented. Numerical demonstrations suggest also that similar theorems would hold for more general shape of segment of low regularity. Theorems related to uniform and pointwise Hölder regularity are presented as well. Although none of the theorems presented give full characterization of regularity, the su cient and necessary conditions are very similar. Another theme of the thesis is the study of convergence of non-linear M ─term approximation of functions that have discontinuous on some curves and otherwise are smooth. With particular smoothness assumptions, it is well known that squared L2 approximation error is O(M-2(logM)3) for curvelet, shearlet or contourlet bases. Here it is shown that assuming higher smoothness properties, the log-factor can be removed, even if the function still is discontinuous.

Convergence withEU environmental legislation in Russia and Kyoto Protocol effects on certain power plants in Russia

Venäjällä uudistetaan sähkömarkkinoita. Uudistamisella pyritään vapauttamaan sähkömarkkinat ja lisäämään kilpailua energiasektorilla. Sähkömarkkinoiden vapauttamisen tarkoitus on energiasektorin hyötysuhteen nostaminen ja investointien houkutteleminen sektorille. Venäjä on ratifioinut Kioton protokollan, mikä energiasektorin kannalta on tärkeää, koska protokollan yhteistoteutusmekanismin kautta saadaan houkuteltua investointeja sektorille. Venäjän sähkömarkkinoiden vapauttamisen pitkäaikainen tähtäin on Venäjän ja Euroopan sähkömarkkinoiden integroituminen, joka tarkoittaa myös ympäristölainsäädännönyhtenäistämistä. Tämä tutkimus on osa Fortum Oyj:n tarjoamaa teknistä katselmusta Venäjällä toimivalle sähköyhtiölle, TGC-9:lle. Tässä työssä keskitytään TGC-9:n omistamien energiatuotantolaitoksien happamoitumista aiheuttaviin ilmapäästöihin ja pölypäästöihin. Tutkimuksessa pyritään myös löytämään Kioton protokollan yhteistoteutusmekanismi hyödyntämiskohteita. NOx -päästöt tulevat olemaan suurin haaste TGC-9:lle, jos ympäristöstandardit yhdenmukaistetaan. Yhteistoteutusmekanismin hyödyntämiskohteita löydettiin neljä: koksaamokaasun hyödyntäminen, maakaasun korvaaminen kuoren poltolla ja kaksi tapausta liittyen laitoksien hyötysuhteen nostamiseen.

Understanding change processes in business networks : a study of convergence in Finnish telecommunications 1985-2005

Aktörer inom telekommunikationsbranschen i Finland har genomgått en intensiv förändring under de senaste 25 åren, från 1980-talets självständiga företag till företag beroende av varandra, och även av aktörer inom närliggande branscher. I dag skapas telekommunikationsmarknaden inte endast av operatörerna, utan också av mediebolag (t.ex. MTV Media) och IT-företag (t.ex. TietoEnator). Gränserna mellan olika industrier håller därmed på att suddas ut - ett fenomen som allmänt benämns som teknologisk konvergens. Konvergens innebär att någonting integreras; det kan handla om t.ex. teknologier (telefoni och Internet), företag (AOL och Time Warner), industrier (telekom, media och IT-branscherna), tjänster (mobilt TV), produkter (PDA) osv. Detta innebär att ytterst få telekomaktörer ensamma kan vidareutveckla marknaden och tekniska lösningar. Samarbete mellan aktörer krävs; mobiltelefontillverkare, innehållsproducenter, operatörer osv. bör intesifiera sitt samarbete för att kunna erbjuda attraktiva tjänster och produkter till kunder och slutanvändare. Avhandlingen fokuserar speciellt på affärsnätverk och samarbetsmönster mellan nätverksaktörer som medel för att få tillgång till resurser som krävs i en konvergenskarakteriserad affärsomgivning. Avhandlingen lyfter fram vad den teknologiska konvergensen har inneburit för telekomaktörer, dvs. att företag tvingats förändra sina strategier och verksamhetsmodeller. För många företag i branschen har anpassningen till konvergenstänkande varit utmanande, och i vissa fall kan man till och med tala om att företagen upplevt en identitetskris. Den utförda forskningen visar att konvergens uppfattas på marknaden som en pågående förändringsprocess, där varje telekomaktör är tvungen att utvärdera sin roll och position i relation till andra aktörer inom branschen. Konvergensprocesser forsätter i framtiden med ökad intensitet. Aktörerna skapar medvetet sin omgivning genom att agera i olika roller, som kan sträcka sig över industrigränser. Avhandlingen påvisar även att externa händelser och industrikontexten påverkar dynamiken i ett affärsnätverk.

Convergence and divergence in global economy and social development : global perspectives on the contents of economic and soical development policy and its effects on rich and poor countries

The study of convergence and divergence in global economy and social development utilises comparative indicators to investigate the contents of economic and social development policy and their effects on the global samples that represent the rich industrial, semi-industrial and the poor developing nations. The study searchesfor answers to questions such as "what are the objectives of economic growth policies in globalisation under the imperatives of convergence and divergence, and how do these affect human well-being in consideration to the objectives of social policy in various nations?" The empirical verification of data utilises the concepts of the `logic of industrialism´ for comparative analysis that focuses mainly on identifying the levels of well-being in world nations after the Second World War. The perspectives of convergence and divergence in global economy and social development critically examine the stages of early development processes in global economy, distinguish the differences between economy and social development, illustrate the contents of economic and social development policies, their effects on rich and poor countries, and the nature of convergence and divergence in propelling economic growth and unequal social development in world nations. The measurement of convergence and divergence in global economy and social development utilised both economic and social data that were combined into an index that measures the precise levels of the effects of economic and social development policies on human well-being in the rich and poor nations. The task of finding policy solutions to resolve the controversies are reviewed through empirical investigations and the analyses of trends indicated within economic and social indicators and data. These revealed how the adoption of social policy measures in translating the gains from economic growth, towards promoting education, public health, and equity, generate social progress and longer life expectancy, higher economic growth, and sustain more stable macro economy for the nations. Social policy is concerned with the translation of benefits from objectives of global economic growth policies, to objectives of social development policy in nation states. Social policy, therefore, represents an open door whereby benefits of economic growth policies are linked with the broader objectives of social development policy, thereby enhancing the possibility of extending benefits from economic growth to all human being in every nation.

Convergence in Industry Evolution

The objective of the thesis is to enhance understanding of the evolution of convergence. Previous research has shown that the technological interfaces between distinct industries are one of the major sources of new radical cross-industry innovations. Despite the fact that convergence in industry evolution has attracted a substantial managerial interest, the conceptual confusion within the field of convergence exists. Firstly, this study clarifies the convergence phenomenon and its impact to industry evolution. Secondly, the study creates novel patent analysis methods to analyze technological convergence and provide tools for anticipating the early stages of convergence. Overall the study combines the industry evolution perspective and the convergence view of industrial evolution. The theoretical background for the study consists of the industry life cycle theories, technology evolution, and technological trajectories. The study links several important concepts in analyzing industry evolution, technological discontinuities, path-dependency, technological interfaces as a source of industry transformation, and the evolutionary stagesof convergence. Based on reviewing the literature a generic understanding of industry transformation and industrial dynamics was generated. In the convergence studies, the theoretical basis is in the discussion of different convergence types and their impacts on industry evolution, and in anticipating and monitoring the stages of convergence. The study is divided in two parts. The first part gives a general overview, and the second part comprises eight research publications. Our case study is based historically on two very distinct industries of the paper and electronics companies as a test environment to evaluate the importance of emerging business sectors and technological convergence as a source of industry transformation. Both qualitative and quantitative research methodology are utilized. The results of this study reveal that technological convergence and complementary innovations from different fields have significant effect to the emerging new business sector formation. The patent-based indicators in the analysis of technological convergence can be utilized on analyzing technology competition, capability and competence development, knowledge accumulation, knowledge spill-overs, and technology-based industry transformation. The patent-based indicators can provide insights to the future competitive environment. Results and conclusions from empirical part seem not be in conflict with real observations in the industry.

The time series convergence of dispersion in financial analysts' forecasts

Finansanalytiker har en stor betydelse för finansmarknaderna, speciellt igenom att förmedla information genom resultatprognoser. Typiskt är att analytiker i viss grad är oeniga i sina resultatprognoser, och det är just denna oenighet analytiker emellan som denna avhandling studerar. Då ett företag rapporterar förluster tenderar oenigheten gällande ett företags framtid att öka. På ett intuitivt plan är det lätt att tolka detta som ökad osäkerhet. Det är även detta man finner då man studerar analytikerrapporter - analytiker ser ut att bli mer osäkra då företag börjar gå med förlust, och det är precis då som även oenigheten mellan analytikerna ökar. De matematisk-teoretiska modeller som beskriver analytikers beslutsprocesser har däremot en motsatt konsekvens - en ökad oenighet analytiker emellan kan endast uppkomma ifall analytikerna blir säkrare på ett individuellt plan, där den drivande kraften är asymmetrisk information. Denna avhandling löser motsägelsen mellan ökad säkerhet/osäkerhet som drivkraft bakom spridningen i analytikerprognoser. Genom att beakta mängden publik information som blir tillgänglig via resultatrapporter är det inte möjligt för modellerna för analytikers beslutsprocesser att ge upphov till de nivåer av prognosspridning som kan observeras i data. Slutsatsen blir därmed att de underliggande teoretiska modellerna för prognosspridning är delvis bristande och att spridning i prognoser istället mer troligt följer av en ökad osäkerhet bland analytikerna, i enlighet med vad analytiker de facto nämner i sina rapporter. Resultaten är viktiga eftersom en förståelse av osäkerhet runt t.ex. resultatrapportering bidrar till en allmän förståelse för resultatrapporteringsmiljön som i sin tur är av ytterst stor betydelse för prisbildning på finansmarknader. Vidare används typiskt ökad prognosspridning som en indikation på ökad informationsasymmetri i redovisningsforskning, ett fenomen som denna avhandling därmed ifrågasätter.

Kunnianosoitus Paulo Freirelle

Kirjoittaja referoi ICAE:n kirjaa XXXI (1998) 1 & 2, Convergence. A tribute to Paulo Freire, joka on lämmin kunnianosoitus 2.5.1997 edemenneelle Paulo Freiren elämäntyölle

Kirjallisuutta

Virallisen vastaväittäjän 30.11.2001 päivätty, vähäisessä määrin lyhennetty lausunto.

On Modelling, System Identification and Control of Servo-Systems with a Flexible Load

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Distance Transforms on Gray-Level Surfaces

This thesis studies gray-level distance transforms, particularly the Distance Transform on Curved Space (DTOCS). The transform is produced by calculating distances on a gray-level surface. The DTOCS is improved by definingmore accurate local distances, and developing a faster transformation algorithm. The Optimal DTOCS enhances the locally Euclidean Weighted DTOCS (WDTOCS) with local distance coefficients, which minimize the maximum error from the Euclideandistance in the image plane, and produce more accurate global distance values.Convergence properties of the traditional mask operation, or sequential localtransformation, and the ordered propagation approach are analyzed, and compared to the new efficient priority pixel queue algorithm. The Route DTOCS algorithmdeveloped in this work can be used to find and visualize shortest routes between two points, or two point sets, along a varying height surface. In a digital image, there can be several paths sharing the same minimal length, and the Route DTOCS visualizes them all. A single optimal path can be extracted from the route set using a simple backtracking algorithm. A new extension of the priority pixel queue algorithm produces the nearest neighbor transform, or Voronoi or Dirichlet tessellation, simultaneously with the distance map. The transformation divides the image into regions so that each pixel belongs to the region surrounding the reference point, which is nearest according to the distance definition used. Applications and application ideas for the DTOCS and its extensions are presented, including obstacle avoidance, image compression and surface roughness evaluation.

Moniprotokollapalveluiden luontiympäristö

Tieto- ja teleliikenneverkkojen konvergenssi on tuonut uusia vaatimuksia palvelukehitysympäristöille ja aiheuttanut haasteita ympäristöjen kehitykselle. Moderneilla palvelukehitysympäristöillä on pystyttävä tuottamaan nopeasti monimutkaisia ja samalla varmatoimisia palveluja. Lisäksi moniprotokollapalveluiden luontiympäristöjen on mukauduttava uusiin olosuhteisiin, jotta palveluntarjoajat pysyisivät kilpailukykyisinä. Tämän työn tarkoituksena oli etsiä menetelmiä ja apuvälineitä nopeaan ja luotettavaan konvergoivissa verkoissa tarjottavien palveluiden luontiin. Työssä tutustuttiin markkinoilla oleviin palvelukehitysympäristöihin ja esiteltiin Intellitel OSN:n palvelukehitysympäristö ja sen palvelunluontimalli, joka tukee palvelunkehitystä läpi koko palvelunluontiprosessin. Työn käytäntöosuudessa parannettiin Intellitelin palvelunluontimallia ja palvelukehitysympäristön tarjoamia työkaluja ja apuohjelmia. Työssä toteutettiin Intellitelin palvelukehitysympäristöllä vaiheittain palvelunluontimallin mukaisesti numeronmuunnospalvelu.

IP Telephony in Third Generation Mobile Systems: Transport Layer Dimensioning

Tämä diplomityö käsittelee kolmannen sukupolven matkaviestinjärjestelmien kuljetuskerroksen mitoitusta. Nykyisten matkapuhelinverkkojen korvaajiksi suunnitellut kolmannen sukupolven matkaviestinjärjestelmät tulevat yhdistämään perinteisen puhelinviestinnän ja uudenlaiset datapalvelut. Uudet verkot tulevat perustumaan pakettivälitteiseen tiedonsiirtoon joka mahdollistaa molempien liikennetyyppien, puheen sekä datan, siirtämisen samassa verkossa. Tämän ratkaisun uskotaan tarjoavan paremmat mahdollisuudet uusien palvelujen luomiseen ja parantavan tiedonsiirtokapasiteettia. Siirtyminen pakettivälitteiseen tiedonsiirtoon aiheuttaa kuitenkin suuria muutoksia verkkoarkkitehtuurissa. Tässä diplomityössä tarkastellaan tulevien runkoverkkojen mitoitukseen liittyviä näkökohtia sekä muodostetaan alustavia kuljetuskerroksen mitoitusohjeita. Diplomityö on tehty osaksi diplomi-insinöörin tutkintoa Lappeenrannan teknillisessä korkeakoulussa. Työ on tehty Nokia Networksin palveluksessa Helsingissä, vuoden 2000 toisella puoliskolla.

Using time and stochastic models for software reliability forecasting and analysis

Tämä työ luo katsauksen ajallisiin ja stokastisiin ohjelmien luotettavuus malleihin sekä tutkii muutamia malleja käytännössä. Työn teoriaosuus sisältää ohjelmien luotettavuuden kuvauksessa ja arvioinnissa käytetyt keskeiset määritelmät ja metriikan sekä varsinaiset mallien kuvaukset. Työssä esitellään kaksi ohjelmien luotettavuusryhmää. Ensimmäinen ryhmä ovat riskiin perustuvat mallit. Toinen ryhmä käsittää virheiden ”kylvöön” ja merkitsevyyteen perustuvat mallit. Työn empiirinen osa sisältää kokeiden kuvaukset ja tulokset. Kokeet suoritettiin käyttämällä kolmea ensimmäiseen ryhmään kuuluvaa mallia: Jelinski-Moranda mallia, ensimmäistä geometrista mallia sekä yksinkertaista eksponenttimallia. Kokeiden tarkoituksena oli tutkia, kuinka syötetyn datan distribuutio vaikuttaa mallien toimivuuteen sekä kuinka herkkiä mallit ovat syötetyn datan määrän muutoksille. Jelinski-Moranda malli osoittautui herkimmäksi distribuutiolle konvergaatio-ongelmien vuoksi, ensimmäinen geometrinen malli herkimmäksi datan määrän muutoksille.