93 research outputs found

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    DNA Computing: Modelling in Formal Languages and Combinatorics on Words, and Complexity Estimation

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    DNA computing, an essential area of unconventional computing research, encodes problems using DNA molecules and solves them using biological processes. This thesis contributes to the theoretical research in DNA computing by modelling biological processes as computations and by studying formal language and combinatorics on words concepts motivated by DNA processes. It also contributes to the experimental research in DNA computing by a scaling comparison between DNA computing and other models of computation. First, for theoretical DNA computing research, we propose a new word operation inspired by a DNA wet lab protocol called cross-pairing polymerase chain reaction (XPCR). We define and study a word operation called word blending that models and generalizes an unexpected outcome of XPCR. The input words are uwx and ywv that share a non-empty overlap w, and the output is the word uwv. Closure properties of the Chomsky families of languages under this operation and its iterated version, the existence of a solution to equations involving this operation, and its state complexity are studied. To follow the XPCR experimental requirement closely, a new word operation called conjugate word blending is defined, where the subwords x and y are required to be identical. Closure properties of the Chomsky families of languages under this operation and the XPCR experiments that motivate and implement it are presented. Second, we generalize the sequence of Fibonacci words inspired by biological concepts on DNA. The sequence of Fibonacci words is an infinite sequence of words obtained from two initial letters f(1) = a and f(2)= b, by the recursive definition f(n+2) = f(n+1)*f(n), for all positive integers n, where * denotes word concatenation. After we propose a unified terminology for different types of Fibonacci words and corresponding results in the extensive literature on the topic, we define and explore involutive Fibonacci words motivated by ideas stemming from theoretical studies of DNA computing. The relationship between different involutive Fibonacci words and their borderedness and primitivity are studied. Third, we analyze the practicability of DNA computing experiments since DNA computing and other unconventional computing methods that solve computationally challenging problems often have the limitation that the space of potential solutions grows exponentially with their sizes. For such problems, DNA computing algorithms may achieve a linear time complexity with an exponential space complexity as a trade-off. Using the subset sum problem as the benchmark problem, we present a scaling comparison of the DNA computing (DNA-C) approach with the network biocomputing (NB-C) and the electronic computing (E-C) approaches, where the volume, computing time, and energy required, relative to the input size, are compared. Our analysis shows that E-C uses a tiny volume compared to that required by DNA-C and NB-C, at the cost of the E-C computing time being outperformed first by DNA-C and then by NB-C. In addition, NB-C appears to be more energy efficient than DNA-C for some input sets, and E-C is always an order of magnitude less energy efficient than DNA-C

    Automatic Pain Assessment by Learning from Multiple Biopotentials

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    Garbling Schemes and Applications

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    The topic of this thesis is garbling schemes and their applications. A garbling scheme is a set of algorithms for realizing secure two-party computation. A party called a client possesses a private algorithm as well as a private input and would like to compute the algorithm with this input. However, the client might not have enough computational resources to evaluate the function with the input on his own. The client outsources the computation to another party, called an evaluator. Since the client wants to protect the algorithm and the input, he cannot just send the algorithm and the input to the evaluator. With a garbling scheme, the client can protect the privacy of the algorithm, the input and possibly also the privacy of the output.  The increase in network-based applications has arisen concerns about the privacy of user data. Therefore, privacy-preserving or privacy-enhancing techniques have gained interest in recent research. Garbling schemes seem to be an ideal solution for privacy-preserving applications. First of all, secure garbling schemes hide the algorithm and its input. Secondly, garbling schemes are known to have efficient implementations.  In this thesis, we propose two applications utilizing garbling schemes. The first application provides privacy-preserving electronic surveillance. The second application extends electronic surveillance to more versatile monitoring, including also health telemetry. This kind of application would be ideal for assisted living services.  In this work, we also present theoretical results related to garbling schemes. We present several new security definitions for garbling schemes which are of practical use. Traditionally, the same garbled algorithm can be evaluated once with garbled input. In applications, the same function is often evaluated several times with different inputs. Recently, a solution based on fully homomorphic encryption provides arbitrarily reusable garbling schemes. The disadvantage in this approach is that the arbitrary reuse cannot be efficiently implemented due to the inefficiency of fully homomorphic encryption.  We propose an alternative approach. Instead of arbitrary reusability, the same garbled algorithm could be used a limited number of times. This gives us a set of new security classes for garbling schemes. We prove several relations between new and established security definitions. As a result, we obtain a complex hierarchy which can be represented as a product of three directed graphs. The three graphs in turn represent the different flavors of security: the security notion, the security model and the level of reusability.  In addition to defining new security classes, we improve the definition of side-information function, which has a central role in defining the security of a garbling scheme. The information allowed to be leaked by the garbled algorithm and the garbled input depend on the representation of the algorithm. The established definition of side-information models the side-information of circuits perfectly but does not model side-information of Turing machines as well. The established model requires that the length of the argument, the length of the final result and the length of the function can be efficiently computable from the side-information function. Moreover, the side-information depends only on the function. In other words, the length of the argument, the length of the final result and the length of the function should only depend on the function. For circuits this is a natural requirement since the number of input wires tells the size of the argument, the number of output wires tells the size of the final result and the number of gates and wires tell the size of the function. On the other hand, the description of a Turing machine does not set any limitation to the size of the argument. Therefore, side-information that depends only on the function cannot provide information about the length of the argument. To tackle this problem, we extend the model of side-information so that side-information depends on both the function and the argument. The new model of side information allows us to define new security classes. We show that the old security classes are compatible with the new model of side-information. We also prove relations between the new security classes.</p

    On the Properties and Structure of Bordered Words and Generalizations

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    Combinatorics on words is a field of mathematics and theoretical computer science that is concerned with sequences of symbols called words, or strings. One class of words that are ubiquitous in combinatorics on words, and theoretical computer science more broadly, are the bordered words. The word w has a border u if u is a non-empty proper prefix and suffix of w. The word w is said to be bordered if it has a border. Otherwise w is said to be unbordered. This thesis is primarily concerned with variations and generalizations of bordered and unbordered words. In Chapter 1 we introduce the field of combinatorics on words and give a brief overview of the literature on borders relevant to this thesis. In Chapter 2 we give necessary definitions, and we present a more in-depth literature review on results on borders relevant to this thesis. In Chapter 3 we complete the characterization due to Harju and Nowotka of binary words with the maximum number of unbordered conjugates. We also show that for every number, up to this maximum, there exists a binary word with that number of unbordered conjugates. In Chapter 4 we give results on pairs of words that almost commute and anti-commute. Two words x and y almost commute if xy and yx differ in exactly two places, and they anti-commute if xy and yx differ in all places. We characterize and count the number of pairs of words that almost and anti-commute. We also characterize and count variations of almost-commuting words. Finally we conclude with some asymptotic results related to the number of almost-commuting pairs of words. In Chapter 5 we count the number of length-n bordered words with a unique border. We also show that the probability that a length-n word has a unique border tends to a constant. In Chapter 6 we present results on factorizations of words related to borders, called block palindromes. A block palindrome is a factorization of a word into blocks that turns into a palindrome if each identical block is replaced by a distinct character. Each block is a border of a central block. We call the number of blocks in a block palindrome the width of the block palindrome. The largest block palindrome of a word is the block palindrome of the word with the maximum width. We count all length-n words that have a width-t largest block palindrome. We also show that the expected width of a largest block palindrome tends to a constant. Finally we conclude with some results on another extremal variation of block palindromes, the smallest block palindrome. In Chapter 7 we present the main results of the thesis. Roughly speaking, a word is said to be closed if it contains a non-empty proper border that occurs exactly twice in the word. A word is said to be privileged if it is of length ≤ 1 or if it contains a non-empty proper privileged border that occurs exactly twice in the word. We give new and improved bounds on the number of length-n closed and privileged words over a k-letter alphabet. In Chapter 8 we work with a generalization of bordered words to pairs of words. The main result of this chapter is a characterization and enumeration result for this generalization of bordered words to multiple dimensions. In Chapter 9 we conclude by summarizing the results of this thesis and presenting avenues for future research

    The Use of digital games to enhance the physical exercise activity of the elderly : a case of Finland

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    According to the World Health Organization (WHO), population ageing is a global phenomenon, which brings both challenges and opportunities for society. The current longer expected lifespan can create opportunities for the elderly to contribute in many ways to their families and communities. However, it greatly depends on their quality of life, which is affected by many factors, including physical and functional health, social well-being, and cognitive abilities. The WHO (2012) states that physical health is one of the indicators for the elderly’s quality of life, and it declines with increasing age. Participation in regular physical exercises can help the elderly improve their physical and mental health, and this has been aided by the use of modern technologies to promote the elderly’s physical and functional health. Of these latest technologies, digital games have shown promise to improve and enhance the elderly’s physical activities through fun and engaging gameplay. The literature highlights that some commercial games in the market (e.g. Microsoft Kinect- Sports and Nintendo Wii Sports games) have the potential to improve the elderly’s physical health such as gait, balance, and fall prevention. However, researchers argue that these commercial games are not designed specifically for the elderly and their physical exercise activities. They state that most commercial games are not user-friendly for the elderly whose functional and physical abilities are limited due to their advanced years. The literature points out that more studies need to be undertaken to understand the usability and usefulness of digital games for physical exercise activities so that game designers can create elderly-friendly digital games in the future. In Finland, the government has been focusing on promoting healthy ageing and increasing home care services for the elderly. In recent years, Finnish researchers have used digital games to promote older Finns’ healthy and active ageing. The existing literature, whilst showing the potential of digital games for elderly Finns’ physical health, also acknowledges further research is needed particularly in the context of Finland. Thus, in this study, we aimed at investigating digital games to specifically assess their applications for older Finns’ physical activities, focusing on the quality of users’ experiences, and their reported ease of use and perceived usefulness. We used the mixed methods approach, which applies both qualitative and quantitative research methods. The study design included four stages: requirements gathering, analysis and design, prototyping, and evaluation. Firstly, we conducted pre-studies to elicit users’ requirements. This was followed by the analysis of the resulting data to identify trends and patterns, which fuelled ideas in the brainstorming game design and development phases. The final product was a digital game-based physical exercise called the Skiing Game. We then evaluated the Skiing Game in Finland with 21 elderly Finns (M=7, F=14, Average Age =76). By using questionnaires, observation, and interviews, we investigated user experiences, focusing on the game’s usability, and usefulness for enhancing the physical activity and wellbeing of the elderly. We also conducted a comparative test of the Skiing Game in Japan with 24 elderly Japanese participants (M=12, F=12, Average Age = 72) to further understand non-Finnish elderly users’ experiences. The findings from the usability study of the Skiing Game in Finland demonstrated that elderly Finns had a positive experience in the gameplay, and their motivation was noticeably high. It also confirmed that elderly Finns have a genuine interest in digital game-based exercises and strong intentions to play digital games as a form of physical exercise in the future. Although prior to the study most of them had negative views and misconceptions about digital games, after the gameplay their attitudes were decidedly positive. They acknowledged that whilst playing digital games could be an alternative way of exercising for them their use would primarily be when they don’t have access to their usual non-digital physical exercise. The Japanese usability of the Skiing Game showed that the elderly Japanese people also had positive user experiences in playing digital games, and also intend to use them in the future. Similarly, after playing the game they reported that their attitudes towards digital games become positive, and indicated playing digital games could be an alternative way of exercising. Although the comparison of the two studies suggests that the elderly Finns had relatively more positive experiences whilst playing the Skiing Game, compared to their Japanese counterparts, in general, both groups had a positive experience in the gameplay and showed interest in digital games as an alternative exercise. Based on the usability lessons learned from these two studies, recommendations for practitioners and designers regarding improvements in game design and development are made in this report. Implementing these modifications into future designs and further development of digital games for the elderly will improve their commercial viability and user uptake. The findings from this study can provide valuable insights, particularly for Finnish policymakers and healthcare practitioners who are keen to introduce digital games into the aged-care sector in Finland. The studies have also provided valuable insights into the optimal methods for introducing Finnish digital games to international markets, in particular, digital games tailored specifically for the physical exercise needs and motivations of the elderly. By taking into consideration the limitations of the study, we provide our future studies and further improvements of the game to be conducted

    Security and trust in cloud computing and IoT through applying obfuscation, diversification, and trusted computing technologies

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    Cloud computing and Internet of Things (IoT) are very widely spread and commonly used technologies nowadays. The advanced services offered by cloud computing have made it a highly demanded technology. Enterprises and businesses are more and more relying on the cloud to deliver services to their customers. The prevalent use of cloud means that more data is stored outside the organization’s premises, which raises concerns about the security and privacy of the stored and processed data. This highlights the significance of effective security practices to secure the cloud infrastructure. The number of IoT devices is growing rapidly and the technology is being employed in a wide range of sectors including smart healthcare, industry automation, and smart environments. These devices collect and exchange a great deal of information, some of which may contain critical and personal data of the users of the device. Hence, it is highly significant to protect the collected and shared data over the network; notwithstanding, the studies signify that attacks on these devices are increasing, while a high percentage of IoT devices lack proper security measures to protect the devices, the data, and the privacy of the users. In this dissertation, we study the security of cloud computing and IoT and propose software-based security approaches supported by the hardware-based technologies to provide robust measures for enhancing the security of these environments. To achieve this goal, we use obfuscation and diversification as the potential software security techniques. Code obfuscation protects the software from malicious reverse engineering and diversification mitigates the risk of large-scale exploits. We study trusted computing and Trusted Execution Environments (TEE) as the hardware-based security solutions. Trusted Platform Module (TPM) provides security and trust through a hardware root of trust, and assures the integrity of a platform. We also study Intel SGX which is a TEE solution that guarantees the integrity and confidentiality of the code and data loaded onto its protected container, enclave. More precisely, through obfuscation and diversification of the operating systems and APIs of the IoT devices, we secure them at the application level, and by obfuscation and diversification of the communication protocols, we protect the communication of data between them at the network level. For securing the cloud computing, we employ obfuscation and diversification techniques for securing the cloud computing software at the client-side. For an enhanced level of security, we employ hardware-based security solutions, TPM and SGX. These solutions, in addition to security, ensure layered trust in various layers from hardware to the application. As the result of this PhD research, this dissertation addresses a number of security risks targeting IoT and cloud computing through the delivered publications and presents a brief outlook on the future research directions.Pilvilaskenta ja esineiden internet ovat nykyään hyvin tavallisia ja laajasti sovellettuja tekniikkoja. Pilvilaskennan pitkälle kehittyneet palvelut ovat tehneet siitä hyvin kysytyn teknologian. Yritykset enenevässä määrin nojaavat pilviteknologiaan toteuttaessaan palveluita asiakkailleen. Vallitsevassa pilviteknologian soveltamistilanteessa yritykset ulkoistavat tietojensa käsittelyä yrityksen ulkopuolelle, minkä voidaan nähdä nostavan esiin huolia taltioitavan ja käsiteltävän tiedon turvallisuudesta ja yksityisyydestä. Tämä korostaa tehokkaiden turvallisuusratkaisujen merkitystä osana pilvi-infrastruktuurin turvaamista. Esineiden internet -laitteiden lukumäärä on nopeasti kasvanut. Teknologiana sitä sovelletaan laajasti monilla sektoreilla, kuten älykkäässä terveydenhuollossa, teollisuusautomaatiossa ja älytiloissa. Sellaiset laitteet keräävät ja välittävät suuria määriä informaatiota, joka voi sisältää laitteiden käyttäjien kannalta kriittistä ja yksityistä tietoa. Tästä syystä johtuen on erittäin merkityksellistä suojata verkon yli kerättävää ja jaettavaa tietoa. Monet tutkimukset osoittavat esineiden internet -laitteisiin kohdistuvien tietoturvahyökkäysten määrän olevan nousussa, ja samaan aikaan suuri osuus näistä laitteista ei omaa kunnollisia teknisiä ominaisuuksia itse laitteiden tai niiden käyttäjien yksityisen tiedon suojaamiseksi. Tässä väitöskirjassa tutkitaan pilvilaskennan sekä esineiden internetin tietoturvaa ja esitetään ohjelmistopohjaisia tietoturvalähestymistapoja turvautumalla osittain laitteistopohjaisiin teknologioihin. Esitetyt lähestymistavat tarjoavat vankkoja keinoja tietoturvallisuuden kohentamiseksi näissä konteksteissa. Tämän saavuttamiseksi työssä sovelletaan obfuskaatiota ja diversifiointia potentiaalisiana ohjelmistopohjaisina tietoturvatekniikkoina. Suoritettavan koodin obfuskointi suojaa pahantahtoiselta ohjelmiston takaisinmallinnukselta ja diversifiointi torjuu tietoturva-aukkojen laaja-alaisen hyödyntämisen riskiä. Väitöskirjatyössä tutkitaan luotettua laskentaa ja luotettavan laskennan suoritusalustoja laitteistopohjaisina tietoturvaratkaisuina. TPM (Trusted Platform Module) tarjoaa turvallisuutta ja luottamuksellisuutta rakentuen laitteistopohjaiseen luottamukseen. Pyrkimyksenä on taata suoritusalustan eheys. Työssä tutkitaan myös Intel SGX:ää yhtenä luotettavan suorituksen suoritusalustana, joka takaa suoritettavan koodin ja datan eheyden sekä luottamuksellisuuden pohjautuen suojatun säiliön, saarekkeen, tekniseen toteutukseen. Tarkemmin ilmaistuna työssä turvataan käyttöjärjestelmä- ja sovellusrajapintatasojen obfuskaation ja diversifioinnin kautta esineiden internet -laitteiden ohjelmistokerrosta. Soveltamalla samoja tekniikoita protokollakerrokseen, työssä suojataan laitteiden välistä tiedonvaihtoa verkkotasolla. Pilvilaskennan turvaamiseksi työssä sovelletaan obfuskaatio ja diversifiointitekniikoita asiakaspuolen ohjelmistoratkaisuihin. Vankemman tietoturvallisuuden saavuttamiseksi työssä hyödynnetään laitteistopohjaisia TPM- ja SGX-ratkaisuja. Tietoturvallisuuden lisäksi nämä ratkaisut tarjoavat monikerroksisen luottamuksen rakentuen laitteistotasolta ohjelmistokerrokseen asti. Tämän väitöskirjatutkimustyön tuloksena, osajulkaisuiden kautta, vastataan moniin esineiden internet -laitteisiin ja pilvilaskentaan kohdistuviin tietoturvauhkiin. Työssä esitetään myös näkemyksiä jatkotutkimusaiheista

    Data-driven method for enhanced corrosion assessment of reinforced concrete structures

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    Corrosion is a major problem affecting the durability of reinforced concrete structures. Corrosion related maintenance and repair of reinforced concrete structures cost multibillion USD per annum globally. It is often triggered by the ingression of carbon dioxide and/or chloride into the pores of concrete. Estimation of these corrosion causing factors using the conventional models results in suboptimal assessment since they are incapable of capturing the complex interaction of parameters. Hygrothermal interaction also plays a role in aggravating the corrosion of reinforcement bar and this is usually counteracted by applying surface protection systems. These systems have different degree of protection and they may even cause deterioration to the structure unintentionally. The overall objective of this dissertation is to provide a framework that enhances the assessment reliability of the corrosion controlling factors. The framework is realized through the development of data-driven carbonation depth, chloride profile and hygrothermal performance prediction models. The carbonation depth prediction model integrates neural network, decision tree, boosted and bagged ensemble decision trees. The ensemble tree based chloride profile prediction models evaluate the significance of chloride ingress controlling variables from various perspectives. The hygrothermal interaction prediction models are developed using neural networks to evaluate the status of corrosion and other unexpected deteriorations in surface-treated concrete elements. Long-term data for all models were obtained from three different field experiments. The performance comparison of the developed carbonation depth prediction model with the conventional one confirmed the prediction superiority of the data-driven model. The variable importance measure revealed that plasticizers and air contents are among the top six carbonation governing parameters out of 25. The discovered topmost chloride penetration controlling parameters representing the composition of the concrete are aggregate size distribution, amount and type of plasticizers and supplementary cementitious materials. The performance analysis of the developed hygrothermal model revealed its prediction capability with low error. The integrated exploratory data analysis technique with the hygrothermal model had identified the surfaceprotection systems that are able to protect from corrosion, chemical and frost attacks. All the developed corrosion assessment models are valid, reliable, robust and easily reproducible, which assist to define proactive maintenance plan. In addition, the determined influential parameters could help companies to produce optimized concrete mix that is able to resist carbonation and chloride penetration. Hence, the outcomes of this dissertation enable reduction of lifecycle costs

    On location, domination and information retrieval

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    The thesis is divided into two main branches: identifying and locatingdominating codes, and information retrieval. The former topics are motivated by the aim to locate objects in sensor networks (or other similar applications) and the latter one by the need to retrieve information in memories such as DNA data storage systems. Albeit the underlying applications, the study on these topics mainly belongs to discrete mathematics; more specically, to the elds of coding and graph theory. The sensor networks are usually represented by graphs where vertices represent the monitored locations and edges the connections between the locations. Moreover, the locations of the sensors are determined by a code. Furthermore, the desired properties of the sensor network are deeply linked with the properties of the underlying code. The number of errors in reading the data is abundant in the DNA data storage systems. In particular, there can occur more errors than a reasonable error-correcting code can handle. However, this problem is somewhat oset by the possibility to obtain multiple approximations of the same information from the data storage. Hence, the information retrieval process can be modelled by the Levenshtein's channel model, where a message is sent through multiple noisy channels and multiple outputs are received. In the rst two papers of the thesis, we introduce and study the new concepts of self- and solid-locating-dominating codes as a natural analogy to self-identifying codes with respect to locating-dominating codes. The rst paper introduces these new codes and considers them in some graphs such as the Hamming graphs. Then, in the second paper, we broaden our view on the topic by considering graph theoretical questions. We give optimal codes in multiple dierent graph classes and some more general results using concepts such as the Dilworth number and graph complements. The third paper focuses on the q-ary Hamming spaces. In particular, we disprove a conjecture proposed by Goddard and Wash related to identifying codes. In the fourth paper, we return to self- and solid-locating-dominating codes and give optimal codes in some graph classes and consider their densities in innite graphs. In the fth paper, we consider information retrieval in memories; in particular, the Levenshtein's channel model. In the channel model, we transmit some codeword belonging to the binary Hamming space through multiple identical channels. With the help of multiple dierent outputs, we give a list of codewords which may have been sent. In the paper, we study the number of channels required to have a rather small (constant) list size when the properties of the channels, the code and the dimension of the Hamming space are xed. In particular, we give an exact relation between the number of channels and the asymptotic value of the maximum list size.Väitöskirja käsittelee kahta aihetta: identioivia ja paikantavia peittokoodeja sekä tiedon noutamista muistista. Ensimmäisen aiheen motivaationa on objektien paikantaminen sensoriverkoista (sekä muut samankaltaiset sovellukset) ja jälkimmäisen tiedonnouto DNA-muisteista. Näiden aiheiden tutkimus kuuluu diskreettiin matematiikkaan, täsmällisemmin koodaus- ja graa-teoriaan. Sensoriverkkoja kuvataan yleensä graafeilla, joissa solmut esittävät tarkkailtuja kohteita ja viivat yhteyksiä näiden kohteiden välillä. Edelleen sensorien paikat määräytyvät annetun koodin perusteella. Tästä johtuen sensoriverkon halutut ominaisuudet pohjautuvat vahvasti alla olevaan koodiin. Luettaessa tietoa DNA-muisteista tapahtuvien virheiden määrä saattaa olla erittäin suuri; erityisesti suurempi kuin kiinnitetyn virheitä korjaavan koodin korjauskyky. Toisaalta tilanne ei ole aivan näin ongelmallinen, sillä DNA-muisteista voidaan saada useita eri arvioita muistiin tallennetusta tiedosta. Näistä syistä johtuen tietojen noutamista DNA-muisteista voidaan mallintaa käyttäen Levenshteinin kanavamallia. Kanavamallissa yksi viesti lähetetään useiden häiriöisten kanavien kautta ja näin vastaanotetaan useita viestejä (yksi jokaisesta kanavasta). Väitöskirjan kahdessa ensimmäisessä julkaisussa esitellään ja tutkitaan uusia paikantavien peittokoodien luokkia, jotka pohjautuvat aiemmin tutkittuihin itse-identioiviin koodeihin. Ensimmäisessä julkaisussa on esitelty nämä koodiluokat sekä tutkittu niitä joissain graafeissa kuten Hammingin graafeissa. Tämän jälkeen toisessa julkaisussa käsitellään yleisiä graa-teoreettisia kysymyksiä. Julkaisussa esitetään optimaaliset koodit useille graaperheille sekä joitain yleisempiä tuloksia käyttäen mm. Dilworthin lukua sekä graakomplementteja. Kolmas julkaisu keskittyy q-arisiin Hammingin avaruuksiin. Erityisesti julkaisussa todistetaan vääräksi Goddardin ja Washin aiemmin esittämä identioivia koodeja koskeva otaksuma. Neljäs artikkeli käsittelee jo kahdessa ensimmäisessä artikkelissa esiteltyjä paikantavien peittokoodien luokkia. Artikkeli esittää optimaalisia koodeja useille graaperheille sekä käsittelee äärettömiä graafeja. Viides artikkeli käsittelee tiedonnoutoa ja erityisesti Levenshteinin kanavamallia. Kanavamallissa binääriseen Hammingin avaruuteen kuuluva koodisana lähetetään useiden identtisten kanavien läpi. Näistä kanavista vastaanotetaan useita eri arvioita lähetetystä koodisanasta ja rakennetaan lista mahdollisesti lähetetyistä sanoista. Artikkelissa tutkitaan kuinka monta kanavaa tarvitaan, jotta tämän listan koko on pieni (vakio), kun kanavien ominaisuudet, koodi ja Hammingin avaruuden dimensio on kiinnitetty. Erityisesti löydetään täsmällinen suhde kanavien lukumäärän ja asymptoottisesti maksimaalisen listan koon välille

    On multiobjective optimization from the nonsmooth perspective

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    Practical applications usually have multiobjective nature rather than having only one objective to optimize. A multiobjective problem cannot be solved with a single-objective solver as such. On the other hand, optimization of only one objective may lead to an arbitrary bad solutions with respect to other objectives. Therefore, special techniques for multiobjective optimization are vital. In addition to multiobjective nature, many real-life problems have nonsmooth (i.e. not continuously differentiable) structure. Unfortunately, many smooth (i.e. continuously differentiable) methods adopt gradient-based information which cannot be used for nonsmooth problems. Since both of these characteristics are relevant for applications, we focus here on nonsmooth multiobjective optimization. As a research topic, nonsmooth multiobjective optimization has gained only limited attraction while the fields of nonsmooth single-objective and smooth multiobjective optimization distinctively have attained greater interest. This dissertation covers parts of nonsmooth multiobjective optimization in terms of theory, methodology and application. Bundle methods are widely considered as effective and reliable solvers for single-objective nonsmooth optimization. Therefore, we investigate the use of the bundle idea in the multiobjective framework with three different methods. The first one generalizes the single-objective proximal bundle method for the nonconvex multiobjective constrained problem. The second method adopts the ideas from the classical steepest descent method into the convex unconstrained multiobjective case. The third method is designed for multiobjective problems with constraints where both the objectives and constraints can be represented as a difference of convex (DC) functions. Beside the bundle idea, all three methods are descent, meaning that they produce better values for each objective at each iteration. Furthermore, all of them utilize the improvement function either directly or indirectly. A notable fact is that none of these methods use scalarization in the traditional sense. With the scalarization we refer to the techniques transforming a multiobjective problem into the single-objective one. As the scalarization plays an important role in multiobjective optimization, we present one special family of achievement scalarizing functions as a representative of this category. In general, the achievement scalarizing functions suit well in the interactive framework. Thus, we propose the interactive method using our special family of achievement scalarizing functions. In addition, this method utilizes the above mentioned descent methods as tools to illustrate the range of optimal solutions. Finally, this interactive method is used to solve the practical case studies of the scheduling the final disposal of the spent nuclear fuel in Finland.Käytännön optimointisovellukset ovat usein luonteeltaan ennemmin moni- kuin yksitavoitteisia. Erityisesti monitavoitteisille tehtäville suunnitellut menetelmät ovat tarpeen, sillä monitavoitteista optimointitehtävää ei sellaisenaan pysty ratkaisemaan yksitavoitteisilla menetelmillä eikä vain yhden tavoitteen optimointi välttämättä tuota mielekästä ratkaisua muiden tavoitteiden suhteen. Monitavoitteisuuden lisäksi useat käytännön tehtävät ovat myös epäsileitä siten, etteivät niissä esiintyvät kohde- ja rajoitefunktiot välttämättä ole kaikkialla jatkuvasti differentioituvia. Kuitenkin monet optimointimenetelmät hyödyntävät gradienttiin pohjautuvaa tietoa, jota ei epäsileille funktioille ole saatavissa. Näiden molempien ominaisuuksien ollessa keskeisiä sovelluksia ajatellen, keskitytään tässä työssä epäsileään monitavoiteoptimointiin. Tutkimusalana epäsileä monitavoiteoptimointi on saanut vain vähän huomiota osakseen, vaikka sekä sileä monitavoiteoptimointi että yksitavoitteinen epäsileä optimointi erikseen ovat aktiivisia tutkimusaloja. Tässä työssä epäsileää monitavoiteoptimointia on käsitelty niin teorian, menetelmien kuin käytännön sovelluksien kannalta. Kimppumenetelmiä pidetään yleisesti tehokkaina ja luotettavina menetelminä epäsileän optimointitehtävän ratkaisemiseen ja siksi tätä ajatusta hyödynnetään myös tässä väitöskirjassa kolmessa eri menetelmässä. Ensimmäinen näistä yleistää yksitavoitteisen proksimaalisen kimppumenetelmän epäkonveksille monitavoitteiselle rajoitteiselle tehtävälle sopivaksi. Toinen menetelmä hyödyntää klassisen nopeimman laskeutumisen menetelmän ideaa konveksille rajoitteettomalle tehtävälle. Kolmas menetelmä on suunniteltu erityisesti monitavoitteisille rajoitteisille tehtäville, joiden kohde- ja rajoitefunktiot voidaan ilmaista kahden konveksin funktion erotuksena. Kimppuajatuksen lisäksi kaikki kolme menetelmää ovat laskevia eli ne tuottavat joka kierroksella paremman arvon jokaiselle tavoitteelle. Yhteistä on myös se, että nämä kaikki hyödyntävät parannusfunktiota joko suoraan sellaisenaan tai epäsuorasti. Huomattavaa on, ettei yksikään näistä menetelmistä hyödynnä skalarisointia perinteisessä merkityksessään. Skalarisoinnilla viitataan menetelmiin, joissa usean tavoitteen tehtävä on muutettu sopivaksi yksitavoitteiseksi tehtäväksi. Monitavoiteoptimointimenetelmien joukossa skalarisoinnilla on vankka jalansija. Esimerkkinä skalarisoinnista tässä työssä esitellään yksi saavuttavien skalarisointifunktioiden perhe. Yleisesti saavuttavat skalarisointifunktiot soveltuvat hyvin interaktiivisten menetelmien rakennuspalikoiksi. Täten kuvaillaan myös esiteltyä skalarisointifunktioiden perhettä hyödyntävä interaktiivinen menetelmä, joka lisäksi hyödyntää laskevia menetelmiä optimaalisten ratkaisujen havainnollistamisen apuna. Lopuksi tätä interaktiivista menetelmää käytetään aikatauluttamaan käytetyn ydinpolttoaineen loppusijoitusta Suomessa
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