Finitary Abstract Elementary Classes

The research in model theory has extended from the study of elementary classes to non-elementary classes, i.e. to classes which are not completely axiomatizable in elementary logic. The main theme has been the attempt to generalize tools from elementary stability theory to cover more applications arising in other branches of mathematics. In this doctoral thesis we introduce finitary abstract elementary classes, a non-elementary framework of model theory. These classes are a special case of abstract elementary classes (AEC), introduced by Saharon Shelah in the 1980's. We have collected a set of properties for classes of structures, which enable us to develop a 'geometric' approach to stability theory, including an independence calculus, in a very general framework. The thesis studies AEC's with amalgamation, joint embedding, arbitrarily large models, countable Löwenheim-Skolem number and finite character. The novel idea is the property of finite character, which enables the use of a notion of a weak type instead of the usual Galois type. Notions of simplicity, superstability, Lascar strong type, primary model and U-rank are inroduced for finitary classes. A categoricity transfer result is proved for simple, tame finitary classes: categoricity in any uncountable cardinal transfers upwards and to all cardinals above the Hanf number. Unlike the previous categoricity transfer results of equal generality the theorem does not assume the categoricity cardinal being a successor. The thesis consists of three independent papers. All three papers are joint work with Tapani Hyttinen.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Turing and the Trans-Pacific Partnership: Intellectual Property, Public Health, and Access to Essential Medicines

A recent controversy in the United States over drug pricing by Turing Pharmaceuticals AG has raised larger issues in respect of intellectual property, access to medicines, and the Trans-Pacific Partnership (TPP). In August 2015, Turing Pharmaceuticals AG – a private biopharmaceutical company with offices in New York, the United States, and Zug, Switzerland - acquired the exclusive marketing rights to Daraprim in the United States from Impax Laboratories Incorporated. Martin Shkreli, Turing’s Founder and Chief Executive Officer, maintained: “The acquisition of Daraprim and our toxoplasmosis research program are significant steps along Turing’s path of bringing novel medications to patients with serious disorders, some of whom often go undiagnosed and untreated.” He emphasised: “We intend to invest in the development of new drug candidates that we hope will yield an even better clinical profile, and also plan to launch an educational effort to help raise awareness and improve diagnosis for patients with toxoplasmosis.” In September 2015, there was much public controversy over the decision of Martin Shkreli to raise the price of a 62 year old drug, Daraprim, from $US13.50 to $US750 a pill. The drug is particularly useful in respect to the treatment and prevention of malaria, and in the treatment of infections in individuals with HIV/AIDS. Daraprim is listed on the World Health Organization’s (WHO) List of Essential Medicines. In the face of much criticism, Martin Shkreli has said that he will reduce the price of Daraprim. He observed: “We've agreed to lower the price on Daraprim to a point that is more affordable and is able to allow the company to make a profit, but a very small profit.” He maintained: “We think these changes will be welcomed.” However, he has been vague and ambiguous about the nature of the commitment. Notably, the lobby group, Pharmaceutical Research and Manufacturers of America (PhARMA), disassociated itself from the claims of Turing Pharmaceuticals. The group said: “PhRMA members have a long history of drug discovery and innovation that has led to increased longevity and improved lives for millions of patients.” The group noted: “Turing Pharmaceutical is not a member of PhRMA and we do not embrace either their recent actions or the conduct of their CEO.” The biotechnology peak body Biotechnology Industry Organization also sought to distance itself from Turing Pharmaceuticals. A hot topic: United States political debate about access to affordable medicines This controversy over Daraprim is unusual – given the age of drug concerned. Daraprim is not subject to patent protection. Nonetheless, there remains a monopoly in respect of the marketplace. Drug pricing is not an isolated problem. There have been many concerns about drug pricing – particularly in respect of essential medicines for HIV/AIDS, tuberculosis, and malaria. This recent controversy is part of a larger debate about access to affordable medicines. The dispute raises larger issues about healthcare, consumer rights, competition policy, and trade. The Daraprim controversy has provided impetus for law reform in the US. US Presidential Candidate Hillary Clinton commented: “Price gouging like this in this specialty drug market is outrageous.” In response to her comments, the Nasdaq Biotechnology Index fell sharply. Hillary Clinton has announced a prescription drug reform plan to protect consumers and promote innovation – while putting an end to profiteering. On her campaign site, she has emphasised that “affordable healthcare is a basic human right.” Her rival progressive candidate, Bernie Sanders, was also concerned about the price hike. He wrote a letter to Martin Shkreli, complaining about the price increase for the drug Daraprim. Sanders said: “The enormous, overnight price increase for Daraprim is just the latest in a long list of skyrocketing price increases for certain critical medications.” He has pushed for reforms to intellectual property to make medicines affordable. The TPP and intellectual property The Daraprim controversy and political debate raises further issues about the design of the TPP. The dispute highlights the dangers of extending the rights of pharmaceutical drug companies under intellectual property, investor-state dispute settlement, and drug administration. Recently, the civil society group Knowledge Ecology International published a leaked draft of the Intellectual Property Chapter of the TPP. Knowledge Ecology International Director, James Love, was concerned the text revealed that the US “continues to be the most aggressive supporter of expanded intellectual property rights for drug companies.” He was concerned that “the proposals contained in the TPP will harm consumers and in some cases block innovation.” James Love feared: “In countless ways, the Obama Administration has sought to expand and extend drug monopolies and raise drug prices.” He maintained: “The astonishing collection of proposals pandering to big drug companies make more difficult the task of ensuring access to drugs for the treatment of cancer and other diseases and conditions.” Love called for a different approach to intellectual property and trade: “Rather than focusing on more intellectual property rights for drug companies, and a death-inducing spiral of higher prices and access barriers, the trade agreement could seek new norms to expand the funding of medical research and development (R&D) as a public good, an area where the US has an admirable track record, such as the public funding of research at the National Institutes of Health (NIH) and other federal agencies.” In addition, there has been much concern about the Investment Chapter of the TPP. The investor-state dispute settlement regime would enable foreign investors to challenge government policy making, which affected their investments. In the context of healthcare, there is a worry that pharmaceutical drug companies will deploy their investor rights to challenge public health measures – such as, for instance, initiatives to curb drug pricing and profiteering. Such concerns are not merely theoretical. Eli Lilly has brought an investor action against the Canadian Government over the rejection of its drug patents under the investor-state dispute settlement regime of the North American Free Trade Agreement (NAFTA). The Health Annex to the TPP also raises worries that pharmaceutical drug companies will able to object to regulatory procedures in respect of healthcare. It is disappointing that the TPP – in the leaks that we have seen – has only limited recognition of the importance of access to essential medicines. There is a need to ensure that there are proper safeguards to provide access to essential medicines – particularly in respect of HIV/AIDs, malaria, and tuberculosis. Moreover, there must be protection against drug profiteering and price gouging in any trade agreement. There should be strong measures against the abuse of intellectual property rights. The dispute over Turing Pharmaceuticals AG and Daraprim is an important cautionary warning in respect of some of the dangers present in the secret negotiations in respect of the TPP. There is a need to preserve consumer rights, competition policy, and public health in trade negotiations over an agreement covering the Pacific Rim.

Save Left Shark: Katy Perry, Intellectual Property, and 3D Printing

There has been much interest in how intellectual property law, policy and practice will adapt to the emergence of 3D printing and the maker movement. Intellectual property lawyers will have to grapple with the impact of additive manufacturing upon a variety of forms of intellectual property — including copyright law, trade mark law, designs law, patent law and trade secrets. The disruptive technology of 3D printing will both pose opportunities and challenges for legal practitioners and policy makers.A performance by pop princess Katy Perry at the 2015 Super Bowl has sparked a public controversy over intellectual property, internet memes and 3D printing.

Inventing the Future: Intellectual Property and 3D Printing

A new technology – 3D printing – has the potential to make radical changes to aspects of the way in which we live. Put simply, it allows people to download designs and turn them into physical objects by laying down successive layers of material. Replacements or parts for household objects such as toys, utensils and gadgets could become available at the press of a button. With this innovation, however, comes the need to consider impacts on a wide range of forms of intellectual property, as Dr Matthew Rimmer explains. 3D Printing is the latest in a long line of disruptive technologies – including photocopiers, cassette recorders, MP3 players, personal computers, peer to peer networks, and wikis – which have challenged intellectual property laws, policies, practices, and norms. As The Economist has observed, ‘Tinkerers with machines that turn binary digits into molecules are pioneering a whole new way of making things—one that could well rewrite the rules of manufacturing in much the same way as the PC trashed the traditional world of computing.’

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Digitaalisten teosten maailmanlaajuinen rekisteröinti ja käyttömaksujen kerääminen internetissä

The vastly increased popularity of the Internet as an effective publication and distribution channel of digital works has created serious challenges to enforcing intellectual property rights. Works are widely disseminated on the Internet, with and without permission. This thesis examines the current problems with licence management and copy protection and outlines a new method and system that solve these problems. The WARP system (Works, Authors, Royalties, and Payments) is based on global registration and transfer monitoring of digital works, and accounting and collection of Internet levy funded usage fees payable to the authors and right holders of the works. The detection and counting of downloads is implemented with origrams, short and original parts picked from the contents of the digital work. The origrams are used to create digests, digital fingerprints that identify the piece of work transmitted over the Internet without the need to embed ID tags or any other easily removable metadata in the file.

Sirex woodwasp range expansion in Australia: performance and parasitism on two commercial pine species

Sirex woodwasp was detected in Queensland in 2009 and rapidly established in softwood plantations (Pinus radiata and P. taeda) in southern border regions. Biocontrol inoculations of Deladenus siricidicola began soon after, and adults were monitored to assess the success of the programme. Wasp size, sex ratios, emergence phenology and nematode parasitism rates were recorded, along with the assessment of wild-caught females. Patterns varied within and among seasons, but overall, P. taeda appeared to be a less suitable host than P. radiata, producing smaller adults, lower fat body content and fewer females. Sirex emerging from P. taeda also showed lower levels of nematode parasitism, possibly due to interactions with the more abundant blue-stain fungus in this host. Sirex adults generally emerged between November and March, with distinct peaks in January and March, separated by a marked drop in emergence in early February. Temperature provided the best correlate of seasonal emergence, with fortnights with higher mean minimum temperatures having higher numbers of Sirex emerging. This has implications for the anticipated northward spread of Sirex into sub-tropical coastal plantation regions. Following four seasons of inundative release of nematodes in Queensland, parasitism rates remain low and have resulted in only partial sterilization of infected females.

Letter of trustees to congregation regarding opening of Oliver Street and affect on congregation's property

Digital image

On-farm Campylobacter and Escherichia coli in commercial broiler chickens: Re-used bedding does not influence Campylobacter emergence and levels across sequential farming cycles

Limitations in quality bedding material have resulted in the growing need to re-use litter during broiler farming in some countries, which can be of concern from a food-safety perspective. The aim of this study was to compare the Campylobacter levels in ceca and litter across three litter treatments under commercial farming conditions. The litter treatments were (a) the use of new litter after each farming cycle; (b) an Australian partial litter re-use practice; and (c) a full litter re-use practice. The study was carried out on two farms over two years (Farm 1, from 2009–2010 and Farm 2, from 2010–2011), across three sheds (35,000 to 40,000 chickens/shed) on each farm, adopting three different litter treatments across six commercial cycles. A random sampling design was adopted to test litter and ceca for Campylobacter and Escherichia coli, prior to commercial first thin-out and final pick-up. Campylobacter levels varied little across litter practices and farming cycles on each farm and were in the range of log 8.0–9.0 CFU/g in ceca and log 4.0–6.0 MPN/g for litter. Similarly the E. coli in ceca were ∼log 7.0 CFU/g. At first thin-out and final pick-up, the statistical analysis for both litter and ceca showed that the three-way interaction (treatments by farms by times) was highly significant (P < 0.01), indicating that the patterns of Campylobacter emergence/presence across time vary between the farms, cycles and pickups. The emergence and levels of both organisms were not influenced by litter treatments across the six farming cycles on both farms. Either C. jejuni or C. coli could be the dominant species across litter and ceca, and this phenomenon could not be attributed to specific litter treatments. Irrespective of the litter treatments in place, cycle 2 on Farm 2 remained campylobacter-free. These outcomes suggest that litter treatments did not directly influence the time of emergence and levels of Campylobacter and E. coli during commercial farming.

Queensland Spanner Crab Fishery: Commercial quota setting for June 2016 – May 2018

The Queensland (QLD) fishery for spanner crabs primarily lands live crab for export overseas, with gross landings valued around A$5 million per year. Quota setting rules are used to assess and adjust total allowable harvest (quota) around an agreed target harvest of 1631 t and capped at a maximum of 2000 t. The quota varies based on catch rate indicators from the commercial fishery and a fishery independent survey. Quota management applies only to ‘Managed Area A’ which includes waters between Rockhampton and the New South Wales (NSW) border. This report has been prepared to inform Fisheries Queensland (Department of Agriculture and Fisheries) and stakeholders of catch trends and the estimated quota of spanner crabs in Managed Area A for the forthcoming annual quota periods (1 June 2016–31 May 2018). The quota calculations followed the methodology developed by the crab fishery Scientific Advisory Group (SAG) between November 2007 and March 2008. The QLD total reported spanner crab harvest was 1170 t for the 2015 calendar year. In 2015, a total of 55 vessels were active in the QLD fishery, down from 262 vessels at the fishery’s peak activity in 1994. Recent spanner crab harvests from NSW waters average about 125 t per year, but fell to 80 t in 2014–2015. The spanner crab Managed Area A commercial standardised catch rate averaged 0.818 kg per net-lift in 2015, 22.5% below the target level of 1.043. Compared to 2014, mean catch rates in 2015 were marginally improved south of Fraser Island. The NSW–QLD survey catch rate in 2015 was 20.541 crabs per ground-line, 33% above the target level of 13.972. This represented an increase in survey catch rates of about four crabs per groundline, compared to the 2014 survey. The QLD spanner crab total allowable harvest (quota) was set at 1923 t in the 2012-13 and 2013-14 fishing years, 1777 t in 2014-15 and 1631 t in 2015-16. The results from the current analysis rules indicate that the quota for the next two fishing years be retained at the base quota of 1631 t.

Queensland Spanner Crab Fishery : Commercial quota setting for June 2015 – May 2016

The Australian fishery for spanner crabs is the largest in the world, with the larger Queensland (QLD) sector’s landings primarily exported live overseas and GVP valued ~A$5 million per year. Spanner crabs are unique in that they may live up to 15 years, significantly more than blue swimmer crabs (Portunus armatus) and mud crabs (Scylla serrata), the two other important crab species caught in Queensland. Spanner crabs are caught using a flat net called a dilly, on which the crabs becoming entangled via the swimming legs. Quota setting rules are used to assess and adjust total allowable harvest (quota) around an agreed target harvest of 1631 t and capped at a maximum of 2000 t. The quota varies based on catch rate indicators from the commercial fishery and a fishery-independent survey from the previous two years, compared to target reference points. Quota management applies only to ‘Managed Area A’ which includes waters between Rockhampton and the New South Wales (NSW) border. This report has been prepared to inform Fisheries Queensland (Department of Agriculture and Fisheries) and stakeholders of catch trends and the estimated quota of spanner crabs in Managed Area A for the forthcoming quota period (1 June 2015–31 May 2016). The quota calculations followed the methodology developed by the crab fishery Scientific Advisory Group (SAG) between November 2007 and March 2008. The total reported spanner crab harvest was 917 t for the 2014 calendar year, almost all of which was taken from Managed Area A. In 2014, a total of 59 vessels were active in the QLD fishery, the lowest number since the peak in 1994 of 262 vessels. Recent spanner crab harvests from NSW waters have been about 125 t per year. The spanner crab Managed Area A commercial standardised catch rate averaged 0.739 kg per net-lift in 2014, 24% below the target level of 1.043. Mean catch rates declined in the commercial fishery in 2014, although the magnitude of the decreases was highest in the area north of Fraser Island. The NSW–QLD survey catch rate in 2014 was 16.849 crabs per ground-line, 22% above the target level of 13.972. This represented a decrease in survey catch rates of 0.366 crabs per ground-line, compared to the 2013 survey. The Queensland spanner crab total allowable harvest (quota) was set at 1923 t in 2012 and 2013. In 2014, the quota was calculated at the base level of 1631 t. However, given that the 2012 fisheryindependent survey was not undertaken for financial reasons, stakeholders proposed that the total allowable commercial catch (TACC) be decreased to 1777 t; a level that was halfway between the 2012/13 quota of 1923 t and the recommended base quota of 1631 t. The results from the current analysis indicate that the quota for the 2015-2016 financial year be decreased from 1777 t to the base quota of 1631 t.

Mikä on ihme ja mitä ihmeistä voidaan tietää? : Keskustelu ihmeistä uusimmassa englanninkielisessä uskonnonfilosofiassa

What is a miracle and what can we know about miracles? A discussion of miracles in anglophone philosophy of religion literature since the late 1960s. The aim of this study is to systematically describe and philosophically examine the anglophone discussion on the subject of miracles since the latter half of the 1960s. The study focuses on two salient questions: firstly, what I will term the conceptual-ontological question of the extent to which we can understand miracles and, secondly, the epistemological question of what we can know about miracles. My main purpose in this study is to examine the various viewpoints that have been submitted in relation to these questions, how they have been argued and on what presuppositions these arguments have been based. In conducting the study, the most salient dimension of the various discussions was found to relate to epistemological questions. In this regard, there was a notable confrontation between those scholars who accept miracles and those who are sceptical of them. On the conceptual-ontological side I recognised several different ways of expressing the concept of miracle . I systematised the discussion by demonstrating the philosophical boundaries between these various opinions. The first and main boundary was related to ontological knowledge. On one side of this boundary I placed the views which were based on realism and objectivism. The proponents of this view assumed that miraculousness is a real property of a miraculous event regardless of how we can perceive it. On the other side I put the views which tried to define miraculousness in terms of subjectivity, contextuality and epistemicity. Another essential boundary which shed light on the conceptual-ontological discussion was drawn in relation to two main views of nature. The realistic-particularistic view regards nature as a certain part of reality. The adherents of this presupposition postulate a supernatural sphere alongside nature. Alternatively, the nominalist-universalist view understands nature without this kind of division. Nature is understood as the entire and infinite universe; the whole of reality. Other, less important boundaries which shed light on the conceptual-ontological discussion were noted in relation to views regarding the laws of nature, for example. I recognised that the most important differences between the epistemological approaches were in the different views of justification, rationality, truth and science. The epistemological discussion was divided into two sides, distinguished by their differing assumptions in relation to the need for evidence. Adherents of the first (and noticeably smaller) group did not see any epistemological need to reach a universal and common opinion about miracles. I discovered that these kinds of views, which I called non-objectivist, had subjectivist and so-called collectivist views of justification and a contextualist view of rationality. The second (and larger) group was mainly interested in discerning the grounds upon which to establish an objective and conclusive common view in relation to the epistemology of miracles. I called this kind of discussion an objectivist discussion and this kind of approach an evidentialist approach. Most of the evidentialists tried to defend miracles and the others attempted to offer evidence against miracles. Amongst both sides, there were many different variations according to emphasis and assumption over how they saw the possibilities to prove their own view. The common characteristic in all forms of evidentialism was a commitment to an objectivist notion of rationality and a universalistic notion of justification. Most evidentialists put their confidence in science in one way or another. Only a couple of philosophers represented the most moderate version of evidentialism; they tried to remove themselves from the apparent controversy and contextualised the different opinions in order to make some critical comments on them. I called this kind of approach a contextualising form of evidentialism. In the final part of the epistemological chapter, I examined the discussion about the evidential value of miracles, but nothing substantially new was discovered concerning the epistemological views of the authors.

Hautamuistomerkki elämän ja kuoleman tulkitsijana : Heikki Häiväojan, Kain Tapperin ja Matti Peltokankaan tekemät hautamuistomerkit 1952-2002

Grave sculpture as interpreter of life and death. Grave sculptures done by Heikki Häiväoja, Kain Tapper and Matti Peltokangas 1952-2002. The thoughts of Philippe Ariès and Erwin Panofsky on western funeral art constitute the starting point of this study. These scholars speak about the 20th century as a period of decline regarding western funeral art. The reason for this situation lies, according to them, in the fact that death has been rejected and become a private affair in modern society. Especially Panofsky sees an important reason for the decay of funeral art also in the separation of death from religion. In this study, I approach the view of Ariès and Panofsky from the angle of Finnish funeral art. The subject of the study is grave sculptures of three Finnish sculptors: Heikki Häiväoja, Kain Tapper and Matti Peltokangas, from 1952 to 2002. (The analysis of the grave sculptures has been performed with the Iconology of Erwin Panofsky. The analysis has been deepened by the ideas of a graveyard as a semiotic text according to Werner Enninger and Christa Schwens. In order to confirm their argumentation, they analyse the graveyard text with the model of communicative functions of Roman Jakobson and verify that the graveyard is a cultural text according to Juri Lotman.) Results of the study In the grave sculptures of the sculptors, different worldviews appear alongside Christian thoughts indicating a new stage in the tradition of funeral art. In the grave sculptures characterised as Christian, the view of life after death is included. In these memorials the direction of life is prospective, pointing to the life beyond. Death is a border, beyond which one is unable to see. Nevertheless the border is open or marked by the cross. On this open border, death is absence of pain, glory and new unity. In memorials with different worldviews, the life beyond is a possibility which is not excluded. Memorials interpret life retrospectively; life is a precious memory which wakens grief and longing. Many memorials have metaphysical and mystic features. In spite of democratization the order and valuation of social classes appear in some memorials. The old order also materializes in the war memorials relating the same destiny of the deceased. Different burial places, nevertheless, do not indicate social inequality but are rather signs of diversity. The sculptors' abstract means of modern funeral art deepen the handling of the subject matter of death and reveal the mystery of it. Grave sculptures are a part of Finnish and sacral modern art, and there is an interaction between funeral art and modern art. Modern art acquires a new dimension, when grave sculptures become a part of its field. Grave sculptures offer an alternative to anonymous burying. The memorial is a sign of the end of life; it gives death significance and publicity and creates a relation to the past of the society. In this way, grave sculptures are a part of the chain of memory of the western funeral art, which extends throughout Antiquity until ancient Egypt. (In this study I have spoken of funeral art as a chain of memory using the thoughts of Danièle Hervieu-Léger.) There are no signs of decay in the grave sculptures, on the contrary the tradition of funeral art continues in them as a search for the meaning of life and death and as an intuitive interpretation of death. As such, grave sculptures are part of the Finnish discussion of death.