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Per Martin-Löf

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Per Erik Rutger Martin-Löf ( / l ɒ f / ; Swedish: [ˈmǎʈːɪn ˈløːv] ; born 8 May 1942) is a Swedish logician , philosopher , and mathematical statistician . He is internationally renowned for his work on the foundations of probability , statistics, mathematical logic, and computer science . Since the late 1970s, Martin-Löf's publications have been mainly in logic . In philosophical logic , Martin-Löf has wrestled with the philosophy of logical consequence and judgment , partly inspired by the work of Brentano , Frege , and Husserl . In mathematical logic , Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics; Martin-Löf's work on type theory has influenced computer science .

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72-434: Until his retirement in 2009, Per Martin-Löf held a joint chair for Mathematics and Philosophy at Stockholm University . His brother Anders Martin-Löf is now emeritus professor of mathematical statistics at Stockholm University; the two brothers have collaborated in research in probability and statistics. The research of Anders and Per Martin-Löf has influenced statistical theory, especially concerning exponential families ,

144-400: A 1966 article The definition of random sequences that gave the first suitable definition of a random sequence. Earlier researchers such as Richard von Mises had attempted to formalize the notion of a test for randomness in order to define a random sequence as one that passed all tests for randomness; however, the precise notion of a randomness test was left vague. Martin-Löf's key insight

216-790: A Danish schoolteacher, using aluminium rings on European starlings . Mortensen had tried using zinc rings as early as 1890 but found these were too heavy. The first ringing scheme was established in Germany by Johannes Thienemann in 1903 at the Rossitten Bird Observatory on the Baltic Coast of East Prussia. This was followed by Hungary in 1908, Great Britain in 1909 (by Arthur Landsborough Thomson in Aberdeen and Harry Witherby in England ), Yugoslavia in 1910 and

288-466: A Swedish zoological journal: This paper was soon cited in leading international journals, and this paper continues to be cited. In the biology and statistics of birds , there are several problems of missing data . Martin-Löf's first paper discussed the problem of estimating the mortality rates of the Dunlin species, using capture-recapture methods. The problem of determining the biological sex of

360-491: A bird, which is extremely difficult for humans, is one of the first examples in Martin-Löf's lectures on statistical models . Martin-Löf wrote a licenciate thesis on probability on algebraic structures, particularly semigroups, while a student of Ulf Grenander at Stockholm University. Martin-Löf developed innovative approaches to statistical theory . In his paper "On Tables of Random Numbers", Kolmogorov observed that

432-469: A constant of their Kolmogorov complexity). Per Martin-Löf has done important research in mathematical statistics , which (in the Swedish tradition) includes probability theory and statistics . Per Martin-Löf began bird watching in his youth and remains an enthusiastic bird-watcher. As a teenager, he published an article on estimating the mortality rates of birds, using data from bird ringing , in

504-556: A department. Stockholm University offers courses at both undergraduate and advanced level. There are 190 study programmes in total, including 75 master's programmes taught in English, and 1,700 courses to choose from within human science and science. Students can choose between studying one or more free-standing courses, that each may last between five weeks and one semester, or apply for a full study programme. Stockholm university offers 4 Bachelor Programmes taught in English, which are

576-543: A detailed analysis of the expectation–maximization (EM) method for estimation using data from exponential families, especially with missing data . Sundberg credits a formula, later known as the Sundberg formula, to previous manuscripts of the Martin-Löf brothers, Per and Anders . Many of these results reached the international scientific community through the 1976 paper on the expectation–maximization (EM) method by Arthur P. Dempster , Nan Laird , and Donald Rubin , which

648-399: A distance without visual confirmation. The use of satellite transmitters for bird movements is currently restricted by transmitter size – to species larger than about 400g. They may be attached to migratory birds (geese, swans, cranes, penguins etc.) or other species such as penguins that undertake long-distance movements. Individuals may be tracked by satellites for immense distances, for

720-401: A letter or letters, and the combination of colour and letters uniquely identifies the bird. These can then be read in the field, through binoculars, meaning that there is no need to re-trap the birds. Because the tags are attached to feathers, they drop off when the bird moults . Another method is imping in a brightly coloured false feather instead of a natural feather. A patagial tag is

792-422: A nasal saddle can plug the nostrils. Neck collars made of expandable, non-heat-conducting plastic are useful for larger birds such as geese. Many institutions that ring birds offer demonstrations for the public, where experts ring live birds while highlighting the steps of the process and answering questions from the public. Educating visitors about the technique helps to spread accurate information about it to

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864-526: A notion of "repetitive structure" and a novel treatment of sufficient statistics, in which one-parameter exponential families were characterized. He provided a category-theoretic approach to nested statistical models , using finite-sample principles. Before (and after) Martin-Löf, such nested models have often been tested using chi-square hypothesis tests, whose justifications are only asymptotic (and so irrelevant to real problems, which always have finite samples). Martin-Löf's student, Rolf Sundberg, developed

936-514: A permanent metal ring. Similar to coloured rings or bands are leg-flags, usually made of darvic and used in addition to numbered metal rings. Although leg-flags may sometimes have individual codes on them, their more usual use is to code for the sites where the birds were ringed in order to elucidate their migration routes and staging areas. The use of colour-coded leg-flags is part of an international program, originated in Australia in 1990, by

1008-402: A permanent tag held onto the wing by a rivet punched through the patagium . Wing tags can be a problem for some smaller raptors like harriers as their conspicuous nature makes them more obvious targets for other more powerful predators like peregrine falcons . Where detailed information is needed on individual movements, tiny radio transmitters can be fitted on to birds. For small species

1080-416: A variety of species, they require supervised training in order to use properly and when they are deployed must be checked frequently. Ringing pliers are an essential tool that helps place the ring around a bird's leg. These pliers come in different sizes as determined by how wide a bird's leg is. Pliers are sized between 0A-1A, 2–3, and 3B, 3A, and 4. The ring size is determined by using a leg gauge. This

1152-568: Is a fundamental property of mathematics and not an accident of Martin-Löf's particular model. The thesis that the definition of Martin-Löf randomness "correctly" captures the intuitive notion of randomness has been called the "Martin-Löf– Chaitin Thesis"; it is somewhat similar to the Church–Turing thesis . Following Martin-Löf's work, algorithmic information theory defines a random string as one that cannot be produced from any computer program that

1224-660: Is a member of the Royal Swedish Academy of Sciences (elected 1990) and of the Academia Europaea (elected 1989). Stockholm University Stockholm University ( SU ) ( Swedish : Stockholms universitet ) is a public research university in Stockholm , Sweden , founded as a college in 1878, with university status since 1960. With over 33,000 students at four different faculties: law, humanities, social sciences, and natural sciences, it

1296-671: Is found, and the ring number read and reported back to the ringer or ringing authority, this is termed a ringing recovery or a control . The finder can contact the address on the ring, give the unique number, and be told the known history of the bird's movements. Many national ringing/banding authorities now also accept reports by phone or on official web sites. The organising body, by collating many such reports, can then determine patterns of bird movements for large populations. Non-ringing/banding scientists can also obtain data for use in bird-related research. At times in North America,

1368-454: Is more readily available and easy to access. Mist nets are fine mesh nets with shelves that create pockets to temporarily restrain birds. Mist nets come in a variety of mesh sizes, heights, lengths, weights, materials, and colours. The mesh size of the net is calculated differently in different countries; in the US and Canada the given mesh size is equivalent to two sides of a mesh square, while in

1440-544: Is now established as a renowned marine research center. Tarfala research station belongs to the Department of Physical Geography. The station is located 1135 meters above sea level in Tarfaladalen, on the east side of Kebnekaise in arctic / alpine surroundings and conducts glaciological, hydrological, meteorological and climatological research. The station has the capacity to accommodate groups of up to 25 people and

1512-602: Is one of the largest universities in Scandinavia . Stockholm University was granted university status in 1960, making it the fourth oldest Swedish university . As with other public universities in Sweden, Stockholm University's mission includes teaching and research anchored in society at large. The initiative for the formation of Stockholm University was taken by the Stockholm City Council. The process

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1584-462: Is placed around the bird's leg, which determines the diameter of the leg. After identifying the size of ring needed, it is then placed on around the leg with the help from the ringing pliers. In Australia, ring sizes range from 1 to 15, plus special sizes for birds whose leg shapes require special rings, such as parrots and pelicans. When looking through the Pyle textbook some birds can be identified by

1656-401: Is shorter than the string ( Chaitin–Kolmogorov randomness ); i.e. a string whose Kolmogorov complexity is at least the length of the string. This is a different meaning from the usage of the term in statistics. Whereas statistical randomness refers to the process that produces the string (e.g. flipping a coin to produce each bit will randomly produce a string), algorithmic randomness refers to

1728-672: The British Trust for Ornithology . In North America the U.S. Bird Banding Laboratory collaborates with Canadian programs and since 1996, partners with the North American Banding Council (NABC). Waterfowl hunters may report the ring number of the bird they killed or observed, and find out the details of that specific bird such as breed, age, and ringing location. Bird rings are often seen as a prize because they are still relatively rare. The European Union for Bird Ringing (EURING) consolidates ringing data from

1800-723: The Middle Ages fitted tags on their falcons with seals of their owners. In England from around 1560 or so, swans were marked with a swan mark , a nick on the bill. Storks injured by hunting arrows (termed as pfeilstorch in German) traceable to African tribes were found in Germany and elsewhere as early as 1822, and constituted some of the earliest definitive evidence of long-distance migration in European birds. In North America John James Audubon and Ernest Thompson Seton were pioneers although their method of marking birds

1872-724: The Migratory Bird Treaty of 1918. Bird ringing is the term used in the UK and in some other parts of Europe and the world. Bird banding is the term used in the United States. Organised ringing efforts are called ringing or banding schemes, and the organisations that run them are ringing or banding authorities. Birds are ringed rather than rung . Those who ring or band birds are known as ringers or banders, and they are typically active at ringing or banding stations. Birds may be captured by being taken as young birds at

1944-525: The Stockholm Metro . The commuter train line Roslagsbanan also stop close to the main campus, at Universitetet railway station . SL buses 50, 540, 608, 624C, 628C, 639, 670 676, 680, 690, 691, 696 and 699 can also be used to get to the campus. The Computer Science campus, Kista, also is close to an underground station called Kista . It is also located close to the pendeltåg station Helenelund , only one or two stops (depending on bus line) from

2016-663: The U.S. News & World Report Rankings , Stockholm University was ranked 114 overall in the world in 2021, 4 in Sweden and 43 within Europe. In the CWTS Leiden Ranking 2022, Stockholm University was placed at 343 on the list of universities in the world. The main part of Stockholm University is in the Frescati area, which extends from the Bergius Botanical Garden in the north to Sveaplan in

2088-531: The United States and Canada . A field-readable is a ring or rings, usually made from plastic and brightly coloured, which may also have conspicuous markings in the form of letters and/or numbers. They are used by biologists working in the field to identify individual birds without recapture and with a minimum of disturbance to their behaviour. Rings large enough to carry numbers are usually restricted to larger birds, although if necessary small extensions to

2160-655: The University of Chicago where he met William Alvin Howard with whom he discussed issues related to the Curry–Howard correspondence . Martin-Löf's first draft article on type theory dates back to 1971. This impredicative theory generalized Girard's System F . However, this system turned out to be inconsistent due to Girard's paradox which was discovered by Girard when studying System U, an inconsistent extension of System F. This experience led Per Martin-Löf to develop

2232-465: The expectation–maximization method for missing data , and model selection . Per Martin-Löf received his PhD in 1970 from Stockholm University , under Andrey Kolmogorov . Martin-Löf is an enthusiastic bird-watcher ; his first scientific publication was on the mortality rates of ringed birds . In 1964 and 1965, Martin-Löf studied in Moscow under the supervision of Andrei N. Kolmogorov . He wrote

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2304-575: The frequency probability notion of the limiting properties of infinite sequences failed to provide a foundation for statistics, which considers only finite samples. Much of Martin-Löf's work in statistics was to provide a finite-sample foundation for statistics. In the 1970s, Per Martin-Löf made important contributions to statistical theory and inspired further research, especially by Scandinavian statisticians including Rolf Sundberg, Thomas Höglund, and Steffan Lauritzen. In this work, Martin-Löf's previous research on probability measures on semigroups led to

2376-457: The nest , or as adults, captured in fine mist nets , baited traps, Heligoland traps , drag nets, cannon nets , or by other methods. Raptors may be caught by many methods, including bal-chatri traps. When a bird is caught, a ring of suitable size (usually made of aluminium or other lightweight material) is attached to the bird's leg, has a unique number, and a contact address. The bird is often weighed and measured, examined for data relevant to

2448-400: The string itself . Algorithmic information theory separates random from nonrandom strings in a way that is relatively invariant to the model of computation being used. An algorithmically random sequence is an infinite sequence of characters, all of whose prefixes (except possibly a finite number of exceptions) are strings that are "close to" algorithmically random (their length is within

2520-546: The taiga . The highly unpredictable movements inherent in these species' lifestyles means that recovery rates are extremely low, especially given generally low population densities within their habitats. Most waterfowl are leg ringed, but some are marked with a plastic neck collar, which can be read at a greater distance. Neck collars can also be used for other long-necked birds such as flamingos . In some surveys, involving larger birds such as eagles, brightly coloured plastic tags are attached to birds' wing feathers. Each has

2592-909: The Bachelor´s Programme in Business, Ethics and Sustainability; Bachelor Programme in Latin America Studies; Bachelor´s Programme in International Business and Politics and the Bachelor´s Programme in Earth Science, Distance Learning. Besides the programmes themselves, the university also offers opportunities for foreign exchange studies during the third year of a bachelor’s degree programme. The university has cooperative agreements with more than 100 universities worldwide. The university's researchers engage in governmental investigations, are active in

2664-490: The Punic Wars in 218 BC a crow was released by a besieged garrison, which suggests that this was an established practice. Quintus Fabius Pictor used a thread on the bird's leg to send a message back. In another case in history, a knight interested in chariot races during the time of Pliny (AD 1) took crows to Volterra, 135 miles (217 km) away and released the crows with information on the race winners. Falconers in

2736-663: The Scandinavian countries between 1911 and 1914. Paul Bartsch of the Smithsonian Institution is credited with the first modern banding in the U.S.: he banded 23 black-crowned night herons in 1902. Leon J. Cole of the University of Wisconsin founded the American Bird Banding Association in 1909; this organisation oversaw banding until the establishment of federal programs in the U.S. (1920) and Canada (1923) pursuant to

2808-664: The Teacher's College's Student Union on transferring its members to it, as it already has a teacher's division. In contrast to common belief, DISK is not an abbreviation. In the Academic Ranking of World Universities 2020, an annual publication of university rankings by Shanghai Ranking Consultancy/ Academic Ranking of World Universities , Stockholm University was placed as the 69th overall best university worldwide. The Times Higher Education (THE) World University Rankings 2018 listed Stockholm University at position 134 on

2880-542: The UK it is equivalent to one side. Ringers must choose a mesh size that appropriately targets the desired species, with smaller birds requiring a smaller mesh size. Nets can range from 1.5 to 18 metres in length, and from 1 to 3 metres in height depending on the number of panels. The weight of the thread and the ply (number of strands) can also vary. Common construction materials include nylon, polyester, and monofilament. Mist nets are typically black, but may also be shades of green or brown. While mist nets are capable of capturing

2952-456: The admission of students. Education and research at Stockholm University is carried out within the natural sciences and the humanities/social sciences. Within these fields, there are four faculties with 56 departments, institutes and centers within the humanities, law, natural sciences and social sciences. Research and training also takes place at a number of centers and institutes with a separate governing board, but that organisationally belong to

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3024-459: The bands have just a unique number (without an address) that is recorded along with other identifying information on the bird. If the bird is recaptured the number on the band is recorded (along with other identifying characteristics) as a retrap . All band numbers and information on the individual birds are then entered into a database and the information often shared throughout North American banding operations. This way information on retrapped birds

3096-484: The bands into a powdery oxide that sticks to the vulture's leg and injures the bird. Dippers are also dangerously handicapped by ringing because the rings induce drag that makes it extremely difficult for them to catch prey in fast-flowing water. Among species which can be safely ringed, there are major limitations among nomadic species of the deserts of the Eastern Hemisphere and cardueline finches of

3168-406: The bus station Torsnäsgatan located next to the campus area. Bird ringing Bird ringing (UK) or bird banding (US) is the attachment of a small, individually numbered metal or plastic tag to the leg or wing of a wild bird to enable individual identification. This helps in keeping track of the movements of the bird and its life history. It is common to take measurements and examine

3240-464: The computer and system science students and the teacher students have their own, independent, student unions called DISK and "The Teacher's College's Student Union" (Lärarhögskolans studentkår) . The law students also have their own student union, as do journalism students ( Studentkåren vid JMK ). The future of the Teacher's College's Student Union is however not entirely safe, as Stockholm University's Student Union has declared it will begin talks with

3312-552: The conditions of feather moult, subcutaneous fat, age indications and sex during capture for ringing. The subsequent recapture, recovery, or observation of the bird can provide information on migration , longevity, mortality, population, territoriality , feeding behaviour , and other aspects that are studied by ornithologists . Other methods of marking birds may also be used to allow for field based identification that does not require capture. The earliest recorded attempts to mark birds were made by Roman soldiers . For instance during

3384-453: The cost of making a ring which is capable of securely fitting their strong, heavy legs is prohibitive. At the other extreme, the smaller species of river and tree kingfishers , todies and certain lories , have such narrow tarsi that a ring placed around the bird's foot may impose danger to blood circulation. For some gamebirds, such as the Indian peafowl , spurs on the legs interfere with

3456-594: The countries of the East Asian - Australasian Flyway to identify important areas and routes used by migratory waders . Head and neck markers are very visible, and may be used in species where the legs are not normally visible (such as ducks and geese). Nasal discs and nasal saddles can be attached to the culmen with a pin looped through the nostrils in birds with perforate nostrils . They should not be used if they obstruct breathing. They should not be used on birds that live in icy climates, as accumulation of ice on

3528-410: The following year, actual operations began. In 1878, the university college Stockholms högskola started its operations with a series of lectures on natural sciences, open to curious citizens (a tradition still upheld by yearly publicly open lectures). Notable in the university's early history is the appointment of Sofia Kovalevskaya to hold a chair in the mathematics department in 1889, making her

3600-461: The late 1700s. After Gustav III's trip to Italy in 1783–84, several places at Brunnsviken were given Italian names. Stockholm University has another campus in Kista , which houses the Department of computer and systems sciences. There are many ways to get to Stockholm University. The main campus Frescati is located near the underground railway station Universitetet metro station , on the red line of

3672-406: The lifetime of the transmitter battery. As with wing tags, the transmitters may be designed to drop off when the bird moults; or they may be recovered by recapturing the bird. Motus wildlife tracking network is a program of Birds Canada , it was launched in 2014 in the US and Canada, by 2022 more than 1,500 receiver stations have been installed in 34 countries, most receivers are concentrated in

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3744-1071: The list of the world's top universities. Times Higher Education World University Rankings are annual university rankings published by British Times Higher Education (THE) magazine. In the QS World University Rankings , Stockholm University was ranked 148 overall in the world in 2021. Its subject rankings were: 23rd in Environmental Sciences, 37th in Sociology, 98th in Natural Sciences, 132nd in Arts & Humanities, 238th in Life Sciences & Medicine, 297th in Engineering and Technology, and 175th in Social Sciences and Management. In

3816-402: The media, provide responses to proposed legislation and are included in several Nobel committees and international expert bodies. Stockholm University Marine Research center (SMF) provides "Askö Laboratory", where Research on ecosystems, ecology and the impact of human interference is carried out. The field station was built in 1961 by Professor Lars Silén, Head of the Department of Zoology, and

3888-468: The original definition, but each of which satisfies our intuitive notion of properties that random sequences ought to have: random sequences should be incompressible, they should pass statistical tests for randomness, and it should be impossible to make money betting on them. The existence of these multiple definitions of Martin-Löf randomness, and the stability of these definitions under different models of computation, give evidence that Martin-Löf randomness

3960-665: The philosophical foundations of type theory , his meaning explanation , a form of proof-theoretic semantics , which justifies predicative type theory as presented in his 1984 Bibliopolis book, and extended in a number of increasingly philosophical texts, such as his influential On the Meanings of the Logical Constants and the Justifications of the Logical Laws . The 1984 type theory was extensional while

4032-405: The public. While live bird ringing is not the only method of educating the public on bird conservation, it can be an especially engaging and unique method for visitors. Ringing activities are often regulated by national agencies but because ringed birds may be found across countries, there are consortiums that ensure that recoveries and reports are collated. In the UK, bird ringing is organised by

4104-401: The ringer's project, and then released. The rings are very light, and are designed to have no adverse effect on the birds – indeed, the whole basis of using ringing to gain data about the birds is that ringed birds should behave in all respects in the same way as the unringed population. The birds so tagged can then be identified when they are re-trapped, or found dead, later. When a ringed bird

4176-433: The rings (leg flags) bearing the identification code allow their use on slightly smaller species. For small species (e.g. most passerines), individuals can be identified by using a combination of small rings of different colours, which are read in a specific order. Most colour-marks of this type are considered temporary (the rings degrade, fade and may be lost or removed by the birds) and individuals are usually also fitted with

4248-508: The rings, which thus can cause injury to the birds. Special rings are needed for long-lived seabirds, such as Manx shearwaters , which can live for over 50 years. The corrosive effects of sea water, combined with wear, result in traditional aluminium rings only lasting around 4 years; for these birds, much tougher and more corrosion-resistant incoloy , monel , or stainless steel alloy rings are now used. Many species of cockatoo , which even if able to be ringed, require special rings to fit

4320-530: The south. It is located in the world's first national urban park and the area is characterized by nature, architecture and modern art, featuring such notable buildings as the Aula Magna (auditorium). Within Frescati, the areas Albano, the Bergius Botanical Garden , Frescati Backe, Frescati Hage, Kräftriket, Lilla Frescati and Sveaplan are located. The names of many of these areas have a history dating back to

4392-647: The staff consists of 2–5 people. Tovetorp Zoological Research Station belongs to the Department of Zoology, and is located about 95 km southwest of Stockholm. It conducts research and training activities in ecology and ethology. Every year Tovetorp is visited by up to 600 students who live and study between 2–10 days on the station. On the research side, over 20 people work today with different research projects. The number of employees are currently 6 people. Prior to 2008, Stockholm University had only one student union called Stockholm University Student Union (Stockholm universitets studentkår, SUS) . However, since 2008

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4464-433: The third female professor in Europe. In 1904 the college became an official degree-granting institution. In 1960, the college was granted university status, becoming Sweden's fourth state university. The university premises were situated in central Stockholm at Observatorielunden but increased enrollment resulted in a lack of space, which required the university campus to be shifted to a bigger facility. Since 1970 most of

4536-593: The transmitter is carried as a 'backpack' fitted over the wing bases, and for larger species it may be attached to a tail feather or looped to the legs. Both types usually have a tiny (10 cm) flexible aerial to improve signal reception. Two field receivers (reading distance and direction) are needed to establish the bird's position using triangulation from the ground. The technique is useful for tracing individuals during landscape-level movements particularly in dense vegetation (such as tropical forests) and for shy or difficult-to-spot species, because birds can be located from

4608-543: The type theory presented in the book by Nordström et al. in 1990, which was heavily influenced by his later ideas, intensional, and more amenable to being implemented on a computer. Martin-Löf's intuitionistic type theory developed the notion of dependent types and directly influenced the development of the calculus of constructions and the logical framework LF . A number of popular computer-based proof systems are based on type theory, for example NuPRL , LEGO, Coq , ALF, Agda , Twelf , Epigram , and Idris . Martin-Löf

4680-508: The unique shape of their legs. With softer metals like aluminium, they can bite off the rings with their powerful bills; tougher alloys also need to be used for these rings. The ability to overcome this problem varies between species, and with some such as the Gang-gang cockatoo , it is known to be too dangerous to attempt banding. New World vultures also cannot be banded on their legs because they urinate onto their legs, causing corrosion of

4752-474: The university operations are located at the main campus at Frescati north of the city center, the former Experimentalfältet, previously used by the Royal Swedish Academy of Agriculture and Forestry . Stockholm University is a state agency and is governed by decisions taken by the government and parliament. The university has the right, within the limits the government provides, to decide on many issues such as their internal organization, educational provision and

4824-647: The wing cord. The next essential piece of equipment is the wing ruler, which is used to determine the length of the wing for data collection, research purposes, or determining species. Once the processing of the bird's morphology has been completed the last piece of equipment used is a digital scale. This helps with determining the weight of the bird. This is the last step before releasing the bird. Certain bird species are for various reasons unsuitable for ringing. In some countries, such as Australia, there exist laws prohibiting ringing of such species. Some very large birds, such as ratites , are difficult to ring because

4896-610: Was completed after a decision in December 1865 regarding the establishment of a fund and a committee to "establish a higher education institution in the capital". The nine members of the committee were respected and prominent citizens whose work had helped the evolution of science and society. The next important step was taken in October 1869, when the Stockholm University College Association

4968-479: Was different from modern ringing. To determine if the same birds returned to his farm, Audubon tied silver threads onto the legs of young eastern phoebes in 1805, although the veracity of Audubon's dates and methods has been questioned, while Seton marked snow buntings in Manitoba with ink in 1882. Ringing of birds for more extensive scientific purposes was started in 1899 by Hans Christian Cornelius Mortensen ,

5040-601: Was established. Several members of the committee became members of the association – including Professor Pehr Henrik Malmsten. The association's mission was to establish a college in Stockholm and would "not be dissolved until the college came into being and its future could be considered secure." The memorandum of the Stockholm University College was adopted in May 1877, and in the autumn semester of

5112-730: Was published in a leading international journal, sponsored by the Royal Statistical Society . In philosophical logic , Per Martin-Löf has published papers on the theory of logical consequence , on judgments , etc. He has been interested in Central-European philosophical traditions, especially of the German-language writings of Franz Brentano , Gottlob Frege , and of Edmund Husserl . Martin-Löf has worked in mathematical logic for many decades. From 1968 to '69 he worked as an assistant professor at

5184-429: Was to use the theory of computation to define formally the notion of a test for randomness. This contrasts with the idea of randomness in probability ; in that theory, no particular element of a sample space can be said to be random. Martin-Löf randomness has since been shown to admit many equivalent characterizations — in terms of compression , randomness tests, and gambling — that bear little outward resemblance to

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