1,375 research outputs found

    New constructions for covering designs

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    A (v,k,t)(v,k,t) {\em covering design}, or {\em covering}, is a family of kk-subsets, called blocks, chosen from a vv-set, such that each tt-subset is contained in at least one of the blocks. The number of blocks is the covering's {\em size}, and the minimum size of such a covering is denoted by C(v,k,t)C(v,k,t). This paper gives three new methods for constructing good coverings: a greedy algorithm similar to Conway and Sloane's algorithm for lexicographic codes~\cite{lex}, and two methods that synthesize new coverings from preexisting ones. Using these new methods, together with results in the literature, we build tables of upper bounds on C(v,k,t)C(v,k,t) for v≀32v \leq 32, k≀16k \leq 16, and t≀8t \leq 8.

    The symphonies of Antonio Brioschi : aspects of sonata form

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    The article investigates tonal, thematic, and textural aspects of sonata form in the movement structures of twenty-six symphonies from the 1730s and early-1740s by the Italian composer Antonio Brioschi (active ca. 1725–ca. 1750). It discusses expository events as well as aspects of development and recapitulation of the musical material. In addition, the article provides an account of the major eighteenth-century manuscript source of the works—a French collection known as Fonds Blancheton—and considers some general stylistic characteristics of the music

    On a C⃗4\vec{C}_4-ultrahomogeneous oriented graph

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    The notion of a C\mathcal C-ultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and subsequently a strongly connected C⃗4\vec{C}_4-ultrahomogeneous oriented graph on 168 vertices and 126 pairwise arc-disjoint 4-cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, by altering a definition of the Coxeter graph via pencils of ordered lines of the Fano plane in which pencils are replaced by ordered pencils.Comment: 4 pages, 2 figures, 2 table

    Space is the machine, part three: the laws of the field

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    Part III of the book, ‘The Laws of the Field’, uses these noted regularities to reconsider the most fundamental question of all in architectural theory: how is the vast field of possible spatial complexes constrained to create those that are actually found as buildings? First, in Chapter Eight, ‘Is architecture an ars combinatoria?’, a general theory of ‘partitioning’ is proposed, in which it is shown that local physical changes in a spatial system always have more or less global configurational effects. It is the laws governing this passage form local physical moves to global spatial effects that are the spatial laws that underlie building. These local-to-global spatial laws are linked to the evolution of real buildings through what will be called ‘generic function’, by which is meant the spatial implications of the most fundamental aspects of human use of space, that is, the fact of occupation and the fact of movement. At this generic level, function imposes restraints on what is spatially viable, and this is responsible for what all buildings have in common as spatial designs. Generic function is the ‘first filter’ between the field of possibility and architectural actuality. The second filter is then the cultural or programmatic requirement of that type of building. The third filter is the idiosyncrasies of structure and expression that then distinguish that building from all others. The passage from the possible to the real passes through these three filters, and without an understanding of each we cannot decipher the form-function relation. Most of all, without a knowledge of generic function and its spatial implications we cannot understand that what all buildings have in common in their spatial structures is already profoundly influenced by human functioning in space. In Chapter 9, ‘The fundamental city’, the theory of generic function and the three filters is applied to cities to show how much of the growth of settlements is governed by these basic laws. A new computer modelling technique of ‘all line analysis’, which begins by conceptualising vacant space as an infinitely dense matrix of lines, containing all possible structures, is used to show how the observable regularities in urban forms from the most local to the most global can be seen to be products of the same underlying processes. A fundamental settlement process is proposed, of which particular cultural types are parameterisations. Finally, it is shown how the fundamental settlement process is essentially realised through a small number of spatial ideas which have an essentially geometrical nature

    From Logical Calculus to Logical Formality—What Kant Did with Euler’s Circles

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    John Venn has the “uneasy suspicion” that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kant’s “disastrous effect on logical method,” namely the “strictest preservation [of logic] from mathematical encroachment.” Kant’s actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Euler’s circles and comparing it with Euler’s own use. I do so in light of the developments in logical calculus from G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations

    THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References

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    and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a

    Una Lampada nella notte [:] L'Ars inventiva per triginta statuas di Giordano Bruno

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    The subject of this thesis, i.e. Giordano Bruno's treatise, known as 'Lampas triginta statuarum', is a text that remained inedited for a long time and was published only in 1891 by Felice Tocco and Girolamo Vitelli in Opera latine conscripta third volume. This philosophic work was written by Bruno during his stay in Wittemberg (1586-88) when he, working as a teacher in Wittemberg Academy, lectured on Aristotle's Organon. During those years he wrote and sent to press other two 'Lampadi' behind this: De Lampade combinatoria Lulliana (a Lullo's Ars Magna comment) and De progressu et Lampade venatoria logicorum (Topici compendium). With Lampas triginta statuarum, that completes the Thrilogy, he intended to improve traditional logical instruments, those derived from Aristotelian and "Porphirian" tradition as well as those derived from Lullian tradition. This treatise was conveyed in its first redaction by Augsburn Codex (A), together with printed test of De Lampade combinatoria Lulliana and with the manuscript Animadversiones circa Lampadem Lullianam, written using the same paper and the same ink already used for the Lampas by a unknown copyist, who was a German Bruno's student. Codex A, preserved in Augsburn Bibliothec, probably belongs to Heinrich Heinzel to whom Bruno dedicated last published work, De imaginum, signorum, et idearum compositione (Francoforte, 1591), that, although written later, can be for many aspects related to Lampas. Having left Wittemberg in 1588, and living in Helmsted (1589 - 90), Bruno devoted himself to the composition of some texts (De magia e Theses de magia, De rerum principiis et elementis et causis, Medicina Lulliana, De magia Mathematica), that remained unedited and were collected in Moscow Codex (M) together with a second manuscript of Lampas triginta statuarum and with De Vinculis in genere. Moscow Codex, also named Norov Codex from the Russian nobleman Avraam Sergeevic Norov that acquired it for his collection from the bookseller Edwin Tross, contains some autograph pages, but it's mostly written by Hyeronimus Besler. In the autumn 1591, while Bruno was living in Padua, Besler transcribed De Vinculis, drafted in Frankfurt, and copied the treatise 'ars inventiva per triginta statuas'. In this work the philosopher leaves the harsh tone used to polemize with his contemporary followers of Aristotle's philosophy, to open to a dialog and a tight mach with the tradition, in particular with the Aristotelian-scholastic one, through a deep analysis of thirty concepts used in philosophic practice, represented by thirty powerful mythologic figures. From this point of view, the treatise is structured like a dictionary of philosophic terms (Bruno appears to be inspired by Aristotle's Metafisica V book.) and also shows some affinity with another text, that was composed some time later in Zurich and that remained unedited (this text was published as a posthumus work by Bruno's student Raphael Egli in two following editions, the first one in 1595 and the second in 1609 comprehensive of the section Praxis descensus seu applicatio entis): it's the Summa terminorum metaphysicorum, a "philosophic nomenclature treatise" as defined by Erminio Troilo) in which fifty two conceptual categories belonging to Aristotelian scholastic lexicom are deeply analysed. In Centum et viginti articuli de natura et mundo adversus Peripateticos (the programmatic phamplet dealing with Cambrai disputation that took place in Paris in 1586), also taken up in Acrotismus (edited in Praga in 1588), the criticism of the natural Aristotle's philosophy is developed through theses regarding some fundamental concepts such as nature, movement, time, place...and so on. In Lampas Bruno goes on in this re-definition of philosophic terms, already started in De la causa, principio et uno: he translates his revolutionary philosophic conceptions into tradition lexicon and in doing this he moulds the meanings and transforms them, joining them in a new plot. In "thirdy statues treatise" the philosopher seems to be moved by a strong systematic intent: that is by the need to proceed in a rigorous and scientific way in the exposition of the foundation of the 'nova filosofia'. Knowledge architecture, within which speculative contents are placed is an imaginary museum filled with statues/concepts: Apollo (unitas), Saturn (principium), Prometheus (agens), Vulcan (forma), Thetis (causa materialis), Sagittarius (causa finalis) and Mount Olympus (finis)...and so on. In moulding the statues, taking from the wide mithology catalogue Bruno uses the "Fidia's seal" (Explicatio triginta sigillorum), as Frances Amelia Yates first guessed (The Art of Memory, 1966). In this thesis my intent is to focus on Bruno's ars memoriae original characters as well as on the forms in which "seals art" is used in Lampas, developing F.A. Yates's insight. One of the most fundamental figure appears to be Prometheus, the imagination architect, the sculptor that first moulded clay statues breathing into them the spiritus. In Bruno's texts, specifically in Lampas and De Imaginum Prometheus became the archetype of the imagination activity, the symbol of the memory artist's praxis. A special emphasis is given to the analysis of the ways used by Bruno to compose the images (consisting in very detailed verbal descriptions) through the research of both literary and iconologic sources (from Boccaccio to Ovidio to the Renaissance mythographers Vincenzo Cartari e Natale Conti). Bruno's work is deeply permeated and inspirited by a didactic intent that is here mostly considered: i.e. the figuration of the most abstract concepts by means of sensitive statues, that appear to sight and mind exploration. The treatise 'ars inventiva per triginta statuas' intends to be mainly a new modus docendi a way of "thinking through images" that is in the same time a way of "thinking through concepts". The "discursiva architectura", hosting the statues must not be considered static or motionless, like physical buildings: in fact the statues can be moved and joined together in many different ways, depending on everybody's own ingenium. Bruno's images are imagini agentes, in other words they have a special effectiveness from the emotional point of view, having the ability to activate cognitive processes. Bruno's opera distinctive features, Lamp structure and functioning, characters and purposes of Bruno's complex logical linguistic system are gradually outlined in this thesis, through text analysis and sources examination. The first chapter presents the great framework inclosing statues gallery: two infigurabilia triads that together represent Bruno's architecture fundamentals and metaphysical basis for ars inventiva that is here applied. In the second chapter "statues and trees" you are introduced to Bruno's use of "statua" mnemonic artifice. By means of the first sequence of statues (Apollo, Saturn, Prometheus, Vulcan, Thetis, Sagittarius and Mount Olympus), it's explained the whole process in natural and human creation. The lexical reference plot is reviewed, with specific consideration to Aristotle's Metafisica fifth Book. "Tree" image in Bruno's texts and "tree" use in the section dedicated to the logic in Lampas treatise is examined for what concerns its relations with both Lullo's and Aristotelian scholastic tradition. Creative activity is represented by Prometheus, the sculptor of alive statues, the creator of natural and artificial things. In the third chapter "Prometheus myth in Lampas triginta statuarum", a deep analysis is carried on about the Statue dedicate by Bruno to Titan, with the purpose to highlight its special relevance in the complete framework. In the two statues dedicated to Minerva (De campo Minervae, seu de noticia e De schala Minervae, seu de habitibus cognitionis) Bruno doesn't provide any goddess image. To Minerva's portrait, outlined by Bruno in Oratio Valedictoria is dedicated the last section (Minerva in light shadow). In Lampas treatise Bruno puts into practice his art of memory, deeply rooted in the living art of nature and represents a new "methodus", suitable for human mind's cognitive structures. The relation among art of memory, theory of knowledge and doctrine of soul is a complex problem of which I pointed out the most important aspects and that in my opinion and in my wishes would be worth further analysing. Beside the figure of the ingenious architect and of the cultivator of imagination "campus", it comes out in my work the image of the other Bruno, the "philosopher", the systematic and rigorous thinker and the fine connoisseur of Aristotelian doctrines, although by himself severely criticized
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