This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows (...) for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle and orthogonal polynomials on the real line, Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC. (shrink)

The Western cultural archetype of Narcissus experiences a significant turning point in the 1400s, thanks to Leon Battista Alberti’s work. Indeed, the myth evolves from being a subject embodying a taboo in the Antiquity to become the glance that generates the image; in so doing this myth assumes the rank of science and philosophy. Alberti does not follow Pliny’s reading of Ovid’s Metamorphosis, but handles Philostratus’s version; with his visual description he represents in the “Eikones” the darting glance towards the (...) water. The rendering of this image anticipates the notion of centric ray, on which Alberti establishes his perspective’s theory based on the diaphanous nature of “velum”. The art of painting is compared to an “open vitreous and translucent window”. Narcissus does not see the water, so to say, but the image, as well as the painting’s observer instantly grasps the iconic value of it, rather than the material support. Because of this immediacy, the art of painting becomes the terrain of revelation: it makes clear the emerging progressive visibility of “something”, thus concurring with philosophy; better, the art of painting overtakes philosophy with the simple representation of polysemous complexities. This is the new art of painting, in which “there is nothing that is not philosophy”. Furthermore, in this synthetic role of representation in which the icon becomes all one with the spectator – in addition to the centric ray and to the orthogonality of the vision, topics already analyzed by the author in previous studies – consists an outstanding resemblance between Alberti and Cusanus. The two philosophers show their synergy in exploring a new anthropology. From this point of view can be read Alberti’s explanation, often misinterpreted, of Narcissus’ transformation into a flower: a synthesis between “imaginatio” and “executio”, or inactiveness versus activeness. Among all Narcissus’ portrayals of that time, it would be useful to consider the Pseudo Boltraffio’s version of London; this rendering applies thematically Alberti’s theory in its essential aspects, introducing it within Leonardo Da Vinci’s circle of artists. (shrink)

We present a mathematically precise derivation of some generalized orthogonality relations for the discrete series representations of SU(1,1). These orthogonality relations are applied to derive tomographical reconstruction formulas. Their physical interpretation is also discussed.

Can robots have significant moral status? This is an emerging topic of debate among roboticists and ethicists. This paper makes three contributions to this debate. First, it presents a theory – ‘ethical behaviourism’ – which holds that robots can have significant moral status if they are roughly performatively equivalent to other entities that have significant moral status. This theory is then defended from seven objections. Second, taking this theoretical position onboard, it is argued that the performative threshold that robots need (...) to cross in order to be afforded significant moral status may not be that high and that they may soon cross it (if they haven’t done so already). Finally, the implications of this for our procreative duties to robots are considered, and it is argued that we may need to take seriously a duty of ‘procreative beneficence’ towards robots. (shrink)

This manuscript explores the orthogonality constraints on configurations and orbitals subject to the property that states are mutually orthogonal. The orthogonality constraints lead to properties that affect the description of chemical systems. When states are described as linear combinations of configurations, the coefficient matrix diagonalises S−1H. Therefore, single-configuration states are only possible in one-electron systems: non-orthogonal configurations yield single-configuration states only if S−1H is diagonal, but this would violate the orthonormalisation constraint. Further, the coefficient matrix is not constrained (...) to be square. Similarly, the orbitals used to construct configurations may also be orthogonal or non-orthogonal; orbitals are only required to be mutually orthogonal at the one-electron limit. Orthogonal orbitals are generally preferred due to their mathematical and conceptual simplicity, leading to fictitious unoccupied orbitals. Since the Fock operator is orthogonality agnostic, non-orthogonal orbitals can be generated by solving the Fock equation independently for each electron; the virtual orbitals produced by this conception are true excitation orbitals as they are eigensolutions of the Fock operator. Additionally, we show that the number of molecular orbitals generated is not restricted to the number of atomic orbitals employed in the computation. This manuscript explores the mathematical relationships that need to be satisfied under the various orthogonality regimes. We also present mathematical relationships that provide results that are independent of the orthogonality approximation within a particular computational method. (shrink)

This paper presents arguments from empirical research and from philosophical considerations to the effect that phenomenality and content are two distinct and independent features of mental representations, which are both relational. Thus, it is argued, classical arguments that infer phenomenality from content have to be rejected. Likewise, theories that try to explain the phenomenal character of experiences by appeal to specific types of content cannot succeed. Instead, a dynamic view of consciousness has to be adopted that seeks to explain consciousness (...) by certain ways of processing representations. Therefore, only empirical methods that are able to investigate the dynamics of the mind can be used for the “quest for consciousness” proper. Moreover, the central intuitions about consciousness are best explained when phenomenality and content are clearly distinguished. (shrink)

Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing the idea of interaction among all parts of a given definable set. A cohesive set is indecomposable, in the sense that if it is internal to the product of two orthogonal sets, then it is internal to one of the two. We prove that a definable group in an o-minimal structure is a product of cohesive (...) orthogonal subsets. If the group has dimension one, or it is definably simple, then it is itself cohesive. As an application, we show that an abelian group definable in the disjoint union of finitely many o-minimal structures is a quotient, by a discrete normal subgroup, of a direct product of locally definable groups in the single structures. (shrink)

Background Immense volumes of personal health information are required to realize the anticipated benefits of artificial intelligence in clinical medicine. To maintain public trust in medical research, consent policies must evolve to reflect contemporary patient preferences. Methods Patients were invited to complete a 27-item survey focusing on: broad versus specific consent; opt-in versus opt-out approaches; comfort level sharing with different recipients; attitudes towards commercialization; and options to track PHI use and study results. Results 222 participants were included in the analysis; (...) 83% were comfortable sharing PHI with researchers at their own hospital, although younger patients were more uncomfortable than older patients. While 56% of patients preferred broad consent, 38% preferred specific consent; 6% preferred not sharing at all. The majority of patients preferred to be asked for permission before entry into a contact pool. Again, this trend was more pronounced for younger patients. Approximately half of patients were uncomfortable sharing PHI with commercial enterprises. Most patients preferred to track PHI usage, with the highest proportion once again reported by the youngest patients. A majority of patients also wished to be notified regarding study results. Conclusions While most patients were willing to share their PHI with researchers within their own institution, many preferred a transparent and reciprocal consent process. These data also suggest a generational shift, wherein younger patients preferred more specific consent options. Modernizing consent policies to reflect increased autonomy is crucial in fostering sustained public engagement with medical research. (shrink)

Hume argues that respect for property (“justice”) is a convention-dependent (“artificial”) virtue. He does so by appeal to a principle, derived from his virtue-based approach to ethics, which requires that, for any kind of virtuous action, there be a “first virtuous motive” that is other than a sense of moral duty. It has been objected, however, that in the case of justice (and also in a parallel argument concerning promise-keeping) Hume (i) does not, (ii) should not, and (iii) cannot recognize (...) such a motive. This paper defends Hume’s argument against these three objections. (shrink)

Summary When dealing with philosophical questions such as the choice of a world system or the substance of heaven, some sixteenth-century astronomers, including Tycho Brahe and Christophe Rothmann, devised more accurate experimental setups so that they could refine their celestial observations. With this desire to listen to nature arose new questions, in particular that of atmospheric refractions, the understanding and resolution of which became decisive to guarantee the best accuracy. However, to solve such practical problems, it was necessary to consider (...) their philosophical and theological background, as well as the knowledge of optics inherited from the medieval period. We examine this heritage and its transmissions through the works of Peter Ramus's assistants, especially Jean Pena and Friedrich Risner. From this first survey, we try to analyse the lively debate on atmospheric refractions in the late sixteenth and early seventeenth centuries by exploring the argumentative structure, the philosophical background, and the epistemological grounds of the discourse of authors such as Tycho Brahe, Christoph Rothmann, and Johannes Kepler. (shrink)

The primary aim of this original work is to provide a more in-depth insight into the relations between control parameters adjustments, learning techniques, inner swarm dynamics and possible hybridization strategies for popular swarm metaheuristic Firefly Algorithm. In this paper, a proven method, orthogonal learning, is fused with FA, specifically with its hybrid modification Firefly Particle Swarm Optimization. The parameters of the proposed Orthogonal Learning Firefly Algorithm are also initially thoroughly explored and tuned. The performance of the developed algorithm (...) is examined and compared with canonical FA and above-mentioned FFPSO. Comparisons have been conducted on well-known CEC 2017 benchmark functions, and the results have been evaluated for statistical significance using the Friedman rank test. (shrink)

The paper is devoted to the presentation and analysis of the philosophical views concerning logic and mathematics of the leading members of Cracow Circle, i.e., of Jan Salamucha, Jan Franciszek Drewnowski and Józef Maria Bocheński. Their views on the problem of possible applicability of logical tools in metaphysical and theological researches is also discussed.

We define and study the notion of an indexed frame. This is a bi-dimensional structure consisting of a Cartesian product equipped with relations which only relate pairs if they coincide in one of their components. We show that these structures are quite ubiquitous in modal logic, showing up in the literature as products of Kripke frames, subset spaces, or temporal frames for STIT logics. We show that indexed frames are completely characterised by their ‘orthogonal’ relations, and we provide their (...) sound and complete logic. Using these ‘orthogonality’ results, we provide necessary and sufficient conditions for an arbitrary Kripke frame to be isomorphic to certain well-known bi-dimensional structures. (shrink)

CONJECTURE: Alongside the innate physical sucking reflex for obtaining milk to be digested, decomposed and used all over the body for growth, repair, and energy, there is a genetically determined information-sucking reflex, which seeks out, sucks in, and decomposes information, which is later recombined in many ways, growing the information-processing architecture and many diverse recombinable competences.

Summary Historical scholars have recently turned their attention to local communities, resulting in a lively debate about the role of regions and provinces in Western Europe. This has quite predictably led many to question this resurgence of local identities in order to discover the cultural roots and the geographical boundaries of these identities and their interaction with the formation of nation-states in the literary, artistic and political practices of the past two centuries. This article provides an introduction to one specific (...) transnational intellectual network, the Guild of Saint Thomas and Saint Luke, which in the latter half of the nineteenth century served as a forum for the different local identities which were influential in the Gothic (and Catholic) Revival of the Low Countries. The interaction among the most influential members during the annual excursions of the Guild and the choice for the locations of these meetings resulted in different ideological discourses about the position and the borders of ‘Christian art’ in the Low Countries. Due to both internal and external influences these discourses very soon integrated into the national frame, making the definition of a potentially common style for the whole area impossible. The analysis is based on existing literature on regionalism and the Neo-Gothic Revival, and on archive material concerning the first meetings of the Guild. The above-mentioned observations offer the opportunity to underline the peculiarity of transnational permanent networks composed by a fluctuating number of participants and to stimulate debate about the applicability of this example to other geo-cultural contexts. (shrink)

This article sets out to throw light on the intellectual and scientific activities of a group of Spanish humanists associated with the diplomat, aristocrat, and writer Diego Hurtado de Mendoza in the course of his fifteen years in Venice, Trent, and Rome, focusing on two aspects that have been neglected to date. These are (a) the integration of practices connected with the study of nature (herborizing expeditions and the production of herbaria) with the work of collating, translating, and commenting on (...) classical texts dealing with natural history and materia medica; and (b) the insertion of these scientific activities in Italy by the Spanish subjects of the Emperor Charles V within the broader context of a specific cultural policy. This policy would later be fleshed out in the scientific project of the Spanish Crown under Philip II, inseparable as it was from the monarch’s political and religious policy. (shrink)

In recent years, neural networks have attracted much attention in the machine learning and the deep learning technologies. Bio-inspired functions and intelligence are also expected to process efficiently and improve existing technologies. In the visual pathway, the prominent features consist of nonlinear characteristics of squaring and rectification functions observed in the retinal and visual cortex networks, respectively. Further, adaptation is an important feature to activate the biological systems, efficiently. Recently, to overcome short-comings of the deep learning techniques, orthogonality for the (...) weights in the networks has been developed for the signal propagation and the efficient optimization of the learning. In this paper, bio-inspired asymmetric networks with nonlinear characteristics are proposed, which are derived from the retinal networks in the biological visual pathway. The asymmetric network proposed here was verified to detect the movement of the object, efficiently in our previous studies. This paper shows a new characteristic of the adaptive orthogonality in the asymmetric networks. First, it is shown that the asymmetric network with nonlinear characteristics is effective for generating orthogonality. Second, the proposed asymmetric network with Gabor filters is compared with the conventional energy model from the point of the orthogonality characteristics. Finally, the asymmetric networks with nonlinear characteristics can generate the extended orthogonal bases in independent subspaces, which are useful for classification and efficient learning. (shrink)

Suppose there are no in-principle restrictions on the contents of arbitrarily intelligent agents’ goals. According to “instrumental convergence” arguments, potentially scary things follow. I do two things in this paper. First, focusing on the influential version of the instrumental convergence argument due to Nick Bostrom, I explain why such arguments require an account of “promotion,” i.e., an account of what it is to “promote” a goal. Then, I consider whether extant accounts of promotion in the literature -- in particular, probabilistic (...) and fit-based views of promotion -- can be used to support dangerous instrumental convergence. I argue that neither account of promotion can do the work. The opposite is true: accepting either account of promotion undermines support for instrumental convergence arguments’ existentially worrying conclusions. The conclusion is that we needn’t be scared -- at least not because of arguments concerning instrumental convergence. (shrink)

In his commentary on Aristotle’s Peri hermeneias,1 Abelard distinguishes the form of an expression2 (oratio) from what it says, that is, its content. The content of an expression is its understanding (intellectus). This distinction is surely the most well-known and central idea in Abelard’s commentary. It provides him with the opportunity to distinguish statements (enuntiationes) from other kinds of expressions without implying a diference in their content, since the ability of a statement to signify something true or false (verum vel (...) falsum)3 cannot be found in its content. More precisely, Abelard distinguishes statements both from complete expressions (orationes perfectae) that are not statements but rather questions, requests, commands, etc. and from incomplete expressions, that is, mere word strings (orationes imperfectae), such as homo albus. These kinds of expressions, according to Abelard, do not differ in the understanding they present but in the way they present it. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 213 Seiten: 307-343.

Classically, an osculating circle at a point of a planar curve is introduced technically, often with formula giving its radius and the coordinates of its center. In this note, we propose a new and intuitive definition of this concept: among all the circles which have, on the considered point, the same tangent as the studied curve and thus seem equal to the curve through a microscope, the osculating circle is this that seems equal to the curve through a (...) microscope within microscope. (shrink)

This article discusses female office workers' own definitions of information technology, based on a study with a group of Finnish office workers, in which they studied and evaluated information systems and analysed their work as well as making proposals for their IT systems. IT is considered as a textuality that is connected with the office workers' subjectivities and their organizational activities. For office workers, defining information systems means a struggle for their own subjectivities. Starting from the concrete practices and interviews (...) with the office workers, the article examines how their 'own' definitions of IT were constructed; how office workers' situated interpretations and textualities interacted; how organizational relations and textualities intervened in the definitions; and how women's mutual support made it possible to approach something that could be considered women's 'own' definitions. (shrink)