Getting Straight on How Russell Underestimated Frege

Bertrand Russell in his essay On Denoting [1905] presented a theory of description developed in response to the one proposed by Gottlob Frege in his paper Über Sinn und Bedeutung [1892]. The aim of our work will be to show that Russell underestimated Frege three times over in presenting the latter’s work: in relation to the Gray’s Elegy argument, to the Ferdinand argument, and to puzzles discussed by Russell. First, we will discuss two claims of Russell’s which do not do justice to Frege: that we speak of a sense by means of quotation marks, and that all Frege does to cope with phrases that might denote nothing is define an arbitrary object as their reference. Second, we will show that Russell omitted the fact that Frege’s theory provided some answers for the puzzles presented by Russell in his essay

Comparison of the Structure of Equation Systems and the GPU Multifrontal Solver for Finite Difference, Collocation and Finite Element Method

AbstractThe article is an in-depth comparison of numerical solvers and corresponding solution pro- cesses of the systems of algebraic equations resulting from finite difference, collocation, and finite element approximations. The paper considers recently developed isogeometric versions of the collocation and finite element methods, employing B-splines for the computations and ensuring Cp−1 continuity on the borders of elements for the B-splines of the order p. For solving the systems, we use our GPU implementation of the state-of-the-art parallel multifrontal solver, which leverages modern GPU architectures and allows to reduce the complexity. We analyze the structures of linear equation systems resulting from each of the methods and how different matrix structures lead to different multifrontal solver elimination trees. The paper also considers the flows of multifrontal solver depending on the originally employed method

An Elementary Theory of Layout Wirability

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySemiconductor Research Corporation / SRC RSCH 84-06-04

Segments, Rectangles, Contours

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424National Science Foundation / NSF MCS-78-1364

Protrusion of the carotid canal into the sphenoid sinuses: evaluation before endonasal endoscopic sinus surgery

Background: Many reports have previously indicated the vast number of anatomical variations of the sphenoid sinuses, e.g. presence of the recesses. Notwithstanding, there are a few crucial neurovascular structures directly neighbouring with the sinuses. The following research aimed to evaluate frequency prevalence of the carotid canal’s protrusion into the sphenoid sinuses in adult population.Materials and methods: Computed tomography (CT) scans of the paranasal sinuses of 296 patients (147 females, 149 males) were analysed in this retrospective study. The patients did not present any pathology in the sinuses. Spiral CT scanner Siemens Somatom Sensation 16 was used in the standard procedure in the option Siemens CARE Dose 4D.Results: Protrusion of the carotid canal was found in the majority of the patients — 55.74%, more frequently in males (65.1% of the patients) than in females (46.26% of the patients). The said variant — regardless of gender — was noted more often bilaterally (41.55% of the cases: 29.93% females, 53.02% males) than unilaterally (14.19% of the cases: 16.33% females, 12.08% males). In the unilateral type (regardless of gender), the protrusion was more common for the left sphenoid sinus — 10.81% of the patients (12.24% females, 9.4% males) than for the right — 3.38% of the patients (4.08% females, 2.68% males).Conclusions: Complicated structure of the paranasal sinuses, derived from the high prevalence of their anatomical variations, may perplex routine surgical interventions. Henceforth, referral for a CT scan is imperative in order to abate the risks associated with an invasive procedure in the said region

Assumptions behind grammatical approaches to code-switching: when the blueprint is a red herring

Many of the so-called ‘grammars’ of code-switching are based on various underlying assumptions, e.g. that informal speech can be adequately or appropriately described in terms of ‘‘grammar’’; that deep, rather than surface, structures are involved in code-switching; that one ‘language’ is the ‘base’ or ‘matrix’; and that constraints derived from existing data are universal and predictive. We question these assumptions on several grounds. First, ‘grammar’ is arguably distinct from the processes driving speech production. Second, the role of grammar is mediated by the variable, poly-idiolectal repertoires of bilingual speakers. Third, in many instances of CS the notion of a ‘base’ system is either irrelevant, or fails to explain the facts. Fourth, sociolinguistic factors frequently override ‘grammatical’ factors, as evidence from the same language pairs in different settings has shown. No principles proposed to date account for all the facts, and it seems unlikely that ‘grammar’, as conventionally conceived, can provide definitive answers. We conclude that rather than seeking universal, predictive grammatical rules, research on CS should focus on the variability of bilingual grammars

Answering Non-Monotonic Queries in Relational Data Exchange

Relational data exchange is the problem of translating relational data from a source schema into a target schema, according to a specification of the relationship between the source data and the target data. One of the basic issues is how to answer queries that are posed against target data. While consensus has been reached on the definitive semantics for monotonic queries, this issue turned out to be considerably more difficult for non-monotonic queries. Several semantics for non-monotonic queries have been proposed in the past few years. This article proposes a new semantics for non-monotonic queries, called the GCWA*-semantics. It is inspired by semantics from the area of deductive databases. We show that the GCWA*-semantics coincides with the standard open world semantics on monotonic queries, and we further explore the (data) complexity of evaluating non-monotonic queries under the GCWA*-semantics. In particular, we introduce a class of schema mappings for which universal queries can be evaluated under the GCWA*-semantics in polynomial time (data complexity) on the core of the universal solutions.Comment: 55 pages, 3 figure

Prevalence of the Onodi cell in the Polish adult population: an anatomical computed tomography study

Background: Onodi cell is a posterior ethmoid air cell with the optic canal bulging into it; the common position of the bulge is into the sphenoid sinus, usually immediately posterior to the posterior ethmoid air cells. Variable pneumatization patterns lead to various structures of lamellae and sinuses occasionally exposing important nerves and vessels, such as the optic and vidian nerves, internal carotid artery and cavernous sinus. In clinical practice, special imaging techniques are used to navigate through the paranasal sinuses and hence avoid injury to these structures. This study is aimed to determine the prevalence of the Onodi cell in the Polish population and compare it with other reported occurrences. Materials and methods: A retrospective analysis of 296 computed tomography (CT) scans of patients treated in Cracow, Poland, using a Siemens Somatom Sensation 16 spiral CT scanner. No contrast medium was administered. Results: The Onodi cell was found in 31 out of the 296 patients, or approximately 10.5%, consistent with the majority of research reporting on Onodi variants. Additionally, there was one presentation of a bilateral Onodi cell in a male patient. No statistically significant difference was found between the male and female populations with a positive identification of the variant (p = 0.095, Chi2 test). Conclusions: This study helped approximate the Onodi variant prevalence of 10.47%, falling within a commonly reported range 8-14%. This gives clinicians and surgeons a better understanding of this variant's structure and significance, and therefore an opportunity to improve treatment outcomes and research