Topological Aspects of Epistemology and Metaphysics

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle

On the isomorphism problem of concept algebras

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in \cite{Kw04}, is whether complete {\wdl}s are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem \ref{T:main}). We also provide a new proof of a well known result due to M.H. Stone \cite{St36}, saying that {\em each Boolean algebra is a field of sets} (Corollary \ref{C:Stone}). Before these, we prove that the boundedness condition on the initial definition of {\wdl}s (Definition \ref{D:wdl}) is superfluous (Theorem \ref{T:wcl}, see also \cite{Kw09}).Comment: 15 page

Resistance training volume load with and without exercise displacement

Monitoring the resistance training volume load (VL) (sets × reps × load) is essential to managing resistance training and the recovery⁻adaptation process. Eight trained weightlifters, seven of which were at national level, participated in the study. VL was measured both with (VLwD) and without (VL) the inclusion of barbell displacement, across twenty weeks of training, in order to allow for comparisons to be made of these VL calculating methods. This consisted of recording the load, repetition count, and barbell displacement for every set executed. Comparisons were made between VL and VLwD for individual blocks of training, select training weeks, and select training days. Strong, statistically significant correlations (r ≥ 0.78, < 0.001) were observed between VL and VLwD between all training periods analyzed. -tests revealed statistically significant ( ≤ 0.018) differences between VL and VLwD in four of the seven training periods analyzed. The very strong relationship between VL and VLwD suggest that a coach with time constraints and a large number of athletes can potentially spare the addition of displacement. However, differences in percent change indicate that coaches with ample time should include displacement in VL calculations, in an effort to acquire more precise workload totals

Normalization of early isometric force production as a percentage of peak force during multijoint isometric assessment

Purpose: To determine the reliability of early force production (50-, 100-, 150-, 200-, 250 ms) relative to peak force (PF) during an isometric mid-thigh pull (IMTP) and assess the relationships between these variables. Methods: Male collegiate athletes (n = 29; age: 21.1 ± 2.9 years; height: 1.71 ± 0.07 m; body mass: 71.3 ± 13.6 kg) performed IMTPs during two separate testing sessions. Net PF and net force produced at each epoch were calculated. Within- and between-session reliability were determined by using intraclass correlation coefficients (ICC) and coefficient of variation (CV%). Additionally, Pearson’s correlation coefficients and coefficient of determination, were calculated to examine the relationships between PF and time-specific force production. Results: Net PF and time-specific force demonstrated very high to almost perfect reliability both within- and between-sessions (ICCs 0.82-0.97; CV% 0.35-1.23%). Similarly, time-specific force expressed as a percentage of PF demonstrated very high to almost perfect reliability both within- and between-sessions (ICCs 0.76-0.86; CV% 0.32-2.51%). Strong to nearly perfect relationships (r = 0.615-0.881) exist between net PF and time-specific net force, with relationships improving over longer epochs. Conclusion: Based on the smallest detectable difference, a change in force at 50 ms expressed relative to PF >10% and early force production (100-, 150-, 200- and 250 ms) expressed relative to PF of >2% should be considered meaningful. Expressing early force production as a percentage of PF is reliable and may provide greater insight into the adaptations to the previous training phase than PF alone

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established

Epistemic and Ontic Quantum Realities

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position

Is a questionnaire and radiograph-based follow-up model for patients with primary hip and knee arthroplasty a viable alternative to traditional regular outpatient follow-up clinic?

Aims Increasing demand for total hip and knee arthroplasty (THA/TKA) and associated follow-up has placed huge demands on orthopaedic services. Feasible follow-up mechanisms are therefore essential. Methods We conducted an audit of clinical follow-up decision-making for THA/TKA based on questionnaire/radiograph review compared with local practice of Arthroplasty Care Practitioner (ACP)-led outpatient follow-up. In all 599 patients attending an ACP-led THA/TKA follow-up clinic had a pelvic/knee radiograph, completed a pain/function questionnaire and were reviewed by an ACP. An experienced orthopaedic surgeon reviewed the same radiographs and questionnaires, without patient contact or knowledge of the ACP’s decision. Each pathway classified patients into: urgent review, annual monitoring, routine follow-up or discharge. Results In total, 401 hip and 198 knee patients were included. There was substantial agreement between the ACP and surgeon for both hip (kappa = 0.69, 95% confidence interval (CI) 0.62 to 0.76) and knee (kappa = 0.81, 95% CI 0.74 to 0.88). Positive agreement was very high for discharge and routine follow-up; however the ACP was more likely to select annual monitoring and the surgeon urgent review. Discussion Review of the questionnaire/radiograph together identified all patients in need of increased surveillance, with good agreement for on-going patient management. However, review of the radiograph or questionnaire alone missed some patients with potential problems. A radiograph in conjunction with a questionnaire as a review may represent a cost effective THA/TKA follow-up mechanism. Take home message: A questionnaire and radiograph-based remote review may represent a cost-effective total joint arthroplasty follow-up mechanism; thereby reducing the considerable burden that follow-up currently places on the NHS. Cite this article: Bone Joint J 2016;98-B:201–8. </jats:sec

Constructive pointfree topology eliminates non-constructive representation theorems from Riesz space theory

In Riesz space theory it is good practice to avoid representation theorems which depend on the axiom of choice. Here we present a general methodology to do this using pointfree topology. To illustrate the technique we show that almost f-algebras are commutative. The proof is obtained relatively straightforward from the proof by Buskes and van Rooij by using the pointfree Stone-Yosida representation theorem by Coquand and Spitters

Moduli spaces of toric manifolds

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version, 19 pages, 6 figure

Panic disorder and locomotor activity

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens