Charles S. Peirce introduced in the late 19th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from (...) their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.Keywords: Abduction; Inference to the best explanation; Inverse problems; Peirce; Radon’s theorem; Tomography. (shrink)

In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase (...) space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables. (shrink)

IntroductionDeep brain stimulation is an effective treatment for advanced Parkinson’s disease with the targeting bilateral subthalamic nucleus or globus pallidus internus. So far, detailed studies on the efficacy of unilateral STN-DBS for motor symptoms have been reported, but few studies have been conducted on unilateral GPi-DBS.Materials and MethodsSeventeen patients with Parkinson’s disease who underwent unilateral GPi-DBS were selected. We conducted comparison analyses between scores obtained 6–42 months pre- and postoperatively using the following measurement tools: the Movement Disorder Society Unified Parkinson’s (...) Disease Rating Scale part III, the Hoehn and Yahr stage, the presence/absence of dyskinesia, Mini-Mental State Examination, Frontal Assessment Battery, Geriatric Depression Scale, levodopa equivalent dose, and cerebral blood flow by single photon emission computed tomography. Patient backgrounds were compared between four cohorts with favorable and unfavorable postoperative outcome.ResultsSignificant improvement was observed postoperatively in the following: total MDS-UPDRS Part III scores during the off period, contralateral scores, ipsilateral scores, and axial scores. Similarly, the Hoehn and Yahr stages during the off period, and GDS also showed significant decrease. In contrast, LED, MMSE, and FAB remained unchanged while the number of patients who scored positive for dyskinesia decreased by 40%. Abnormal cerebral blood flow preoperatively seen in the cerebral cortex had normalized in the total score-based good responder cohort. In the ipsilateral score-based good responder cohort, cerebral blood flow increased in the contralateral frontal lobe including in the premotor cortex, contralateral to the DBS. Compared to the poor responders, postoperative good responders demonstrated significantly higher preoperative MMSE scores.DiscussionUnilateral GPi-DBS therapy was effective in improving contralateral, ipsilateral, and axial motor symptoms of patients with advanced PD; in particular, it was found to be especially beneficial in PwPD whose cognitive function was unimpaired; the treatment efficacy rivaled that of bilateral counterparts up till at least 6 months postoperatively. Finally, normalization of preoperative abnormalities in cerebral blood flow and increased cerebral blood flow in the contralateral frontal lobe indicated the beneficial potential of this therapy on ipsilateral motor symptoms. (shrink)

Stiff Person Syndrome is a rare autoimmune disorder associated with antibodies against glutamic acid decarboxylase, the key enzyme in γ -aminobutyric acid synthesis. In order to investigate the role of cerebral benzodiazepinereceptor binding in SPS, we performed [ 11 C]flumazenil positron emission tomography in a female patient with SPS compared to nine healthy controls. FMZ is a radioligand to the postsynaptic central benzodiazepine receptor which is co-localized with the GABA-A receptor. In the SPS patient, we found a global reduction (...) of cortical FMZ binding. In addition, distinct local clusters of reduced radiotracer binding were observed. These data provide first in vivo evidence for a reduced postsynaptic GABA-A receptor availability which may reflect the loss of GABAergic neuronal inhibition in SPS. (shrink)

This paper aims to trace individual as well as collective aspects of ‘sight styles’ in diagnostic computed tomography. Radiologists need to efficiently translate the visualized data from the living human body into a reliable and significant diagnosis. During this process, their visual thinking and the created images are incorporated into a complex network of other visualizations, communication strategies, professional traditions, and (tacit) visual knowledge. To investigate the interplay of collective as well as individual dimensions of diagnostic seeing, the concept (...) of ‘sight collective’ (Sehkollektiv) is developed. On the one hand, this concept is based on critical reading of Ludwik Fleck’s epistemological writings and his notions of thought collective (Denkkollektiv) and thought style (Denkstil). On the other hand, it is tested by means of qualitative empirical studies in a radiological university clinic (participatory observations and informal interviews). By employing this approach, the paper traces the collective foundations of a certain diagnostic sight. Moreover, it shows how the individual abilities of radiologists to perform stylized seeing rely remarkably on software-based interactions with the processed images and on tacit dimensions of visual knowledge. (shrink)

High throughput time-resolved observations of accreting collapsed objects at X-ray energies provide key information on the motions of matter orbiting a few gravitational radii away from black holes. Predictions of general relativity in the strong field regime, such as relativistic epicyclic motions, precession, light bending and the presence and radius of an innermost stable circular orbit in the close vicinity of a black hole can be verified by making use of two powerful diagnostics, namely relativistically broadened \ lines and variability (...) on dynamical timescales, quasi periodic oscillations in particular. Moreover tomography and reverberation techniques relying upon combined spectral timing and polarimetric timing provide an entirely new perspective in the field. Both the low and high spacetime curvature regimes of gravity can be probed by studying black holes of vastly different masses in X-ray binaries and Active Galactic Nuclei, opening up the possibility of testing also some alternative theories of gravity. To achieve these goals, very large area X-ray instrumentation with good spectral resolution and polarimetric capability is required. Prospects and projects in this area of research are briefly surveyed. (shrink)

Here we review 37 modern neuroimaging studies in an attempt to address this question posed by Halstead (1947) as he and other icons of the last century endeavored to understand how brain and behavior are linked through the expression of intelligence and reason. Reviewing studies from functional (i.e., functional magnetic resonance imaging, positron emission tomography) and structural (i.e., magnetic resonance spectroscopy, diffusion tensor imaging, voxel-based morphometry) neuroimaging paradigms, we report a striking consensus suggesting that variations in a distributed network (...) predict individual differences found on intelligence and reasoning tasks. We describe this network as the Parieto-Frontal Integration Theory (P-FIT). The P-FIT model includes, by Brodmann areas (BAs): the dorsolateral prefrontal cortex (BAs 6, 9, 10, 45, 46, 47), the inferior (BAs 39, 40) and superior (BA 7) parietal lobule, the anterior cingulate (BA 32), and regions within the temporal (BAs 21, 37) and occipital (BAs 18, 19) lobes. White matter regions (i.e., arcuate fasciculus) are also implicated. The P-FIT is examined in light of findings from human lesion studies, including missile wounds, frontal lobotomy/leukotomy, temporal lobectomy, and lesions resulting in damage to the language network (e.g., aphasia), as well as findings from imaging research identifying brain regions under significant genetic control. Overall, we conclude that modern neuroimaging techniques are beginning to articulate a biology of intelligence. We propose that the P-FIT provides a parsimonious account for many of the empirical observations, to date, which relate individual differences in intelligence test scores to variations in brain structure and function. Moreover, the model provides a framework for testing new hypotheses in future experimental designs. (shrink)

Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in a (...) single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated. (shrink)

Advanced medical imaging, such as CT, fMRI and PET, has undergone enormous progress in recent years, both in accuracy and utilization. Such techniques often bring with them an illusion of immediacy, the idea that the body and its diseases can be directly inspected. In this paper we target this illusion and address the issue of the reliability of advanced imaging tests as knowledge procedures, taking positron emission tomography in oncology as paradigmatic case study. After individuating a suitable notion of (...) reliability, we argue that PET is a highly theory-laden and non-immediate knowledge procedure, in spite of the photographic-like quality of the images it delivers; the diagnostic conclusions based on the interpretation of PET images are population-dependent; PET images require interpretation, which is inherently observer-dependent and therefore variable. We conclude with a three-step methodological proposal for enhancing the reliability of advanced medical imaging. (shrink)

ObjectivesTo simulate hemodynamic changes after extraluminal compression in pulsatile tinnitus patients with a prominent transverse-sigmoid sinus junction.MethodsOne patient-specific case was reconstructed based on computed tomography venography images of a PT patient. The compression degree served as a new index in this study. Cases with 10, 20, 30, 40, 50, 60, 70, 80, and 90% of the compression degree of the control subject were constructed. Steady-state computational fluid dynamics were assessed. The wall pressure distribution, wall maximum pressure and flow pattern (...) of the PTSJ were calculated to evaluate hemodynamic differences among all cases.ResultsWith increasing compression, the wall pressure at the compression point and downstream of the PTSJ decreased but increased upstream. When the compression degree exceeded 70%, the upstream pressure increased significantly. Above 50% compression, the blood flow pattern downstream of the sigmoid sinus tended to spiral, especially after 80% compression. Beyond 60% compression, the blood flow pattern under the compression axis became more medial.ConclusionMechanical compression of PTSJ changes wall pressure and blood flow patterns. The degree of compression should be carefully observed to avoid possible complications or reoccurrence. (shrink)

Continuous recordings of brain electrical activity were obtained from a group of 176 patients throughout surgical procedures using general anesthesia. Artifact-free data from the 19 electrodes of the International 10/20 System were subjected to quantitative analysis of the electroencephalogram (QEEG). Induction was variously accomplished with etomidate, propofol or thiopental. Anesthesia was maintained throughout the procedures by isoflurane, desflurane or sevoflurane (N = 68), total intravenous anesthesia using propofol (N = 49), or nitrous oxide plus narcotics (N = 59). A set (...) of QEEG measures were found which reversibly displayed high heterogeneity of variance between four states as follows: (1) during induction; (2) just after loss of consciousness (LOC); (3) just before return of consciousness (ROC); (4) just after ROC. Homogeneity of variance across all agents within states was found. Topographic statistical probability images were compared between states. At LOC, power increased in all frequency bands in the power spectrum with the exception of a decrease in gamma activity, and there was a marked anteriorization of power. Additionally, a significant change occurred in hemispheric relationships, with prefrontal and frontal regions of each hemisphere becoming more closely coupled, and anterior and posterior regions on each hemisphere, as well as homologous regions between the two hemispheres, uncoupling. All of these changes reversed upon ROC. Variable resolution electromagnetic tomography (VARETA) was performed to localize salient features of power anteriorization in three dimensions. A common set of neuroanatomical regions appeared to be the locus of the most probable generators of the observed EEG changes. (shrink)

The method of positron emission tomography (PET imaging) illustrates the circular logic popular in subtractive neuroimaging and linear reductive cognitive psychology. Both require that strictly feed-forward, modular, cognitive components exist, before the fact, to justify the inference of particular components from images (or other observables) after the fact. Also, both require a "true" componential theory of cognition and laboratory tasks, before the fact, to guarantee reliable choices for subtractive contrasts. None of these possibilities are likely. Consequently, linear reductive analysis (...) has failed to yield general, reliable, componential accounts. (shrink)

A great variety of medical conditions are subject to the placebo effect. Although there is mounting evidence to suggest that the placebo effect is related to the expectation of clinical benefit, little is still known about the biochemical bases underlying placebo responses. Positron emission tomography studies have recently shown that the placebo effect in Parkinson’s disease, pain, and depression is related to the activation of the limbic circuitry. The observation that placebo administration induces the release of dopamine in the (...) ventral striatum of patients with Parkinson’s disease suggests a link between the placebo effect and reward mechanisms. In addition to Parkinson’s disease, the placebo-reward model may also apply to other disorders. However, the relative contribution of the different neurotransmitters and neuropeptides that are known to be involved in modulating the activity of the limbic system may be disease-specific. Thus, while the placebo-induced clinical benefit observed in Parkinson’s disease would mostly reflect the release of dopamine in the dorsal striatum, the activation of opioid and serotonin pathways could be particularly implicated in mediating placebo responses encountered in pain and depression, respectively. (shrink)

The neural substrates of context effects in word perception are still largely unclear. Interhemispheric priming phenomena in word recognition, typically observed in normal subjects, are absent in commissurotomized patients. This suggests that callosal fibers may provide contextual integration. In addition, certain characteristics of human frontal cortical fields subserving sensorimotor learning, as investigated by positron emission tomography, provide evidence for contextual integration not confined to the visual system. This supports the notion of common aspects of cortical computations in different cerebral (...) areas. (shrink)

While philosophers have, for centuries, pondered upon the relation between mind and brain, neuroscientists have only recently been able to explore the connection analytically — to peer inside the black box. This ability stems from recent advances in technology and emerging neuroimaging modalities. It is now possible not only to produce remarkably detailed images of the brain’s structure (i.e. anatomical imaging) but also to capture images of the physiology associated with mental processes (i.e. functional imaging). We are able to see (...) how specific regions of the brain ‘light up’ when activities such as reading this book are performed, and how our neurons and their elaborate cast of supporting cells organize and coordinate their tasks. As demonstrated in the other chapters of this book, the mapping of the human mind (mostly by measuring regional changes in blood flow, initially by positron emission tomography (PET) and recently by functional magnetic resonance imaging or (fMRI)) has provided insight into the functional neuroanatomy of neuropsychiatric diseases. Amazingly, the idea that regional cerebral blood flow (rCBF) is related intimately to brain function goes back more than a century. As is often the case in science, this idea was initially the result of unexpected observations. The Italian physiologist Angelo Mosso first expressed the idea while studying pulsations of the living human brain that keep pace with the heartbeat (Mosso, 1881). These brain pulsations can be observed on the surface of the fontanelles in newborn children. Mosso believed that they reflected blood flow to the brain. He observed similar pulsations in an adult with a post-traumatic skull defect over the frontal lobes. While studying this subject, a peasant named Bertino, Mosso observed a sudden increase in the magnitude of the ‘brain’s heart-beats’ when the church bells signalled 12 o’clock, the time for a required prayer. The changes in brain pulsations occurred independently of any change in pulsations in the forearm.. (shrink)

Here we report that a specific form of yoga can generate controlled high-frequency gamma waves. For the first time, paroxysmal gamma waves were observed in eight subjects practicing a yoga technique of breathing control called Bhramari Pranayama . To obtain new insights into the nature of the EEG during BhPr, we analyzed EEG signals using time-frequency representations , independent component analysis , and EEG tomography . We found that the PGW consists of high-frequency biphasic ripples. This unusual activity is (...) discussed in relation to previous reports on yoga and meditation. It is concluded this EEG activity is most probably non-epileptic, and that applying the same methodology to other meditation recordings might yield an improved understanding of the neurocorrelates of meditation. (shrink)

This article presents a case study of a recent controversy over the use of computed tomography as a diagnostic technology in South Korean hospitals. The controversy occurred in the wake of a series of conflicts in the late twentieth century over the legitimate placement of healing practices, medicinal substances, and medical technologies within Korea’s separate “Western Medicine” and “Korean Medicine” systems of health care and pharmaceutical distribution. The controversy concerned an attempt to use hi-tech imaging technology—the epitome of modern (...) medicine—in a clinic that maintains a strong ideological attachment to Korean healing traditions. A close study of this dispute, based on interviews, participant observation, and documentary analysis, showed that discursive positions taken about the translatability of medical technologies changed with the context of dispute, and did not reflect a stable epistemic boundary between rival medical paradigms. (shrink)

A great variety of medical conditions are subject to the placebo effect. Although there is mounting evidence to suggest that the placebo effect is related to the expectation of clinical benefit, little is still known about the biochemical bases underlying placebo responses. Positron emission tomography studies have recently shown that the placebo effect in Parkinson’s disease, pain, and depression is related to the activation of the limbic circuitry. The observation that placebo administration induces the release of dopamine in the (...) ventral striatum of patients with Parkinson’s disease suggests a link between the placebo effect and reward mechanisms. In addition to Parkinson’s disease, the placebo-reward model may also apply to other disorders. However, the relative contribution of the different neurotransmitters and neuropeptides that are known to be involved in modulating the activity of the limbic system may be disease-specific. Thus, while the placebo-induced clinical benefit observed in Parkinson’s disease would mostly reflect the release of dopamine in the dorsal striatum, the activation of opioid and serotonin pathways could be particularly implicated in mediating placebo responses encountered in pain and depression, respectively. (shrink)

Centriole duplication has been an area of interest since the late 1800s when Boveri suggested that these structures were central organizers for mitosis and cell division. Two groups1, 2 have delineated a linear pathway for centriole assembly. In C. elegans, Pelletier and coworkers1 have identified intermediates in the pathway using cryo‐electron tomography. Surprising, the first intermediate is a hollow tube of 60 nm that increases in diameter and then elongates before acquiring microtubules. Similar structures have not been observed to (...) date in other centrioles. BioEssays 29:630–634, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

Revonsuo argues that current brain imaging methods do not allow us to ‘discover’ consciousness. While all observational methods in science have limitations, consciousness is such a massive and pervasive phenomenon that we cannot fail to observe its effects at every level of brain organization: molecular, cellular, electrical, anatomical, metabolic, and even the ‘higher levels of electrophysiological organization that are crucial for the empirical discovery and theoretical explanation of consciousness’ . Indeed, the first major discovery in that respect was Hans Berger's (...) finding that scalp EEG is massively different between waking and deep sleep, already seven decades ago. We now have perhaps a dozen sophisticated methods for monitoring consciousness-related activity at multiple levels of brain observation. Theoretical progress has come quite rapidly. Recently, E.R. John and colleagues have made fundamental findings using Quantitative EEG, showing consistent brainwide changes as a result of several types of general anaesthetics . John has proposed a neuronal ‘field theory’ to account for those results. Another promising new method involves frequency-tagging of competing stimuli, allowing us to follow the activity of billions of neurons synchronized to particular conscious stimuli, always compared to very similar unconscious input . A fundamental theoretical account of such results has been provided by Tononi & Edelman . Such results and theory are in broad agreement with the cognitive theory proposed by Baars. (shrink)

Several arguments are considered which purport to demonstrate the impossibility of theory-neutral observation. The most important of these infers the continuity of observation with theory from the presumed continuity of perception with cognition, a doctrine widely espoused in recent cognitive psychology. An alternative psychological account of the relation between cognition and perception is proposed and its epistemological consequences for the observation/theory distinction are then explored.

The concept of generalized observable in the scheme of Hilbert quantum mechanics is discussed. We give an example of a possible ambiguity of this notion. The role of interpretation and the strong connection with concrete experimental procedures in the discussion of generalized observables are stressed to explain the above ambiguity.

The circular arc swept out by the angular displacement of a clock indicator (or its equivalent representation) measuring time is shown to be a Lorentz invariant, representing “universal” time. The concepts of time dilation and transverse Doppler effect are accordingly not physically observable. The experiments on these effects when examined critically are found to be inconclusive. Length contraction, also experimentally unconfirmed, and kinematic temporal phase, both consequences of the Lorentz transformations, are as a matter of logical consistency also physically (...) unobservable. (shrink)

This is an entry to the Compendium of Quantum Physics, edited by F Weinert, K Hentschel and D Greenberg, to be published by Springer-Verlag.

Psychologists sometimes discuss the need to refine clear designations of the observable units comprising their subject matter. This paper links such discussions to (a) Dewey and Bentley's (1949) account of specification as relatively accurate unit-designation, and (b) the logical base of scientific classifications and abstractions in observable particulars. The paper then reviews, clarifies, evaluates, and contrasts the psychological units proposed by Kantor (behavior segment), Skinner (operant), and Lee (deed). Overall, Lee's deed is found to be the sharpest, least (...) ambiguous designation, and the only specification. Deeds, fields of contributors, and contingencies are then used to selectively integrate aspects of all three units. The resulting integration is consistent with field-based approaches to causal relations within and among units, where the noun cause is synonymous with one of many contributors. It is also applicable to the analysis of feedback loops, which are designated as circular networks of dependency among subclasses of deeds. (shrink)

In a recent paper in this journal, Kosso ([2000]) discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by 't Hooft ([1980]) has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper, we present our preferred approach to the empirical significance of symmetries, re-analysing (...) the cases of gauge symmetry and general covariance. Direct and indirect empirical significance Global and local continuous symmetries Gauge symmetry 3.1 Local gauge symmetry 3.1.1 Discussion of the first claim 3.1.2 Discussion of the second claim 3.2 Global gauge symmetry Space-time symmetries Direct and indirect empirical significance again Conclusion. (shrink)

: I reformulate and elaborate on important claims relevantly put for debate by the commentators, i.e., counterfactuals are a form of observable experience rather than a plurality of ….

In his recent 2018 book, Resisting Scientific Realism, K. Brad Wray provides a detailed, full-fledged defense of anti-realism about science. In this paper, I argue against the two main claims that constitute Wray’s positive and novel argument for his position, viz., his suggested Darwinian-selectionist explanation of the success of science and his skepticism about unobservables based on radical theory change. My goal is not wholly negative though. Instead, I aim to identify the type of work that an anti-realist like Wray (...) would need to undertake in order to further substantiate their position, viz., taking a stance on inductive inference and support, and the type of realist and anti-realist positions that seem viable. (shrink)

Most versions of the knowledge argument say that if a scientist observing my brain does not know what my consciousness 'is like,' then consciousness is not identical with physical brain processes. This unwarrantedly equates 'physical' with 'empirically observable.' However, we can conclude only that consciousness is not identical with anything empirically observable. Still, given the intimate connection between each conscious event and a corresponding empirically observable physiological event, what P-C relation could render C empirically unobservable? Some suggest (...) that C is a relation among Ps which is distinguishable because it is multi-realizable; that is, C could have been realized by P2 rather than P1 and still have been the same relation. C might even be a 'self-organizing' process, appropriating and replacing its own material substrata. How can this account explain the empirical unobservability of consciousness? Because the emotions motivating attention direction, partly constitutive of phenomenal states, are executed, not undergone, by organisms. Organisms-self-organizing processes actively appropriating their needed physical substrata-feel motivations by generating them. Thus, experiencing someone's consciousness entails executing his or her motivations. (shrink)

Most versions of the knowledge argument say that, since scientists observing my brain wouldn't know what my consciousness "is like," consciousness isn't describable as a physical process. Although this argument unwarrantedly equates the physical with the empirically observable, we can conclude, not that consciousness is nonphysical but that consciousness isn't identical with anything empirically observable. But what kind of mind&endash;body relation would render possible this empirical inaccessibility of consciousness? Even if multiple realizability may allow a distinction between consciousness (...) and its physical substrata, why does this distinction make consciousness empirically unobservable? The reason must be that the emotions motivating attention direction, partly constitutive of phenomenal states, are executed, not undergone by self-organizing processes actively appropriating and replacing needed physical substrata; we feel motivations by generating them. But all consciousness is motivated; visual cortex activation is unconscious of red unless the emotional limbic system and anterior cingulate motivatedly "look for" red. Experiencing entails executing motivations. Experimenters do know what subjects' brain events "are like" ---; but from the standpoint of the experimenter's motivational processes. (shrink)