Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.Comment: 20 page

The patient acceptable symptom state for knee pain - a systematic literature review and meta-analysis

Purpose: Knee pain is highly prevalent, most commonly attributed to osteoarthritis in older people, and in younger people often due to internal derangements. Knee pain can be measured using numerical patient-reported outcome measures (PROMs). Several pain measurement questionnaires have been used for OA pain. These questionnaires each purport to measure the participant’s experience of pain, but may address different pain characteristics (recollection over different time periods, pain impact on function, constant or intermittent or other qualitative aspects of pain). Pooling pain data between studies using different PROMs requires demonstration or transformation to ensure that each PROM would give the same value for pain in a single participant. The Patient Acceptable Symptoms State (PASS) indicates a clinical benchmark that permits comparison between PROMs. Current treatments might relieve but often do not eliminate pain, and PASS is the threshold representing pain which a patient would accept for the remainder of their life. We aimed to systematically review PASS thresholds for different pain PROMs used with people with knee pain, and to identify factors that might influence PASS heterogeneity.Methods: We systematically reviewed literature for PASS scores in knee pain using searches of CENTRAL, MEDLINE, EMBASE, AMED, CINAHL, and SPORTDiscus databases from their inception date up to June 2020. PROMs of interest were pain-specific questionnaires (or their related domains). Title screening, data extraction, and methodological quality assessments were performed independently by 2 reviewers. Outcome scores were standardised and included in meta-analysis models as a 0-100 scale (0: no pain, 100: highest pain severity). Based on a-priori hypotheses (PROMs, diagnoses, interventions, follow-up timepoints and methodological quality) and following review of data from included studies (PASS score derivation methods), potential effects of study and patient characteristics on PASS were explored. Post-hoc meta-regression explored the relationship between baseline pain and PASS scores. The significance of differences observed between subgroups was evaluated via a Cochran's Q-test. Study heterogeneity was evaluated with the I2 statistic. Results: Eighteen eligible studies (n=7766 participants) reported PASS from pain PROMs in people with knee pain. All studies were longitudinal and observational, undertaken within the context of a treatment for knee pain. Identified PROMS were the Knee Injury and Osteoarthritis Outcome Score (KOOS), Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), the Numerical Rating Scale (NRS) and the Visual Analogue Scale (VAS). Most studies were of low risk of bias (8/18), with 6/18 of moderate and 4/18 of high risk of bias. Thirteen studies (n=6339 participants) reported data that allowed their inclusion in metaanalysis models. The pooled pain PASS score was 27 (95%CI: 21 to 35; n=6339 participants) with significant heterogeneity (I2 =96%, p <0.01) (Figure). No significant differences (Q=2.07, p = 0.36) were observed between PASS scores derived for the different knee pain PROMs (KOOS: 23, 95%CI: 16 to 30; WOMAC: 28, 95% CI: 23 to 32; NRS or VAS: 35, 95%CI: 24 to 45). Lower estimates of PASS were associated with lower baseline pain (β=0.60, p=0.02), longer time to follow up at which PASS was estimated (6-months 30, 95%CI: 20 to 40; 12-months: 24, 95%CI: 17 to 30; more than 12-months: 16, 95% CI: 9 to 22), and with surgical (24, 95%CI: 17 to 30) rather than non-surgical interventions (40, 95%CI: 29 to 52). PASS scores were similar between knee osteoarthritis (31, 95%CI: 26 to 36) and meniscal tear (27, 95%CI: 20 to 35) but lower for ligament tears (12, 95%CI: 11 to 13). Observed differences in estimates of PASS due to risk of bias (low: 23, 95%CI: 11 to 35; moderate: 34, 95%CI: 24 to 45; high: 26, 95%CI: 21 to 31) were not significant (Q=1.93, p = 0.38).Conclusions: Standardised knee pain PROMs scores of approximately 30/100 are considered acceptable by people with knee pain. The level of pain that is acceptable might depend upon the baseline pain severity (higher with worse baseline pain), decrease with time from commencing an intervention and vary according to diagnostic or treatment group. However, different knee pain PROMs when transformed produce similar PASS scores, suggesting that standardised scores derived from multiple instruments might be validly combined in large multicentre studies using historically collected data

CCL2 and CCR2 regulate pain-related behaviour and early gene expression in post-traumatic murine osteoarthritis but contribute little to chondropathy

SummaryObjectiveThe role of inflammation in structural and symptomatic osteoarthritis (OA) remains unclear. One key mediator of inflammation is the chemokine CCL2, primarily responsible for attracting monocytes to sites of injury. We investigated the role of CCL2 and its receptor CCR2 in experimental OA.DesignOA was induced in 10 weeks old male wild type (WT), Ccl2−/− and Ccr2−/− mice, by destabilisation of the medial meniscus (DMM). RNA was extracted from whole joints at 6 h and 7 days post-surgery and examined by reverse transcription polymerase chain reaction (RT-PCR). Gene expression changes between naïve and DMM-operated mice were compared. Chondropathy scores, from mice at 8, 12, 16 and 20 weeks post DMM were calculated using modified Osteoarthritis Research Society International (OARSI) grading systems. Changes in hind paw weight distribution, as a measure of pain, were assessed by Linton incapacitance.ResultsAbsence of CCL2 strongly suppressed (>90%) selective inflammatory response genes in the joint 6 h post DMM, including arginase 1, prostaglandin synthase 2, nitric oxide synthase 2 and inhibin A. IL6, MMP3 and tissue inhibitor of metalloproteinase 1 were also significantly suppressed. Similar trends were also observed in the absence of CCR2. A lower average chondropathy score was observed in both Ccl2−/− and Ccr2−/− mice at 12, 16 and 20 weeks post DMM compared with WT mice, but this was only statistically significant at 20 weeks in Ccr2−/− mice. Pain-related behaviour in Ccl2−/− and Ccr2−/− mice post DMM was delayed in onset.ConclusionThe CCL2/CCR2 axis plays an important role in the development of pain in murine OA, but contributes little to cartilage damage

From Linear to Nonlinear Response in Spin Glasses: Importance of Mean-Field-Theory Predictions

Deviations from spin-glass linear response in a single crystal Cu:Mn 1.5 at % are studied for a wide range of changes in magnetic field, $\Delta H$. Three quantities, the difference $TRM-(MFC-ZFC)$, the effective waiting time, $t_{w}^{eff}$, and the difference $TRM(t_{w})-TRM(t_{w}=0)$ are examined in our analysis. Three regimes of spin-glass behavior are observed as $\Delta H$ increases. Lines in the $(T,\Delta H)$ plane, corresponding to ``weak'' and ``strong'' violations of linear response under a change in magnetic field, are shown to have the same functional form as the de Almeida-Thouless critical line. Our results demonstrate the existence of a fundamental link between static and dynamic properties of spin glasses, predicted by the mean-field theory of aging phenomena.Comment: 9 pages, 10 figure

Mechanical forces couple bone matrix mineralization with inhibition of angiogenesis to limit adolescent bone growth

Bone growth requires a specialised, highly angiogenic blood vessel subtype, so-called type H vessels, which pave the way for osteoblasts surrounding these vessels. At the end of adolescence, type H vessels differentiate into quiescent type L endothelium lacking the capacity to promote bone growth. Until now, the signals that switch off type H vessel identity and thus limit adolescent bone growth have remained ill defined. Here we show that mechanical forces, associated with increased body weight at the end of adolescence, trigger the mechanoreceptor PIEZO1 and thereby mediate enhanced production of the kinase FAM20C in osteoblasts. FAM20C, the major kinase of the secreted phosphoproteome, phosphorylates dentin matrix protein 1, previously identified as a key factor in bone mineralization. Thereupon, dentin matrix protein 1 is secreted from osteoblasts in a burst-like manner. Extracellular dentin matrix protein 1 inhibits vascular endothelial growth factor signalling by preventing phosphorylation of vascular endothelial growth factor receptor 2. Hence, secreted dentin matrix protein 1 transforms type H vessels into type L to limit bone growth activity and enhance bone mineralization. The discovered mechanism may suggest new options for the treatment of diseases characterised by aberrant activity of bone and vessels such as osteoarthritis, osteoporosis and osteosarcoma

Energy and decay width of the pi-K atom

The energy and decay width of the pi-K atom are evaluated in the framework of the quasipotential-constraint theory approach. The main electromagnetic and isospin symmetry breaking corrections to the lowest-order formulas for the energy shift from the Coulomb binding energy and for the decay width are calculated. They are estimated to be of the order of a few per cent. We display formulas to extract the strong interaction S-wave pi-K scattering lengths from future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra

Translation of clinical problems in osteoarthritis into pathophysiological research goals

Osteoarthritis (OA) accounts for more disability among the elderly than any other disease and is associated with an increased mortality rate. The prevalence in Europe will rise in the future since this continent has a strongly ageing population and an obesity epidemic; obesity and age both being major risk factors for OA. No adequate therapeutic options, besides joint replacement, are available, although they are greatly needed and should be acquired by adequate research investments. However, the perspective on OA from a researcher's point of view is not always aligned with the perspective of a patient with OA. Researchers base their views on OA mainly on abnormalities in structure and function while patients consider OA as a collection of symptoms. In this viewpoint paper, we discuss the possibility of translating the most important clinical problems into pathophysiological research goals to facilitate the translation from bench to bedside and vice versa. This viewpoint is the outcome of a dialogue within the 'European League Against Rheumatism study group on OA' and People with Arthritis/Rheumatism across Europe (PARE) representatives

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics