Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Hyperacute Directional Hearing and Phonotactic Steering in the Cricket (Gryllus bimaculatus deGeer)

Background: Auditory mate or prey localisation is central to the lifestyle of many animals and requires precise directional hearing. However, when the incident angle of sound approaches 0u azimuth, interaural time and intensity differences gradually vanish. This poses a demanding challenge to animals especially when interaural distances are small. To cope with these limitations imposed by the laws of acoustics, crickets employ a frequency tuned peripheral hearing system. Although this enhances auditory directionality the actual precision of directional hearing and phonotactic steering has never been studied in the behaviourally important frontal range. Principal Findings: Here we analysed the directionality of phonotaxis in female crickets (Gryllus bimaculatus) walking on an open-loop trackball system by measuring their steering accuracy towards male calling song presented at frontal angles of incidence. Within the range of 630u, females reliably discriminated the side of acoustic stimulation, even when the sound source deviated by only 1u from the animal’s length axis. Moreover, for angles of sound incidence between 1u and 6u the females precisely walked towards the sound source. Measuring the tympanic membrane oscillations of the front leg ears with a laser vibrometer revealed between 0u and 30u a linear increasing function of interaural amplitude differences with a slope of 0.4 dB/u. Auditory nerve recordings closely reflected these bilateral differences in afferent response latency and intensity that provide the physiological basis for precise auditory steering

Comparison of bacterial microbiota of the predatory mite Neoseiulus cucumeris (Acari: Phytoseiidae) and its factitious prey Tyrophagus putrescentiae (Acari: Acaridae)

Neoseiulus cucumeris is a predatory mite used for biological control of arthropod pests. Mass-reared predators are fed with factitious prey mites such as Tyrophagus putrescentiae. Although some information on certain endosymbionts of N. cucumeris and T. putrescentiae exists, it is unclear whether both species share bacterial communities. The bacterial communities in populations of predator and prey mites, as well as the occurence of potential acaropathogenic bacteria were analyzed. The comparisons were based on the following groups: (i) N. cucumeris mass-production; (ii) N. cucumeris laboratory population with disease symptoms; (iii) T. putrescentiae pure populations and; (iv) T. putrescentiae from rearing units of N. cucumeris. Only 15% of OTUs were present in all samples from predatory and prey mite populations (core OTUs): the intracellular symbionts Wolbachia, Cardinium, plus other Blattabacterium-like, Solitalea-like, and Bartonella-like symbionts. Environmental bacteria were more abundant in predatory mites, while symbiotic bacteria prevailed in prey mites. Relative numbers of certain bacterial taxa were significantly different between the microbiota of prey mites reared with and without N. cucumeris. No significant differences were found in the bacterial communities of healthy N. cucumeris compared to N. cucumeris showing disease symptoms. We did not identify any confirmed acaropathogenic bacteria among microbiota

Error correction in bimanual coordination benefits from bilateral muscle activity: evidence from kinesthetic tracking

Although previous studies indicated that the stability properties of interlimb coordination largely result from the integrated timing of efferent signals to both limbs, they also depend on afference-based interactions. In the present study, we examined contributions of afference-based error corrections to rhythmic bimanual coordination using a kinesthetic tracking task. Furthermore, since we found in previous research that subjects activated their muscles in the tracked (motor-driven) arm, we examined the functional significance of this activation to gain more insight into the processes underlying this phenomenon. To these aims, twelve subjects coordinated active movements of the right hand with motor-driven oscillatory movements of the left hand in two coordinative patterns: in-phase (relative phase 0°) and antiphase (relative phase 180°). They were either instructed to activate the muscles in the motor-driven arm as if moving along with the motor (active condition), or to keep these muscles as relaxed as possible (relaxed condition). We found that error corrections were more effective in in-phase than in antiphase coordination, resulting in more adequate adjustments of cycle durations to compensate for timing errors detected at the start of each cycle. In addition, error corrections were generally more pronounced in the active than in the relaxed condition. This activity-related difference was attributed to the associated bilateral neural control signals (as estimated using electromyography), which provided an additional reference (in terms of expected sensory consequences) for afference-based error corrections. An intimate relation was revealed between the (integrated) motor commands to both limbs and the processing of afferent feedback

A Policy-into-Practice Intervention to Increase the Uptake of Evidence-Based Management of Low Back Pain in Primary Care: A Prospective Cohort Study

BACKGROUND: Persistent non-specific low back pain (nsLBP) is poorly understood by the general community, by educators, researchers and health professionals, making effective care problematic. This study evaluated the effectiveness of a policy-into-practice intervention developed for primary care physicians (PCPs). METHODS: To encourage PCPs to adopt practical evidence-based approaches and facilitate time-efficient, integrated management of patients with nsLBP, we developed an interdisciplinary evidence-based, practical pain education program (gPEP) based on a contemporary biopsychosocial framework. One hundred and twenty six PCPs from primary care settings in Western Australia were recruited. PCPs participated in a 6.5-hour gPEP. Self-report measures recorded at baseline and at 2 months post-intervention included PCPs' attitudes, beliefs (modified Health Care Providers Pain and Impairment Relationship Scale (HC-PAIRS), evidence-based clinical practices (knowledge and skills regarding nsLBP management: 5-point Likert scale with 1  =  nil and 5  =  excellent) and practice behaviours (recommendations based on a patient vignette; 5-point Likert scale). RESULTS: Ninety one PCPs participated (attendance rate of 72%; post-intervention response rate 88%). PCP-responders adopted more positive, guideline-consistent beliefs, evidenced by clinically significant HC-PAIRS score differences (mean change  =  -5.6±8.2, p<0.0001; 95% confidence interval: -7.6 to -3.6) and significant positive shifts on all measures of clinical knowledge and skills (p<0.0001 for all questions). Self management strategies were recommended more frequently post-intervention. The majority of responders who were guideline-inconsistent for work and bed rest recommendations (82% and 62% respectively) at pre-intervention, gave guideline-consistent responses at post-intervention. CONCLUSION: An interprofessional pain education program set within a framework that aligns health policy and practice, encourages PCPs to adopt more self-reported evidence-based attitudes, beliefs and clinical behaviours in their management of patients with nsLBP. However, further research is required to determine cost effectiveness of this approach when compared with other modes of educational delivery and to examine PCP behaviours in actual clinical practice

Rasiowa–Sikorski deduction systems in computer science applications

AbstractA Rasiowa-Sikorski system is a sequence-type formalization of logics. The system uses invertible decomposition rules which decompose a formula into sequences of simpler formulae whose validity is equivalent to validity of the original formula. There may also be expansion rules which close indecomposable sequences under certain properties of relations appearing in the formulae, like symmetry or transitivity. Proofs are finite decomposition trees with leaves having “fundamental”, valid labels. The author describes a general method of applying the R-S formalism to develop complete deduction systems for various brands of C.S and A.I. logic, including a logic for reasoning about relative similarity, a three-valued software specification logic with McCarthy's connectives and Kleene quantifiers, a logic for nondeterministic specifications, many-sorted FOL with possibly empty carriers of some sorts, and a three-valued logic for reasoning about concurrency

Evaluation of a Theory-Informed Implementation Intervention for the Management of Acute Low Back Pain in General Medical Practice: The IMPLEMENT Cluster Randomised Trial

Introduction: This cluster randomised trial evaluated an intervention to decrease x-ray referrals and increase giving advice to stay active for people with acute low back pain (LBP) in general practice. Methods: General practices were randomised to either access to a guideline for acute LBP (control) or facilitated interactive workshops (intervention). We measured behavioural predictors (e.g. knowledge, attitudes and intentions) and fear avoidance beliefs. We were unable to recruit sufficient patients to measure our original primary outcomes so we introduced other outcomes measured at the general practitioner (GP) level: behavioural simulation (clinical decision about vignettes) and rates of x-ray and CT-scan (medical administrative data). All those not involved in the delivery of the intervention were blinded to allocation. Results: 47 practices (53 GPs) were randomised to the control and 45 practices (59 GPs) to the intervention. The number of GPs available for analysis at 12 months varied by outcome due to missing confounder information; a minimum of 38 GPs were available from the intervention group, and a minimum of 40 GPs from the control group. For the behavioural constructs, although effect estimates were small, the intervention group GPs had greater intention of practising consistent with the guideline for the clinical behaviour of x-ray referral. For behavioural simulation, intervention group GPs were more likely to adhere to guideline recommendations about x-ray (OR 1.76, 95%CI 1.01, 3.05) and more likely to give advice to stay active (OR 4.49, 95%CI 1.90 to 10.60). Imaging referral was not statistically significantly different between groups and the potential importance of effects was unclear; rate ratio 0.87 (95%CI 0.68, 1.10) for x-ray or CT-scan. Conclusions: The intervention led to small changes in GP intention to practice in a manner that is consistent with an evidence-based guideline, but it did not result in statistically significant changes in actual behaviour. Trial Registration: Australian New Zealand Clinical Trials Registry ACTRN01260600009853

A New Direction to Athletic Performance: Understanding the Acute and Longitudinal Responses to Backward Running

Backward running (BR) is a form of locomotion that occurs in short bursts during many overground field and court sports. It has also traditionally been used in clinical settings as a method to rehabilitate lower body injuries. Comparisons between BR and forward running (FR) have led to the discovery that both may be generated by the same neural circuitry. Comparisons of the acute responses to FR reveal that BR is characterised by a smaller ratio of braking to propulsive forces, increased step frequency, decreased step length, increased muscle activity and reliance on isometric and concentric muscle actions. These biomechanical differences have been critical in informing recent scientific explorations which have discovered that BR can be used as a method for reducing injury and improving a variety of physical attributes deemed advantageous to sports performance. This includes improved lower body strength and power, decreased injury prevalence and improvements in change of direction performance following BR training. The current findings from research help improve our understanding of BR biomechanics and provide evidence which supports BR as a useful method to improve athlete performance. However, further acute and longitudinal research is needed to better understand the utility of BR in athletic performance programs

Mechanisms of progression of chronic kidney disease

Chronic kidney disease (CKD) occurs in all age groups, including children. Regardless of the underlying cause, CKD is characterized by progressive scarring that ultimately affects all structures of the kidney. The relentless progression of CKD is postulated to result from a self-perpetuating vicious cycle of fibrosis activated after initial injury. We will review possible mechanisms of progressive renal damage, including systemic and glomerular hypertension, various cytokines and growth factors, with special emphasis on the renin–angiotensin–aldosterone system (RAAS), podocyte loss, dyslipidemia and proteinuria. We will also discuss possible specific mechanisms of tubulointerstitial fibrosis that are not dependent on glomerulosclerosis, and possible underlying predispositions for CKD, such as genetic factors and low nephron number