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The aim of this study was to compare the interlimb coordination, asymmetry, and variability between older adults who participated in sports (n = 25; age = 72.6 ± 6.46 years) and sedentary older adults (n = 20; age = 70.85 ± 3.82 years). The sport participants were selected from tennis and badminton clubs, whereas the sedentary participants were recruited from local community centers. The participants walked at their preferred speed in a 10-m walkway for 2 min. The interlimb coordination was measured by the phase coordination index. Other walking metrics were speed, cadence, swing time, stance time, double-support time, stride time, and swing time asymmetry. The results showed that the sport participants relative to the sedentary group had better interlimb coordination, higher walking speed and cadence, and less swing time variability. Young older adults also had a better interlimb coordination. In conclusion, the findings of this study showed that long-term participation in sports has some antiaging benefits on gait coordination and symmetry in older adults. [ABSTRACT FROM AUTHOR]

The Sullivan dictionary provides a beautiful correspondence between Kleinian groups acting on hyperbolic space and rational maps of the extended complex plane. We focus on the setting of geometrically finite Kleinian groups with parabolic elements and parabolic rational maps. In this context an especially direct correspondence exists concerning the dimension theory of the associated limit sets and Julia sets. In recent work we established formulae for the Assouad type dimensions and spectra for these fractal sets and certain conformal measures they support. This allows a rather more nuanced comparison of the two families in the context of dimension. In this expository article we discuss how these results provide new entries in the Sullivan dictionary, as well as revealing striking differences between the two families. [ABSTRACT FROM AUTHOR]

Unicondylar knee replacement is a relatively common elective orthopedic procedure but is not often seen in the Emergency Department setting. Familiarity with normal clinical and radiological appearances is difficult to gain. Dislocation of the mobile bearing component “spacer” is a known complication of unicondylar knee replacements, and these patients will initially present to the accident and Emergency Department. In this setting, an accurate and prompt diagnosis is necessary to appropriately manage the patient's condition. There is normally a radiological challenge in identifying dislocated mobile bearings on plain radiographs. These patients may need to have further imaging, such as a computer tomographic scan to identify the dislocated mobile bearing.

Given a non-empty bounded subset of hyperbolic space and a Kleinian group acting on that space, the orbital set is the orbit of the given set under the action of the group. We may view orbital sets as bounded (often fractal) subsets of Euclidean space. We prove that the upper box dimension of an orbital set is given by the maximum of three quantities: the upper box dimension of the given set, the Poincaré exponent of the Kleinian group, and the upper box dimension of the limit set of the Kleinian group. Since we do not make any assumptions about the Kleinian group, none of the terms in the maximum can be removed in general. We show by constructing an explicit example that our assumption that the given set is bounded (in the hyperbolic metric) cannot be removed in general. [ABSTRACT FROM AUTHOR]

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of "well‐spread" points, which we refer to as abstract rationals. We prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness. [ABSTRACT FROM AUTHOR]

We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensions : a family of dimensions depending on a parameter \theta \in [0,1] which interpolate between the Hausdorff and box dimensions. Our main results are in the case when all the contractions are conformal. Under a natural separation condition we prove that the intermediate dimensions of the limit set are the maximum of the Hausdorff dimension of the limit set and the intermediate dimensions of the set of fixed points of the contractions. This builds on work of Mauldin and Urbański concerning the Hausdorff and upper box dimension. We give several (often counter-intuitive) applications of our work to dimensions of projections, fractional Brownian images, and general Hölder images. These applications apply to well-studied examples such as sets of numbers which have real or complex continued fraction expansions with restricted entries. We also obtain several results without assuming conformality or any separation conditions. We prove general upper bounds for the Hausdorff, box and intermediate dimensions of infinitely generated attractors in terms of a topological pressure function. We also show that the limit set of a 'generic' infinite iterated function system has box and intermediate dimensions equal to the ambient spatial dimension, where 'generic' can refer to any one of (i) full measure; (ii) prevalent; or (iii) comeagre. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology suggests, we show that it can be used to characterise the Minkowski dimension of a compact metric space. We also study its relationship with other concepts in dimension theory. [ABSTRACT FROM AUTHOR]

We prove a general nonlinear projection theorem for Assouad dimension. This theorem has several applications including to distance sets, radial projections, and sum‐product phenomena. In the setting of distance sets, we are able to completely resolve the planar version of Falconer's distance set problem for Assouad dimension, both dealing with the awkward 'critical case' and providing sharp estimates for sets with Assouad dimension less than 1. In the higher dimensional setting, we connect the problem to the dimension of the set of exceptions in a related (orthogonal) projection theorem. We also obtain results on pinned distance sets and our results still hold when distances are taken with respect to a sufficiently curved norm. As another application we prove a radial projection theorem for Assouad dimension with sharp estimates on the Hausdorff dimension of the exceptional set. [ABSTRACT FROM AUTHOR]

The 'popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erdős inequality from probability theory. [ABSTRACT FROM AUTHOR]

La Crosse virus (LACV) is a major cause of pediatric encephalitis and aseptic meningitis in the Midwestern, Mid-Atlantic, and Southern United States, where it is an emerging pathogen. The LACV Gc glycoprotein plays a critical role in the neuropathogenesis of LACV encephalitis as the putative virus attachment protein. Previously, we identified and experimentally confirmed the location of the LACV fusion peptide within Gc and generated a panel of recombinant LACVs (rLACVs) containing mutations in the fusion peptide as well as the wild-type sequence. These rLACVs retained their ability to cause neuronal death in a primary embryonic rat neuronal culture system, despite decreased replication and fusion phenotypes. To test the role of the fusion peptide in vivo, we tested rLACVs in an age-dependent murine model of LACV encephalitis. When inoculated directly into the CNS of young adult mice (P28), the rLACV fusion peptide mutants were as neurovirulent as the rLACV engineered with a wild-type sequence, confirming the results obtained in tissue culture. In contrast, the fusion peptide mutant rLACVs were less neuroinvasive when suckling (P3) or weanling (P21) mice were inoculated peripherally, demonstrating that the LACV fusion peptide is a determinant of neuroinvasion, but not of neurovirulence. In a challenge experiment, we found that peripheral challenge of weanling (P21) mice with fusion peptide mutant rLACVs protected from a subsequent WT-LACV challenge, suggesting that mutations in the fusion peptide are an attractive target for generating live-attenuated virus vaccines. Importantly, the high degree of conservation of the fusion peptide amongst the Bunyavirales and, structurally, other arboviruses suggests that these findings are broadly applicable to viruses that use a class II fusion mechanism and cause neurologic disease. [ABSTRACT FROM AUTHOR]

Kleinian groups are discrete groups of isometries of hyperbolic space. Their actions give rise to intricate fractal limit sets on the boundary at infinity and there is great interest in estimating the "dimension" of these limit sets. As an invitation to this fascinating area, we provide a proof of the (well-known) result that the Poincaré exponent of a nonelementary Kleinian group is a lower bound for the upper box dimension of the limit set. Our proof uses only elementary hyperbolic and fractal geometry. [ABSTRACT FROM AUTHOR]

We study the Lq-spectrum of measures in the plane generated by certain nonlinear maps. In particular, we consider attractors of iterated function systems consisting of maps whose components are C1+α and for which the Jacobian is a lower triangular matrix at every point subject to a natural domination condition on the entries. We calculate the Lq-spectrum of Bernoulli measures supported on such sets by using an appropriately defined analogue of the singular value function and an appropriate pressure function. [ABSTRACT FROM AUTHOR]

We derive the almost sure Assouad spectrum and quasi-Assouad dimension of one-variable random self-affine Bedford–McMullen carpets. Previous work has revealed that the (related) Assouad dimension is not sufficiently sensitive to distinguish between subtle changes in the random model, since it tends to be almost surely 'as large as possible' (a deterministic quantity). This has been verified in conformal and non-conformal settings. In the conformal setting, the Assouad spectrum and quasi-Assouad dimension behave rather differently, tending to almost surely coincide with the upper box dimension. Here we investigate the non-conformal setting and find that the Assouad spectrum and quasi-Assouad dimension generally do not coincide with the box dimension or Assouad dimension. We provide examples highlighting the subtle differences between these notions. Our proofs combine deterministic covering techniques with suitably adapted Chernoff estimates and Borel–Cantelli-type arguments. [ABSTRACT FROM AUTHOR]

Let pn denote the n th prime, and consider the function 1/n ↦ 1 / pn which maps the reciprocals of the positive integers bijectively to the reciprocals of the primes. We show that Hölder continuity of this function is equivalent to a parametrised family of Cramér type estimates on the gaps between successive primes. Here the parametrisation comes from the Hölder exponent. In particular, we show that Cramér's conjecture is equivalent to the map 1 / n ↦ 1 / p n being Lipschitz. On the other hand, we show that the inverse map 1 / p n ↦ 1 / n is Hölder of all orders but not Lipschitz and this is independent of Cramér's conjecture. [ABSTRACT FROM AUTHOR]