Maximum Weight Spectrum Codes

In the recent work \cite{shi18}, a combinatorial problem concerning linear codes over a finite field \F_q was introduced. In that work the authors studied the weight set of an $[n,k]_q$ linear code, that is the set of non-zero distinct Hamming weights, showing that its cardinality is upper bounded by $\frac{q^k-1}{q-1}$. They showed that this bound was sharp in the case $q=2$, and in the case $k=2$. They conjectured that the bound is sharp for every prime power $q$ and every positive integer $k$. In this work quickly establish the truth of this conjecture. We provide two proofs, each employing different construction techniques. The first relies on the geometric view of linear codes as systems of projective points. The second approach is purely algebraic. We establish some lower bounds on the length of codes that satisfy the conjecture, and the length of the new codes constructed here are discussed.Comment: 19 page

On the Weights of General MDS Codes

The weight spectra of MDS codes of length $n$ and dimension $k$ over the arbitrary alphabets are studied. For all $q$-ary MDS codes of dimension $k$ containing the zero codeword, it is shown that all $k$ weights from $n$ to $n-k+1$ are realized. The remaining case $n=q+k-1$ is also determined. Additionally, we prove that all binary MDS codes are equivalent to linear MDS codes. The proofs are combinatorial, and self contained

A note on full weight spectrum codes

A linear $[n,k]_q$ code $C$ is said to be a full weight spectrum (FWS) code if there exist codewords of each nonzero weight less than or equal to $n$. In this brief communication we determine necessary and sufficient conditions for the existence of linear $[n,k]_q$ full weight spectrum (FWS) codes. Central to our approach is the geometric view of linear codes, whereby columns of a generator matrix correspond to points in $PG(k-1,q)$

THE SYMMETRY ANGLE IDENTIFIES LESS CLINICALLY RELEVANT INTER-LIMB ASYMMETRIES THAN THE SYMMETRY INDEX IN HEALTHY ADULTS

There are several methods for calculating inter-limb symmetry, an inter-limb difference ≥15% has been suggested as an indicator of sporting injury risk. The purpose of this study was to compare three common methods for determining symmetry: the Symmetry Index (percentage difference; SI) when referenced to the left limb (SILeft) or the average of both limbs (SIAverage), and the Symmetry Angle (vector difference; SA). 15 recreationally active participants completed a sprint protocol on a non-motorised treadmill. Accelerometers were positioned on both tibias to measure peak resultant acceleration (PRA). The SA identified less clinically relevant PRA inter-limb asymmetries than the SI in healthy adults. Once an appropriate level of asymmetry as measured by the SA is determined, this may help to more correctly identify asymmetry in athletes and patients than the SI

Measurement of lower-limb asymmetry in professional rugby league: a technical note describing the use of inertial measurement units

Background. Quantifying lower-limb load and asymmetry during team sport match play may be important for injury prevention and understanding performance. However, current analysis methods of lower-limb symmetry during match-play employ wearable microtechnology that may not be best suited to the task. A popular microtechnology is global positioning systems (GPS), which are torso worn. The torso location, and the summary workload measures calculated by GPS are not suited to the calculation of lower-limb load. Instead, research grade accelerometers placed directly on the lower-limb may provide better load information than GPS. This study proposes a new technique to quantify external mechanical load, and lower-limb asymmetry during on-field team sport play using inertial measurement units. Methods. Four professional rugby league players (Age: 23.4 ± 3.1 years; Height: 1.89 ± 0.05 m; Mass: 107.0 ± 12.9 kg) wore two accelerometers, one attached to each foot by the boot laces, during match simulations. Custom Matlab (R2017b, The Mathworks Inc, Natick, MA) code was used to calculate total time, area under the curve (AUC), and percentage of time (%Time) spent in seven acceleration categories (negative to very high, <0 g to >16 g), as well as minimum and maximum acceleration during match simulations. Lower-limb AUC and %Time asymmetry was calculated using the Symmetry Angle Equation, which does not require normalization to a reference leg. Results. The range of accelerations experienced across all participants on the left and right sides were 15.68–17.53 g, and 16.18–17.69 g, respectively. Clinically significant asymmetry in AUC and %Time was observed for all but one participant, and only in negative (<0 g) and very high accelerations (>16 g). Clinically significant AUC differences in very high accelerations ranged from 19.10%–26.71%. Clinically significant %Time differences in negative accelerations ranged from 12.65%–25.14%, and in very high accelerations from 18.59%–25.30%. All participants experienced the most AUC at very low accelerations (2–4 g), and the least AUC at very high accelerations (165.00–194.00 AU vs. 0.32–3.59 AU). The %Time results indicated that all participants spent the majority of match-play (73.82–92.06%) in extremely low (0–2 g) to low (4–6 g) acceleration intensities, and the least %Time in very high accelerations (0.01%–0.05%). Discussion. A wearable located on the footwear to measure lower-limb load and asymmetry is feasible to use during rugby league match-play. The location of the sensor on the boot is suited to minimize injury risk occurring from impact to the sensor. This technique is able to quantify external mechanical load and detect inter limb asymmetries during match-play at the source of impact and loading, and is therefore likely to be better than current torso based methods. The results of this study may assist in preparing athletes for match-play, and in preventing injury

The Demands of Professional Rugby League Match-Play: a Meta-analysis

Background Rugby league is a collision sport, where players are expected to be physically competent in a range of areas, including aerobic fitness, strength, speed and power. Several studies have attempted to characterise the physical demands of rugby league match-play, but these studies often have relatively small sample sizes based on one or two clubs, which makes generalisation of the findings difficult. Therefore, the aim of this review was to synthesise studies that investigated the physical demands of professional rugby league match-play. Methods SPORTDiscus, CINAHL, MEDLINE (EBSCO) and Embase (EBSCO) databases were systematically searched from inception until October 2018. Articles were included if they (1) recruited professional rugby league athletes aged ≥ 18 years and (2) provided at least one match-play relevant variable (including playing time, total and relative distance, repeat high-intensity efforts (RHIE), efforts per RHIE, accelerations and decelerations, total and relative collisions). Meta-analyses were used to provide pooled estimates ± 95% confidence intervals. Results A total of 30 studies were included. Pooled estimates indicated that, compared to adjustables and backs, forwards have less playing time (− 17.2 ± 5.6 and − 25.6 ± 5.8 min, respectively), cover less ‘slow-speed’ (− 2230 ± 735 and − 1348 ± 655 m, respectively) and ‘high-speed’ distance (− 139 ± 108 and − 229 ± 101 m, respectively), but complete more relative RHIEs (+ 0.05 ± 0.05 and + 0.08 ± 0.04 per minute, respectively), and total (+ 12.0 ± 8.1 and + 12.8 ± 7.2 collisions, respectively) and relative collisions (+ 0.32 ± 0.22 and + 0.41 ± 0.22 collisions per minute, respectively). Notably, when the distance was expressed relative to playing time, forwards were not different from adjustables and backs in slow-speed (P ≥ 0.295) and high-speed (P ≥ 0.889) relative distance. The adjustables and backs subgroups were similar in most variables, except playing time (shorter for adjustables, − 8.5 ± 6.2 min), slow-speed distance (greater for adjustables, + 882 ± 763 m) and total relative distance (greater for adjustables, + 11.3 ± 5.2 m·min−1). There were no significant differences between positional groups for efforts per RHIE, accelerations and decelerations (P ≥ 0.745). Conclusions These results indicate the unique physical demands of each playing position and should be considered by strength and conditioning and tactical coaches when planning for professional rugby league performance

Understanding and supporting block play: video observation research on preschoolers’ block play to identify features associated with the development of abstract thinking

This article reports on a study conducted to investigate the development of abstract thinking in preschool children (ages from 3 years to 4 years old) in a nursery school in England. Adopting a social influence approach, the researcher engaged in 'close listening' to document children's ideas expressed in various representations through video observation. The aim was to identify behaviours connected with features of the functional dependency relationship – a cognitive function that connects symbolic representations with abstract thinking. The article presents three episodes to demonstrate three dominating features, which are i) child/child sharing of thinking and adult and child sharing of thinking; ii) pause for reflection; and iii) satisfaction as a result of self-directed play. These features were identified as signs of learning, and were highlighted as phenomena that can help practitioners to understand the value of quality play and so provide adequate time and space for young children and plan for a meaningful learning environment. The study has also revealed the importance of block play in promoting abstract thinking. Keywords: abstract thinking; functional dependency relationship; social influence approach; block play; preschool; video observation; qualitative researc

Equipoise across the patient population: Optimising recruitment to a randomised controlled trial

© 2016 The Author(s). Background: This paper proposes a novel perspective on the value of qualitative research for improving trial design and optimising recruitment. We report findings from a qualitative study set within the OPEN trial, a surgical randomised controlled trial (RCT) comparing two interventions for recurrent bulbar urethral stricture, a common cause of urinary problems in men. Methods: Interviews were conducted with men meeting trial eligibility criteria (n = 19) to explore reasons for accepting or declining participation and with operating urologists (n = 15) to explore trial acceptability. Results: Patients expressed various preferences and understood these in the context of relative severity and tolerability of their symptoms. Accounts suggest a common trajectory of worsening symptoms with a particular window within which either treatment arm would be considered acceptable. Interviews with clinician recruiters found that uncertainty varied between general and specialist sites, which reflect clinicians' relative exposure to different proportions of the patient population. Conclusion: Recruitment post referral, at specialist sites, was challenging due to patient (and clinician) expectations. Trial design, particularly where there are fixed points for recruitment along the care pathway, can enable or constrain the possibilities for effective accrual depending on how it aligns with the optimum point of patient equipoise. Qualitative recruitment investigations, often focussed on information provision and patient engagement, may also look to better understand the target patient population in order to optimise the point at which patients are approached. Trial registration: ISRCTN Registry, ISRCTN98009168. Registered on 29 November 2012

Life, time, and the organism:Temporal registers in the construction of life forms

In this paper, we articulate how time and temporalities are involved in the making of living things. For these purposes, we draw on an instructive episode concerning Norfolk Horn sheep. We attend to historical debates over the nature of the breed, whether it is extinct or not, and whether presently living exemplars are faithful copies of those that came before. We argue that there are features to these debates that are important to understanding contemporary configurations of life, time and the organism, especially as these are articulated within the field of synthetic biology. In particular, we highlight how organisms are configured within different material and semiotic assemblages that are always structured temporally. While we identify three distinct structures, namely the historical, phyletic and molecular registers, we do not regard the list as exhaustive. We also highlight how these structures are related to the care and value invested in the organisms at issue. Finally, because we are interested ultimately in ways of producing time, our subject matter requires us to think about historiographical practice reflexively. This draws us into dialogue with other scholars interested in time, not just historians, but also philosophers and sociologists, and into conversations with them about time as always multiple and never an inert background

Aspects of microbial communities in peatland carbon cycling under changing climate and land use pressures

This is the final version. Available on open access from the Finnish Peatland Society via the DOI in this record. Globally, major efforts are being made to restore peatlands to maximise their resilience to anthropogenic climate change, which puts continuous pressure on peatland ecosystems and modifies the geography of the environmental envelope that underpins peatland functioning. A probable effect of climate change is reduction in the waterlogged conditions that are key to peatland formation and continued accumulation of carbon (C) in peat. C sequestration in peatlands arises from a delicate imbalance between primary production and decomposition, and microbial processes are potentially pivotal in regulating feedbacks between environmental change and the peatland C cycle. Increased soil temperature, caused by climate warming or disturbance of the natural vegetation cover and drainage, may result in reductions of long-term C storage via changes in microbial community composition and metabolic rates. Moreover, changes in water table depth alter the redox state and hence have broad consequences for microbial functions, including effects on fungal and bacterial communities especially methanogens and methanotrophs. This article is a perspective review of the effects of climate change and ecosystem restoration on peatland microbial communities and the implications for C sequestration and climate regulation. It is authored by peatland scientists, microbial ecologists, land managers and non-governmental organisations who were attendees at a series of three workshops held at The University of Manchester (UK) in 2019–2020. Our review suggests that the increase in methane flux sometimes observed when water tables are restored is predicated on the availability of labile carbon from vegetation and the absence of alternative terminal electron acceptors. Peatland microbial communities respond relatively rapidly to shifts in vegetation induced by climate change and subsequent changes in the quantity and quality of below-ground C substrate inputs. Other consequences of climate change that affect peatland microbial communities and C cycling include alterations in snow cover and permafrost thaw. In the face of rapid climate change, restoration of a resilient microbiome is essential to sustaining the climate regulation functions of peatland systems. Technological developments enabling faster characterisation of microbial communities and functions support progress towards this goal, which will require a strongly interdisciplinary approach.Natural Environment Research Council (NERC