On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

Locally recurrent chondrosarcoma of the pelvis and limbs can only be controlled by wide local excision

Aims The purpose of this study was to investigate the potential for achieving local and systemic control after local recurrence of a chondrosarcoma of bone. Patients and Methods A total of 126 patients with local recurrence (LR) of chondrosarcoma (CS) of the pelvis or a limb bone were identified from a prospectively maintained database, between 1990 and 2015 at the Royal Orthopaedic Hospital, Birmingham, United Kingdom. There were 44 female patients (35%) and 82 male patients (65%) with a mean age at the time of LR of 56 years (13 to 96). The 126 patients represented 24.3% of the total number of patients with a primary CS (519) who had been treated during this period. Clinical data collected at the time of primary tumour and LR included the site (appendicular, extremity, or pelvis); primary and LR tumour size (in centimetres); type of operation at the time of primary or LR (limb-salvage or amputation); surgical margin achieved at resection of the primary tumour and the LR; grade of the primary tumour and the LR; gender; age; and oncological outcomes, including local recurrence-free survival and disease-specific survival. A minimum two years' follow-up and complete histopathology records were available for all patients included in the study. Results For patients without metastases prior to or at the time of local recurrence, the disease-specific survival after local recurrence was 62.5% and 45.5% at one and five years, respectively, After univariable analysis, significant factors predicting disease-specific survival were grade (p <0.001) and surgical margin (p = 0.044). After multivariable analysis, grade, increasing age at the time of diagnosis of local recurrence, and a greater time interval from primary surgery to local recurrence were significant factors for disease-specific survival. A secondary local recurrence was seen in 26% of patients. Wide margins were a good predictor of local recurrence-free survival for subsequent recurrences after univariable analysis when compared with intralesional margins (p = 0.002) but marginal margins did not reach statistical significance when compared with intralesional margins (p = 0.084). Conclusion In cases of local recurrence of a chondrosarcoma of bone, we have shown that if the tumour is non-metastatic at re-staging, an increase in disease-specific survival and in local recurrence-free survival is achievable, but only by resection of the local recurrence with a wide margin.Peer reviewe

Solar interacting protons versus interplanetary protons in the core plus halo model of diffusive shock acceleration and stochastic re-acceleration

With the first observations of solar γ-rays from the decay of pions, the relationship of protons producing ground level enhancements (GLEs) on the Earth to those of similar energies producing the γ-rays on the Sun has been debated. These two populations may be either independent and simply coincident in large flares, or they may be, in fact, the same population stemming from a single accelerating agent and jointly distributed at the Sun and also in space. Assuming the latter, we model a scenario in which particles are accelerated near the Sun in a shock wave with a fraction transported back to the solar surface to radiate, while the remainder is detected at Earth in the form of a GLE. Interplanetary ions versus ions interacting at the Sun are studied for a spherical shock wave propagating in a radial magnetic field through a highly turbulent radial ray (the acceleration core) and surrounding weakly turbulent sector in which the accelerated particles can propagate toward or away from the Sun. The model presented here accounts for both the first-order Fermi acceleration at the shock front and the second-order, stochastic re-acceleration by the turbulence enhanced behind the shock. We find that the re-acceleration is important in generating the γ-radiation and we also find that up to 10% of the particle population can find its way to the Sun as compared to particles escaping to the interplanetary space

Factors associated with parental recognition of a child's overweight status - a cross sectional study

<p>Abstract</p> <p>Background</p> <p>Very few studies have evaluated the association between a child's lifestyle factors and their parent's ability to recognise the overweight status of their offspring. The aim of this study was to analyze the factors associated with a parent's ability to recognise their own offspring's overweight status.</p> <p>Methods</p> <p>125 overweight children out of all 1,278 school beginners in Northern Finland were enrolled.</p> <p>Weight and height were measured in health care clinics. Overweight status was defined by BMI according to internationally accepted criteria. A questionnaire to be filled in by parents was delivered by the school nurses. The parents were asked to evaluate their offspring's weight status. The child's eating habits and physical activity patterns were also enquired about. Factor groups of food and physical activity habits were formed by factor analysis. Binary logistic regression was performed using all variables associated with recognition of overweight status in univariate analyses. The significant risk factors in the final model are reported using odds ratios (ORs) and their 95% confidence intervals (CIs).</p> <p>Results</p> <p>Fifty-seven percent (69/120) of the parents of the overweight children considered their child as normal weight. Child's BMI was positively associated with parental recognition of overweight (OR 3.59, CI 1.8 to 7.0). Overweight boys were less likely to be recognised than overweight girls (OR 0.14, CI 0.033 to 0.58). Child's healthy diet (OR 0.22, CI 0.091 to 0.54) and high physical activity (OR 0.29, CI 0.11 to 0.79) were inversely related to parental recognition of overweight status.</p> <p>Conclusions</p> <p>Child's healthy eating habits and physical activity are inversely related to parental recognition of their offspring's overweight. These should be taken into account when planning prevention and treatment strategies for childhood obesity.</p

Chondroblastoma of bone in extremities. - A single centre study of 177 cases

Introduction Chondroblastoma is a rare benign bone tumour that usually occurs in children and young adults. They are cartilaginous tumours arising in the epiphysis or apophysis of a long bone. The tumour is classified as benign, although rare cases of pulmonary metastases have been reported. The aims of this study were to describe clinical, radiographic characteristics of chondroblastoma; to analyse the local recurrence rate and complications associated with surgery. Material and methods This retrospective study included 177 patients, who had been diagnosed with a chondroblastoma in extremity between 1990 and 2015. Results The most common site was proximal tibia 20%, followed by proximal humerus 19%, proximal femur 18%, distal femur 16% and foot 15%. One patient has died of the disease and one patient is alive after being operated for lung metastases. There was local recurrence in 25/177 (14%) patients. The median time to local recurrence was 10 months (range 3-158 months). The most common site for local recurrence was proximal tibia (22.2%). The proximal femur was the location in 32/178 (18%) of the cases. 18/32 (56%) were in the greater trochanter and 14/32 (44%) in the femoral head. The mean age was lower in tumours located in femoral head when compared to the greater trochanter; 19.5 years and 13.9 years respectively (p=0.004). Tumours located in greater trochanter were all curetted without further complications. Local recurrence was seen more often in femoral head tumours, though without statistical significance; 3/14 (21%) and none, respectively (p=0.073). Conclusions Chondroblastoma is a rare benign to intermediate grade bone tumour with a potential to metastasise. Femoral head chondroblastoma is rare, presenting 4.5% of all chondroblastoma cases. Around 50% of the chondroblastoma in femoral head. occur in patients with open growth plates.Peer reviewe

Drift-induced deceleration of Solar Energetic Particles

We investigate the deceleration of Solar Energetic Particles (SEPs) during their propagation from the Sun through interplanetary space, in the presence of weak to strong scattering in a Parker spiral configuration, using relativistic full orbit test particle simulations. The calculations retain all three spatial variables describing particles’ trajectories, allowing to model any transport across the magnetic field. Large energy change is shown to occur for protons, due to the combined effect of standard adiabatic deceleration and a significant contribution from particle drift in the direction opposite to that of the solar wind electric field. The latter drift-induced deceleration is found to have a stronger effect for SEP energies than for galactic cosmic rays. The kinetic energy of protons injected at 1 MeV is found to be reduced by between 35 and 90% after four days, and for protons injected at 100 MeV by between 20 and 55%. The overall degree of deceleration is a weak function of the scattering mean free path, showing that, although adiabatic deceleration plays a role, a large contribution is due to particle drift. Current SEP transport models are found to account for drift-induced deceleration in an approximate way and their accuracy will need to be assessed in future work

From Sun to Interplanetary Space: What is the Pathlength of Solar Energetic Particles?

Solar energetic particles (SEPs), accelerated during solar eruptions, propagate in turbulent solar wind before being observed with in situ instruments. In order to interpret their origin through comparison with remote sensing observations of the solar eruption, we thus must deconvolve the transport effects due to the turbulent magnetic fields from the SEP observations. Recent research suggests that the SEP propagation is guided by the turbulent meandering of the magnetic fieldlines across the mean magnetic field. However, the lengthening of the distance the SEPs travel, due to the fieldline meandering, has so far not been included in SEP event analysis. This omission can cause significant errors in estimation of the release times of SEPs at the Sun. We investigate the distance traveled by the SEPs by considering them to propagate along fieldlines that meander around closed magnetic islands that are inherent in turbulent plasma. We introduce a fieldline random walk model which takes into account the physical scales associated to the magnetic islands. Our method remedies the problem of the diffusion equation resulting in unrealistically short pathlengths, and the fractal dependence of the pathlength of random walk on the length of the random-walk step. We find that the pathlength from the Sun to 1au can be below the nominal Parker spiral length for SEP events taking place at solar longitudes 45E to 60W, whereas the western and behind-the-limb particles can experience pathlengths longer than 2au due to fieldline meandering

Aural CT characteristics of American Cocker Spaniels have features of both mesaticephalic and brachycephalic breeds

Otitis externa and otitis media are common in American Cocker Spaniels, however breed-specific aural CT descriptions are currently lacking. This prospective and retrospective, observational, analytical study aimed to describe quantitative CT characteristics of the horizontal ear canal and the tympanic bulla in American Cocker Spaniels versus similar-sized mesaticephalic dogs. We prospectively performed clinical examinations and aural CT scanning for 38 American Cocker Spaniels. Computed tomographic transverse area of the osseous horizontal ear canal (TA1), transverse area of the widest air-filled part of the cartilaginous horizontal ear canal (TA2), tympanic bulla volume, and tympanic bulla wall thickness were measured. The TA1 and TA2 measurements were compared with those of 23 retrospectively recruited, similar-sized mesaticephalic dogs that had undergone CT-scanning of the head for non-ear-related reasons. The TA1 and TA2 did not differ for healthy American Cocker Spaniels and mesaticephalic dogs. Severely affected American Cocker Spaniels had significantly smaller TA2 (P <.001). The intraclass correlation coefficient for intraobserver and interobserver repeatability was 0.972 and 0.983 for TA1 and 0.994 and 0.998 for TA2, respectively. Variation between individuals was subjectively noted in healthy and affected American Cocker Spaniels, but mean tympanic bulla volume was slightly smaller in relation to body weight, and the tympanic bulla wall was thicker than in previous reports for mesaticephalic dogs. The tympanic bulla wall appeared thicker rostro-ventrally than caudo-ventrally in 44% of the dogs. Our results imply that a relatively thick tympanic bulla wall may be a normal CT variation and should be interpreted cautiously in this breed.Peer reviewe