On the independence ratio of distance graphs

A distance graph is an undirected graph on the integers where two integers are adjacent if their difference is in a prescribed distance set. The independence ratio of a distance graph $G$ is the maximum density of an independent set in $G$. Lih, Liu, and Zhu [Star extremal circulant graphs, SIAM J. Discrete Math. 12 (1999) 491--499] showed that the independence ratio is equal to the inverse of the fractional chromatic number, thus relating the concept to the well studied question of finding the chromatic number of distance graphs. We prove that the independence ratio of a distance graph is achieved by a periodic set, and we present a framework for discharging arguments to demonstrate upper bounds on the independence ratio. With these tools, we determine the exact independence ratio for several infinite families of distance sets of size three, determine asymptotic values for others, and present several conjectures.Comment: 39 pages, 12 figures, 6 table

Rehabilitation Settings After Joint Replacement: An Application of Multiattribute Preference Elicitation

While advances in medical treatment and technologies have the potential to improve the delivery of health care, their use typically involves making multiple, complex decisions. Patients and their medical providers may share in the decision-making processes and balance a variety of criteria and/or attributes in the pursuit of improved health. This necessitates a stronger understanding of the role of human behavior in health care processes and presents a timely opportunity to use decision analysis tools to contribute to this important aspect of health care operations. This article reports on the application of multiattribute preference elicitation to identify postsurgical rehabilitation setting options for elective hip and knee replacement patients and their discharge planning team prior to placement in these settings. These preferences are analyzed to identify trends in emphases across patients and the discharge planning team, including a comparison with actual outcomes to determine the extent of congruence with each other, an important component of patient-centered care. Variances are identified in what patients and the discharge planning team expected and what actually happened. Reasons for these variances are discussed

Short communication: relationship between body growth and mammary development in dairy heifers

Our objective was to determine if prepubertal rate of body weight (BW) gain, independent of diet, was related to mammary development of dairy heifers. Data from two studies recently conducted at Michigan State University were used to identify factors, within a dietary treatment group, that would account for variation in first lactation milk production or amount of mammary parenchymal DNA at the time of puberty. Factors analyzed for variation in milk production during first lactation were: postpartum BW, prepubertal BW gain, gestational BW gain, postpartum BW gain, body condition score (BCS) at breeding, and BCS at calving. Factors analyzed for variation in mammary parenchymal DNA at puberty were: BW at slaughter, age at puberty, prepubertal BW gain and body protein and body fat content at slaughter. For both analyses, prepubertal BW gain did not account for any of the variation in mammary development. The only significant covariate for the milk production model (r2 = 0.44) was BCS at breeding. Similarly, the only significant covariate in the parenchymal DNA model (r2 = 0.22) was body fat content at slaughter. These results suggest that, within a dietary treatment, heifers that grow faster do not have impaired mammary development, and increased body fatness may be a better predictor of impaired mammary development than BW gain

Short communication: relationship between body growth and mammary development in dairy heifers

Our objective was to determine if prepubertal rate of body weight (BW) gain, independent of diet, was related to mammary development of dairy heifers. Data from two studies recently conducted at Michigan State University were used to identify factors, within a dietary treatment group, that would account for variation in first lactation milk production or amount of mammary parenchymal DNA at the time of puberty. Factors analyzed for variation in milk production during first lactation were: postpartum BW, prepubertal BW gain, gestational BW gain, postpartum BW gain, body condition score (BCS) at breeding, and BCS at calving. Factors analyzed for variation in mammary parenchymal DNA at puberty were: BW at slaughter, age at puberty, prepubertal BW gain and body protein and body fat content at slaughter. For both analyses, prepubertal BW gain did not account for any of the variation in mammary development. The only significant covariate for the milk production model (r2 = 0.44) was BCS at breeding. Similarly, the only significant covariate in the parenchymal DNA model (r2 = 0.22) was body fat content at slaughter. These results suggest that, within a dietary treatment, heifers that grow faster do not have impaired mammary development, and increased body fatness may be a better predictor of impaired mammary development than BW gain

Duration of symptoms resulting from lumbar disc herniation: effect on treatment outcomes: analysis of the Spine Patient Outcomes Research Trial (SPORT).

BACKGROUND: The purpose of the present study was to determine if the duration of symptoms affects outcomes following the treatment of intervertebral lumbar disc herniation. METHODS: An as-treated analysis was performed on patients enrolled in the Spine Patient Outcomes Research Trial (SPORT) for the treatment of intervertebral lumbar disc herniation. Randomized and observational cohorts were combined. A comparison was made between patients who had had symptoms for six months or less (n = 927) and those who had had symptoms for more than six months (n = 265). Primary and secondary outcomes were measured at baseline and at regular follow-up intervals up to four years. The treatment effect for each outcome measure was determined at each follow-up period for the duration of symptoms for both groups. RESULTS: At all follow-up intervals, the primary outcome measures were significantly worse in patients who had had symptoms for more than six months prior to treatment, regardless of whether the treatment was operative or nonoperative. When the values at the time of the four-year follow-up were compared with the baseline values, patients in the operative treatment group who had had symptoms for six months or less had a greater increase in the bodily pain domain of the Short Form-36 (SF-36) (mean change, 48.3 compared with 41.9; p \u3c 0.001), a greater increase in the physical function domain of the SF-36 (mean change, 47.7 compared with 41.2; p \u3c 0.001), and a greater decrease in the Oswestry Disability Index score (mean change, -41.1 compared with -34.6; p \u3c 0.001) as compared with those who had had symptoms for more than six months (with higher scores indicating less severe symptoms on the SF-36 and indicating more severe symptoms on the Oswestry Disability Index). When the values at the time of the four-year follow-up were compared with the baseline values, patients in the nonoperative treatment group who had had symptoms for six months or less had a greater increase in the bodily pain domain of the SF-36 (mean change, 31.8 compared with 21.4; p \u3c 0.001), a greater increase in the physical function domain of the SF-36 (mean change, 29.5 compared with 22.6; p = 0.015), and a greater decrease in the Oswestry Disability Index score (mean change, -24.9 compared with -18.5; p = 0.006) as compared with those who had had symptoms for more than six months. Differences in treatment effect between the two groups related to the duration of symptoms were not significant. CONCLUSIONS: Increased symptom duration due to lumbar disc herniation is related to worse outcomes following both operative and nonoperative treatment. The relative increased benefit of surgery compared with nonoperative treatment was not dependent on the duration of the symptoms

Coherent States of the SU(N) groups

Coherent states $(CS)$ of the $SU(N)$ groups are constructed explicitly and their properties are investigated. They represent a nontrivial generalization of the spining $CS$ of the $SU(2)$ group. The $CS$ are parametrized by the points of the coset space, which is, in that particular case, the projective space $CP^{N-1}$ and plays the role of the phase space of a corresponding classical mechanics. The $CS$ possess of a minimum uncertainty, they minimize an invariant dispersion of the quadratic Casimir operator. The classical limit is ivestigated in terms of symbols of operators. The role of the Planck constant playes $h=P^{-1}$, where $P$ is the signature of the representation. The classical limit of the so called star commutator generates the Poisson bracket in the $CP^{N-1}$ phase space. The logarithm of the modulus of the $CS$ overlapping, being interpreted as a symmetric in the space, gives the Fubini-Study metric in $CP^{N-1}$. The $CS$ constructed are useful for the quasi-classical analysis of the quantum equations of the $SU(N)$ gauge symmetric theories.Comment: 19pg, IFUSP/P-974 March/199

Does the load-sharing classification predict ligamentous injury, neurological injury, and the need for surgery in patients with thoracolumbar burst fractures?: Clinical article.

OBJECT: The load-sharing score (LSS) of vertebral body comminution is predictive of results after short-segment posterior instrumentation of thoracolumbar burst fractures. Some authors have posited that an LSS \u3e 6 is predictive of neurological injury, ligamentous injury, and the need for surgical intervention. However, the authors of the present study hypothesized that the LSS does not predict ligamentous or neurological injury. METHODS: The prospectively collected spinal cord injury database from a single institution was queried for thoracolumbar burst fractures. Study inclusion criteria were acute (\u3c 24 hours) burst fractures between T-10 and L-2 with preoperative CT and MRI. Flexion-distraction injuries and pathological fractures were excluded. Four experienced spine surgeons determined the LSS and posterior ligamentous complex (PLC) integrity. Neurological status was assessed from a review of the medical records. RESULTS: Forty-four patients were included in the study. There were 4 patients for whom all observers assigned an LSS \u3e 6, recommending operative treatment. Eleven patients had LSSs ≤ 6 across all observers, suggesting that nonoperative treatment would be appropriate. There was moderate interobserver agreement (0.43) for the overall LSS and fair agreement (0.24) for an LSS \u3e 6. Correlations between the LSS and the PLC score averaged 0.18 across all observers (range -0.02 to 0.34, p value range 0.02-0.89). Correlations between the LSS and the American Spinal Injury Association motor score averaged -0.12 across all observers (range -0.25 to -0.03, p value range 0.1-0.87). Correlations describing the relationship between an LSS \u3e 6 and the treating physician\u27s decision to operate averaged 0.17 across all observers (range 0.11-0.24, p value range 0.12-0.47). CONCLUSIONS: The LSS does not uniformly correlate with the PLC injury, neurological status, or empirical clinical decision making. The LSSs of only one observer correlated significantly with PLC injury. There were no significant correlations between the LSS as determined by any observer and neurological status or clinical decision making

Early Experience With Uniplanar Versus Biplanar Expandable Interbody Fusion Devices in Single-Level Minimally Invasive Transforaminal Lumbar Interbody Fusion

ObjectiveTo compare the early radiographic and clinical outcomes of expandable uniplanar versus biplanar interbody cages used for single-level minimally invasive transforaminal lumbar interbody fusion (MIS-TLIF). MethodA retrospective review of 1-level MIS-TLIFs performed with uniplanar and biplanar polyetheretherketone cages was performed. Radiographic measurements were performed on radiographs taken preoperatively, at 6-week follow-up, and 1-year follow-up. Oswestry Disability Index (ODI) and visual analogue scale (VAS) for back and leg at 3-month and 1-year follow-up. ResultsA total of 93 patients (41 uniplanar, 52 biplanar) were included. Both cage types provided significant postoperative improvements in anterior disc height, posterior disc height, and segmental lordosis at 1 year. No significant differences in cage subsidence rates were found between uniplanar (21.9%) and biplanar devices (32.7%) at 6 weeks (odds ratio, 2.015; 95% confidence interval, 0.651–6.235; p = 0.249) with no additional instances of subsidence at 1 year. No significant differences in the magnitude of improvements based on ODI, VAS back, or VAS leg at 3-month or 1-year follow-up between groups and the proportion of patients achieving the minimal clinically important difference in ODI, VAS back, or VAS leg at 1 year were not statistically significantly different (p \u3e 0.05). Finally, there were no significant differences in complication rates (p = 0.283), 90-day readmission rates (p = 1.00), revision surgical procedures (p = 0.423), or fusion rates at 1 year (p = 0.457) between groups. ConclusionsBiplanar and uniplanar expandable cages offer a safe and effective means of improving anterior disc height, posterior disc height, segmental lordosis, and patient-reported outcome measures at 1 year postoperatively. No significant differences in radiographic outcomes, subsidence rates, mean subsidence distance, 1-year patient-reported outcomes, and postoperative complications were noted between groups

Negative energy balance in dairy cows is associated with specific changes in IGF-binding protein expression in the oviduct

Negative energy balance (NEB) during early lactation in dairy cows leads to an altered metabolic state that has major effects on the production of IGF family members. Low IGF-I concentrations are associated with poor fertility and therefore we aimed to determine whether NEB exerts a direct effect on IGF expression in the postpartum oviduct. Multiparous Holstein cows were allocated to two treatments (each n=6) designed using differential feeding and milking regimes to produce either mild NEB (MNEB) or severe NEB (SNEB). Animals were slaughtered in week 2 of lactation when divergent metabolic profiles were evident. Oviducts were collected for RNA analysis by real-time RT-PCR and in situ hybridisation. Quantitative measures in oviduct gene expression were obtained for all members of the IGF family (IGF-I/II, IGF-binding proteins (IGFBP) 1–6 and receptors for IGF types 1 and 2), insulin A/B, GH, glucocorticoid and oestrogen α/β. Expression of IGFBP-2 and IGFBP-6 (both of which have a high affinity for IGF-II) was decreased in SNEB relative to MNEB (P<0.05). No other gene was altered by NEB, but IGF-II, IGFBP-3, IGFBP-5 and IGFBP-6 all showed differential expression in different regions of the oviduct. These results indicate that, in addition to low circulating IGF-I after calving, NEB may also influence IGF availability in the oviduct indirectly through changes in specific IGFBP expression. It is possible that the predicted increased signalling by IGF-II may perturb embryo development, contributing to the high rates of embryonic mortality in dairy cows