On the Functional Integral Theory of Systems with Kinematical Interaction

We propose a systematic way to investigate the low-temperature thermodynamic properties of quantum spin systems subject to the restriction that only a finite number of bosons may occupy a single lattice site. Such a kinematical interaction results in appearance of a temperature dependent chemical potential. Its low-temperature asymptotics is calculated self-consistently using the functional integration technique.Comment: 3 pages (REVTeX), 2 PS figure

Baryogenesis in Cosmological Model with Superstring-Inspired E_6 Unification

We have developed a concept of parallel existence of the ordinary (O) and hidden (H) worlds with a superstring-inspired E_6 unification, broken at the early stage of the Universe into SO(10) X U(1) - in the O-world, and SU(6)' X SU(2)' - in the H-world. As a result, we have obtained in the hidden world the low energy symmetry group G'_SM X SU(2)'_\theta, instead of the Standard Model group G_SM. The additional non-Abelian SU(2)'_\theta group with massless gauge fields, "thetons", is responsible for the dark energy. We present a baryogenesis mechanism with the B-L asymmetry produced by the conversion of ordinary leptons into particles of the hidden sector.Comment: 15 pages, 2 figure

Fast evaluation of appointment schedules for outpatients in health care

We consider the problem of evaluating an appointment schedule for outpatients in a hospital. Given a fixed-length session during which a physician sees K patients, each patient has to be given an appointment time during this session in advance. When a patient arrives on its appointment, the consultations of the previous patients are either already finished or are still going on, which respectively means that the physician has been standing idle or that the patient has to wait, both of which are undesirable. Optimising a schedule according to performance criteria such as patient waiting times, physician idle times, session overtime, etc. usually requires a heuristic search method involving a huge number of repeated schedule evaluations. Hence, the aim of our evaluation approach is to obtain accurate predictions as fast as possible, i.e. at a very low computational cost. This is achieved by (1) using Lindley's recursion to allow for explicit expressions and (2) choosing a discrete-time (slotted) setting to make those expression easy to compute. We assume general, possibly distinct, distributions for the patient's consultation times, which allows us to account for multiple treatment types, as well as patient no-shows. The moments of waiting and idle times are obtained. For each slot, we also calculate the moments of waiting and idle time of an additional patient, should it be appointed to that slot. As we demonstrate, a graphical representation of these quantities can be used to assist a sequential scheduling strategy, as often used in practice

Low body condition predisposes cattle to lameness: An 8-year study of one dairy herd

Lameness in dairy cows is a multifactorial and progressive disease with complex interactions between risk factors contributing to its occurrence. Detailed records were obtained from one United Kingdom dairy herd over an 8-yr period. Weekly locomotion scores were used to classify cows as not lame (score 1 to 2), mildly lame (score 3) and severely lame (score 4 to 5). These outcomes were used to investigate the hypothesis that low body condition score (BCS) is associated with an increased risk of lameness in dairy cows. Mixed effect multinomial logistic regression models were used to investigate the association between prior BCS and repeat lameness events during the longitudinal period of the study. Discrete time survival models were used to explore the relationship between prior BCS and first lifetime lameness events. In total, 79,565 cow weeks at risk were obtained for 724 cows. The number of lameness events was 17,114, of which 8,799 were categorized as mildly lame and 8,315 as severely lame. The median BCS was 2.25 (range, 0.75 to 4.25) and the mean body weight (BW) and age at first calving were 619.5 kg (range, 355.6 to 956.4 kg) and 25.8 mo (range, 20.5 to 37.8 mo), respectively. Subsets of the data were used in the discrete time survival models: 333 mild and 211 severe first lifetime lameness events in heifers (first lactation cows), and 81 mild and 49 severe first lifetime lameness events in cows second lactation or greater. Low BCS 3 wk before a repeated lameness event was associated with a significantly increased risk of lameness. Cows with BCS <2 were at greatest risk of mild or severe lameness, and an increased BCS above 2 was associated with a reduced risk of mild or severe lameness. Low BCS 16 or 8 wk before a first mild or severe lifetime lameness event, respectively, also had a positive association with risk of lameness in cows second lactation or greater. This provides evidence to support targeting management toward maintaining BCS to minimize the risk of lameness. Low BW (independent of BCS) and increased age at first calving above 24 mo were also associated with increased long-term risk of repeated lameness events. Overall, the model explained 62 and 60% of the variability for mild and severe lameness, respectively, highlighting the importance of these variables as risk factors and hence where management could be targeted to significantly affect reducing the risk of lameness

Lameness in dairy heifers; impacts of hoof lesions present around first calving on future lameness, milk yield and culling risk

The importance of lameness in primiparous dairy heifers is increasingly recognised. Although it is accepted that clinical lameness in any lactation increases the risk of future lameness, the impact of foot lesions during the first lactation on long-term lameness risk is less clear. This retrospective cohort study aimed to investigate the impacts of foot lesions occurring around the time of first calving in heifers on future lameness risk, daily milk yield and survival within a dairy herd. Records were obtained for 158 heifers from one UK dairy herd. Heifers were examined in 2 month blocks from 2 months pre-calving through to 4 months post-calving. Sole lesions and white line lesions were scored on a zero to 10 scale and digital dermatitis on a zero to 3 scale. Outcomes investigated were; lameness risk based on weekly locomotion scores, average daily milk yield and culling risk. Mixed effect models were used to investigate associations between maximum lesion scores and outcomes. Lesion scores in the highest score categories for claw horn lesions (sole lesions and white line lesions) in the 2 to 4 month post-calving period were associated with an increased risk of future lameness; heifers with white line lesion scores ≥3 compared with scores zero to 1 and heifers with sole lesion scores ≥4 compared with score 2, at this time point, had a predicted increased risk of future lameness of 1.6 and 2.6 respectively. Sole lesions ≥4 were also associated with a reduction in average daily milk yield of 2.68 kg. Managing heifers to reduce claw horn lesions during this time period post-calving may provide health, welfare and production benefits for the long-term future of those animals. A novel finding from the study was that mild lesion scores compared with scores zero to 1, were associated with a reduced risk of future lameness for white line lesions and sole lesions occurring in the pre-calving or 2 to 4 months post-calving periods respectively. Mild sole lesions in the pre-calving period were also associated with a reduced risk of premature culling. One hypothesis for this result is that a mild insult may result in adaptive changes to the foot leading to greater biomechanical resilience and so increased longevity

The contribution of previous lameness events and body condition score to the occurrence of lameness in dairy herds: a study of 2 herds

It has been demonstrated that low body condition and previous occurrence of lameness increase the risk of future lameness in dairy cows. To date the population attributable fraction (PAF), which provides an estimate of the contribution that a risk factor makes toward the total number of disease events in a population, has not been explored for lameness using longitudinal data with repeated measures. Estimation of PAF helps to identify control measures that could lead to the largest improvements on-farm. The aim of this study was to use longitudinal data to evaluate the proportion of lameness that could be avoided in 2 separate herds (2 populations) through (1) reduced recurrence of previous lameness events, (2) and moving body condition score (BCS) into more optimal ranges. Data were obtained from 2 UK dairy herds: herd A, a 200-cow herd with 8 yr of data from a total of 724 cows where lameness events were based on weekly locomotion scores (LS; 1 to 5 scale), and herd B, a 600-cow herd with data recorded over 44 mo from a total of 1,040 cows where treatment of clinical cases was used to identify lameness events. The PAF for categories of BCS were estimated using a closed equation appropriate for multiple exposure categories. Simulation models were used to explore theoretical scenarios to reflect changes in BCS and recurrence of previous lameness events in each herd. For herd A, 21.5% of the total risk periods (cow-weeks) contained a lameness event (LS 3, 4, or 5), 96% of which were repeat events and 19% were recorded with BCS 16 wk before a risk period. The median PAF estimated for changes in BCS were in the region of 4 to 11%, depending on severity of lameness. Repeated bouts of lameness made a very large contribution to the total number of lameness events. This could either be because certain cows are initially susceptible and remain susceptible, due to the increased risk associated with previous lameness events, or due to interactions with environmental factors. This area requires further research

PP-Wave Light-Cone Free String Field Theory at Finite Temperature

In this paper, a real-time formulation of light-cone pp-wave string field theory at finite temperature is presented. This is achieved by developing the thermo field dynamics (TFD) formalism in a second quantized string scenario. The equilibrirum thermodynamic quantities for a pp-wave ideal string gas are derived directly from expectation values on the second quantized string thermal vacuum. Also, we derive the real-time thermal pp-wave closed string propagator. In the flat space limit it is shown that this propagator can be written in terms of Theta functions, exactly as the zero temperature one. At the end, we show how supestrings interactions can be introduced, making this approach suitable to study the BMN dictionary at finite temperature.Comment: 27 pages, revtex

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and remarks added) To appear in Inventione

The Taming of Closed Time-like Curves

We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space reversal, also known as the embedding space of the elliptic de Sitter space. The background has two potentially dangerous problems: time-nonorientability and the existence of closed time-like curves. We first show that closed causal curves disappear after a proper definition of the time function. We then consider the one-loop vacuum expectation value of the stress tensor. A naive QFT analysis yields a divergent result. We then analyze the stress tensor in bosonic string theory, and find the same result as if the target space would be just the Minkowski space $R^{1,d}$, suggesting a zero result for the superstring. This leads us to propose a proper reformulation of QFT, and recalculate the stress tensor. We find almost the same result as in Minkowski space, except for a potential divergence at the initial time slice of the orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that it is possible to define local S-matrices, even if the spacetime is globally time-nonorientable.Comment: 37 pages, LaTeX2e, uses amssymb, amsmath and epsf macros, 8 eps and 3 ps figures; (v2): Two additional comments + one reference added; (v3): corrections in discussion of CTCs + some clarification