The average crossing number of equilateral random polygons.

In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form . A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type can be described by a function of the form where a, b and c are constants depending on and n0 is the minimal number of segments required to form . The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the ACN profile of all closed walks. These points of intersection define the equilibrium length of , i.e., the chain length at which a statistical ensemble of configurations with given knot type -upon cutting, equilibration and reclosure to a new knot type -does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration Rg.

Weaning made easy: moving from milk to family meals

This booklet provides advice about the stages involved in helping babies make the move from milk only to joining in family meals.

Implementing A vision for change: moving towards a modern, quality and responsive mental health service. Carlow / Kilkenny / South Tipperary.

The key element of the HSE South’s Programme is to enhance and develop community mental health services in Carlow, Kilkenny and South Tipperary, to enable the service user to remain in the community to the greatest extent possible. HSE South has prioritised the implementation of the change programme and has allocated more than €20m capital funding and over €1.75m revenue funding to support this comprehensive development programme. Speaking at the briefings Mr. Pat Healy, Regional Director of Operations, HSE South said, “When this plan is delivered, clients will have access to the highest standards of services in all three counties, which should significantly improve these clients’ treatment programmes and quality of life. The National Service Users Executive are supporting the change programme, which is of immense importance to HSE South. The programme heralds the enhancement and development of community mental health services, the closure of old long stay institutions, the separation of North and South Tipperary acute inpatient mental health services and development of appropriate acute inpatient services, for the extended catchment area, in line with the national strategy for mental health “A Vision for Change”. The programme also acts on recommendations of the Mental Health Commission.”This resource was contributed by The National Documentation Centre on Drug Use.

Weaning made easy moving from milk to family meals (English and translations)

As a parent you want the best start for your baby. What your child eats and drinks is important for his/her health now and in the future. The information in this leaflet may be quite different from what you have read before, or what your friends or family may tell you they did. New research is constantly being carried out into infant nutrition and the information and advice in this leaflet is based on up-to-date scientific evidence. It will help you make sure that your child is getting a good start. (Note: translations are of the 2007 version)

Continuous monitoring of cerebrovascular pressure reactivity in patients with head injury.

OBJECT: Cerebrovascular pressure reactivity is the ability of cerebral vessels to respond to changes in transmural pressure. A cerebrovascular pressure reactivity index (PRx) can be determined as the moving correlation coefficient between mean intracranial pressure (ICP) and mean arterial blood pressure. METHODS: The authors analyzed a database consisting of 398 patients with head injuries who underwent continuous monitoring of cerebrovascular pressure reactivity. In 298 patients, the PRx was compared with a transcranial Doppler ultrasonography assessment of cerebrovascular autoregulation (the mean index [Mx]), in 17 patients with the PET-assessed static rate of autoregulation, and in 22 patients with the cerebral metabolic rate for O(2). Patient outcome was assessed 6 months after injury. RESULTS: There was a positive and significant association between the PRx and Mx (R(2) = 0.36, p < 0.001) and with the static rate of autoregulation (R(2) = 0.31, p = 0.02). A PRx > 0.35 was associated with a high mortality rate (> 50%). The PRx showed significant deterioration in refractory intracranial hypertension, was correlated with outcome, and was able to differentiate patients with good outcome, moderate disability, severe disability, and death. The graph of PRx compared with cerebral perfusion pressure (CPP) indicated a U-shaped curve, suggesting that too low and too high CPP was associated with a disturbance in pressure reactivity. Such an optimal CPP was confirmed in individual cases and a greater difference between current and optimal CPP was associated with worse outcome (for patients who, on average, were treated below optimal CPP [R(2) = 0.53, p < 0.001] and for patients whose mean CPP was above optimal CPP [R(2) = -0.40, p < 0.05]). Following decompressive craniectomy, pressure reactivity initially worsened (median -0.03 [interquartile range -0.13 to 0.06] to 0.14 [interquartile range 0.12-0.22]; p < 0.01) and improved in the later postoperative course. After therapeutic hypothermia, in 17 (70.8%) of 24 patients in whom rewarming exceeded the brain temperature threshold of 37 degrees C, ICP remained stable, but the average PRx increased to 0.32 (p < 0.0001), indicating significant derangement in cerebrovascular reactivity. CONCLUSIONS: The PRx is a secondary index derived from changes in ICP and arterial blood pressure and can be used as a surrogate marker of cerebrovascular impairment. In view of an autoregulation-guided CPP therapy, a continuous determination of a PRx is feasible, but its value has to be evaluated in a prospective controlled trial.

Reuse of paths in light source animation

In this paper we extend the reuse of paths to the shot from a moving light source. In the classical algorithm new paths have to be cast from each new position of a light source. We show that we can reuse all paths for all positions, obtaining in this way a theoretical maximum speed-up equal to the average length of the shooting path

Digital beamforming and moving target indication for future spaceborne synthetic aperture radar

During the last decade the interest on space-borne Synthetic Aperture Radars (SAR) for remote sensing applications has grown as testified by the number of recent and forthcoming missions as TerraSAR-X, RADARSAT-2, COSMO-kyMed, TanDEM-X and the Spanish SEOSAR/PAZ. In this sense, this thesis proposes to study and analyze the performance of the state-of-the-Art space-borne SAR systems, with modes able to provide Moving Target Indication capabilities (MTI), i.e. moving object detection and estimation. The research will focus on the MTI processing techniques as well as the architecture and/ or configuration of the SAR instrument, setting the limitations of the current systems with MTI capabilities, and proposing efficient solutions for the future missions. Two European projects, to which the Universitat Politècnica de Catalunya provides support, are an excellent framework for the research activities suggested in this thesis. NEWA project proposes a potential European space-borne radar system with MTI capabilities in order to fulfill the upcoming European security policies. This thesis will critically review the state-of-the-Art MTI processing techniques as well as the readiness and maturity level of the developed capabilities. For each one of the techniques a performance analysis will be carried out based on the available technologies, deriving a roadmap and identifying the different technological gaps. In line with this study a simulator tool will be developed in order to validate and evaluate different MTI techniques in the basis of a flexible space-borne radar configuration. The calibration of a SAR system is mandatory for the accurate formation of the SAR images and turns to be critical in the advanced operation modes as MTI. In this sense, the SEOSAR/PAZ project proposes the study and estimation of the radiometric budget. This thesis will also focus on an exhaustive analysis of the radiometric budget considering the current calibration concepts and their possible limitations. In the framework of this project a key point will be the study of the Dual Receive Antenna (DRA) mode, which provides MTI capabilities to the mission. An additional aspect under study is the applicability of the Digital Beamforming on multichannel and/or multistatic radar platforms, which conform potential solutions for the NEWA project with the aim to fully exploit its capability jointly with MTI techniques.

Real-time recording of circadian liver gene expression in freely moving mice reveals the phase-setting behavior of hepatocyte clocks.

The mammalian circadian timing system consists of a master pacemaker in the suprachiasmatic nucleus (SCN) in the hypothalamus, which is thought to set the phase of slave oscillators in virtually all body cells. However, due to the lack of appropriate in vivo recording technologies, it has been difficult to study how the SCN synchronizes oscillators in peripheral tissues. Here we describe the real-time recording of bioluminescence emitted by hepatocytes expressing circadian luciferase reporter genes in freely moving mice. The technology employs a device dubbed RT-Biolumicorder, which consists of a cylindrical cage with reflecting conical walls that channel photons toward a photomultiplier tube. The monitoring of circadian liver gene expression revealed that hepatocyte oscillators of SCN-lesioned mice synchronized more rapidly to feeding cycles than hepatocyte clocks of intact mice. Hence, the SCN uses signaling pathways that counteract those of feeding rhythms when their phase is in conflict with its own phase.

The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

Nuclear magnetic resonance chemical shifts with the statistical average of orbital-dependent model potentials in Kohn-Sham density functional theory

The performance of the SAOP potential for the calculation of NMR chemical shifts was evaluated. SAOP results show considerable improvement with respect to previous potentials, like VWN or BP86, at least for the carbon, nitrogen, oxygen, and fluorine chemical shifts. Furthermore, a few NMR calculations carried out on third period atoms (S, P, and Cl) improved when using the SAOP potential

Guidelines for the Conversion of Urban Four-Lane Undivided Roadways to Three-Lane Two-Way Left-turn Lane Facilities, April 2001

Four-lane undivided roadways in urban areas can experience a degradation of service and/or safety as traffic volumes increase. In fact, the existence of turning vehicles on this type of roadway has a dramatic effect on both of these factors. The solution identified for these problems is typically the addition of a raised median or two-way left-turn lane (TWLTL). The mobility and safety benefits of these actions have been proven and are discussed in the “Past Research” chapter of this report along with some general cross section selection guidelines. The cost and right-of-way impacts of these actions are widely accepted. These guidelines focus on the evaluation and analysis of an alternative to the typical four-lane undivided cross section improvement approach described above. It has been found that the conversion of a four-lane undivided cross section to three lanes (i.e., one lane in each direction and a TWLTL) can improve safety and maintain an acceptable level of service. These guidelines summarize the results of past research in this area (which is almost nonexistent) and qualitative/quantitative before-and-after safety and operational impacts of case study conversions located throughout the United States and Iowa. Past research confirms that this type of conversion is acceptable or feasible in some situations but for the most part fails to specifically identify those situations. In general, the reviewed case study conversions resulted in a reduction of average or 85th percentile speeds (typically less than five miles per hour) and a relatively dramatic reduction in excessive speeding (a 60 to 70 percent reduction in the number of vehicles traveling five miles per hour faster than the posted speed limit was measured in two cases) and total crashes (reductions between 17 to 62 percent were measured). The 13 roadway conversions considered had average daily traffic volumes of 8,400 to 14,000 vehicles per day (vpd) in Iowa and 9,200 to 24,000 vehicles per day elsewhere. In addition to past research and case study results, a simulation sensitivity analysis was completed to investigate and/or confirm the operational impacts of a four-lane undivided to three-lane conversion. First, the advantages and disadvantages of different corridor simulation packages were identified for this type of analysis. Then, the CORridor SIMulation (CORSIM) software was used x to investigate and evaluate several characteristics related to the operational feasibility of a four-lane undivided to three-lane conversion. Simulated speed and level of service results for both cross sections were documented for different total peak-hour traffic, access densities, and access-point left-turn volumes (for a case study corridor defined by the researchers). These analyses assisted with the identification of the considerations for the operational feasibility determination of a four -lane to three-lane conversion. The results of the simulation analyses primarily confirmed the case study impacts. The CORSIM results indicated only a slight decrease in average arterial speed for through vehicles can be expected for a large range of peak-hour volumes, access densities, and access-point left-turn volumes (given the assumptions and design of the corridor case study evaluated). Typically, the reduction in the simulated average arterial speed (which includes both segment and signal delay) was between zero and four miles per hour when a roadway was converted from a four-lane undivided to a three-lane cross section. The simulated arterial level of service for a converted roadway, however, showed a decrease when the bi-directional peak-hour volume was about 1,750 vehicles per hour (or 17,500 vehicles per day if 10 percent of the daily volume is assumed to occur in the peak hour). Past research by others, however, indicates that 12,000 vehicles per day may be the operational capacity (i.e., level of service E) of a three-lane roadway due to vehicle platooning. The simulation results, along with past research and case study results, appear to support following volume-related feasibility suggestions for four-lane undivided to three-lane cross section conversions. It is recommended that a four-lane undivided to three-lane conversion be considered as a feasible (with respect to volume only) option when bi-directional peak-hour volumes are less than 1,500 vehicles per hour, but that some caution begin to be exercised when the roadway has a bi-directional peak-hour volume between 1,500 and 1,750 vehicles per hour. At and above 1,750 vehicles per hour, the simulation indicated a reduction in arterial level of service. Therefore, at least in Iowa, the feasibility of a four-lane undivided to three-lane conversion should be questioned and/or considered much more closely when a roadway has (or is expected to have) a peak-hour volume of more than 1,750 vehicles. Assuming that 10 percent of the daily traffic occurs during the peak-hour, these volume recommendations would correspond to 15,000 and 17,500 vehicles per day, respectively. These suggestions, however, are based on the results from one idealized case xi study corridor analysis. Individual operational analysis and/or simulations should be completed in detail once a four-lane undivided to three-lane cross section conversion is considered feasible (based on the general suggestions above) for a particular corridor. All of the simulations completed as part of this project also incorporated the optimization of signal timing to minimize vehicle delay along the corridor. A number of determination feasibility factors were identified from a review of the past research, before-and-after case study results, and the simulation sensitivity analysis. The existing and expected (i.e., design period) statuses of these factors are described and should be considered. The characteristics of these factors should be compared to each other, the impacts of other potentially feasible cross section improvements, and the goals/objectives of the community. The factors discussed in these guidelines include • roadway function and environment • overall traffic volume and level of service • turning volumes and patterns • frequent-stop and slow-moving vehicles • weaving, speed, and queues • crash type and patterns • pedestrian and bike activity • right-of-way availability, cost, and acquisition impacts • general characteristics, including - parallel roadways - offset minor street intersections - parallel parking - corner radii - at-grade railroad crossings xii The characteristics of these factors are documented in these guidelines, and their relationship to four-lane undivided to three-lane cross section conversion feasibility identified. This information is summarized along with some evaluative questions in this executive summary and Appendix C. In summary, the results of past research, numerous case studies, and the simulation analyses done as part of this project support the conclusion that in certain circumstances a four-lane undivided to three-lane conversion can be a feasible alternative for the mitigation of operational and/or safety concerns. This feasibility, however, must be determined by an evaluation of the factors identified in these guidelines (along with any others that may be relevant for a individual corridor). The expected benefits, costs, and overall impacts of a four-lane undivided to three-lane conversion should then be compared to the impacts of other feasible alternatives (e.g., adding a raised median) at a particular location.