Set Systems Containing Many Maximal Chains

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed $\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$ such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

Outer planet mission guidance and navigation for spinning spacecraft

The orbit determination accuracies, maneuver results, and navigation system specification for spinning Pioneer planetary probe missions are analyzed to aid in determining the feasibility of deploying probes into the atmospheres of the outer planets. Radio-only navigation suffices for a direct Saturn mission and the Jupiter flyby of a Jupiter/Uranus mission. Saturn ephemeris errors (1000 km) plus rigid entry constraints at Uranus result in very high velocity requirements (140 m/sec) on the final legs of the Saturn/Uranus and Jupiter/Uranus missions if only Earth-based tracking is employed. The capabilities of a conceptual V-slit sensor are assessed to supplement radio tracking by star/satellite observations. By processing the optical measurements with a batch filter, entry conditions at Uranus can be controlled to acceptable mission-defined levels (+ or - 3 deg) and the Saturn-Uranus leg velocity requirements can be reduced by a factor of 6 (from 139 to 23 m/sec) if nominal specified accuracies of the sensor can be realized

Hovering and Low-Speed Performance and Control Characteristics of the Kaman Helicopter Rotor System as Determined on the Langley Helicopter Tower. TED No. NACA DE 205

An investigation has been conducted with the Langley helicopter tower to obtain basic performance and control characteristics of the Raman rotor system. Blade-pitch control is obtained in this configuration by utilizing an auxiliary flap to twist the blades. Rotor thrust and power required were measured for the hovering condition and over a range of wind velocities from 0 to 30 miles per hour. The control characteristics and the transient response of the rotor to various control movements were also measured. The hovering-performance data are presented as a survey of the wake velocities and the variation of torque coefficient with thrust coefficient. The power required for the test rotor to hover at a thrust of 1350 pounds and a rotor speed of 240 rpm is approximately 6.5 percent greater than that estimated for a conventional rotor of the same diameter and solidity. It is believed that most of this difference is caused by th e flap servomechanism. The reduction in total power required for sustentation of the single-rotor configuration tested at various wind velocities and at the normal operating rotor thrust was found to be similar to the theoretical and experimental results for ro tors with conventionally actuated pitch. The control effectiveness was determined as a function of rotor speed. Sufficient control was available to give a thrust range of 0 to 1500 pounds and a rotor tilt of plus or minus 7 degrees. The time lag between flap motion and blade-pitch response is approximately 0.02 to 0.03 second. The response of the rotor following the blade-pitch response is similar to that of a rotor with conventionally actuated pitch changes. The over-all characteristics of the rotor investigated indicate that satisfactory performance and control characteristics were obtained

The intrinsic stiffness of human trabecular meshwork cells increases with senescence.

Dysfunction of the human trabecular meshwork (HTM) plays a central role in the age-associated disease glaucoma, a leading cause of irreversible blindness. The etiology remains poorly understood but cellular senescence, increased stiffness of the tissue, and the expression of Wnt antagonists such as secreted frizzled related protein-1 (SFRP1) have been implicated. However, it is not known if senescence is causally linked to either stiffness or SFRP1 expression. In this study, we utilized in vitro HTM senescence to determine the effect on cellular stiffening and SFRP1 expression. Stiffness of cultured cells was measured using atomic force microscopy and the morphology of the cytoskeleton was determined using immunofluorescent analysis. SFRP1 expression was measured using qPCR and immunofluorescent analysis. Senescent cell stiffness increased 1.88±0.14 or 2.57±0.14 fold in the presence or absence of serum, respectively. This was accompanied by increased vimentin expression, stress fiber formation, and SFRP1 expression. In aggregate, these data demonstrate that senescence may be a causal factor in HTM stiffening and elevated SFRP1 expression, and contribute towards disease progression. These findings provide insight into the etiology of glaucoma and, more broadly, suggest a causal link between senescence and altered tissue biomechanics in aging-associated diseases

Cell fate patterning during C. elegans vulval development

Precursor cells of the vulva of the C. elegans hermaphrodite choose between two vulval cell fates (1° and 2°) and a non-vulval epidermal fate (3°) in response to three intercellular signals. An inductive signal produced by the anchor cell induces the vulval precursors to assume the 1° and 2° vulval fates. This inductive signal is an EGF-like growth factor encoded by the gene lin-3. An inhibitory signal mediated by lin-15, and which may originate from the surrounding epidermis, prevents the vulval precursors from assuming vulval fates in the absence of the inductive signal. A short range lateral signal, which acts through the gene lin-12, regulates the pattern of 1° and 2° fates assumed by the induced vulval precursors. The combined action of the three signals precisely directs the six vulval precursors to adopt a 3° 3° 2° 1° 2 ° 3° pattern of fates. The amount of inductive signal produced by the anchor cell appears to determine the number or vulval precursors that assume vulval fates. The three induced vulval precursors most proximal to the anchor cell are proposed to adopt the 2° 1° 2° pattern of fates in response to a gradient of the inductive signal and also in response to lateral signalling that inhibits adjacent vulval precursor cells from both assuming the 1° fate

Modelling the influence of the process inputs on the removal of surface contaminants from Ti-6Al-4V linear friction welds

The linear friction welding (LFW) process is finding increasing interest from industry for the fabrication of near-net-shape, titanium alloy Ti–6Al–4V, aerospace components. Currently, the removal of surface contaminants, such as oxides and foreign particles, from the weld interface into the flash is not fully understood. To address this problem, two-dimensional (2D) computational models were developed using the finite element analysis (FEA) software DEFORM and validated with experiments. The key findings showed that the welds made with higher applied forces required less burn-off to completely remove the surface contaminants from the interface into the flash; the interface temperature increased as the applied force was decreased or the rubbing velocity increased; and the boundary temperature between the rapid flash formation and negligible material flow was approximately 970 °C. An understanding of these phenomena is of particular interest for the industrialisation of near-net-shape titanium alloy aerospace components.EPSRC, Boeing Company, Welding Institut

Equity of colorectal cancer screening: which groups have inequitable participation and what can we do about it?

The National Bowel Cancer Screening Program (NBCSP) offers population-based screening for colorectal cancer (CRC) across Australia. The aims of this paper were to highlight the inequities in CRC screening in South Australia (SA) and the system-related barriers and enablers to CRC screening from the perspective of participants identified as having inequitable participation. First, de-identified data for the SA population of the NBCSP were statistically analysed and then mapped. Second, 117 in-depth interviews were conducted with culturally and linguistically diverse (CALD) groups, Indigenous and Anglo-Saxon Australians. Participation rates in the NBCSP were geographically and statistically significantly different (P < 0.0001) on the basis of gender (higher for women), age (higher for older people) and socioeconomic status (higher for more affluent people). The main system-related barriers were the lack of awareness of CRC or CRC screening within these groups, the problems with language due to most of the information being in English and the lack of recommendation by a doctor. This study revealed that inequity exists in the NBCSP participation in SA, and we identified both barriers and facilitators to CRC screening that require action at the level of both policy and practice. There is a large role in primary health care of both recommending CRC screening and facilitating equitable participation

Modeling associations between public understanding, engagement and forest conditions in theInland Northwest, USA

Opinions about public lands and the actions of private non-industrial forest owners in the western United States play important roles in forested landscape management as both public and private forests face increasing risks from large wildfires, pests and disease. This work presents the responses from two surveys, a random-sample telephone survey of more than 1500 residents and a mail survey targeting owners of parcels with 10 or more acres of forest. These surveys were conducted in three counties (Wallowa, Union, and Baker) in northeast Oregon, USA. We analyze these survey data using structural equation models in order to assess how individual characteristics and understanding of forest management issues affect perceptions about forest conditions and risks associated with declining forest health on public lands. We test whether forest understanding is informed by background, beliefs, and experiences, and whether as an intervening variable it is associated with views about forest conditions on publicly managed forests. Individual background characteristics such as age, gender and county of residence have significant direct or indirect effects on our measurement of understanding. Controlling for background factors, we found that forest owners with higher self-assessed understanding, and more education about forest management, tend to hold more pessimistic views about forest conditions. Based on our results we argue that self-assessed understanding, interest in learning, and willingness to engage in extension activities together have leverage to affect perceptions about the risks posed by declining forest conditions on public lands, influence land owner actions, and affect support for public policies. These results also have broader implications for management of forested landscapes on public and private lands amidst changing demographics in rural communities across the Inland Northwest where migration may significantly alter the composition of forest owner goals, understanding, and support for various management actions

Modelling Associations between Public Understanding, Engagement and Forest Conditions in the Inland Northwest, USA.

Abstract Opinions about public lands and the actions of private non-industrial forest owners in the western United States play important roles in forested landscape management as both public and private forests face increasing risks from large wildfires, pests and disease. This work presents the responses from two surveys, a random-sample telephone survey of more than 1500 residents and a mail survey targeting owners of parcels with 10 or more acres of forest. These surveys were conducted in three counties (Wallowa, Union, and Baker) in northeast Oregon, USA. We analyze these survey data using structural equation models in order to assess how individual characteristics and understanding of forest management issues affect perceptions about forest conditions and risks associated with declining forest health on public lands. We test whether forest understanding is informed by background, beliefs, and experiences, and whether as an intervening variable it is associated with views about forest conditions on publicly managed forests. Individual background characteristics such as age, gender and county of residence have significant direct or indirect effects on our measurement of understanding. Controlling for background factors, we found that forest owners with higher self-assessed understanding, and more education about forest management, tend to hold more pessimistic views about forest conditions. Based on our results we argue that self-assessed understanding, interest in learning, and willingness to engage in extension activities together have leverage to affect perceptions about the risks posed by declining forest conditions on public lands, influence land owner actions, and affect support for public policies. These results also have broader implications for management of forested landscapes on public and private lands amidst changing demographics in rural communities across the Inland Northwest where migration may significantly alter the composition of forest owner goals, understanding, and support for various management actions