Intervals of Permutations with a Fixed Number of Descents are Shellable

The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the M\"obius function of these intervals. We present an alternative proof for a result on the M\"obius function of intervals $[1,\pi]$ such that $\pi$ has exactly one descent. We prove that if $\pi$ has exactly one descent and avoids 456123 and 356124, then the intervals $[1,\pi]$ have no nontrivial disconnected subintervals; we conjecture that these intervals are shellable

On the M\"obius Function of Permutations With One Descent

The set of all permutations, ordered by pattern containment, is a poset. We give a formula for the M\"obius function of intervals $[1,\pi]$ in this poset, for any permutation $\pi$ with at most one descent. We compute the M\"obius function as a function of the number and positions of pairs of consecutive letters in $\pi$ that are consecutive in value. As a result of this we show that the M\"obius function is unbounded on the poset of all permutations. We show that the M\"obius function is zero on any interval $[1,\pi]$ where $\pi$ has a triple of consecutive letters whose values are consecutive and monotone. We also conjecture values of the M\"obius function on some other intervals of permutations with at most one descent

An Experimental Information Gathering and Utilization Systems (IGUS) Robot to Demonstrate the Physics of Now

The past, present and future are not fundamental properties of Minkowski spacetime. It has been suggested that they are properties of a class of information gathering and utilizing systems (IGUSs).The past, present and future are psychologically created phenomena not actually properties of spacetime. A human is a model IGUS robot. We develop a way to establish that the past, present, and future do not follow from the laws of physics by constructing robots that process information differently and therefore experience different nows (presents). We construct a customized virtual reality (VR) system which allows an observer to switch between present and past. This robot (human with VR system) can experience immersion in the immediate past ad libitum. Being able to actually construct an IGUS that has the same present at two different coordinates along the worldline lends support to the IGUS hypothesis.Comment: 8 pages, 5 figure

Are You Used To It Yet? Braking Performance and Adaptation in a Fixed-base Driving Simulator.

During braking-to-stop manoeuvres in a fixed-base driving simulator, the paucity of visual and vestibular cues can lead to driver misperception and produce different patterns of braking response between real and simulated driving. For these reasons, drivers must adapt their behaviour in a simulator to affect a comfortable and efficient braking manoeuvre. Such behavioural adaptation is likely to have negative consequences by increasing a driver’s attentional demand. In this study, 48 participants underwent a series of braking-to-stop manoeuvres in an instrumented vehicle on a test-track. Each participant was instructed to drive at 40mph. A set of traffic lights, on occasions, changed to red as the vehicle was 58m from the lights. Deceleration profiles provided the baseline data. The same scenario was modelled in a fixed-base driving simulator. Two groups, each of 24 participants, one familiar with the simulator from previous investigations and one with no prior simulator experience, underwent the simulated traffic light scenario ten times. This paper suggests a method of objectively assessing driver braking performance between the real and simulated environments. Results appear to suggest that in as little as five or six practice stops drivers can adapt their simulator driving style to closely match that observed in a real vehicle on a test track. However, any process of adaptation from prior exposure to the simulator is short-lived

Teachers’ views of teaching sex education: pedagogies and models of delivery

This paper is based on a study of 17 secondary schools in an inner-city area of England deemed to have very high levels of teenage pregnancies. The New Labour Government argued that academic achievements and effective labour-market participation are inhibited by early or 'premature' parenthood (Social Exclusion Unit 1999). It therefore set in place policies to address these issues efectively in schools, through a revised school achievement agenda and a revised Sex & Relationship Education (SRE) programme. In this paper, we concentrate on the role and views of personal, social and/or health education coordinators charged with the delivery of SRE in secondary schools. We consider the way a broad-based, inclusive curriculum and pastoral programme fits into the subject-based and assessed curriculum of secondary schools for 11-16 where there is no tradition of open discussion of sexual matters. The legitimacy of teaching about sex and relationships in school has been hotly contested. The question of how to deal with teenage pregnancy and sexuality remains politically charged and sensitive and the teacher's role is thus contentious. We present a range of views about the professional or other pressures on schools, especially teachers, discussing difficulties within each of the main models of delivery. Teachers reprt considerable anxiety about SRE as a subject and its low status inthe curriculum, committed though they are to teaching it. This links with what is now seen as an overarching culture of anxiety regarding sex in contemporary society. Many teachers think that attending to young people's personal and social development - and especially their sexual identities - could help their education careers and academic achievement. Thus, from the teachers' accounts, we argue that there are important links between the revised sex education curriculum and the new emphasis on the achievement agenda in secondary schools in the UK