How do elderly pedestrians perceive hazards in the street? - An initial investigation towards development of a pedestrian simulation that incorporates reaction of various pedestrians to environments

In order to evaluate the accessibility of street and transport environments, such as railway stations, we are now developing a pedestrian simulation that incorporates elderly and disable pedestrians and their interaction with various environments including hazards on the street. For this development, it is necessary to understand how elderly and disabled pedestrians perceive hazards in the street and transport environments. Many elderly people suffer from some visual impairment. A study in the UK suggested 12% of people aged 65 or over have binocular acuity of 6/18 or less (Van der Pols et al, 2000). It should be noted that a quarter of the UK population will be aged 65 or over by 2031 (The Government Actuary's Department, 2004). Because of age-related changes of visual perception organs, elderly people suffer not only visual acuity problems but also other forms of visual disabilities, such as visual field loss and less contrast sensitivity. Lighting is considered to be an effective solution to let elderly and disable pedestrians perceive possible hazards in the street. Interestingly, British Standards for residential street lighting have not considered lighting needs of elderly pedestrians or pedestrians with visual disabilities (e.g. Fujiyama et al, 2005). In order to design street lighting that incorporates elderly and visually disabled pedestrians, it would be useful to understand how lighting improves the perception of hazards by elderly and disable pedestrians. The aim of this paper is to understand how elderly pedestrians perceive different hazards and to address issues to be investigated in future research. This paper focuses on fixation patterns of elderly pedestrians on different hazards in the street under different lighting conditions. Analysing fixation patterns helps us understand how pedestrians perceive environments or hazards (Fujiyama, 2006). This paper presents the initial results of our analysis of the eye tracker data of an ordinary elderly participant

Investigation of Lighting Levels for Pedestrians - Some questions about lighting levels of current lighting standards

22-23 September, 200

Scaffolds and Generalized Integral Galois Module Structure

Let $L/K$ be a finite, totally ramified $p$-extension of complete local fields with residue fields of characteristic $p > 0$, and let $A$ be a $K$-algebra acting on $L$. We define the concept of an $A$-scaffold on $L$, thereby extending and refining the notion of a Galois scaffold considered in several previous papers, where $L/K$ was Galois and $A=K[G]$ for $G=\mathrm{Gal}(L/K)$. When a suitable $A$-scaffold exists, we show how to answer questions generalizing those of classical integral Galois module theory. We give a necessary and sufficient condition, involving only numerical parameters, for a given fractional ideal to be free over its associated order in $A$. We also show how to determine the number of generators required when it is not free, along with the embedding dimension of the associated order. In the Galois case, the numerical parameters are the ramification breaks associated with $L/K$. We apply these results to biquadratic Galois extensions in characteristic 2, and to totally and weakly ramified Galois $p$-extensions in characteristic $p$. We also apply our results to the non-classical situation where $L/K$ is a finite primitive purely inseparable extension of arbitrary exponent that is acted on, via a higher derivation (but in many different ways), by the divided power $K$-Hopf algebra.Comment: Further minor corrections and improvements to exposition. Reference [BE] updated. To appear in Ann. Inst. Fourier, Grenobl

On the Galois correspondence for Hopf Galois structures arising from finite radical algebras and Zappa-Sz\'ep products

Let $L/K$ be a $G$-Galois extension of fields with an $H$-Hopf Galois structure of type $N$. We study the ratio $GC(G, N)$, which is the number of intermediate fields $E$ with $K \subseteq E \subseteq L$ that are in the image of the Galois correspondence for the $H$-Hopf Galois structure on $L/K$, divided by the number of intermediate fields. By Galois descent, $L \otimes_K H = LN$ where $N$ is a $G$-invariant regular subgroup of $\mathrm{Perm}(G)$, and then $GC(G, N)$ is the number of $G$-invariant subgroups of $N$, divided by the number of subgroups of $G$. We look at the Galois correspondence ratio for a Hopf Galois structure by translating the problem into counting certain subgroups of the corresponding skew brace. We look at skew braces arising from finite radical algebras $A$ and from Zappa-Sz\'ep products of finite groups, and in particular when $A^3 = 0$ or the Zappa-Sz\'ep product is a semidirect product, in which cases the corresponding skew brace is a bi-skew brace, that is, a set $G$ with two group operations $\circ$ and $\star$ in such a way that $G$ is a skew brace with either group structure acting as the additive group of the skew brace. We obtain the Galois correspondence ratio for several examples. In particular, if $(G, \circ, \star)$ is a bi-skew brace of squarefree order $2m$ where $(G, \circ) \cong Z_{2m}$ is cyclic and $(G, \star) = D_m$ is dihedral, then for large $m$, $GC(Z_{2m},D_m),$ is close to 1/2 while $GC(D_m, Z_{2m})$ is near 0.Comment: 23 pages. Some computations in the examples were corrected. The final dihedral example was generalized. Submitted to Publ. Mat. (Barcelona

On the Galois correspondence for Hopf Galois structures arising from finite radical algebras and Zappa-Szép products

Let L/K be a G-Galois extension of fields with an H-Hopf Galois structure of type N. We study the Galois correspondence ratio GC(G, N), which is the proportion of intermediate fields E with K ⊆ E ⊆ L that are in the image of the Galois correspondence for the H-Hopf Galois structure on L/K. The Galois correspondence ratio for a Hopf Galois structure can be found by translating the problem into counting certain subgroups of the corresponding skew brace. We look at skew braces arising from finite radical algebras A and from Zappa-Sz'ep products of finite groups, and in particular when A3 = 0 or the Zappa-Sz'ep product is a semidirect product, in which cases the corresponding skew brace is a bi-skew brace, that is, a set G with two group operations ◦ and ? in such a way that G is a skew brace with either group structure acting as the additive group of the skew brace. We obtain the Galois correspondence ratio for several examples. In particular, if (G, ◦, ?) is a biskew brace of squarefree order 2m where (G, ◦) ∼= Z2m is cyclic and (G, ?) ∼= Dm is dihedral, then for large m, GC(Z2m, Dm) is close to 1/2 while GC(Dm, Z2m) is near 0