Cohomology of preimages with local coefficients

Let M,N and B\subset N be compact smooth manifolds of dimensions n+k,n and \ell, respectively. Given a map f from M to N, we give homological conditions under which g^{-1}(B) has nontrivial cohomology (with local coefficients) for any map g homotopic to f. We also show that a certain cohomology class in H^j(N,N-B) is Poincare dual (with local coefficients) under f^* to the image of a corresponding class in H_{n+k-j}(f^{-1}(B)) when f is transverse to B. This generalizes a similar formula of D Gottlieb in the case of simple coefficients.Comment: This is the version published by Algebraic & Geometric Topology on 4 October 200

Sprague-Grundy values and complexity for LCTR

Given a Young diagram on $n$ boxes as a non-increasing sequence of integers, we consider the impartial combinatorial game LCTR in which moves consist of removing either the left column or top row of boxes. We show that for both normal and mis\`ere play, the optimal strategy can consist mostly of mirroring the opponent's moves. This allows for computing the Sprague-Grundy value of the given game in $O(\log(n))$ time units, where time unit allows for reading an integer, or performing a basic arithmetic operation. This improves on the previous bound of $O(n)$ time units, due to by Ili\'c (2019), which can be obtained by an improvement of the Sprague-Grundy recursion.Comment: 24 pages, 7 figures, 1 tabl

Tumour Suppressor Genes—One Hit Can Be Enough

A paper published in 1998 showed that loss of only one copy of the p53 tumor suppressor gene is sometimes enough to initiate carcinogenesi

Context-Dependent Information Elements in the Car: Explorative Analysis of Static and Dynamic Head-Up-Displays

Head-up-displays (HUDs) illustrate a particular static number of information elements in the driver’s primary field of view. Since the display can obscure the reality, a dynamic HUD presents context-dependent information elements. To become familiar with a user-optimal number of information elements and its essential information elements, we conducted a user study with n = 183 participants. We focused the context on an urban, a rural and a highway trip. Afterwards, a within-subject experiment using a high-fidelity driving simulator (n = 27) reveals the following: Dynamic HUDs significantly lower the average over speeding by 3.45 km/h compared to static HUDs. This speed above the speed limit equals 15.33% of the average speed in urban areas. Steering angle and speed can capture the context. Practitioners can use these findings to decrease the number of information elements in HUDs, thereby possibly increasing traffic safety