Recontamination Helps a Lot to Hunt a Rabbit

The Hunters and Rabbit game is played on a graph G where the Hunter player shoots at k vertices in every round while the Rabbit player occupies an unknown vertex and, if it is not shot, must move to a neighbouring vertex after each round. The Rabbit player wins if it can ensure that its position is never shot. The Hunter player wins otherwise. The hunter number h(G) of a graph G is the minimum integer k such that the Hunter player has a winning strategy (i.e., allowing him to win whatever be the strategy of the Rabbit player). This game has been studied in several graph classes, in particular in bipartite graphs (grids, trees, hypercubes...), but the computational complexity of computing h(G) remains open in general graphs and even in more restricted graph classes such as trees. To progress further in this study, we propose a notion of monotonicity (a well-studied and useful property in classical pursuit-evasion games such as Graph Searching games) for the Hunters and Rabbit game imposing that, roughly, a vertex that has already been shot "must not host the rabbit anymore". This allows us to obtain new results in various graph classes. More precisely, let the monotone hunter number mh(G) of a graph G be the minimum integer k such that the Hunter player has a monotone winning strategy. We show that pw(G) ? mh(G) ? pw(G)+1 for any graph G with pathwidth pw(G), which implies that computing mh(G), or even approximating mh(G) up to an additive constant, is NP-hard. Then, we show that mh(G) can be computed in polynomial time in split graphs, interval graphs, cographs and trees. These results go through structural characterisations which allow us to relate the monotone hunter number with the pathwidth in some of these graph classes. In all cases, this allows us to specify the hunter number or to show that there may be an arbitrary gap between h and mh, i.e., that monotonicity does not help. In particular, we show that, for every k ? 3, there exists a tree T with h(T) = 2 and mh(T) = k. We conclude by proving that computing h (resp., mh) is FPT parameterised by the minimum size of a vertex cover

Further results on the Hunters and Rabbit game through monotonicity

Hunters and Rabbit game is played on a graph $G$ where the Hunter player shoots at $k$ vertices in every round while the Rabbit player occupies an unknown vertex and, if not shot, must move to a neighbouring vertex after each round. The Rabbit player wins if it can ensure that its position is never shot. The Hunter player wins otherwise. The hunter number $h(G)$ of a graph $G$ is the minimum integer $k$ such that the Hunter player has a winning strategy (i.e., allowing him to win whatever be the strategy of the Rabbit player). This game has been studied in several graph classes, in particular in bipartite graphs (grids, trees, hypercubes...), but the computational complexity of computing $h(G)$ remains open in general graphs and even in trees. To progress further, we propose a notion of monotonicity for the Hunters and Rabbit game imposing that, roughly, a vertex that has already been shot ``must not host the rabbit anymore''. This allows us to obtain new results in various graph classes. Let the monotone hunter number be denoted by $mh(G)$. We show that $pw(G) \leq mh(G) \leq pw(G)+1$ for any graph $G$ with pathwidth $pw(G)$, implying that computing $mh(G)$, or even approximating $mh(G)$ up to an additive constant, is NP-hard. Then, we show that $mh(G)$ can be computed in polynomial time in split graphs, interval graphs, cographs and trees. These results go through structural characterisations which allow us to relate the monotone hunter number with the pathwidth in some of these graph classes. In all cases, this allows us to specify the hunter number or to show that there may be an arbitrary gap between $h$ and $mh$, i.e., that monotonicity does not help. In particular, we show that, for every $k\geq 3$, there exists a tree $T$ with $h(T)=2$ and $mh(T)=k$. We conclude by proving that computing $h$ (resp., $mh$) is FPT parameterised by the minimum size of a vertex cover.Comment: A preliminary version appeared in MFCS 2023. Abstract shortened due to Arxiv submission requirement

Visualization of the distribution of autophosphorylated calcium/calmodulin-dependent protein kinase II after tetanic stimulation in the CA1 area of the hippocampus

Autophosphorylation of calcium/calmodulin-dependent protein kinase II (CaMKII) at threonine-286 produces Ca2+-independent kinase activity and has been proposed to be involved in induction of long-term potentiation by tetanic stimulation in the hippocampus. We have used an immunocytochemical method to visualize and quantify the pattern of autophosphorylation of CaMKII in hippocampal slices after tetanization of the Schaffer collateral pathway. Thirty minutes after tetanic stimulation, autophosphorylated CaM kinase II (P-CaMKII) is significantly increased in area CA1 both in apical dendrites and in pyramidal cell somas. In apical dendrites, this increase is accompanied by an equally significant increase in staining for nonphosphorylated CaM kinase II. Thus, the increase in P-CaMKII appears to be secondary to an increase in the total amount of CaMKII. In neuronal somas, however, the increase in P-CaMKII is not accompanied by an increase in the total amount of CaMKII. We suggest that tetanic stimulation of the Schaffer collateral pathway may induce new synthesis of CaMKII molecules in the apical dendrites, which contain mRNA encoding its alpha-subunit. In neuronal somas, however, tetanic stimulation appears to result in long-lasting increases in P-CaMKII independent of an increase in the total amount of CaMKII. Our findings are consistent with a role for autophosphorylation of CaMKII in the induction and/or maintenance of long-term potentiation, but they indicate that the effects of tetanus on the kinase and its activity are not confined to synapses and may involve induction of new synthesis of kinase in dendrites as well as increases in the level of autophosphorylated kinase

Tiam1 interaction with the PAR complex promotes talin-mediated Rac1 activation during polarized cell migration.

Migrating cells acquire front-rear polarity with a leading edge and a trailing tail for directional movement. The Rac exchange factor Tiam1 participates in polarized cell migration with the PAR complex of PAR3, PAR6, and atypical protein kinase C. However, it remains largely unknown how Tiam1 is regulated and contributes to the establishment of polarity in migrating cells. We show here that Tiam1 interacts directly with talin, which binds and activates integrins to mediate their signaling. Tiam1 accumulated at adhesions in a manner dependent on talin and the PAR complex. The interactions of talin with Tiam1 and the PAR complex were required for adhesion-induced Rac1 activation, cell spreading, and migration toward integrin substrates. Furthermore, Tiam1 acted with talin to regulate adhesion turnover. Thus, we propose that Tiam1, with the PAR complex, binds to integrins through talin and, together with the PAR complex, thereby regulates Rac1 activity and adhesion turnover for polarized migration

Paradox lost : the cost of a virtual world

This paper touches on a number of seemingly disparate topics-Artificial Intelligence, Fuzzy Logic, String Theory, the search for extra-terrestrial intelligence, the Cantorian concept of infinite sets-in order to support the thesis that for a large part of the educated public in the Western world, the very concept of reality has been changing over the last few generations, and that the change is being accelerated by our increasing acceptance of the Virtual as a substitute for the traditional Real. This, as I hope to convince you, is a momentous shift in the our world view, and like so many profound but gradual shifts, has gone largely unnoticed. Whether the shift is ultimately a good thing or a bad, it ought not to go unscrutinized; this paper aims to bring it to public attention. (The paradox whose loss is referred to in the title is discussed at the end of the paper.

Farming Inside Invisible Worlds

This book is available as open access through the Bloomsbury Open Access programme and is available on www.bloomsburycollections.com. It is funded by the University of Otago, New Zealand. Farming Inside Invisible Worlds argues that the farm is a key player in the creation and stabilisation of political, economic and ecological power-particularly in colonised landscapes like New Zealand, America and Australia. This open access book reviews and rejects the way that farms are characterised in orthodox economics and agricultural science and then shows how re-centring the farm using the theoretical idea of political ontology can transform the way we understand the power of farming. Starting with the colonial history of farms in New Zealand, Hugh Campbell goes on to describe the rise of modernist farming and its often hidden political, racial and ecological effects. He concludes with an examination of alternative ways to farm in New Zealand, showing how the prior histories of colonisation and modernisation reveal important ways to farm differently in post-colonial worlds. Hugh Campbell's book has wide-ranging implications for understanding the role farms play in both our food systems and landscapes, and is an exciting new addition to food studies

The APC/C recruits cyclin B1–Cdk1–Cks in prometaphase before D box recognition to control mitotic exit

Prior associations with the APC/C complex during prometaphase makes cyclin B1 a better substrate for the cell cycle–regulating ubiquitin ligase in metaphase (see also a related paper by Di Fiore et al. in this issue)