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Discovering nothing : in pursuit of an elusive Northwest Passage
\"The many attempts by navigators to find a Northwest Passage via its Pacific portal all ended in failure; however, their discoveries spurred expansionist developments that would forever alter the landscape of North America. In Discovering Nothing, David L. Nicandri maps a cast of geographic visionaries and practical explorers as they promoted or sought a workable commercial route linking the Pacific Ocean to the Atlantic. The discovery of the legendary northern passage proved elusive, but the equivalent land bridges that were built in the form of two transcontinental railroads changed the futures of Canada and the United States. Drawing from close readings of explorers' personal journals, Nicandri provides readers a detailed, engaging, and multifaceted investigation into the many players and failed enterprises at the core of this search, beginning in the eighteenth century through to today--and to the unexpected impact of climate change on this fabled passage.\"-- Provided by publisher.
Book
From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of N random walkers
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N2 for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
Journal Article
Northwest Passage
This portrayal of early efforts to explore Canada's Northwest Passage presents Rogers' 1981 song in combination with color illustrations, historical commentary and a gallery of explorers.
Book
First passage and first hitting times of Lévy flights and Lévy walks
For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.
Journal Article
Time consciousness: the missing link in theories of consciousness
Abstract
There are plenty of issues to be solved in order for researchers to agree on a neural model of consciousness. Here we emphasize an often under-represented aspect in the debate: time consciousness. Consciousness and the present moment both extend in time. Experience flows through a succession of moments and progresses from future predictions, to present experiences, to past memories. However, a brief review finds that many dominant theories of consciousness only refer to brief, static, and discrete “functional moments” of time. Very few refer to more extended, dynamic, and continuous time, which is associated with conscious experience (cf. the “experienced moment”). This confusion between short and discrete versus long and continuous is, we argue, one of the core issues in theories of consciousness. Given the lack of work dedicated to time consciousness, its study could test novel predictions of rival theories of consciousness. It may be that different theories of consciousness are compatible/complementary if the different aspects of time are taken into account. Or, if it turns out that no existing theory can fully accommodate time consciousness, then perhaps it has something new to add. Regardless of outcome, the crucial step is to make subjective time a central object of study.
Journal Article
Non-Markovian modeling of protein folding
We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine₉ for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.
Journal Article
Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices
We analyze a random walk strategy on undirected regular networks involving power matrix functions of the typeL^((α/2))whereLindicates a `simple' Laplacian matrix.We refer such walks to as `Fractional Random Walks' with admissible interval0<α ≤ 2 .We deduce for the Fractional Random Walk probability generating functions (network Green's functions). From these analytical resultswe establish a generalization of Polya's recurrence theorem for Fractional Random Walks ond -dimensional infinite lattices:The Fractional Random Walk is transient for dimensionsd > α(recurrent ford≤α ) of the lattice.As a consequence for0<α< 1the Fractional Random Walk istransient for all lattice dimensionsd=1,2,..and in the range1≤α < 2for dimensionsd≥ 2 . Finally, forα=2 Polya's classical recurrence theorem is recovered, namelythe walk is transient only for lattice dimensionsd≥ 3 . The generalization of Polya's recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps.We also analyze for the Fractional Random Walkmean first passage probabilities, mean first passage times, and global mean first passage times (Kemeny constant).For the infinite 1D lattice (infinite ring) we obtain forthe transient regime0<α<1closed form expressions for the fractional lattice Green's function matrix containing the escape and ever passage probabilities. The ever passage probabilities fulfill Riesz potential power law decay asymptotic behavior for nodes far from the departure node.The non-locality of the Fractional Random Walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy type heavy tailed inverse power law decay for the probability of long-range moves.This non-local and asymptotic behavior of the Fractional random Walk introduces small world properties with emergence of Lévy flights on large (infinite) lattices.
Journal Article