12,297 research outputs found
The output distribution of important LULU-operators
Two procedures to compute the output distribution phi_S of certain stack
filters S (so called erosion-dilation cascades) are given. One rests on the
disjunctive normal form of S and also yields the rank selection probabilities.
The other is based on inclusion-exclusion and e.g. yields phi_S for some
important LULU-operators S. Properties of phi_S can be used to characterize
smoothing properties of S. One of the methods discussed also allows for the
calculation of the reliability polynomial of any positive Boolean function
(e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be
published in Quaestiones Mathematicae 201
Sustainable growth and synchronization in protocell models
The growth of a population of protocells requires that the two key processes of replication of the protogenetic material and reproduction of the whole protocell take place at the same rate. While in many ODE-based models such synchronization spontaneously develops, this does not happen in the important case of quadratic growth terms. Here we show that spontaneous synchronization can be recovered (i) by requiring that the transmembrane diffusion of precursors takes place at a finite rate, or (ii) by introducing a finite lifetime of the molecular complexes. We then consider reaction networks that grow by the addition of newly synthesized chemicals in a binary polymer model, and analyze their behaviors in growing and dividing protocells, thereby confirming the importance of (i) and (ii) for synchronization. We describe some interesting phenomena (like long-term oscillations of duplication times) and show that the presence of food-generated autocatalytic cycles is not sufficient to guarantee synchronization: in the case of cycles with a complex structure, it is often observed that only some subcycles survive and synchronize, while others die out. This shows the importance of truly dynamic models that can uncover effects that cannot be detected by static graph theoretical analyses
Irreversibility and the arrow of time in a quenched quantum system
Irreversibility is one of the most intriguing concepts in physics. While
microscopic physical laws are perfectly reversible, macroscopic average
behavior has a preferred direction of time. According to the second law of
thermodynamics, this arrow of time is associated with a positive mean entropy
production. Using a nuclear magnetic resonance setup, we measure the
nonequilibrium entropy produced in an isolated spin-1/2 system following fast
quenches of an external magnetic field and experimentally demonstrate that it
is equal to the entropic distance, expressed by the Kullback-Leibler
divergence, between a microscopic process and its time-reverse. Our result
addresses the concept of irreversibility from a microscopic quantum standpoint.Comment: 8 pages, 7 figures, RevTeX4-1; Accepted for publication Phys. Rev.
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