A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues

We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single clones. Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters.Comment: 4 figures, to appear in Royal Society Interfac

Four-dimensional understanding of quantum mechanics and Bell violation

While our natural intuition suggests us that we live in 3D space evolving in time, modern physics presents fundamentally different picture: 4D spacetime, Einstein's block universe, in which we travel in thermodynamically emphasized direction: arrow of time. Suggestions for such nonintuitive and nonlocal living in kind of "4D jello" come among others from: Lagrangian mechanics we use from QFT to GR saying that history between fixed past and future situation is the one optimizing action, special relativity saying that different velocity observers have different present 3D hypersurface and time direction, general relativity deforming shape of the entire spacetime up to switching time and space below the black hole event horizon, or the CPT theorem concluding fundamental symmetry between past and future. Accepting this nonintuitive living in 4D spacetime: with present moment being in equilibrium between past and future - minimizing tension as action of Lagrangian, leads to crucial surprising differences from intuitive "evolving 3D" picture, in which we for example conclude satisfaction of Bell inequalities - violated by the real physics. Specifically, particle in spacetime becomes own trajectory: 1D submanifold of 4D, making that statistical physics should consider ensembles like Boltzmann distribution among entire paths, what leads to quantum behavior as we know from Feynman's Euclidean path integrals or similar Maximal Entropy Random Walk (MERW). It results for example in Anderson localization, or the Born rule with squares - allowing for violation of Bell inequalities. Specifically, quantum amplitude turns out to describe probability at the end of half-spacetime from a given moment toward past or future, to randomly get some value of measurement we need to "draw it" from both time directions, getting the squares of Born rules.Comment: 13 pages, 18 figure

First-passage phenomena in hierarchical networks

In this paper we study Markov processes and related first passage problems on a class of weighted, modular graphs which generalize the Dyson hierarchical model. In these networks, the coupling strength between two nodes depends on their distance and is modulated by a parameter $\sigma$. We find that, in the thermodynamic limit, ergodicity is lost and the "distant" nodes can not be reached. Moreover, for finite-sized systems, there exists a threshold value for $\sigma$ such that, when $\sigma$ is relatively large, the inhomogeneity of the coupling pattern prevails and "distant" nodes are hardly reached. The same analysis is carried on also for generic hierarchical graphs, where interactions are meant to involve $p$-plets ($p>2$) of nodes, finding that ergodicity is still broken in the thermodynamic limit, but no threshold value for $\sigma$ is evidenced, ultimately due to a slow growth of the network diameter with the size

An anatomy of a quantum adiabatic algorithm that transcends the Turing computability

We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.Comment: 7 pages, no figure. Submitted to the Proceedings of the conference "Foundations of Quantum Information" (April 2004, Camerino, Italy

On quantum vs. classical probability

Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry, probabilities, composition of systems, state preparation and reductionism. The essential distinction between classical and quantum theory, on the other hand, is shown to be joint decidability versus smoothness; for the latter in particular I supply ample explanation and motivation. Finally, I argue that beyond quantum theory there are no other generalisations of classical probability theory that are relevant to physics.Comment: Major revision: key results unchanged, but derivation and discussion completely rewritten; 33 pages, no figure