1,880 research outputs found
Towards Cancer Hybrid Automata
This paper introduces Cancer Hybrid Automata (CHAs), a formalism to model the
progression of cancers through discrete phenotypes. The classification of
cancer progression using discrete states like stages and hallmarks has become
common in the biology literature, but primarily as an organizing principle, and
not as an executable formalism. The precise computational model developed here
aims to exploit this untapped potential, namely, through automatic verification
of progression models (e.g., consistency, causal connections, etc.),
classification of unreachable or unstable states and computer-generated
(individualized or universal) therapy plans. The paper builds on a
phenomenological approach, and as such does not need to assume a model for the
biochemistry of the underlying natural progression. Rather, it abstractly
models transition timings between states as well as the effects of drugs and
clinical tests, and thus allows formalization of temporal statements about the
progression as well as notions of timed therapies. The model proposed here is
ultimately based on hybrid automata, and we show how existing controller
synthesis algorithms can be generalized to CHA models, so that therapies can be
generated automatically. Throughout this paper we use cancer hallmarks to
represent the discrete states through which cancer progresses, but other
notions of discretely or continuously varying state formalisms could also be
used to derive similar therapies.Comment: In Proceedings HSB 2012, arXiv:1208.315
Mean-payoff Automaton Expressions
Quantitative languages are an extension of boolean languages that assign to
each word a real number. Mean-payoff automata are finite automata with
numerical weights on transitions that assign to each infinite path the long-run
average of the transition weights. When the mode of branching of the automaton
is deterministic, nondeterministic, or alternating, the corresponding class of
quantitative languages is not robust as it is not closed under the pointwise
operations of max, min, sum, and numerical complement. Nondeterministic and
alternating mean-payoff automata are not decidable either, as the quantitative
generalization of the problems of universality and language inclusion is
undecidable.
We introduce a new class of quantitative languages, defined by mean-payoff
automaton expressions, which is robust and decidable: it is closed under the
four pointwise operations, and we show that all decision problems are decidable
for this class. Mean-payoff automaton expressions subsume deterministic
mean-payoff automata, and we show that they have expressive power incomparable
to nondeterministic and alternating mean-payoff automata. We also present for
the first time an algorithm to compute distance between two quantitative
languages, and in our case the quantitative languages are given as mean-payoff
automaton expressions
Index theory of one dimensional quantum walks and cellular automata
If a one-dimensional quantum lattice system is subject to one step of a
reversible discrete-time dynamics, it is intuitive that as much "quantum
information" as moves into any given block of cells from the left, has to exit
that block to the right. For two types of such systems - namely quantum walks
and cellular automata - we make this intuition precise by defining an index, a
quantity that measures the "net flow of quantum information" through the
system. The index supplies a complete characterization of two properties of the
discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the
sense that there is a system S which locally acts like S_1 in one region and
like S_2 in some other region, if and only if S_1 and S_2 have the same index.
Second, the index labels connected components of such systems: equality of the
index is necessary and sufficient for the existence of a continuous deformation
of S_1 into S_2. In the case of quantum walks, the index is integer-valued,
whereas for cellular automata, it takes values in the group of positive
rationals. In both cases, the map S -> ind S is a group homomorphism if
composition of the discrete dynamics is taken as the group law of the quantum
systems. Systems with trivial index are precisely those which can be realized
by partitioned unitaries, and the prototypes of systems with non-trivial index
are shifts.Comment: 38 pages. v2: added examples, terminology clarifie
A particulate basis for a lattice-gas model of amphiphilic fluids
We show that the flux-field expansion derived by Boghosian and Coveney for
the Rothman-Keller immiscible fluid model can be derived in a simpler and more
general way in terms of the completely symmetric tensor kernels introduced by
those authors. Using this generalised flux-field expansion we show that the
more complex amphiphilic model of Boghosian Coveney and Emerton can also be
derived from an underlying model of particle interactions. The consequences of
this derivation are discussed in the context of previous equilibrium Ising-like
lattice models and other non-equilibrium mesoscale models.Comment: To appear in Phil. Trans. Roy. Soc. (Proceedings of the Xth
International Conference on Discrete Simulation of Fluid Dynamics.
Mathematical open problems in Projected Entangled Pair States
Projected Entangled Pair States (PEPS) are used in practice as an efficient
parametrization of the set of ground states of quantum many body systems. The
aim of this paper is to present, for a broad mathematical audience, some
mathematical questions about PEPS.Comment: Notes associated to the Santal\'o Lecture 2017, Universidad
Complutense de Madrid (UCM), minor typos correcte
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