36,073 research outputs found
Rank-frequency relation for Chinese characters
We show that the Zipf's law for Chinese characters perfectly holds for
sufficiently short texts (few thousand different characters). The scenario of
its validity is similar to the Zipf's law for words in short English texts. For
long Chinese texts (or for mixtures of short Chinese texts), rank-frequency
relations for Chinese characters display a two-layer, hierarchic structure that
combines a Zipfian power-law regime for frequent characters (first layer) with
an exponential-like regime for less frequent characters (second layer). For
these two layers we provide different (though related) theoretical descriptions
that include the range of low-frequency characters (hapax legomena). The
comparative analysis of rank-frequency relations for Chinese characters versus
English words illustrates the extent to which the characters play for Chinese
writers the same role as the words for those writing within alphabetical
systems.Comment: To appear in European Physical Journal B (EPJ B), 2014 (22 pages, 7
figures
Real-Reward Testing for Probabilistic Processes (Extended Abstract)
We introduce a notion of real-valued reward testing for probabilistic
processes by extending the traditional nonnegative-reward testing with negative
rewards. In this richer testing framework, the may and must preorders turn out
to be inverses. We show that for convergent processes with finitely many states
and transitions, but not in the presence of divergence, the real-reward
must-testing preorder coincides with the nonnegative-reward must-testing
preorder. To prove this coincidence we characterise the usual resolution-based
testing in terms of the weak transitions of processes, without having to
involve policies, adversaries, schedulers, resolutions, or similar structures
that are external to the process under investigation. This requires
establishing the continuity of our function for calculating testing outcomes.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Quantum Levy flights and multifractality of dipolar excitations in a random system
We consider dipolar excitations propagating via dipole-induced exchange among
immobile molecules randomly spaced in a lattice. The character of the
propagation is determined by long-range hops (Levy flights). We analyze the
eigen-energy spectra and the multifractal structure of the wavefunctions. In 1D
and 2D all states are localized, although in 2D the localization length can be
extremely large leading to an effective localization-delocalization crossover
in realistic systems. In 3D all eigenstates are extended but not always
ergodic, and we identify the energy intervals of ergodic and non-ergodic
states. The reduction of the lattice filling induces an ergodic to non-ergodic
transition, and the excitations are mostly non-ergodic at low filling.Comment: 5 pages, 6 figure
Characterising Probabilistic Processes Logically
In this paper we work on (bi)simulation semantics of processes that exhibit
both nondeterministic and probabilistic behaviour. We propose a probabilistic
extension of the modal mu-calculus and show how to derive characteristic
formulae for various simulation-like preorders over finite-state processes
without divergence. In addition, we show that even without the fixpoint
operators this probabilistic mu-calculus can be used to characterise these
behavioural relations in the sense that two states are equivalent if and only
if they satisfy the same set of formulae.Comment: 18 page
Optimal nonlocal multipartite entanglement concentration based on projection measurements
We propose an optimal nonlocal entanglement concentration protocol (ECP) for
multi-photon systems in a partially entangled pure state, resorting to the
projection measurement on an additional photon. One party in quantum
communication first performs a parity-check measurement on her photon in an
N-photon system and an additional photon, and then she projects the additional
photon into an orthogonal Hilbert space for dividing the original -photon
systems into two groups. In the first group, the N parties will obtain a subset
of -photon systems in a maximally entangled state. In the second group, they
will obtain some less-entangled N-photon systems which are the resource for the
entanglement concentration in the next round. By iterating the entanglement
concentration process several times, the present ECP has the maximal success
probability which is just equivalent to the entanglement of the partially
entangled state. That is, this ECP is an optimal one.Comment: 5 pages, 4 figure
Work Function of Single-wall Silicon Carbide Nanotube
Using first-principles calculations, we study the work function of single
wall silicon carbide nanotube (SiCNT). The work function is found to be highly
dependent on the tube chirality and diameter. It increases with decreasing the
tube diameter. The work function of zigzag SiCNT is always larger than that of
armchair SiCNT. We reveal that the difference between the work function of
zigzag and armchair SiCNT comes from their different intrinsic electronic
structures, for which the singly degenerate energy band above the Fermi level
of zigzag SiCNT is specifically responsible. Our finding offers potential
usages of SiCNT in field-emission devices.Comment: 3 pages, 3 figure
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