1,694 research outputs found
Quantum and random walks as universal generators of probability distributions
Quantum walks and random walks bear similarities and divergences. One of the
most remarkable disparities affects the probability of finding the particle at
a given location: typically, almost a flat function in the first case and a
bell-shaped one in the second case. Here I show how one can impose any desired
stochastic behavior (compatible with the continuity equation for the
probability function) on both systems by the appropriate choice of time- and
site-dependent coins. This implies, in particular, that one can devise quantum
walks that show diffusive spreading without loosing coherence, as well as
random walks that exhibit the characteristic fast propagation of a quantum
particle driven by a Hadamard coin.Comment: 8 pages, 2 figures; revised and enlarged versio
Model Fractional Chern Insulators
We devise local lattice models whose ground states are model fractional Chern
insulators---Abelian and non-Abelian topologically ordered states characterized
by exact ground state degeneracies at any finite size and infinite entanglement
gaps. Most saliently, we construct exact parent Hamiltonians for two distinct
families of bosonic lattice generalizations of the parafermion
quantum Hall states: (i) color-entangled fractional Chern insulators at band
filling fractions and (ii) nematic states at ,
where is the Chern number of the lowest band in our models. In
spite of a fluctuating Berry curvature, our construction is partially
frustration free: the ground states reside entirely within the lowest band and
exactly minimize a local -body repulsion term by term. In addition to
providing the first known models hosting intriguing states such as higher Chern
number generalizations of the Fibonacci anyon quantum Hall states, the
remarkable stability and finite-size properties make our models particularly
well-suited for the study of novel phenomena involving e.g. twist defects and
proximity induced superconductivity, as well as being a guide for designing
experiments.Comment: 9 pages, 5 figure
A Simulator for LLVM Bitcode
In this paper, we introduce an interactive simulator for programs in the form
of LLVM bitcode. The main features of the simulator include precise control
over thread scheduling, automatic checkpoints and reverse stepping, support for
source-level information about functions and variables in C and C++ programs
and structured heap visualisation. Additionally, the simulator is compatible
with DiVM (DIVINE VM) hypercalls, which makes it possible to load, simulate and
analyse counterexamples from an existing model checker
The role of human ventral visual cortex in motion perception.
Visual motion perception is fundamental to many aspects of visual perception. Visual motion perception has long been associated with the dorsal (parietal) pathway and the involvement of the ventral 'form' (temporal) visual pathway has not been considered critical for normal motion perception. Here, we evaluated this view by examining whether circumscribed damage to ventral visual cortex impaired motion perception. The perception of motion in basic, non-form tasks (motion coherence and motion detection) and complex structure-from-motion, for a wide range of motion speeds, all centrally displayed, was assessed in five patients with a circumscribed lesion to either the right or left ventral visual pathway. Patients with a right, but not with a left, ventral visual lesion displayed widespread impairments in central motion perception even for non-form motion, for both slow and for fast speeds, and this held true independent of the integrity of areas MT/V5, V3A or parietal regions. In contrast with the traditional view in which only the dorsal visual stream is critical for motion perception, these novel findings implicate a more distributed circuit in which the integrity of the right ventral visual pathway is also necessary even for the perception of non-form motion
Bounded Model Checking of State-Space Digital Systems: The Impact of Finite Word-Length Effects on the Implementation of Fixed-Point Digital Controllers Based on State-Space Modeling
The extensive use of digital controllers demands a growing effort to prevent
design errors that appear due to finite-word length (FWL) effects. However,
there is still a gap, regarding verification tools and methodologies to check
implementation aspects of control systems. Thus, the present paper describes an
approach, which employs bounded model checking (BMC) techniques, to verify
fixed-point digital controllers represented by state-space equations. The
experimental results demonstrate the sensitivity of such systems to FWL effects
and the effectiveness of the proposed approach to detect them. To the best of
my knowledge, this is the first contribution tackling formal verification
through BMC of fixed-point state-space digital controllers.Comment: International Symposium on the Foundations of Software Engineering
201
Two-Player Reachability-Price Games on Single-Clock Timed Automata
We study two player reachability-price games on single-clock timed automata.
The problem is as follows: given a state of the automaton, determine whether
the first player can guarantee reaching one of the designated goal locations.
If a goal location can be reached then we also want to compute the optimum
price of doing so. Our contribution is twofold. First, we develop a theory of
cost functions, which provide a comprehensive methodology for the analysis of
this problem. This theory allows us to establish our second contribution, an
EXPTIME algorithm for computing the optimum reachability price, which improves
the existing 3EXPTIME upper bound.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Summation of Series Defined by Counting Blocks of Digits
We discuss the summation of certain series defined by counting blocks of
digits in the -ary expansion of an integer. For example, if denotes
the sum of the base-2 digits of , we show that . We recover this previous
result of Sondow in math.NT/0508042 and provide several generalizations.Comment: 12 pages, Introduction expanded, references added, accepted by J.
Number Theor
Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)
The B\"uchi non-emptiness problem for timed automata refers to deciding if a
given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting
condition. The standard solution to this problem involves adding an auxiliary
clock to take care of the non-Zenoness. In this paper, it is shown that this
simple transformation may sometimes result in an exponential blowup. A
construction avoiding this blowup is proposed. It is also shown that in many
cases, non-Zenoness can be ascertained without extra construction. An
on-the-fly algorithm for the non-emptiness problem, using non-Zenoness
construction only when required, is proposed. Experiments carried out with a
prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV
2010; Formal Methods in System Design, 201
- …