1,199 research outputs found
Superposition as memory: unlocking quantum automatic complexity
Imagine a lock with two states, "locked" and "unlocked", which may be
manipulated using two operations, called 0 and 1. Moreover, the only way to
(with certainty) unlock using four operations is to do them in the sequence
0011, i.e., where . In this scenario one might think that the
lock needs to be in certain further states after each operation, so that there
is some memory of what has been done so far. Here we show that this memory can
be entirely encoded in superpositions of the two basic states "locked" and
"unlocked", where, as dictated by quantum mechanics, the operations are given
by unitary matrices. Moreover, we show using the Jordan--Schur lemma that a
similar lock is not possible for .
We define the semi-classical quantum automatic complexity of a
word as the infimum in lexicographic order of those pairs of nonnegative
integers such that there is a subgroup of the projective unitary
group PU with and with such that, in terms of a
standard basis and with , we have
and for all with . We show that is
unbounded and not constant for strings of a given length. In particular, and
.Comment: Lecture Notes in Computer Science, UCNC (Unconventional Computation
and Natural Computation) 201
Persistent fluctuations in stride intervals under fractal auditory stimulation
Copyright @ 2014 Marmelat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.Commission of the European Community and the Netherlands Organisation for Scientific Research
Gait and Cognition: A Complementary Approach to Understanding Brain Function and the Risk of Falling
Until recently, clinicians and researchers have performed gait assessments and cognitive assessments separately when evaluating older adults, but increasing evidence from clinical practice, epidemiological studies, and clinical trials shows that gait and cognition are interrelated in older adults. Quantifiable alterations in gait in older adults are associated with falls, dementia, and disability. At the same time, emerging evidence indicates that early disturbances in cognitive processes such as attention, executive function, and working memory are associated with slower gait and gait instability during single- and dual-task testing and that these cognitive disturbances assist in the prediction of future mobility loss, falls, and progression to dementia. This article reviews the importance of the interrelationship between gait and cognition in aging and presents evidence that gait assessments can provide a window into the understanding of cognitive function and dysfunction and fall risk in older people in clinical practice. To this end, the benefits of dual-task gait assessments (e.g., walking while performing an attention-demanding task) as a marker of fall risk are summarized. A potential complementary approach for reducing the risk of falls by improving certain aspects of cognition through nonpharmacological and pharmacological treatments is also presented. Untangling the relationship between early gait disturbances and early cognitive changes may be helpful in identifying older adults at risk of experiencing mobility decline, falls, and progression to dementia. J Am Geriatr Soc 60: 2127-2136, 2012
Neuron dynamics in the presence of 1/f noise
Interest in understanding the interplay between noise and the response of a
non-linear device cuts across disciplinary boundaries. It is as relevant for
unmasking the dynamics of neurons in noisy environments as it is for designing
reliable nanoscale logic circuit elements and sensors. Most studies of noise in
non-linear devices are limited to either time-correlated noise with a
Lorentzian spectrum (of which the white noise is a limiting case) or just white
noise. We use analytical theory and numerical simulations to study the impact
of the more ubiquitous "natural" noise with a 1/f frequency spectrum.
Specifically, we study the impact of the 1/f noise on a leaky integrate and
fire model of a neuron. The impact of noise is considered on two quantities of
interest to neuron function: The spike count Fano factor and the speed of
neuron response to a small step-like stimulus. For the perfect (non-leaky)
integrate and fire model, we show that the Fano factor can be expressed as an
integral over noise spectrum weighted by a (low pass) filter function. This
result elucidates the connection between low frequency noise and disorder in
neuron dynamics. We compare our results to experimental data of single neurons
in vivo, and show how the 1/f noise model provides much better agreement than
the usual approximations based on Lorentzian noise. The low frequency noise,
however, complicates the case for information coding scheme based on interspike
intervals by introducing variability in the neuron response time. On a positive
note, the neuron response time to a step stimulus is, remarkably, nearly
optimal in the presence of 1/f noise. An explanation of this effect elucidates
how the brain can take advantage of noise to prime a subset of the neurons to
respond almost instantly to sudden stimuli.Comment: Phys. Rev. E in pres
A note on the Zassenhaus product formula
We provide a simple method for the calculation of the terms c_n in the
Zassenhaus product for
non-commuting a and b. This method has been implemented in a computer program.
Furthermore, we formulate a conjecture on how to translate these results into
nested commutators. This conjecture was checked up to order n=17 using a
computer
The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
Fractional Brownian motion (fBm) has been used as a theoretical framework to
study real time series appearing in diverse scientific fields. Because its
intrinsic non-stationarity and long range dependence, its characterization via
the Hurst parameter H requires sophisticated techniques that often yield
ambiguous results. In this work we show that fBm series map into a scale free
visibility graph whose degree distribution is a function of H. Concretely, it
is shown that the exponent of the power law degree distribution depends
linearly on H. This also applies to fractional Gaussian noises (fGn) and
generic f^(-b) noises. Taking advantage of these facts, we propose a brand new
methodology to quantify long range dependence in these series. Its reliability
is confirmed with extensive numerical simulations and analytical developments.
Finally, we illustrate this method quantifying the persistent behavior of human
gait dynamics.Comment: 5 pages, submitted for publicatio
Investigating the correlation between paediatric stride interval persistence and gross energy expenditure
<p>Abstract</p> <p>Background</p> <p>Stride interval persistence, a term used to describe the correlation structure of stride interval time series, is thought to provide insight into neuromotor control, though its exact clinical meaning has not yet been realized. Since human locomotion is shaped by energy efficient movements, it has been hypothesized that stride interval dynamics and energy expenditure may be inherently tied, both having demonstrated similar sensitivities to age, disease, and pace-constrained walking.</p> <p>Findings</p> <p>This study tested for correlations between stride interval persistence and measures of energy expenditure including mass-specific gross oxygen consumption per minute (<inline-formula><graphic file="1756-0500-3-47-i1.gif"/></inline-formula>), mass-specific gross oxygen cost per meter (<it>VO</it><sub>2</sub>) and heart rate (HR). Metabolic and stride interval data were collected from 30 asymptomatic children who completed one 10-minute walking trial under each of the following conditions: (i) overground walking, (ii) hands-free treadmill walking, and (iii) handrail-supported treadmill walking. Stride interval persistence was not significantly correlated with <inline-formula><graphic file="1756-0500-3-47-i1.gif"/></inline-formula> (p > 0.32), <it>VO</it><sub>2 </sub>(p > 0.18) or HR (p > 0.56).</p> <p>Conclusions</p> <p>No simple linear dependence exists between stride interval persistence and measures of gross energy expenditure in asymptomatic children when walking overground and on a treadmill.</p
Scaling of Horizontal and Vertical Fixational Eye Movements
Eye movements during fixation of a stationary target prevent the adaptation
of the photoreceptors to continuous illumination and inhibit fading of the
image. These random, involuntary, small, movements are restricted at long time
scales so as to keep the target at the center of the field of view. Here we use
the Detrended Fluctuation Analysis (DFA) in order to study the properties of
fixational eye movements at different time scales. Results show different
scaling behavior between horizontal and vertical movements. When the small
ballistics movements, i.e. micro-saccades, are removed, the scaling exponents
in both directions become similar. Our findings suggest that micro-saccades
enhance the persistence at short time scales mostly in the horizontal component
and much less in the vertical component. This difference may be due to the need
of continuously moving the eyes in the horizontal plane, in order to match the
stereoscopic image for different viewing distance.Comment: 5 pages, 4 figure
Interpretations of Presburger Arithmetic in Itself
Presburger arithmetic PrA is the true theory of natural numbers with
addition. We study interpretations of PrA in itself. We prove that all
one-dimensional self-interpretations are definably isomorphic to the identity
self-interpretation. In order to prove the results we show that all linear
orders that are interpretable in (N,+) are scattered orders with the finite
Hausdorff rank and that the ranks are bounded in terms of the dimension of the
respective interpretations. From our result about self-interpretations of PrA
it follows that PrA isn't one-dimensionally interpretable in any of its finite
subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201
Quantum Noise Limits for Nonlinear, Phase-Invariant Amplifiers
Any quantum device that amplifies coherent states of a field while preserving
their phase generates noise. A nonlinear, phase-invariant amplifier may
generate less noise, over a range of input field strengths, than any linear
amplifier with the same amplification. We present explicit examples of such
nonlinear amplifiers, and derive lower bounds on the noise generated by a
nonlinear, phase-invariant quantum amplifier.Comment: RevTeX, 6 pages + 4 figures (included in file; hard copy sent on
request
- …