2,745 research outputs found
Sharp nonasymptotic bounds on the norm of random matrices with independent entries
We obtain nonasymptotic bounds on the spectral norm of random matrices with
independent entries that improve significantly on earlier results. If is
the symmetric matrix with , we show that
This bound is optimal in the sense that a matching
lower bound holds under mild assumptions, and the constants are sufficiently
sharp that we can often capture the precise edge of the spectrum. Analogous
results are obtained for rectangular matrices and for more general sub-Gaussian
or heavy-tailed distributions of the entries, and we derive tail bounds in
addition to bounds on the expected norm. The proofs are based on a combination
of the moment method and geometric functional analysis techniques. As an
application, we show that our bounds immediately yield the correct phase
transition behavior of the spectral edge of random band matrices and of sparse
Wigner matrices. We also recover a result of Seginer on the norm of Rademacher
matrices.Comment: Published at http://dx.doi.org/10.1214/15-AOP1025 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Spatiotemporal complexity of the universe at subhorizon scales
This is a short note on the spatiotemporal complexity of the dynamical
state(s) of the universe at subhorizon scales (up to 300 Mpc). There are
reasons, based mainly on infrared radiative divergences, to believe that one
can encounter a flicker noise in the time domain, while in the space domain,
the scaling laws are reflected in the (multi)fractal distribution of galaxies
and their clusters. There exist recent suggestions on a unifying treatment of
these two aspects within the concept of spatiotemporal complexity of dynamical
systems driven out of equilibrium. Spatiotemporal complexity of the subhorizon
dynamical state(s) of the universe is a conceptually nice idea and may lead to
progress in our understanding of the material structures at large scalesComment: references update
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
On the exchange of intersection and supremum of sigma-fields in filtering theory
We construct a stationary Markov process with trivial tail sigma-field and a
nondegenerate observation process such that the corresponding nonlinear
filtering process is not uniquely ergodic. This settles in the negative a
conjecture of the author in the ergodic theory of nonlinear filters arising
from an erroneous proof in the classic paper of H. Kunita (1971), wherein an
exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page
Langevin Thermostat for Rigid Body Dynamics
We present a new method for isothermal rigid body simulations using the
quaternion representation and Langevin dynamics. It can be combined with the
traditional Langevin or gradient (Brownian) dynamics for the translational
degrees of freedom to correctly sample the NVT distribution in a simulation of
rigid molecules. We propose simple, quasi-symplectic second-order numerical
integrators and test their performance on the TIP4P model of water. We also
investigate the optimal choice of thermostat parameters.Comment: 15 pages, 13 figures, 1 tabl
Sound Transformation: Applying Image Neural Style Transfer Networks to Audio Spectrograms
Image style transfer networks are used to blend images, producing images that are a mix of source images. The process is based on controlled extraction of style and content aspects of images, using pre-trained Convolutional Neural Networks (CNNs). Our interest lies in adopting these image style transfer networks for the purpose of transforming sounds. Audio signals can be presented as grey-scale images of audio spectrograms. The purpose of our work is to investigate whether audio spectrogram inputs can be used with image neural transfer networks to produce new sounds. Using musical instrument sounds as source sounds, we apply and compare three existing image neural style transfer networks for the task of sound mixing. Our evaluation shows that all three networks are successful in producing consistent, new sounds based on the two source sounds. We use classification models to demonstrate that the new audio signals are consistent and distinguishable from the source instrument sounds. We further apply t-SNE cluster visualisation to visualise the feature maps of the new sounds and original source sounds, confirming that they form different sound groups from the source sounds. Our work paves the way to using CNNs for creative and targeted production of new sounds from source sounds, with specified source qualities, including pitch and timbre
Smartphone placement within vehicles
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordSmartphone-based driver monitoring is quickly gaining ground as a feasible alternative to competing in-vehicle and aftermarket solutions. Currently the main challenges for data analysts studying smartphone-based driving data stem from the mobility of the smartphone. In this paper, we use kernel-based k-means clustering to infer the placement of smartphones within vehicles. The trip segments are mapped into fifteen different placement clusters. As a part of the presented framework, we discuss practical considerations concerning e.g., trip segmentation, cluster initialization, and parameter selection. The proposed method is evaluated on more than 10 000 kilometers of driving data collected from approximately 200 drivers. To validate the interpretation of the clusters, we compare the data associated with different clusters and relate the results to real-world knowledge of driving behavior. The clusters associated with the label “Held by hand” are shown to display high gyroscope variances, low maximum speeds, low correlations between the measurements from smartphone-embedded and vehicle-fixed accelerometers, and short segment durations
Sliding mode control of quantum systems
This paper proposes a new robust control method for quantum systems with
uncertainties involving sliding mode control (SMC). Sliding mode control is a
widely used approach in classical control theory and industrial applications.
We show that SMC is also a useful method for robust control of quantum systems.
In this paper, we define two specific classes of sliding modes (i.e.,
eigenstates and state subspaces) and propose two novel methods combining
unitary control and periodic projective measurements for the design of quantum
sliding mode control systems. Two examples including a two-level system and a
three-level system are presented to demonstrate the proposed SMC method. One of
main features of the proposed method is that the designed control laws can
guarantee desired control performance in the presence of uncertainties in the
system Hamiltonian. This sliding mode control approach provides a useful
control theoretic tool for robust quantum information processing with
uncertainties.Comment: 18 pages, 4 figure
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The dry country
Set in the dryland farming country of Eastern Oregon in the late 1950's, this novel follows a year and a half in the life of a young girl as she comes of age. A water rights dispute, the plight of nearby ranchers, disappointments in her own family and a harrowing encounter with a neighbor all contribute to her perception that, contrary to what her father has taught her, what matters most isn't owning the oldest water rights. She comes to recognize that the world is much larger and more complex than it had appeared from her remote mountain valley home
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