10,700 research outputs found
Schwinger-Dyson equations and disorder
Using simple models in D=0+0 and D=0+1 dimensions we construct partition
functions and compute two-point correlations. The exact result is compared with
saddle-point approximation and solutions of Schwinger-Dyson equations. When
integrals are dominated by more than one saddle-point we find Schwinger-Dyson
equations do not reproduce the correct results unless the action is first
transformed into dual variables.Comment: 7 pages, 6 figure
Enhancing the Performance of Integrated Optical Sensor by Slow-light: Theoretical Study on Ring-Resonator Based Structures
In this work, the performance of three kinds of integrated optical ring-resonator based slow-light structures for sensing applications is theoretically studied using the transfer matrix method and the complex transmission coefficient approach. Enhancement of sensing performance due to the slowlight phenomenon is quantitatively formulated. The modeling results show that using realistic structure parameters, a refractive index detection limit of one order better than the state of the art Mach-Zehnder interferometer sensing structure is possible by the inclusion of such a slow-light structure. The role of ring(s) attenuation constant in limiting the usable light slowness and the achievable sensor resolution is also discussed. For a sufficiently small ring attenuation constant, the optimal sensing performance of a single resonator circuit can be better than that of multiple resonator circuits, while offering less fabrication complexities, cleaner spectra, shorter device length, and higher figure of merit
Practical Bayesian Optimization of Machine Learning Algorithms
Machine learning algorithms frequently require careful tuning of model
hyperparameters, regularization terms, and optimization parameters.
Unfortunately, this tuning is often a "black art" that requires expert
experience, unwritten rules of thumb, or sometimes brute-force search. Much
more appealing is the idea of developing automatic approaches which can
optimize the performance of a given learning algorithm to the task at hand. In
this work, we consider the automatic tuning problem within the framework of
Bayesian optimization, in which a learning algorithm's generalization
performance is modeled as a sample from a Gaussian process (GP). The tractable
posterior distribution induced by the GP leads to efficient use of the
information gathered by previous experiments, enabling optimal choices about
what parameters to try next. Here we show how the effects of the Gaussian
process prior and the associated inference procedure can have a large impact on
the success or failure of Bayesian optimization. We show that thoughtful
choices can lead to results that exceed expert-level performance in tuning
machine learning algorithms. We also describe new algorithms that take into
account the variable cost (duration) of learning experiments and that can
leverage the presence of multiple cores for parallel experimentation. We show
that these proposed algorithms improve on previous automatic procedures and can
reach or surpass human expert-level optimization on a diverse set of
contemporary algorithms including latent Dirichlet allocation, structured SVMs
and convolutional neural networks
Training Restricted Boltzmann Machines on Word Observations
The restricted Boltzmann machine (RBM) is a flexible tool for modeling
complex data, however there have been significant computational difficulties in
using RBMs to model high-dimensional multinomial observations. In natural
language processing applications, words are naturally modeled by K-ary discrete
distributions, where K is determined by the vocabulary size and can easily be
in the hundreds of thousands. The conventional approach to training RBMs on
word observations is limited because it requires sampling the states of K-way
softmax visible units during block Gibbs updates, an operation that takes time
linear in K. In this work, we address this issue by employing a more general
class of Markov chain Monte Carlo operators on the visible units, yielding
updates with computational complexity independent of K. We demonstrate the
success of our approach by training RBMs on hundreds of millions of word
n-grams using larger vocabularies than previously feasible and using the
learned features to improve performance on chunking and sentiment
classification tasks, achieving state-of-the-art results on the latter
Towards Complexity for Quantum Field Theory States
We investigate notions of complexity of states in continuous quantum-many
body systems. We focus on Gaussian states which include ground states of free
quantum field theories and their approximations encountered in the context of
the continuous version of Multiscale Entanglement Renormalization Ansatz. Our
proposal for quantifying state complexity is based on the Fubini-Study metric.
It leads to counting the number of applications of each gate (infinitesimal
generator) in the transformation, subject to a state-dependent metric. We
minimize the defined complexity with respect to momentum preserving quadratic
generators which form algebras. On the manifold of
Gaussian states generated by these operations the Fubini-Study metric
factorizes into hyperbolic planes with minimal complexity circuits reducing to
known geodesics. Despite working with quantum field theories far outside the
regime where Einstein gravity duals exist, we find striking similarities
between our results and holographic complexity proposals.Comment: 6+7 pages, 6 appendices, 2 figures; v2: references added;
acknowledgments expanded; appendix F added, reviewing similarities and
differences with hep-th/1707.08570; v3: version published in PR
CP4 miracle: shaping Yukawa sector with CP symmetry of order four
We explore the phenomenology of a unique three-Higgs-doublet model based on
the single CP symmetry of order 4 (CP4) without any accidental symmetries. The
CP4 symmetry is imposed on the scalar potential and Yukawa interactions,
strongly shaping both sectors of the model and leading to a very characteristic
phenomenology. The scalar sector is analyzed in detail, and in the Yukawa
sector we list all possible CP4-symmetric structures which do not run into
immediate conflict with experiment, namely, do not lead to massless or
mass-degenerate quarks nor to insufficient mixing or CP-violation in the CKM
matrix. We show that the parameter space of the model, although very
constrained by CP4, is large enough to comply with the electroweak precision
data and the LHC results for the 125 GeV Higgs boson phenomenology, as well as
to perfectly reproduce all fermion masses, mixing, and CP violation. Despite
the presence of flavor changing neutral currents mediated by heavy Higgs
scalars, we find through a parameter space scan many points which accurately
reproduce the kaon CP-violating parameter as well as oscillation
parameters in K and mesons. Thus, CP4 offers a novel minimalistic
framework for building models with very few assumptions, sufficient predictive
power, and rich phenomenology yet to be explored.Comment: 39 pages, 8 figures, 1 table; v2: expanded discussion, extra
references, matches published versio
Ultra-sharp soliton switching in a directional coupler
By a numerical investigation it is shown that a directional coupler, described by two linearly coupled non-linear Schrošdinger equations, can be used to construct a soliton switch with an extremely narrow transition region
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