595 research outputs found
Complexity of randomized algorithms for underdamped Langevin dynamics
We establish an information complexity lower bound of randomized algorithms
for simulating underdamped Langevin dynamics. More specifically, we prove that
the worst strong error is of order , for
solving a family of -dimensional underdamped Langevin dynamics, by any
randomized algorithm with only queries to , the driving Brownian
motion and its weighted integration, respectively. The lower bound we establish
matches the upper bound for the randomized midpoint method recently proposed by
Shen and Lee [NIPS 2019], in terms of both parameters and .Comment: 27 pages; some revision (e.g., Sec 2.1), and new supplementary
materials in Appendice
Multiple Descent in the Multiple Random Feature Model
Recent works have demonstrated a double descent phenomenon in
over-parameterized learning. Although this phenomenon has been investigated by
recent works, it has not been fully understood in theory. In this paper, we
investigate the multiple descent phenomenon in a class of multi-component
prediction models. We first consider a ''double random feature model'' (DRFM)
concatenating two types of random features, and study the excess risk achieved
by the DRFM in ridge regression. We calculate the precise limit of the excess
risk under the high dimensional framework where the training sample size, the
dimension of data, and the dimension of random features tend to infinity
proportionally. Based on the calculation, we further theoretically demonstrate
that the risk curves of DRFMs can exhibit triple descent. We then provide a
thorough experimental study to verify our theory. At last, we extend our study
to the ''multiple random feature model'' (MRFM), and show that MRFMs ensembling
types of random features may exhibit -fold descent. Our analysis
points out that risk curves with a specific number of descent generally exist
in learning multi-component prediction models.Comment: 89 pages, 9 figures. Version 3 adds new description of triple descent
in certain double random feature model, deletes the discussion of NTK
regimes, and adds more literature reference
On explicit -convergence rate estimate for underdamped Langevin dynamics
We provide a new explicit estimate of exponential decay rate of underdamped
Langevin dynamics in distance. To achieve this, we first prove a
Poincar\'{e}-type inequality with Gibbs measure in space and Gaussian measure
in momentum. Our new estimate provides a more explicit and simpler expression
of decay rate; moreover, when the potential is convex with Poincar\'{e}
constant , our new estimate offers the decay rate of
after optimizing the choice of friction coefficient,
which is much faster compared to for the overdamped Langevin
dynamics.Comment: We have fixed the bug
Background Traffic-Based Retransmission Algorithm for Multimedia Streaming Transfer over Concurrent Multipaths
The content-rich multimedia streaming will be the most attractive services in the next-generation networks. With function of distribute data across multipath end-to-end paths based on SCTP's multihoming feature, concurrent multipath transfer SCTP (CMT-SCTP) has been regarded as the most promising technology for the efficient multimedia streaming transmission. However, the current researches on CMT-SCTP mainly focus on the algorithms related to the data delivery performance while they seldom consider the background traffic factors. Actually, background traffic of realistic network environments has an important impact on the performance of CMT-SCTP. In this paper, we firstly investigate the effect of background traffic on the performance of CMT-SCTP based on a close realistic simulation topology with reasonable background traffic in NS2, and then based on the localness nature of background flow, a further improved retransmission algorithm, named RTX_CSI, is proposed to reach more benefits in terms of average throughput and achieve high users' experience of quality for multimedia streaming services
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Localized Ridge Wrinkling of Stiff Films on Compliant Substrates
Wrinkling of thin stiff films on thick compliant elastomeric substrates subject to plane strain compression is considered for cases in which the substrate is pre-stretched prior to film attachment. Advanced wrinkling modes are investigated that evolve as the systems are compressed beyond the onset of the primary sinusoidal wrinkling mode. If the substrate pre-stretch is greater than about 40%, an advanced mode in the form of a series of well-spaced ridges separated by relatively flat film is observed in the simulations. Our experiments reveal a localization mode in the form of alternating packets of large and small amplitude wrinkles, but not ridges, while ridge formation has been observed in other recent experiments. Measurements of undulation amplitudes have been made for wrinkle fields of stiff films formed by oxidation of the surface of pre-stretched PDMS substrates. Simulations have been performed with a finite element model and an analytical film/substrate model. The formation of the ridge mode is a consequence of the altered nonlinearity of the substrate produced by the pre-stretch. The role of the tangential substrate stiffness in suppressing localization at the ridges is also highlighted. If there is no substrate pre-stretch, or if the substrate is pre-compressed, the primary sinusoidal mode gives way to an entirely different sequence of advanced modes usually entailing period doubling followed by folding. The nature of substrate nonlinearity that leads to ridges or folds is discussed.Engineering and Applied Science
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