7,078 research outputs found
On the Homology of the Space of Curves Immersed in The Sphere with Curvature Constrained to a Prescribed Interval
While the topology of the space of all smooth immersed curves on the
-sphere that start and end at given points in given
directions is well known, it is an open problem to understand the homotopy type
of its subspaces consisting of the curves whose geodesic curvatures are
constrained to a prescribed proper open interval. In this article we prove
that, under certain circumstances for endpoints and end directions, these
subspaces are not homotopically equivalent to the whole space. Moreover, we
give an explicit construction of exotic generators for some homotopy and
cohomology groups. It turns out that the dimensions of these generators depend
on endpoints and end directions. A version of the h-principle is used to prove
these results.Comment: 62 Pages, 19 figures. This is the article version of author's PhD
Thesis advised by Nicolau C. Saldanh
Event-Trigger Based Robust-Optimal Control for Energy Harvesting Transmitter
This paper studies an online algorithm for an energy harvesting transmitter,
where the transmission (completion) time is considered as the system
performance. Unlike the existing online algorithms which more or less require
the knowledge on the future behavior of the energy-harvesting rate, we consider
a practical but significantly more challenging scenario where the
energy-harvesting rate is assumed to be totally unknown. Our design is
formulated as a robust-optimal control problem which aims to optimize the
worst-case performance. The transmit power is designed only based on the
current battery energy level and the data queue length directly monitored by
the transmitter itself. Specifically, we apply an event-trigger approach in
which the transmitter continuously monitors the battery energy and triggers an
event when a significant change occurs. Once an event is triggered, the
transmit power is updated according to the solution to the robust-optimal
control problem, which is given in a simple analytic form. We present numerical
results on the transmission time achieved by the proposed design and
demonstrate its robust-optimality.Comment: The paper is accepted for publication in IEEE Transactions on
Wireless Communication
A Distributed Hierarchical SGD Algorithm with Sparse Global Reduction
Reducing communication in training large-scale machine learning applications
on distributed platform is still a big challenge. To address this issue, we
propose a distributed hierarchical averaging stochastic gradient descent
(Hier-AVG) algorithm with infrequent global reduction by introducing local
reduction. As a general type of parallel SGD, Hier-AVG can reproduce several
popular synchronous parallel SGD variants by adjusting its parameters. We show
that Hier-AVG with infrequent global reduction can still achieve standard
convergence rate for non-convex optimization problems. In addition, we show
that more frequent local averaging with more participants involved can lead to
faster training convergence. By comparing Hier-AVG with another popular
distributed training algorithm K-AVG, we show that through deploying local
averaging with fewer number of global averaging, Hier-AVG can still achieve
comparable training speed while frequently get better test accuracy. This
indicates that local averaging can serve as an alternative remedy to
effectively reduce communication overhead when the number of learners is large.
Experimental results of Hier-AVG with several state-of-the-art deep neural nets
on CIFAR-10 and IMAGENET-1K are presented to validate our analysis and show its
superiority.Comment: 38 page
Stabilization and Consensus of Linear Systems with Multiple Input Delays by Truncated Pseudo-Predictor Feedback
This paper provides an alternative approach referred to as pseudo-predictor
feedback (PPF) for stabilization of linear systems with multiple input delays.
Differently from the traditional predictor feedback which is from the model
reduction appoint of view, the proposed PPF utilizes the idea of prediction by
generalizing the corresponding results for linear systems with a single input
delay to the case of multiple input delays. Since the PPF will generally lead
to distributed controllers, a truncated pseudopredictor feedback (TPPF)
approach is established instead which gives finite dimensional controllers. It
is shown that the TPPF can compensate arbitrarily large yet bounded delays as
long as the open-loop system is only polynomially unstable. The proposed TPPF
approach is then used to solve the consensus problems for multi-agent systems
characterized by linear systems with multiple input delays. Numerical examples
show the effectiveness of the proposed approach.Comment: 19pages, 4 figures. submitted to a journal for publication
consideratio
Probing the linear polarization of photons in ultraperipheral heavy ion collisions
We propose to measure the linear polarization of the external electromagnetic
fields of a relativistic heavy ion through azimuthal asymmetries in dilepton
production in ultraperipheral collisions. The asymmetries estimated with the
equivalent photon approximation are shown to be sizable.Comment: The version accepted by the journal, 7 pages, 4 figure
Fast Simulation of Hyperplane-Truncated Multivariate Normal Distributions
We introduce a fast and easy-to-implement simulation algorithm for a
multivariate normal distribution truncated on the intersection of a set of
hyperplanes, and further generalize it to efficiently simulate random variables
from a multivariate normal distribution whose covariance (precision) matrix can
be decomposed as a positive-definite matrix minus (plus) a low-rank symmetric
matrix. Example results illustrate the correctness and efficiency of the
proposed simulation algorithms.Comment: To appear in Bayesian Analysi
Gamma Belief Networks
To infer multilayer deep representations of high-dimensional discrete and
nonnegative real vectors, we propose an augmentable gamma belief network (GBN)
that factorizes each of its hidden layers into the product of a sparse
connection weight matrix and the nonnegative real hidden units of the next
layer. The GBN's hidden layers are jointly trained with an upward-downward
Gibbs sampler that solves each layer with the same subroutine. The
gamma-negative binomial process combined with a layer-wise training strategy
allows inferring the width of each layer given a fixed budget on the width of
the first layer. Example results illustrate interesting relationships between
the width of the first layer and the inferred network structure, and
demonstrate that the GBN can add more layers to improve its performance in both
unsupervisedly extracting features and predicting heldout data. For exploratory
data analysis, we extract trees and subnetworks from the learned deep network
to visualize how the very specific factors discovered at the first hidden layer
and the increasingly more general factors discovered at deeper hidden layers
are related to each other, and we generate synthetic data by propagating random
variables through the deep network from the top hidden layer back to the bottom
data layer.Comment: 44 pages, 24 figure
Towards Efficient Scheduling of Federated Mobile Devices under Computational and Statistical Heterogeneity
Originated from distributed learning, federated learning enables
privacy-preserved collaboration on a new abstracted level by sharing the model
parameters only. While the current research mainly focuses on optimizing
learning algorithms and minimizing communication overhead left by distributed
learning, there is still a considerable gap when it comes to the real
implementation on mobile devices. In this paper, we start with an empirical
experiment to demonstrate computation heterogeneity is a more pronounced
bottleneck than communication on the current generation of battery-powered
mobile devices, and the existing methods are haunted by mobile stragglers.
Further, non-identically distributed data across the mobile users makes the
selection of participants critical to the accuracy and convergence. To tackle
the computational and statistical heterogeneity, we utilize data as a tuning
knob and propose two efficient polynomial-time algorithms to schedule different
workloads on various mobile devices, when data is identically or
non-identically distributed. For identically distributed data, we combine
partitioning and linear bottleneck assignment to achieve near-optimal training
time without accuracy loss. For non-identically distributed data, we convert it
into an average cost minimization problem and propose a greedy algorithm to
find a reasonable balance between computation time and accuracy. We also
establish an offline profiler to quantify the runtime behavior of different
devices, which serves as the input to the scheduling algorithms. We conduct
extensive experiments on a mobile testbed with two datasets and up to 20
devices. Compared with the common benchmarks, the proposed algorithms achieve
2-100x speedup epoch-wise, 2-7% accuracy gain and boost the convergence rate by
more than 100% on CIFAR10
Regional Multi-Armed Bandits
We consider a variant of the classic multi-armed bandit problem where the
expected reward of each arm is a function of an unknown parameter. The arms are
divided into different groups, each of which has a common parameter. Therefore,
when the player selects an arm at each time slot, information of other arms in
the same group is also revealed. This regional bandit model naturally bridges
the non-informative bandit setting where the player can only learn the chosen
arm, and the global bandit model where sampling one arms reveals information of
all arms. We propose an efficient algorithm, UCB-g, that solves the regional
bandit problem by combining the Upper Confidence Bound (UCB) and greedy
principles. Both parameter-dependent and parameter-free regret upper bounds are
derived. We also establish a matching lower bound, which proves the
order-optimality of UCB-g. Moreover, we propose SW-UCB-g, which is an extension
of UCB-g for a non-stationary environment where the parameters slowly vary over
time.Comment: AISTATS 201
Scaling parameters in anomalous and nonlinear Hall effects depend on temperature
In the study of the anomalous Hall effect, the scaling relations between the
anomalous Hall and longitudinal resistivities play the central role. The
scaling parameters by definition are fixed as the scaling variable
(longitudinal resistivity) changes. Contrary to this paradigm, we unveil that
the electron-phonon scattering can result in apparent temperature-dependence of
scaling parameters when the longitudinal resistivity is tuned through
temperature. An experimental approach is proposed to observe this hitherto
unexpected temperature-dependence. We further show that this phenomenon also
exists in the nonlinear Hall effect in nonmagnetic inversion-breaking materials
and may help identify experimentally the presence of the side-jump contribution
besides the Berry-curvature dipole.Comment: 4 pages, 2 figures, considerable change of the presentation in this
versio
- …