2,150 research outputs found
On type-II singularities in Ricci flow on
In each dimension and for each real number , we
construct a family of complete rotationally symmetric solutions to Ricci flow
on which encounter a global singularity at a finite time .
The singularity forms arbitrarily slowly with the curvature blowing up
arbitrarily fast at the rate . Near the origin, blow-ups
of such a solution converge uniformly to the Bryant soliton. Near spatial
infinity, blow-ups of such a solution converge uniformly to the shrinking
cylinder soliton. As an application of this result, we prove that there exist
standard solutions of Ricci flow on whose blow-ups near the
origin converge uniformly to the Bryant soliton.Comment: Revised version, typos correcte
Robustness of Information Diffusion Algorithms to Locally Bounded Adversaries
We consider the problem of diffusing information in networks that contain
malicious nodes. We assume that each normal node in the network has no
knowledge of the network topology other than an upper bound on the number of
malicious nodes in its neighborhood. We introduce a topological property known
as r-robustness of a graph, and show that this property provides improved
bounds on tolerating malicious behavior, in comparison to traditional concepts
such as connectivity and minimum degree. We use this topological property to
analyze the canonical problems of distributed consensus and broadcasting, and
provide sufficient conditions for these operations to succeed. Finally, we
provide a construction for r-robust graphs and show that the common
preferential-attachment model for scale-free networks produces a robust graph.Comment: Preprint of results to appear at 2012 American Control Conferenc
Two-stage Deep Reinforcement Learning for Inverter-based Volt-VAR Control in Active Distribution Networks
Model-based Vol/VAR optimization method is widely used to eliminate voltage
violations and reduce network losses. However, the parameters of active
distribution networks(ADNs) are not onsite identified, so significant errors
may be involved in the model and make the model-based method infeasible. To
cope with this critical issue, we propose a novel two-stage deep reinforcement
learning (DRL) method to improve the voltage profile by regulating
inverter-based energy resources, which consists of offline stage and online
stage. In the offline stage, a highly efficient adversarial reinforcement
learning algorithm is developed to train an offline agent robust to the model
mismatch. In the sequential online stage, we transfer the offline agent safely
as the online agent to perform continuous learning and controlling online with
significantly improved safety and efficiency. Numerical simulations on IEEE
test cases not only demonstrate that the proposed adversarial reinforcement
learning algorithm outperforms the state-of-art algorithm, but also show that
our proposed two-stage method achieves much better performance than the
existing DRL based methods in the online application.Comment: 8 page
Joint Stochastic Approximation learning of Helmholtz Machines
Though with progress, model learning and performing posterior inference still
remains a common challenge for using deep generative models, especially for
handling discrete hidden variables. This paper is mainly concerned with
algorithms for learning Helmholz machines, which is characterized by pairing
the generative model with an auxiliary inference model. A common drawback of
previous learning algorithms is that they indirectly optimize some bounds of
the targeted marginal log-likelihood. In contrast, we successfully develop a
new class of algorithms, based on stochastic approximation (SA) theory of the
Robbins-Monro type, to directly optimize the marginal log-likelihood and
simultaneously minimize the inclusive KL-divergence. The resulting learning
algorithm is thus called joint SA (JSA). Moreover, we construct an effective
MCMC operator for JSA. Our results on the MNIST datasets demonstrate that the
JSA's performance is consistently superior to that of competing algorithms like
RWS, for learning a range of difficult models.Comment: Fixing typos. Published at ICLR-2016 Workshop Trac
A Trend-following Trading Indicator on Homomorphically Encrypted Data
Algorithmic trading has proliferated the area of quantitative finance for
already over a decade. The decisions are made without human intervention using
the data provided by brokerage firms and exchanges. There is an emerging
intermediate layer of financial players that are placed in between a broker and
algorithmic traders. The role of these players is to aggregate market decisions
from the algorithmic traders and send a final market order to a broker. In
return, the quantitative analysts receive incentives proportional to the
correctness of their predictions. In such a setup, the intermediate player - an
aggregator - does not provide the market data in plaintext but encrypts it.
Encrypting market data prevents quantitative analysts from trading on their
own, as well as keeps valuable financial data private. This paper proposes an
implementation of a popular trend-following indicator with two different
homomorphic encryption libraries - SEAL and HEAAN - and compares it to the
trading indicator implemented for plaintext. Then an attempt to implement a
trading strategy is presented and analysed. The trading indicator implemented
with SEAL and HEAAN is almost identical to that implemented on the plaintext,
the percentage error is of 0.14916% and 0.00020% respectively. Despite many
limitations that homomorphic encryption imposes on this algorithm's
implementation, quantitative finance has a high potential of benefiting from
the methods of homomorphic encryption.Comment: Accepted as a short paper by the 17th International Conference on
Security and Cryptography (SECRYPT 2020
Dynamical stability of algebraic Ricci solitons
We consider dynamical stability for a modified Ricci flow equation whose
stationary solutions include Einstein and Ricci soliton metrics. Our focus is
on homogeneous metrics on non-compact manifolds. Following the program of
Guenther, Isenberg, and Knopf, we define a class of weighted little H\"older
spaces with certain interpolation properties that allow the use of maximal
regularity theory and the application of a stability theorem of Simonett. With
this, we derive two stability theorems, one for a class of Einstein metrics and
one for a class of non-Einstein Ricci solitons. Using linear stability results
of Jablonski, Petersen, and the first author, we obtain dynamical stability for
many specific Einstein and Ricci soliton metrics on simply connected solvable
Lie groups.Comment: 18 pages, updated reference and statement of Theorems 1.3 and 2.1,
revised introduction and fixed typos, final version to appear in Journal
f\"ur die reine und angewandte Mathemati
Simple Applications of BERT for Ad Hoc Document Retrieval
Following recent successes in applying BERT to question answering, we explore
simple applications to ad hoc document retrieval. This required confronting the
challenge posed by documents that are typically longer than the length of input
BERT was designed to handle. We address this issue by applying inference on
sentences individually, and then aggregating sentence scores to produce
document scores. Experiments on TREC microblog and newswire test collections
show that our approach is simple yet effective, as we report the highest
average precision on these datasets by neural approaches that we are aware of
An efficient model reduction method for solving viscous G-equations in incompressible cellular flows
The G-equation is a well-known model for studying front propagation in
turbulent combustion. In this paper, we shall develop an efficient model
reduction method for solving viscous G-equations in incompressible steady and
time-periodic cellular flows. Our method is based on the Galerkin proper
orthogonal decomposition (POD) methods. To facilitate the algorithm design and
convergence analysis, we decompose the solution of the viscous G-equation into
a mean-free part and a mean part, where their evolution equations can be
derived accordingly. We construct the POD basis from the solution snapshots of
the mean-free part. With the POD basis, we can efficiently solve the evolution
equation for the mean-free part of the solution to the viscous G-equation.
After we get the mean-free part of the solution, the mean of the solution can
be recovered. We also provide rigorous convergence analysis for our numerical
method. Numerical results are presented to demonstrate the accuracy and
efficiency of the proposed method. Specifically, we study the turbulent flame
speeds of the viscous G-equations in incompressible cellular flows based on the
POD method and fully resolved computations.Comment: 25 page
Practical Algorithms for Best-K Identification in Multi-Armed Bandits
In the Best- identification problem (Best--Arm), we are given
stochastic bandit arms with unknown reward distributions. Our goal is to
identify the arms with the largest means with high confidence, by drawing
samples from the arms adaptively. This problem is motivated by various
practical applications and has attracted considerable attention in the past
decade. In this paper, we propose new practical algorithms for the Best--Arm
problem, which have nearly optimal sample complexity bounds (matching the lower
bound up to logarithmic factors) and outperform the state-of-the-art algorithms
for the Best--Arm problem (even for ) in practice
Robustness of Complex Networks with Implications for Consensus and Contagion
We study a graph-theoretic property known as robustness, which plays a key
role in certain classes of dynamics on networks (such as resilient consensus,
contagion and bootstrap percolation). This property is stronger than other
graph properties such as connectivity and minimum degree in that one can
construct graphs with high connectivity and minimum degree but low robustness.
However, we show that the notions of connectivity and robustness coincide on
common random graph models for complex networks (Erdos-Renyi, geometric random,
and preferential attachment graphs). More specifically, the properties share
the same threshold function in the Erdos-Renyi model, and have the same values
in one-dimensional geometric graphs and preferential attachment networks. This
indicates that a variety of purely local diffusion dynamics will be effective
at spreading information in such networks. Although graphs generated according
to the above constructions are inherently robust, we also show that it is
coNP-complete to determine whether any given graph is robust to a specified
extent.Comment: Extended version of paper appearing at the 2012 Conference on
Decision and Contro
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