336 research outputs found
The fundamental gap of a kind of two dimensional sub-elliptic operator
This paper is concerned at the minimization fundamental gap problem for a
class of two-dimensional degenerate sub-elliptic operators. We establish
existence results for weak solutions, Sobolev embedding theorem and spectral
theory of sub-elliptic operators. We provide the existence and characterization
theorems for extremizing potentials when is subject to
norm constraint
Some controllability results of a class of N-dimensional parabolic equations with internal single-point degeneracy
This paper investigates the controllability of a class of -dimensional
degenerate parabolic equations with interior single-point degeneracy. We employ
the Galerkin method to prove the existence of solutions for the equations. The
analysis is then divided into two cases based on whether the degenerate point
lies within the control region or not. For each case, we
establish specific Carleman estimates. As a result, we achieve null
controllability in the first case and unique continuation and
approximate controllability in the second case
Efficient Semi-Supervised Federated Learning for Heterogeneous Participants
Federated Learning (FL) has emerged to allow multiple clients to
collaboratively train machine learning models on their private data. However,
training and deploying large-scale models on resource-constrained clients is
challenging. Fortunately, Split Federated Learning (SFL) offers a feasible
solution by alleviating the computation and/or communication burden on clients.
However, existing SFL works often assume sufficient labeled data on clients,
which is usually impractical. Besides, data non-IIDness across clients poses
another challenge to ensure efficient model training. To our best knowledge,
the above two issues have not been simultaneously addressed in SFL. Herein, we
propose a novel Semi-SFL system, which incorporates clustering regularization
to perform SFL under the more practical scenario with unlabeled and non-IID
client data. Moreover, our theoretical and experimental investigations into
model convergence reveal that the inconsistent training processes on labeled
and unlabeled data have an influence on the effectiveness of clustering
regularization. To this end, we develop a control algorithm for dynamically
adjusting the global updating frequency, so as to mitigate the training
inconsistency and improve training performance. Extensive experiments on
benchmark models and datasets show that our system provides a 3.0x speed-up in
training time and reduces the communication cost by about 70.3% while reaching
the target accuracy, and achieves up to 5.1% improvement in accuracy under
non-IID scenarios compared to the state-of-the-art baselines.Comment: 16 pages, 12 figures, conferenc
Nonlinear vibrations of beams with spring and damping delayed feedback control
The primary, subharmonic, and superharmonic resonances of an Euler–Bernoulli beam subjected to harmonic excitations are studied with damping and spring delayed-feedback controllers. By method of multiple scales, the non-linear governing partial differential equation is transformed into linear differential equations directly. Effects of the feedback gains and time-delays on the steady state responses are investigated. The velocity and displacement delayed-feedback controllers are employed to suppress the primary and superharmonic resonances of the forced nonlinear oscillator. The stable vibration regions of the feedback gains and time-delays are worked out based on stablility conditions of the resonances. It is found that proper selection of feedback gains and time-delays can enhance the control performance of beam’s nonlinear vibration. Position of the bifurcation point can be changed or the bifurcation can be eliminated
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