2,146 research outputs found
On the Convergence of Decentralized Gradient Descent
Consider the consensus problem of minimizing where
each is only known to one individual agent out of a connected network
of agents. All the agents shall collaboratively solve this problem and
obtain the solution subject to data exchanges restricted to between neighboring
agents. Such algorithms avoid the need of a fusion center, offer better network
load balance, and improve data privacy. We study the decentralized gradient
descent method in which each agent updates its variable , which is
a local approximate to the unknown variable , by combining the average of
its neighbors' with the negative gradient step .
The iteration is where the averaging coefficients form a symmetric doubly stochastic matrix
. We analyze the convergence of this
iteration and derive its converge rate, assuming that each is proper
closed convex and lower bounded, is Lipschitz continuous with
constant , and stepsize is fixed. Provided that where , the objective error at the averaged
solution, , reduces at a speed of
until it reaches . If are further (restricted) strongly
convex, then both and each converge
to the global minimizer at a linear rate until reaching an
-neighborhood of . We also develop an iteration for
decentralized basis pursuit and establish its linear convergence to an
-neighborhood of the true unknown sparse signal
The induced interaction in a Fermi gas with a BEC-BCS crossover
We study the effect of the induced interaction on the superfluid transition
temperature of a Fermi gas with a BEC-BCS crossover. The
Gorkov-Melik-Barkhudarov theory about the induced interaction is extended from
the BCS side to the entire crossover, and the pairing fluctuation is treated in
the approach by Nozi\`{e}res and Schmitt-Rink. At unitarity, the induced
interaction reduces the transition temperature by about twenty percent. In the
BCS limit, the transition temperature is reduced by a factor about 2.22, as
found by Gorkov and Melik-Barkhudarov. Our result shows that the effect of the
induced interaction is important both on the BCS side and in the unitary
region.Comment: 11 pages, 3 figures, to be published in PR
Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover
The Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover is
derived by the path-integral method. In addition to the standard
Ginzburg-Landau equation, a second equation describing the total atom density
is obtained. These two coupled equations are necessary to describe both
homogeneous and inhomogeneous systems. The Ginzburg-Landau theory is valid near
the transition temperature on both sides of the crossover. In the
weakly-interacting BEC region, it is also accurate at zero temperature where
the Ginzburg-Landau equation can be mapped onto the Gross-Pitaevskii (GP)
equation. The applicability of GP equation at finite temperature is discussed.
On the BEC side, the fluctuation of the order parameter is studied and the
renormalization to the molecule coupling constant is obtained.Comment: 16 pages, 2 figures, to be published in PR
Electron self-energy and effective mass in a single heterostructure
In this paper, we investigate the electron self-energy and effective mass in
a single heterostructure using Green-function method. Numerical calculations of
the electron self-energy and effective mass for GaAs/AlAs heterostructure are
performed. The results show that the self energy (effective mass) of electron,
which incorporate the energy of electron coupling to interface-optical phonons
and half three-dimension LO phonons, monotonically increase(decrease) from that
of interface polaron to that of 3D bulk polaron with the increase of the
distance between the position of the electron and interface.Comment: 10 pages, 2 figure
The TRRAP-HAT-Sp1 axis maintains brain homeostasis
The homeostasis of the brain is tightly controlled by the viability and functionality of various cell types, including neurons and glial cells, like oligodendrocytes, astrocytes as well as microglia. Defects of neurogenesis and maintenance of neural cells are associated with multiple neuropathologies, such as Intellectual Disability (ID) and Autism Spectrum Disorders (ASD) among other diseases. HAT and HDAC modulate brain functionality, e.g. memory formation, cognitive function, and neuroprotection, whereas the disturbance of the acetylation profiles has been related to multiple neuropathological diseases. However, how epigenetic regulation participates in the neurodevelopmental, neural differentiation and neurodegenerative processes remains largely unknown. In our studies, we have chosen the HAT adaptor, Trrap, to investigate how the disturbance of acetylation would affect brain functionality. We show that Trrap deletion in post-mitotic neurons results in neurodegeneration. In addition, Trrap deficiency in adult neural stem cells compromises their self-renewal and differentiation. With integrated transcriptomics, epigenomics, and proteomics we identify Sp1 as the master regulator controlled by Trrap-HAT and demonstrate that the Trrap-HAT-Sp1 axis ensures the proper expression of genes involved in microtubule dynamics. We find that Trrap mediates Sp1 binding through the maintenance of the acetylation profile on Sp1 and that acetylation of Sp1 plays an important role, dependent and independent of Trrap, in its transcription activation. Taken together, we demonstrate that Trrap, through its mediated acetylation, is involved in neuroprotection and neural differentiation via the regulation of Sp1 activity. My dissertation provides a novel insight into the role of epigenetic regulation of transcription factors in the maintenance of brain homeostasis and preventing neurodegeneration
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