4,021 research outputs found
Unsupervised Generative Modeling Using Matrix Product States
Generative modeling, which learns joint probability distribution from data
and generates samples according to it, is an important task in machine learning
and artificial intelligence. Inspired by probabilistic interpretation of
quantum physics, we propose a generative model using matrix product states,
which is a tensor network originally proposed for describing (particularly
one-dimensional) entangled quantum states. Our model enjoys efficient learning
analogous to the density matrix renormalization group method, which allows
dynamically adjusting dimensions of the tensors and offers an efficient direct
sampling approach for generative tasks. We apply our method to generative
modeling of several standard datasets including the Bars and Stripes, random
binary patterns and the MNIST handwritten digits to illustrate the abilities,
features and drawbacks of our model over popular generative models such as
Hopfield model, Boltzmann machines and generative adversarial networks. Our
work sheds light on many interesting directions of future exploration on the
development of quantum-inspired algorithms for unsupervised machine learning,
which are promisingly possible to be realized on quantum devices.Comment: 11 pages, 12 figures (not including the TNs) GitHub Page:
https://congzlwag.github.io/UnsupGenModbyMPS
Experimental observations of dynamic critical phenomena in a lipid membrane
Near a critical point, the time scale of thermally-induced fluctuations
diverges in a manner determined by the dynamic universality class. Experiments
have verified predicted 3D dynamic critical exponents in many systems, but
similar experiments in 2D have been lacking for the case of conserved order
parameter. Here we analyze time-dependent correlation functions of a quasi-2D
lipid bilayer in water to show that its critical dynamics agree with a recently
predicted universality class. In particular, the effective dynamic exponent
crosses over from to as the correlation
length of fluctuations exceeds a hydrodynamic length set by the membrane and
bulk viscosities.Comment: 5 pages, 3 figures and 2 additional pages of supplemen
Bursts of activity in collective cell migration
Dense monolayers of living cells display intriguing relaxation dynamics,
reminiscent of soft and glassy materials close to the jamming transition, and
migrate collectively when space is available, as in wound healing or in cancer
invasion. Here we show that collective cell migration occurs in bursts that are
similar to those recorded in the propagation of cracks, fluid fronts in porous
media and ferromagnetic domain walls. In analogy with these systems, the
distribution of activity bursts displays scaling laws that are universal in
different cell types and for cells moving on different substrates. The main
features of the invasion dynamics are quantitatively captured by a model of
interacting active particles moving in a disordered landscape. Our results
illustrate that collective motion of living cells is analogous to the
corresponding dynamics in driven, but inanimate, systems
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