Commensurate and Incommensurate Structure of the Neutron Cross Section in LaSrCuO and YBaCuO

We study the evolution of the d-wave neutron cross-section with variable frequency \omega and fixed T (below and above Tc) in two different cuprate families. The evolution from incommensurate to commensurate to incommensurate peaks is rather generic within an RPA-like scheme. This behavior seems to be in reasonable accord with experiments, and may help distinguish between this and the "stripe" scenario.Comment: 2 pages; submitted to Proceedings of M2S-HTSC-V

Frequency Evolution of Neutron Peaks Below Tc: Commensurate and Incommensurate Structure in LaSrCuO and YBaCuO

We study the evolution of the neutron cross-section with variable frequency $\omega$ and fixed $T$ below $T_c$ in two different cuprate families. Our calculations, which predominantly probe the role of d-wave pairing, lead to generic features, independent of Fermi surface shapes. Among our findings, reasonably consistent with experiment, are (i) for $\omega$ near the gap energy $\Delta$, both optimal {LaSrCuO} and slightly underdoped YBCO exhibit (comparably) incommensurate peaks (ii) peak sharpening below $T_c$ is seen in {LaSrCuO}, (iii) quite generically, a frequency evolution from incommensurate to commensurate and then back to incommensurate structure is found with increasing $\omega$. Due to their narrow $\omega$ regime of stability, commensurate peaks in {LaSrCuO} should be extremely difficult to observe.Comment: RevTex 5pages, 4figures; Manuscript rewritten, figures revised, and direct comparisons with experiments adde

Closed-loop control of complex networks : A trade-off between time and energy

W. L. is supported by the National Science Foundation of China (NSFC) (Grants No. 11322111 and No. 61773125). Y.-Z. S. is supported by the NSFC (Grant No. 61403393). Y.-C. L. acknowledges support from the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through Grant No. N00014-16-1-2828. Y.-Z. S. and S.-Y. L. contributed equally to this work.Peer reviewedPublisher PD

Learning Active Basis Models by EM-Type Algorithms

EM algorithm is a convenient tool for maximum likelihood model fitting when the data are incomplete or when there are latent variables or hidden states. In this review article we explain that EM algorithm is a natural computational scheme for learning image templates of object categories where the learning is not fully supervised. We represent an image template by an active basis model, which is a linear composition of a selected set of localized, elongated and oriented wavelet elements that are allowed to slightly perturb their locations and orientations to account for the deformations of object shapes. The model can be easily learned when the objects in the training images are of the same pose, and appear at the same location and scale. This is often called supervised learning. In the situation where the objects may appear at different unknown locations, orientations and scales in the training images, we have to incorporate the unknown locations, orientations and scales as latent variables into the image generation process, and learn the template by EM-type algorithms. The E-step imputes the unknown locations, orientations and scales based on the currently learned template. This step can be considered self-supervision, which involves using the current template to recognize the objects in the training images. The M-step then relearns the template based on the imputed locations, orientations and scales, and this is essentially the same as supervised learning. So the EM learning process iterates between recognition and supervised learning. We illustrate this scheme by several experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimization and resilience of complex supply-demand networks

Acknowledgments This work was supported by NSF under Grant No. 1441352. SPZ and ZGH were supported by NSF of China under Grants No. 11135001 and No. 11275003. ZGH thanks Prof Liang Huang and Xin-Jian Xu for helpful discussions.Peer reviewedPublisher PD