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

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

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

Hall of Fame Scientists: Exploring identity through the examples of famous scientists using biology and English

In the Hall of Fame Scientists Unit, we hope introduce to students the concept of success and practice skills they will need for the rest of their high school career. The interdisciplinary unit is meant for ninth graders taking biology and English I. The unit concentrates on foundational writing skills: properly formatted paragraph (A.P.E.), citing scholarly sources, and research. Students should also communicate and apply scientific information extracted from various sources. We hope that after this unit, students will be able to independently recognize different perspectives, develop a cross-cultural understanding of what it means to be young, develop a growth mindset, and recognize the different avenues to success. We approached these transfer goals through a 6 day unit (of 90 minute block classes), in which we taught students skills through a research project. The unit concludes with students presenting a famous scientist’s journey to success, focusing on their years of adolescence and their identity

Torsion Vanishing for Some Shimura Varieties

We generalize the torsion vanishing results of Caraiani-Scholze and Koshikawa. Our results apply to the cohomology of general Shimura varieties $(\mathbf{G},X)$ of PEL type $A$ or $C$, localized at a suitable maximal ideal $\mathfrak{m}$ in the spherical Hecke algebra at primes $p$ such that $\mathbf{G}_{\mathbb{Q}_{p}}$ is a group for which we know the Fargues-Scholze local Langlands correspondence is the semi-simplification of a suitably nice local Langlands correspondence. This is accomplished by combining Koshikawa's technique, the theory of geometric Eisenstein series over the Fargues-Fontaine curve, the work of Santos describing the structure of the fibers of the minimally and toroidally compactified Hodge-Tate period morphism for general PEL type Shimura varieties of type $A$ or $C$, and ideas developed by Zhang on comparing Hecke correspondences on the moduli stack of $G$-bundles with the cohomology of Shimura varieties. In the process, we also establish a description of the generic part of the cohomology that bears resemblance to the work of Xiao-Zhu. Moreover, we also construct a filtration on the compactly supported cohomology that differs from Manotovan's filtration in the case that the Shimura variety is non-compact, allowing us to circumvent some of the circumlocutions taken by Cariani-Scholze. Our method showcases a very general strategy for proving such torsion vanishing results, and should bear even more fruit once the inputs are generalized. Motivated by this, we formulate an even more general torsion vanishing conjecture

Study Majorana Neutrino Contribution to B-meson Semi-leptonic Rare Decays

B meson semi-leptonic rare decays are sensitive to new physics beyond standard model. We study the $B^{-}\to \pi^{-}\mu^{+}\mu^{-}$ process and investigate the Majorana neutrino contribution to its decay width. The constraints on the Majorana neutrino mass and mixing parameter are obtained from this decay channel with the latest LHCb data. Utilizing the best fit for the parameters, we study the lepton number violating decay $B^{-}\to \pi^{+}\mu^{-}\mu^{-}$, and find its branching ratio is about $6.4\times10^{-10}$, which is consistent with the LHCb data reported recently.Comment: 10 pages, 3 figure

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