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For $G={\rm GL}(n,q)$, the proportion $P_{n,q}$ of pairs $(\chi,g)$ in ${\rm Irr}(G)\times G$ with $\chi(g)\neq 0$ satisfies $P_{n,q}\to 0$ as $n\to\infty$.

Understanding the mechanism of high temperature (high Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high Tc superconductivity arises from a doped Mott insulator as described by the Hubbard model. An exact solution of the Hubbard model, however, is extremely challenging due to the strong electron-electron correlation. Therefore, it is highly desirable to experimentally study a model Hubbard system in which the unconventional superconductivity can be continuously tuned by varying the Hubbard parameters. Here we report signatures of tunable superconductivity in ABC-trilayer graphene (TLG) / boron nitride (hBN) moir\'e superlattice. Unlike "magic angle" twisted bilayer graphene, theoretical calculations show that under a vertical displacement field the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 Kelvin at 1/4 and 1/2 fillings, corresponding to 1 and 2 holes per unit cell, respectively. Upon further cooling, signatures of superconducting domes emerge below 1 kelvin for the electron- and hole-doped sides of the 1/4 filling Mott state. The electronic behavior in the TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron-electron interaction and the miniband bandwidth, which can be tuned continuously with the displacement field D. By simply varying the D field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that TLG/hBN heterostructures offer an attractive model system to explore rich correlated behavior emerging in the tunable triangular Hubbard model., Comment: 14 pages, 4 figures

Rational design of artificial lattices yields effects unavailable in simple solids, and vertical superlattices of multilayer semiconductors are already used in optical sensors and emitters. Manufacturing lateral superlattices remains a much bigger challenge, with new opportunities offered by the use of moire patterns in van der Waals heterostructures of graphene and hexagonal crystals such as boron nitride (h-BN). Experiments to date have elucidated the novel electronic structure of highly aligned graphene/h-BN heterostructures, where miniband edges and saddle points in the electronic dispersion can be reached by electrostatic gating. Here we investigate the dynamics of electrons in moire minibands by transverse electron focusing, a measurement of ballistic transport between adjacent local contacts in a magnetic field. At low temperatures, we observe caustics of skipping orbits extending over hundreds of superlattice periods, reversals of the cyclotron revolution for successive minibands, and breakdown of cyclotron motion near van Hove singularities. At high temperatures, we study the suppression of electron focusing by inelastic scattering.

The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are successfully explained by the composite fermion (CF) model, in which an even number of magnetic flux quanta are attached to an electron and where states form the sequence of filling factors $\nu = p/(2mp \pm 1)$, with $m$ and $p$ positive integers. In the widely-studied GaAs-based system, the CF picture is thought to become unstable for the $N \geq 2$ LL, where larger residual interactions between CFs are predicted and competing many-body phases have been observed. Here we report transport measurements of FQH states in the $N=2$ LL (filling factors $4 < \nu < 8$) in bilayer graphene, a system with spin and valley degrees of freedom in all LLs, and an additional orbital degeneracy in the 8-fold degenerate $N=0$/$N=1$ LLs. In contrast with recent observations of particle-hole asymmetry in the $N=0$/$N=1$ LLs of bilayer graphene, the FQH states we observe in the $N=2$ LL are consistent with the CF model: within a LL, they form a complete sequence of particle-hole symmetric states whose relative strength is dependent on their denominators. The FQH states in the $N=2$ LL display energy gaps of a few Kelvin, comparable to and in some cases larger than those of fractional states in the $N=0$/$N=1$ LLs. The FQH states we observe form, to the best of our knowledge, the highest set of particle-hole symmetric pairs seen in any material system.

Top-down information plays a central role in human perception, but plays relatively little role in many current state-of-the-art deep networks, such as Convolutional Neural Networks (CNNs). This work seeks to explore a path by which top-down information can have a direct impact within current deep networks. We explore this path by learning and using "generators" corresponding to the network internal effects of three types of transformation (each a restriction of a general affine transformation): rotation, scaling, and translation. We demonstrate how these learned generators can be used to transfer top-down information to novel settings, as mediated by the "feature flows" that the transformations (and the associated generators) correspond to inside the network. Specifically, we explore three aspects: 1) using generators as part of a method for synthesizing transformed images --- given a previously unseen image, produce versions of that image corresponding to one or more specified transformations, 2) "zero-shot learning" --- when provided with a feature flow corresponding to the effect of a transformation of unknown amount, leverage learned generators as part of a method by which to perform an accurate categorization of the amount of transformation, even for amounts never observed during training, and 3) (inside-CNN) "data augmentation" --- improve the classification performance of an existing network by using the learned generators to directly provide additional training "inside the CNN".

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in place of average or max pooling. We experimentally demonstrate that the proposed pooling operations provide a boost in invariance properties relative to conventional pooling and set the state of the art on several widely adopted benchmark datasets; they are also easy to implement, and can be applied within various deep neural network architectures. These benefits come with only a light increase in computational overhead during training and a very modest increase in the number of model parameters., Comment: Patent disclosure, UCSD Docket No. SD2015-184, "Forest Convolutional Neural Network", filed on March 4, 2015. UCSD Docket No. SD2016-053, "Generalizing Pooling Functions in Convolutional Neural Network", filed on Sept 23, 2015

Graphene monolayers are known to display domains of anisotropic friction with twofold symmetry and anisotropy exceeding 200 percent. This anisotropy has been thought to originate from periodic nanoscale ripples in the graphene sheet, which enhance puckering around a sliding asperity to a degree determined by the sliding direction. Here we demonstrate that these frictional domains derive not from structural features in the graphene, but from self-assembly of atmospheric adsorbates into a highly regular superlattice of stripes with period 4 to 6 nm. The stripes and resulting frictional domains appear on monolayer and multilayer graphene on a variety of substrates, as well as on exfoliated flakes of hexagonal boron nitride. We show that the stripe-superlattices can be reproducibly and reversibly manipulated with submicron precision using a scanning probe microscope, allowing us to create arbitrary arrangements of frictional domains within a single flake. Our results suggest a revised understanding of the anisotropic friction observed in graphene and bulk graphite in terms of atmospheric adsorbates., Comment: This version contains new data which show that the stripes observed in AFM are adsorbates rather than structural ripples. We also clarify that the stripe axis is parallel to the axis of high friction, rather than perpendicular, as we previously claimed following others' studies; our revised conclusion is based on a more careful imaging sequence which avoided reorienting frictional domains

Electrolyte gating is a powerful technique for accumulating large carrier densities in surface two-dimensional electron systems (2DES). Yet this approach suffers from significant sources of disorder: electrochemical reactions can damage or alter the surface of interest, and the ions of the electrolyte and various dissolved contaminants sit Angstroms from the 2DES. Accordingly, electrolyte gating is well-suited to studies of superconductivity and other phenomena robust to disorder, but of limited use when reactions or disorder must be avoided. Here we demonstrate that these limitations can be overcome by protecting the sample with a chemically inert, atomically smooth sheet of hexagonal boron nitride (BN). We illustrate our technique with electrolyte-gated strontium titanate, whose mobility improves more than tenfold when protected with BN. We find this improvement even for our thinnest BN, of measured thickness 6 A, with which we can accumulate electron densities nearing 10^14 cm^-2. Our technique is portable to other materials, and should enable future studies where high carrier density modulation is required but electrochemical reactions and surface disorder must be minimized.

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural networks (CNN) style architectures are being looked at: (1) transparency of the intermediate layers to the overall classification; (2) discriminativeness and robustness of learned features, especially in the early layers; (3) effectiveness in training due to the presence of the exploding and vanishing gradients. We introduce "companion objective" to the individual hidden layers, in addition to the overall objective at the output layer (a different strategy to layer-wise pre-training). We extend techniques from stochastic gradient methods to analyze our algorithm. The advantage of our method is evident and our experimental result on benchmark datasets shows significant performance gain over existing methods (e.g. all state-of-the-art results on MNIST, CIFAR-10, CIFAR-100, and SVHN)., Comment: Patent disclosure, UCSD Docket No. SD2014-313, filed on May 22, 2014

Many convex optimization methods are conceived of and analyzed in a largely separate fashion. In contrast to this traditional separation, this manuscript points out and demonstrates the utility of an important but largely unremarked common thread running through many prominent optimization methods. In particular, we show that methods such as successive orthogonal projection, gradient descent, projected gradient descent, the proximal-point method, forward-backward splitting, the alternating direction method of multipliers, and under- or over-relaxed variants of the preceding all involve updates that are of a common type --- namely, the updates satisfy a property known as pseudocontractivity. Moreover, since the property of pseudocontractivity is preserved under both composition and convex combination, updates constructed via these operations from pseudocontractive updates are themselves pseudocontractive. Having demonstrated that pseudocontractive updates are to be found in many optimization methods, we then provide a unified basic analysis of methods with pseudocontractive updates. Specifically, we prove a novel bound satisfied by the norm of the difference in iterates of pseudocontractive updates and we then use this bound to establish that the error criterion $\left\Vert x^{N}-Tx^{N}\right\Vert ^{2}$ is $o(1/N)$ for any method involving pseudocontractive updates (where $N$ is the number of iterations and $T$ is the iteration operator).

A simple surface band structure and a large bulk band gap have allowed Bi2Se3 to become a reference material for the newly discovered three-dimensional topological insulators, which exhibit topologically-protected conducting surface states that reside inside the bulk band gap. Studying topological insulators such as Bi2Se3 in nanostructures is advantageous because of the high surface-to-volume ratio, which enhances effects from the surface states; recently reported Aharonov-Bohm oscillation in topological insulator nanoribbons by some of us is a good example. Theoretically, introducing magnetic impurities in topological insulators is predicted to open a small gap in the surface states by breaking time-reversal symmetry. Here, we present synthesis of magnetically-doped Bi2Se3 nanoribbons by vapor-liquid-solid growth using magnetic metal thin films as catalysts. Although the doping concentration is less than ~ 2%, low-temperature transport measurements of the Fe-doped Bi2Se3 nanoribbon devices show a clear Kondo effect at temperatures below 30 K, confirming the presence of magnetic impurities in the Bi2Se3 nanoribbons. The capability to dope topological insulator nanostructures magnetically opens up exciting opportunities for spintronics., Comment: 16 pages, 4 figures

We study the transport properties of graphene nanoribbons of standardized 30 nm width and varying lengths. We find that the extent of the gap observed in transport as a function of Fermi energy in these ribbons (the "transport gap") does not have a strong dependence on ribbon length, while the extent of the gap as a function of source-drain voltage (the "source-drain gap") increases with increasing ribbon length. We anneal the ribbons to reduce the amplitude of the disorder potential, and find that the transport gap both shrinks and moves closer to zero gate voltage. In contrast, annealing does not systematically affect the source-drain gap. We conclude that the transport gap reflects the overall strength of the background disorder potential, while the source-drain gap is sensitively dependent on its details. Our results support the model that transport in graphene nanoribbons occurs through quantum dots forming along the ribbon due to a disorder potential induced by charged impurities., Comment: 10 pages, 8 figures