Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and largely incoher
ent nature. We report the diffusion-based topological states supported by spatiotemporally-modulated advections stacked over a fluidic surface, thereby imitating a periodic propagating potential in effective thermal lattices. We observe edge and bulk states within purely nontrivial and trivial lattices, respectively. At interfaces between these two types of lattices, the diffusive system exhibits interface states, manifesting inhomogeneous thermal properties on the fluidic surface. Our findings establish a framework for topological diffusion and thermal edge/bulk states, and it may empower a distinct mechanism for flexible manipulation of robust heat and mass transfer.
Recent empirical work on SGD applied to over-parameterized deep learning has shown that most gradient components over epochs are quite small. Inspired by such observations, we rigorously study properties of noisy truncated SGD (NT-SGD), a noisy gradi
ent descent algorithm that truncates (hard thresholds) the majority of small gradient components to zeros and then adds Gaussian noise to all components. Considering non-convex smooth problems, we first establish the rate of convergence of NT-SGD in terms of empirical gradient norms, and show the rate to be of the same order as the vanilla SGD. Further, we prove that NT-SGD can provably escape from saddle points and requires less noise compared to previous related work. We also establish a generalization bound for NT-SGD using uniform stability based on discretized generalized Langevin dynamics. Our experiments on MNIST (VGG-5) and CIFAR-10 (ResNet-18) demonstrate that NT-SGD matches the speed and accuracy of vanilla SGD, and can successfully escape sharp minima while having better theoretical properties.
Differentially private SGD (DP-SGD) is one of the most popular methods for solving differentially private empirical risk minimization (ERM). Due to its noisy perturbation on each gradient update, the error rate of DP-SGD scales with the ambient dimen
sion $p$, the number of parameters in the model. Such dependence can be problematic for over-parameterized models where $p gg n$, the number of training samples. Existing lower bounds on private ERM show that such dependence on $p$ is inevitable in the worst case. In this paper, we circumvent the dependence on the ambient dimension by leveraging a low-dimensional structure of gradient space in deep networks -- that is, the stochastic gradients for deep nets usually stay in a low dimensional subspace in the training process. We propose Projected DP-SGD that performs noise reduction by projecting the noisy gradients to a low-dimensional subspace, which is given by the top gradient eigenspace on a small public dataset. We provide a general sample complexity analysis on the public dataset for the gradient subspace identification problem and demonstrate that under certain low-dimensional assumptions the public sample complexity only grows logarithmically in $p$. Finally, we provide a theoretical analysis and empirical evaluations to show that our method can substantially improve the accuracy of DP-SGD in the high privacy regime (corresponding to low privacy loss $epsilon$).
Atomically thin transition metal dichalcogenide films with distorted trigonal (1T$^prime$) phase have been predicted to be candidates for realizing quantum spin Hall effect. Growth of 1T$^prime$ film and experimental investigation of its electronic s
tructure are critical. Here we report the electronic structure of 1T$^prime$-MoTe$_2$ films grown by molecular beam epitaxy (MBE). Growth of the 1T$^prime$-MoTe$_2$ film depends critically on the substrate temperature, and successful growth of the film is indicated by streaky stripes in the reflection high energy electron diffraction and sharp diffraction spots in low energy electron diffraction. Angle-resolved photoemission spectroscopy measurements reveal a metallic behavior in the as-grown film with an overlap between the conduction and valence bands. First principles calculation suggests that a suitable tensile strain along the a-axis direction is needed to induce a gap to make it an insulator. Our work not only reports the electronic structure of MBE grown 1T$^prime$-MoTe$_2$ films, but also provides insights for strain engineering to make it possible for quantum spin Hall effect.
Atomically thin PtSe2 films have attracted extensive research interests for potential applications in high-speed electronics, spintronics and photodetectors. Obtaining high quality, single crystalline thin films with large size is critical. Here we r
eport the first successful layer-by-layer growth of high quality PtSe2 films by molecular beam epitaxy. Atomically thin films from 1 ML to 22 ML have been grown and characterized by low-energy electron diffraction, Raman spectroscopy and X-ray photoemission spectroscopy. Moreover, a systematic thickness dependent study of the electronic structure is revealed by angle-resolved photoemission spectroscopy (ARPES), and helical spin texture is revealed by spin-ARPES. Our work provides new opportunities for growing large size single crystalline films for investigating the physical properties and potential applications of PtSe2.
Charge-state-resolved ion energy-time-distributions of pulsed Cu arc plasma were obtained by using direct (time dependent) acquisition of the ion detection signal from a commercial ion mass-per-charge and energy-per-charge analyzer. We find a shift o
f energies of Cu2+, Cu3+ and Cu4+ ions to lower values during the first few hundred microseconds after arc ignition, which is evidence for particle collisions in the plasma. The generation of Cu1+ ions in the later part of the pulse, measured by the increase of Cu1+ signal intensity and an associated slight reduction of the mean charge state point to charge exchange reactions between ions and neutrals. At the very beginning of the pulse, when the plasma expands into vacuum and the plasma potential strongly fluctuates, ions with much higher energy (over 200 eV) were observed. Early in the pulse, the ion energies observed are approximately proportional to the ion charge state, and we conclude that the acceleration mechanism is primarily based on acceleration in an electric field. This field is directed away from the cathode, indicative for a potential hump. Measurements by a floating probe suggest that potential structures travel and ions moving in the traveling field can gain high energies up to a few hundred electron-volt. Later in the pulse, the approximate proportionality is lost, which is either related to increased smearing out of different energies due to collisions with neutrals, and/or a change of the acceleration character from electrostatic to gas-dynamic, i.e., dominated by pressure gradient.
