Testing for high-dimensional white noise

Testing for multi-dimensional white noise is an important subject in statistical inference. Such test in the high-dimensional case becomes an open problem waiting to be solved, especially when the dimension of a time series is comparable to or even greater than the sample size. To detect an arbitrary form of departure from high-dimensional white noise, a few tests have been developed. Some of these tests are based on max-type statistics, while others are based on sum-type ones. Despite the progress, an urgent issue awaits to be resolved: none of these tests is robust to the sparsity of the serial correlation structure. Motivated by this, we propose a Fisher's combination test by combining the max-type and the sum-type statistics, based on the established asymptotically independence between them. This combination test can achieve robustness to the sparsity of the serial correlation structure,and combine the advantages of the two types of tests. We demonstrate the advantages of the proposed test over some existing tests through extensive numerical results and an empirical analysis.Comment: 84 page

Fast Network Community Detection with Profile-Pseudo Likelihood Methods

The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks. One prominent work that overcomes this computational challenge is Amini et al.(2013), which proposed a fast pseudo-likelihood approach for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and is not well suited for small- or medium- scale networks. In this article, we propose a novel likelihood based approach that decouples row and column labels in the likelihood function, which enables a fast alternating maximization; the new method is computationally efficient, performs well for both small and large scale networks, and has provable convergence guarantee. We show that our method provides strongly consistent estimates of the communities in a stochastic block model. As demonstrated in simulation studies, the proposed method outperforms the pseudo-likelihood approach in terms of both estimation accuracy and computation efficiency, especially for large sparse networks. We further consider extensions of our proposed method to handle networks with degree heterogeneity and bipartite properties

Almost Tight L0-norm Certified Robustness of Top-k Predictions against Adversarial Perturbations

Top-$k$ predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. $\ell_0$-norm adversarial perturbation characterizes an attack that arbitrarily modifies some features of an input such that a classifier makes an incorrect prediction for the perturbed input. $\ell_0$-norm adversarial perturbation is easy to interpret and can be implemented in the physical world. Therefore, certifying robustness of top-$k$ predictions against $\ell_0$-norm adversarial perturbation is important. However, existing studies either focused on certifying $\ell_0$-norm robustness of top-$1$ predictions or $\ell_2$-norm robustness of top-$k$ predictions. In this work, we aim to bridge the gap. Our approach is based on randomized smoothing, which builds a provably robust classifier from an arbitrary classifier via randomizing an input. Our major theoretical contribution is an almost tight $\ell_0$-norm certified robustness guarantee for top-$k$ predictions. We empirically evaluate our method on CIFAR10 and ImageNet. For instance, our method can build a classifier that achieves a certified top-3 accuracy of 69.2\% on ImageNet when an attacker can arbitrarily perturb 5 pixels of a testing image

The normal-auxeticity mechanical phase transition in graphene

When a solid object is stretched, in general, it shrinks transversely. However, the abnormal ones are auxetic, which exhibit lateral expansion, or negative Poisson ratio. While graphene is a paradigm 2D material, surprisingly, graphene converts from normal to auxetic at certain strains. Here, we show via molecular dynamics simulations that the normal-auxeticity mechanical phase transition only occurs in uniaxial tension along the armchair direction or the nearest neighbor direction. Such a characteristic persists at temperatures up to 2400 K. Besides monolayer, bilayer and multi-layer graphene also possess such a normal-auxeticity transition. This unique property could extend the applications of graphene to new horizons

The DNA–protein interaction modes of FEN-1 with gap substrates and their implication in preventing duplication mutations

Flap endonuclease-1 (FEN-1) is a structure-specific nuclease best known for its involvement in RNA primer removal and long-patch base excision repair. This enzyme is known to possess 5′-flap endo- (FEN) and 5′–3′ exo- (EXO) nuclease activities. Recently, FEN-1 has been reported to also possess a gap endonuclease (GEN) activity, which is possibly involved in apoptotic DNA fragmentation and the resolution of stalled DNA replication forks. In the current study, we compare the kinetics of these activities to shed light on the aspects of DNA structure and FEN-1 DNA-binding elements that affect substrate cleavage. By using DNA binding deficient mutants of FEN-1, we determine that the GEN activity is analogous to FEN activity in that the single-stranded DNA region of DNA substrates interacts with the clamp region of FEN-1. In addition, we show that the C-terminal extension of human FEN-1 likely interacts with the downstream duplex portion of all substrates. Taken together, a substrate-binding model that explains how FEN-1, which has a single active center, can have seemingly different activities is proposed. Furthermore, based on the evidence that GEN activity in complex with WRN protein cleaves hairpin and internal loop substrates, we suggest that the GEN activity may prevent repeat expansions and duplication mutations

Digital photoprogramming of liquid-crystal superstructures featuring intrinsic chiral photoswitches

Dynamic patterning of soft materials in a fully reversible and programmable manner with light enables applications in anti-counterfeiting, displays and labelling technology. However, this is a formidable challenge due to the lack of suitable chiral molecular photoswitches. Here, we report the development of a unique intrinsic chiral photoswitch with broad chirality modulation to achieve digitally controllable, selectable and extractable multiple stable reflection states. An anti-counterfeiting technique, embedded with diverse microstructures, featuring colour-tunability, erasability, reversibility, multi-stability and viewing-angle dependency of pre-recorded patterns, is established with these photoresponsive superstructures. This strategy allows dynamic helical transformation from the molecular and supramolecular to the macroscopic level using light-activated intrinsic chirality, demonstrating the practicality of photoprogramming photonics