On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations

In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler's equations (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data.Comment: A paragraph at the end of Section 2 and an appendix discussing kinetic energy conservation are adde

Gradient descent for sparse rank-one matrix completion for crowd-sourced aggregation of sparsely interacting workers

We consider worker skill estimation for the singlecoin Dawid-Skene crowdsourcing model. In practice skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary, and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completion problem, where the observed components correspond to observed label correlation between workers. We show that the correlation matrix can be successfully recovered and skills identifiable if and only if the sampling matrix (observed components) is irreducible and aperiodic. We then propose an efficient gradient descent scheme and show that skill estimates converges to the desired global optima for such sampling matrices. Our proof is original and the results are surprising in light of the fact that even the weighted rank-one matrix factorization problem is NP hard in general. Next we derive sample complexity bounds for the noisy case in terms of spectral properties of the signless Laplacian of the sampling matrix. Our proposed scheme achieves state-of-art performance on a number of real-world datasets.Published versio

User-Behavior Based Detection of Infection Onset

A major vector of computer infection is through exploiting software or design flaws in networked applications such as the browser. Malicious code can be fetched and executed on a victim’s machine without the user’s permission, as in drive-by download (DBD) attacks. In this paper, we describe a new tool called DeWare for detecting the onset of infection delivered through vulnerable applications. DeWare explores and enforces causal relationships between computer-related human behaviors and system properties, such as file-system access and process execution. Our tool can be used to provide real time protection of a personal computer, as well as for diagnosing and evaluating untrusted websites for forensic purposes. Besides the concrete DBD detection solution, we also formally define causal relationships between user actions and system events on a host. Identifying and enforcing correct causal relationships have important applications in realizing advanced and secure operating systems. We perform extensive experimental evaluation, including a user study with 21 participants, thousands of legitimate websites (for testing false alarms), as well as 84 malicious websites in the wild. Our results show that DeWare is able to correctly distinguish legitimate download events from unauthorized system events with a low false positive rate (< 1%)

Simple and effective data augmentation for compositional generalization

Compositional generalization, the ability to predict complex meanings from training on simpler sentences, poses challenges for powerful pretrained seq2seq models. In this paper, we show that data augmentation methods that sample MRs and backtranslate them can be effective for compositional generalization, but only if we sample from the right distribution. Remarkably, sampling from a uniform distribution performs almost as well as sampling from the test distribution, and greatly outperforms earlier methods that sampled from the training distribution. We further conduct experiments to investigate the reason why this happens and where the benefit of such data augmentation methods come from