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We study the dynamics of ow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on ow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the ow may become uniform and homogenized or become unstable and develop channels. By de ning an order parameter capturing these di erent behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our results. 

We propose a new algorithmic framework for traffic-optimal virtual network function (VNF) placement and migration for policy-preserving data centers (PPDCs). As dy- namic virtual machine (VM) traffic must traverse a sequence of VNFs in PPDCs, it generates more network traffic, consumes higher bandwidth, and causes additional traffic delays than a traditional data center. We design optimal, approximation, and heuristic traffic-aware VNF placement and migration algorithms to minimize the total network traffic in the PPDC. In particular, we propose the first traffic-aware constant-factor approximation algorithm for VNF placement, a Pareto-optimal solution for VNF migration, and a suite of efficient dynamic-programming (DP)-based heuristics that further improves the approximation solution. At the core of our framework are two new graph- theoretical problems that have not been studied. Using flow characteristics found in production data centers and realistic traffic patterns, we show that a) our VNF migration techniques are effective in mitigating dynamic traffic in PPDCs, reducing the total traffic cost by up to 73%, b) our VNF placement algorithms yield traffic costs 56% to 64% smaller than those by existing techniques, and c) our VNF migration algorithms outperform the state-of-the-art VM migration algorithms by up to 63% in reducing dynamic network traffic. 

Deep neural networks (DNNs) have became one of the most high performing tools in a broad rangeof machine learning areas. However, the multilayer non-linearity of the network architectures preventus from gaining a better understanding of the models’ predictions. Gradient based attributionmethods (e.g., Integrated Gradient (IG)) that decipher input features’ contribution to the predictiontask have been shown to be highly effective yet requiring a reference input as the anchor for explainingmodel’s output. The performance of DNN model interpretation can be quite inconsistent withregard to the choice of references. Here we propose an Adversarial Gradient Integration (AGI) methodthat integrates the gradients from adversarial examples to the target example along the curve of steepestascent to calculate the resulting contributions from all input features. Our method doesn’t rely onthe choice of references, hence can avoid the ambiguity and inconsistency sourced from the referenceselection. We demonstrate the performance of our AGI method and compare with competing methodsin explaining image classification results. Code is available from https://github.com/pd90506/AGI.

 

Granular packings display the remarkable phenomenon of dilatancy, wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, also being the related phenomenon of shear-induced jamming, requires frictional interactions. Here, we show that the occurrence of isotropic jamming densities ϕ j above the minimal density (or the J-point density) ϕ J leads both to the emergence of shear-induced jamming and dilatancy in frictionless packings. Under constant pressure shear, the system evolves into a steady-state at sufficiently large strains, whose density only depends on the pressure and is insensitive to the initial jamming density ϕ j . In the limit of vanishing pressure, the steady-state exhibits critical behavior at ϕ J . While packings with different ϕ j values display equivalent scaling properties under compression, they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when ϕ j > ϕ J , contrary to the continuous behaviour in generic packings that jam at ϕ J . Our results thus lead to a more coherent, generalised picture of jamming in frictionless packings, which also have important implications on how dilatancy is understood in the context of frictional granular matter. 

Convolutional neural networks (CNNs) have achieved state-of- the-art performance on various tasks in computer vision. However, recent studies demonstrate that these models are vulnerable to carefully crafted adversarial samples and suffer from a significant performance drop when predicting them. Many methods have been proposed to improve adversarial robustness (e.g., adversarial training and new loss functions to learn adversarially robust feature representations). Here we offer a unique insight into the predictive behavior of CNNs that they tend to misclassify adversarial samples into the most probable false classes. This inspires us to propose a new Probabilistically Compact (PC) loss with logit constraints which can be used as a drop-in replacement for cross-entropy (CE) loss to improve CNN’s adversarial robustness. Specifically, PC loss enlarges the probability gaps between true class and false classes meanwhile the logit constraints prevent the gaps from being melted by a small perturbation. We extensively compare our method with the state-of-the-art using large scale datasets under both white-box and black-box attacks to demonstrate its effectiveness. The source codes are available at https://github.com/xinli0928/PC-LC. 

Deep convolutional neural networks (CNNs) trained with logistic and softmax losses have made significant advancement in visual recognition tasks in computer vision. When training data exhibit class imbalances, the class-wise reweighted version of logistic and softmax losses are often used to boost performance of the unweighted version. In this paper, motivated to explain the reweighting mechanism, we explicate the learning property of those two loss functions by analyzing the necessary condition (e.g., gradient equals to zero) after training CNNs to converge to a local minimum. The analysis immediately provides us explanations for understanding (1) quantitative effects of the class-wise reweighting mechanism: deterministic effectiveness for binary classification using logistic loss yet indeterministic for multi-class classification using softmax loss; (2) disadvantage of logistic loss for single-label multi-class classification via one-vs.-all approach, which is due to the averaging effect on predicted probabilities for the negative class (e.g., non-target classes) in the learning process. With the disadvantage and advantage of logistic loss disentangled, we thereafter propose a novel reweighted logistic loss for multi-class classification. Our simple yet effective formulation improves ordinary logistic loss by focusing on learning hard non-target classes (target vs. non-target class in one-vs.-all) and turned out to be competitive with softmax loss. We evaluate our method on several benchmark datasets to demonstrate its effectiveness.