AutoEncoder Inspired Unsupervised Feature Selection

High-dimensional data in many areas such as computer vision and machine learning tasks brings in computational and analytical difficulty. Feature selection which selects a subset from observed features is a widely used approach for improving performance and effectiveness of machine learning models with high-dimensional data. In this paper, we propose a novel AutoEncoder Feature Selector (AEFS) for unsupervised feature selection which combines autoencoder regression and group lasso tasks. Compared to traditional feature selection methods, AEFS can select the most important features by excavating both linear and nonlinear information among features, which is more flexible than the conventional self-representation method for unsupervised feature selection with only linear assumptions. Experimental results on benchmark dataset show that the proposed method is superior to the state-of-the-art method.Comment: accepted by ICASSP 201

Risk-informed Resilience Planning of Transmission Systems Against Ice Storms

Ice storms, known for their severity and predictability, necessitate proactive resilience enhancement in power systems. Traditional approaches often overlook the endogenous uncertainties inherent in human decisions and underutilize predictive information like forecast accuracy and preparation time. To bridge these gaps, we proposed a two-stage risk-informed decision-dependent resilience planning (RIDDRP) for transmission systems against ice storms. The model leverages predictive information to optimize resource allocation, considering decision-dependent line failure uncertainties introduced by planning decisions and exogenous ice storm-related uncertainties. We adopt a dual-objective approach to balance economic efficiency and system resilience across both normal and emergent conditions. The first stage of the RDDIP model makes line hardening decisions, as well as the optimal sitting and sizing of energy storage. The second stage evaluates the risk-informed operation costs, considering both pre-event preparation and emergency operations. Case studies demonstrate the model's ability to leverage predictive information, leading to more judicious investment decisions and optimized utilization of dispatchable resources. We also quantified the impact of different properties of predictive information on resilience enhancement. The RIDDRP model provides grid operators and planners valuable insights for making risk-informed infrastructure investments and operational strategy decisions, thereby improving preparedness and response to future extreme weather events

Cohomologies, extensions and deformations of differential algebras with any weights

As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie algebra contexts and to the case when the operator identity has a weight in order to include difference operators and difference algebras. This paper provides a cohomology theory for differential algebras of any weights. This gives a uniform approach to both the zero weight case which is similar to the earlier study of differential Lie algebras, and the non-zero weight case which poses new challenges. As applications, abelian extensions of a differential algebra are classified by the second cohomology group. Furthermore, formal deformations of differential algebras are obtained and the rigidity of a differential algebra is characterized by the vanishing of the second cohomology group.Comment: 21 page

Degradation of Cry1Ac Protein Within Transgenic Bacillus thuringiensis Rice Tissues Under Field and Laboratory Conditions

To clarify the environmental fate of the Cry1Ac protein from Bacillus thuringiensis subsp. kurstaki (Bt) contained in transgenic rice plant stubble after harvest, degradation was monitored under field conditions using an enzyme-linked immunosorbent assay. In stalks, Cry1Ac protein concentration decreased rapidly to 50% of the initial amount during the first month after harvest; subsequently, the degradation decreased gradually reaching 21.3% when the experiment was terminated after 7 mo. A similar degradation pattern of the Cry1Ac protein was observed in rice roots. However, when the temperature increased in April of the following spring, protein degradation resumed, and no protein could be detected by the end of the experiment. In addition, a laboratory experiment was conducted to study the persistence of Cry1Ac protein released from rice tissue in water and paddy soil. The protein released from leaves degraded rapidly in paddy soil under flooded conditions during the first 20 d and plateaued until the termination of this trial at 135 d, when 15.3% of the initial amount was still detectable. In water, the Cry1Ac protein degraded more slowly than in soil but never entered a relatively stable phase as in soil. The degradation rate of Cry1Ac protein was significantly faster in nonsterile water than in sterile water. These results indicate that the soil environment can increase the degradation of Bt protein contained in plant residues. Therefore, plowing a field immediately after harvest could be an effective method for decreasing the persistence of Bt protein in transgenic rice field

Homotopy Rota-Baxter operators, homotopy O\mathcal{O}-operators and homotopy post-Lie algebras

Rota-Baxter operators, $\mathcal{O}$-operators on Lie algebras and their interconnected pre-Lie and post-Lie algebras are important algebraic structures with applications in mathematical physics. This paper introduces the notions of a homotopy Rota-Baxter operator and a homotopy $\mathcal{O}$-operator on a symmetric graded Lie algebra. Their characterization by Maurer-Cartan elements of suitable differential graded Lie algebras is provided. Through the action of a homotopy $\mathcal{O}$-operator on a symmetric graded Lie algebra, we arrive at the notion of an operator homotopy post-Lie algebra, together with its characterization in terms of Maurer-Cartan elements. A cohomology theory of post-Lie algebras is established, with an application to 2-term skeletal operator homotopy post-Lie algebras.Comment: 29 page

Adversarially Robust Neural Architectures

Deep Neural Network (DNN) are vulnerable to adversarial attack. Existing methods are devoted to developing various robust training strategies or regularizations to update the weights of the neural network. But beyond the weights, the overall structure and information flow in the network are explicitly determined by the neural architecture, which remains unexplored. This paper thus aims to improve the adversarial robustness of the network from the architecture perspective with NAS framework. We explore the relationship among adversarial robustness, Lipschitz constant, and architecture parameters and show that an appropriate constraint on architecture parameters could reduce the Lipschitz constant to further improve the robustness. For NAS framework, all the architecture parameters are equally treated when the discrete architecture is sampled from supernet. However, the importance of architecture parameters could vary from operation to operation or connection to connection, which is not explored and might reduce the confidence of robust architecture sampling. Thus, we propose to sample architecture parameters from trainable multivariate log-normal distributions, with which the Lipschitz constant of entire network can be approximated using a univariate log-normal distribution with mean and variance related to architecture parameters. Compared with adversarially trained neural architectures searched by various NAS algorithms as well as efficient human-designed models, our algorithm empirically achieves the best performance among all the models under various attacks on different datasets.Comment: 9 pages, 3 figures, 5 table