Joint Asymptotics for Estimating the Fractal Indices of Bivariate Gaussian Processes

Multivariate (or vector-valued) processes are important for modeling multiple variables. The fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structures and statistical properties of the multivariate process. In this paper, under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators of bivariate fractal indices. Our main results quantitatively describe the effect of the cross- dependence structure on the performance of the estimators

Augmenting Knowledge Transfer across Graphs

Given a resource-rich source graph and a resource-scarce target graph, how can we effectively transfer knowledge across graphs and ensure a good generalization performance? In many high-impact domains (e.g., brain networks and molecular graphs), collecting and annotating data is prohibitively expensive and time-consuming, which makes domain adaptation an attractive option to alleviate the label scarcity issue. In light of this, the state-of-the-art methods focus on deriving domain-invariant graph representation that minimizes the domain discrepancy. However, it has recently been shown that a small domain discrepancy loss may not always guarantee a good generalization performance, especially in the presence of disparate graph structures and label distribution shifts. In this paper, we present TRANSNET, a generic learning framework for augmenting knowledge transfer across graphs. In particular, we introduce a novel notion named trinity signal that can naturally formulate various graph signals at different granularity (e.g., node attributes, edges, and subgraphs). With that, we further propose a domain unification module together with a trinity-signal mixup scheme to jointly minimize the domain discrepancy and augment the knowledge transfer across graphs. Finally, comprehensive empirical results show that TRANSNET outperforms all existing approaches on seven benchmark datasets by a significant margin

Reliability model of organization management chain of South-to-North Water Diversion Project during construction period

AbstractIn order to analyze the indispensability of the organization management chain of the South-to-North Water Diversion Project (SNWDP), two basic forms (series connection state and mixed state of both series connection and parallel connection) of the organization management chain can be abstracted. The indispensability of each form has been studied and is described in this paper. Through analysis of the reliability of the two basic forms, reliability models of the organization management chain in the series connection state and the mixed state of both series connection and parallel connection have been set up

A Matrix Ensemble Kalman Filter-based Multi-arm Neural Network to Adequately Approximate Deep Neural Networks

Deep Learners (DLs) are the state-of-art predictive mechanism with applications in many fields requiring complex high dimensional data processing. Although conventional DLs get trained via gradient descent with back-propagation, Kalman Filter (KF)-based techniques that do not need gradient computation have been developed to approximate DLs. We propose a multi-arm extension of a KF-based DL approximator that can mimic DL when the sample size is too small to train a multi-arm DL. The proposed Matrix Ensemble Kalman Filter-based multi-arm ANN (MEnKF-ANN) also performs explicit model stacking that becomes relevant when the training sample has an unequal-size feature set. Our proposed technique can approximate Long Short-term Memory (LSTM) Networks and attach uncertainty to the predictions obtained from these LSTMs with desirable coverage. We demonstrate how MEnKF-ANN can "adequately" approximate an LSTM network trained to classify what carbohydrate substrates are digested and utilized by a microbiome sample whose genomic sequences consist of polysaccharide utilization loci (PULs) and their encoded genes.Comment: 18 pages, 6 Figures, and 6 Table

Dynamic Transfer Learning across Graphs

Transferring knowledge across graphs plays a pivotal role in many high-stake domains, ranging from transportation networks to e-commerce networks, from neuroscience to finance. To date, the vast majority of existing works assume both source and target domains are sampled from a universal and stationary distribution. However, many real-world systems are intrinsically dynamic, where the underlying domains are evolving over time. To bridge the gap, we propose to shift the problem to the dynamic setting and ask: given the label-rich source graphs and the label-scarce target graphs observed in previous T timestamps, how can we effectively characterize the evolving domain discrepancy and optimize the generalization performance of the target domain at the incoming T+1 timestamp? To answer the question, for the first time, we propose a generalization bound under the setting of dynamic transfer learning across graphs, which implies the generalization performance is dominated by domain evolution and domain discrepancy between source and target domains. Inspired by the theoretical results, we propose a novel generic framework DyTrans to improve knowledge transferability across dynamic graphs. In particular, we start with a transformer-based temporal encoding module to model temporal information of the evolving domains; then, we further design a dynamic domain unification module to efficiently learn domain-invariant representations across the source and target domains. Finally, extensive experiments on various real-world datasets demonstrate the effectiveness of DyTrans in transferring knowledge from dynamic source domains to dynamic target domains

An image encryption algorithm based on the double time-delay Lorenz system

The traditional image encryption technology has the disadvantages of low encryption efficiency and low security. According to the characteristics of image information, an image encryption algorithm based on double time-delay chaos is proposed by combining the delay chaotic system with traditional encryption technology. Because of the infinite dimension and complex dynamic behavior of the delayed chaotic system, it is difficult to be simulated by AI technology. Furthermore time delay and time delay position have also become elements to be considered in the key space. The proposed encryption algorithm has good quality. The stability and the existence condition of Hopf bifurcation of Lorenz system with double delay at the equilibrium point are studied by nonlinear dynamics theory, and the critical delay value of Hopf bifurcation is obtained. The system intercepts the pseudo-random sequence in chaotic state and encrypts the image by means of scrambling operation and diffusion operation. The algorithm is simulated and analyzed from key space size, key sensitivity, plaintext image sensitivity and plaintext histogram. The results show that the algorithm can produce satisfactory scrambling effect and can effectively encrypt and decrypt images without distortion. Moreover, the scheme is not only robust to statistical attacks, selective plaintext attacks and noise, but also has high stability

Robust Average Formation Tracking for Multi-Agent Systems With Multiple Leaders

In this paper, the formation tracking problem of the multi-agent system under disturbances and unmodeled uncertainties has been studied. An identifier-based robust control algorithm using the neighboring relative information has been proposed to ensure the followers to maintain a given, and time-varying formation and track the average state of the leaders at the same time. Some sufficient conditions for the second-order multi-agent system with multiple leaders in the presence of disturbances and unmodeled uncertainties have been proposed based on the graph theory and the Lyapunov method. Numerical simulations are provided to testify the validity of the algorithm

Strength and size of phosphorus-rich patches determine the foraging strategy of Neyraudia reynaudiana

BackgroundUnder natural conditions, soil nutrients are heterogeneously distributed, and plants have developed adaptation strategies to efficiently forage patchily distributed nutrient. Most previous studies examined either patch strength or patch size separately and focused mainly on root morphological plasticity (increased root proliferation in nutrient-rich patch), thus the effects of both patch strength and size on morphological and physiological plasticity are not well understood. In this study, we examined the foraging strategy of Neyraudia reynaudiana (Kunth) Keng ex Hithc, a pioneer grass colonizing degraded sites, with respect to patch strength and size in heterogeneously distributed phosphorus (P), and how foraging patchily distributed P affects total plant biomass production. Plants were grown in sand-culture pots divided into 1/2, 1/4, 1/6 compartments and full size and supplied with 0+0/30, 0+7.5/30 and 7.5+0/30mg P/kg dry soil as KH2PO4 or 0+15/15, 0+18.5/ 18.5, 7.5+15/15mgkg-1 in the homogenous treatment. The first amount was the P concentration in the central region, and that the second amount was the P concentration in the outer parts of the pot.ResultsAfter 3months of growth under experimental conditions, significantly (p<0.05) high root elongation, root surface area, root volume and average root diameter was observed in large patches with high patch strength. Roots absorbed significantly more P in P-replete than P-deficient patches. Whole plant biomass production was significantly higher in larger patches with high patch strength than small patches and homogeneous P distribution.ConclusionThe result demonstrates that root morphological and physiological plasticity are important adaptive strategies for foraging patchily distributed P and the former is largely determined by patch strength and size. The results also establish that foraging patchily distributed P resulted in increased total plant biomass production compared to homogeneous P distribution