Theoretical Results Research Articles

A Theoretical View of Linear Backpropagation and its Convergence.

Backpropagation (BP) is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, BP is considered as a de-facto choice in a variety of machine learning tasks including DNN training and adversarial attack/defense. Recently, a linear variant of BP named LinBP was introduced for generating more transferable adversarial examples for performing black-box attacks, by (Guo et al. 2020). Although it has been shown empirically effective in black-box attacks, theoretical studies and convergence analyses of such a method is lacking. This paper serves as a complement and somewhat an extension to Guo et al. (2020) paper, by providing theoretical analyses on LinBP in neural-network-involved learning tasks, including adversarial attack and model training. We demonstrate that, somewhat surprisingly, LinBP can lead to faster convergence in these tasks in the same hyper-parameter settings, compared to BP. We confirm our theoretical results with extensive experiments.

An α-robust error analysis of the [formula omitted] scheme for time-fractional integro-differential initial-boundary value problems

An initial-boundary value problem governed by the time-fractional integro-differential equation Dtαu−κItβΔu−λΔu=f is considered, where (x,t)∈Ω×(0,T]; here Dtα is a Caputo temporal derivative of order α∈(0,1), Itβ is a Riemann-Liouville temporal integral of order β∈(0,1), and Ω is a rectangular-type domain in Rd for some d≥1. The positive constants κ and λ and the function f are given data. A numerical scheme is constructed by employing the L1‾ scheme for the Caputo derivative, an averaged product integration rule for the Riemann-Liouville integral, and a standard discretisation (3 points in each coordinate direction) of Δu. The scheme satisfies a discrete comparison principle, which is used to establish an error bound for the computed solution that is O(N−2) in time on graded temporal meshes with N points. This result is α-robust: it does not blow up as α→1−. Numerical results show the sharpness of our theoretical results.

Growing Like a Tree: Finding Trunks From Graph Skeleton Trees.

The message-passing paradigm has served as the foundation of graph neural networks (GNNs) for years, making them achieve great success in a wide range of applications. Despite its elegance, this paradigm presents several unexpected challenges for graph-level tasks, such as the long-range problem, information bottleneck, over-squashing phenomenon, and limited expressivity. In this study, we aim to overcome these major challenges and break the conventional "node- and edge-centric" mindset in graph-level tasks. To this end, we provide an in-depth theoretical analysis of the causes of the information bottleneck from the perspective of information influence. Building on the theoretical results, we offer unique insights to break this bottleneck and suggest extracting a skeleton tree from the original graph, followed by propagating information in a distinctive manner on this tree. Drawing inspiration from natural trees, we further propose to find trunks from graph skeleton trees to create powerful graph representations and develop the corresponding framework for graph-level tasks. Extensive experiments on multiple real-world datasets demonstrate the superiority of our model. Comprehensive experimental analyses further highlight its capability of capturing long-range dependencies and alleviating the over-squashing problem, thereby providing novel insights into graph-level tasks.

State estimation for linear discrete-time systems with binary-valued quantized innovations against data tampering attacks

In today’s information era, cyber–physical systems (CPS) have been widely used in many industrial and infrastructure fields, and the study of security problems of CPS has become a crucial issue. For linear discrete-time systems, this paper investigates the state estimation problem based on the quantized innovations and transmission data tampering scenarios. From the attacker’s view, by designing the tampering matrix and combining the property of the error function, the optimal attack strategy in the sense of maximizing the prediction error covariance matrix is given. From the defender’s view, the optimal defense scheme based on multiplicative compensation is given in the case of a known attack strategy. Moreover, in the case of unknown attack strategies, a joint estimation algorithm is designed to give the optimal defense scheme subject to error constraints. In this paper, state estimators in recursive form are given for all above cases, and the algorithms are proved to be consistent. The theoretical results obtained are verified by simulations.

Influence of incident angle on spalling damage of underground tunnels subjected to explosion waves

Tensile waves formed by the reflection of explosive stress waves at the free surface of a tunnel can lead to the destruction of the surrounding rock in the form of spalling. The incident angle of stress waves is an important factor affecting the characteristics of spalling. Theoretical calculations were conducted on the spalling thickness, spalling range, ejection velocity of rock fragments, and the furthest spalling distance in cases of normal incidence and oblique incidence, respectively. The variations of the spalling with the incident angle along the axial direction of the tunnel are presented. The results show that when the Poisson’s ratio of the medium is less than 0.26, the reflected longitudinal wave transforms from a tensile wave to a compressive wave within a certain range of the incident angle. As the incident angle increases, the thickness of the first spalling layer increases monotonically, while the total spalling thickness decreases monotonically. The critical condition of spalling is reached when the first spalling thickness equals the total spalling thickness. For an explosion 6 m away from the tunnel, the critical spalling distance obtained by oblique incidence is 1.67 m/kg1/3, and the peak particle velocity is 3.11 m/s. The critical spalling distance obtained by normal incidence is 5.64 m/kg1/3, and the peak particle velocity is 0.42 m/s. The theoretical results agree well with the on-site experimental data, indicating that the results of oblique incidence overestimated the critical peak particle velocity for spalling.

Knockoffs-SPR: Clean Sample Selection in Learning With Noisy Labels.

A noisy training set usually leads to the degradation of the generalization and robustness of neural networks. In this article, we propose a novel theoretically guaranteed clean sample selection framework for learning with noisy labels. Specifically, we first present a Scalable Penalized Regression (SPR) method, to model the linear relation between network features and one-hot labels. In SPR, the clean data are identified by the zero mean-shift parameters solved in the regression model. We theoretically show that SPR can recover clean data under some conditions. Under general scenarios, the conditions may be no longer satisfied; and some noisy data are falsely selected as clean data. To solve this problem, we propose a data-adaptive method for Scalable Penalized Regression with Knockoff filters (Knockoffs-SPR), which is provable to control the False-Selection-Rate (FSR) in the selected clean data. To improve the efficiency, we further present a split algorithm that divides the whole training set into small pieces that can be solved in parallel to make the framework scalable to large datasets. While Knockoffs-SPR can be regarded as a sample selection module for a standard supervised training pipeline, we further combine it with a semi-supervised algorithm to exploit the support of noisy data as unlabeled data. Experimental results on several benchmark datasets and real-world noisy datasets show the effectiveness of our framework and validate the theoretical results of Knockoffs-SPR.

Experimental and theoretical study of the Favipiravir association in water solvent

Favipiravir, also known as T-705, is an antiviral prodrug that was first developed against the influenza virus and was later found to be effective against other RNA viruses, including arenaviruses, bunyaviruses, Zika, Ebola, Lassa, and COVID-19 viruses, in addition to influenza A and B. Due to the global prevalence of SARS-COV-2 in 2019, Favipiravir was used as an antiviral drug for treating COVID-19, but the challenges facing it, including its solubility, tablet ability, and bioavailability, remain. It is critical and challenging to develop a drug with appropriate bioavailability, improved oral absorption, and increased solubility without interfering with other functions and preventing the consumption of high daily doses. For this purpose, in the present study, the interactions of Favipiravir-Favipiravir and Favipiravir-H2O and the association of the Favipiravir molecules were investigated experimentally and theoretically. The theoretical results showed that under normal conditions, all structures were stable, but the most stable structure based on calculations of electronic energy, Gibbs, and solvation Gibbs free energies (minimum value), both in the gas phase and in the aqueous phase, is related to the B-enol isomer. Also, the change in dipole moment in the solvation process for this isomer was less than others. Also, the intense intermolecular hydrogen bonds O-H…O and N-H…O between the Favipiravir and water molecules showed that Favipiravir…Favipiravir interactions are stronger than Favipiravir…H2O interactions in aqueous solutions. These interactions indicate that Favipiravir can participate in the aggregation phenomena in high concentrations. Also, Stokeʼs shift values slightly increased with the decreasing the drug concentration in water (intramolecular charge transfer phenomenon).

Deep Electron Redistributions Induced by Dual Junctions Facilitating Electroreduction of Dilute Nitrate to Ammonia.

The electronic states of metal catalysts can be redistributed by the rectifying contact between metal and semiconductor e.g., N-doped carbon (NC), while the interfacial regulation degree is very limited. Herein, a deep electronic state regulation is achieved by constructing a novel double-heterojunctional Co/Co3O4@NC catalyst containing Co/Co3O4 and Co3O4/NC heterojunctions. When used for dilute electrochemical NO3 - reduction reaction (NO3RR), the as-prepared Co/Co3O4@NC exhibits an outstanding Faradaic efficiency for NH3 formation (FENH3) of 97.9%, -0.4V versus RHE and significant NH3 yield of 303.5mmol h-1 gcat -1 at -0.6V at extremely low nitrate concentrations (100ppm NO3 --N). Experimental and theoretical results reveal that the dual junctions of Co/Co3O4 and Co3O4/NC drive a unidirectional electron transfer from Co to NC (Co→Co3O4→NC), resulting in electron-deficient Co atoms. The electron-deficient Co promotes NO3 - adsorption, the rate-determining step (RDS) for NO3RR, facilitating the dilute NO3RR to NH3. The design strategy provides a novel reference for unidirectional multistage regulation of metal electronic states boosting electrochemical dilute NO3RR, which opens up an avenue for deep electronic state regulation of electrocatalyst breaking the limitation of the electronic regulation degree by rectifying contact.

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system’s Hopf bifurcation. The results indicate that adjusting the control intensity or the control target’s age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems.

A simultaneous measurement method for multi-directional galloping of iced bundled conductors and its application in spatial galloping behavior

Abstract The theoretical results indicate that iced bundled conductors experience spatial gallop-ing due to wind-induced vibration, involving in-plane, out-of-plane, and torsional movements. To better understand the dynamic response of this behavior from an exper-imental perspective, an innovative experimental method has been proposed. The method can simultaneously measure the in-plane, out-of-plane, and torsional vibration signals of iced bundled conductors’ galloping. A testing system was established, and the method is applied in the galloping experiment of continuous iced bundled conductors, validating some theoretical results. This paper describes the construction of a wide-aperture, low-speed wind tunnel suitable for testing the galloping of continuous iced bundled conduc-tors. A “cut-bury-glue” method was proposed to create a model of continuous iced bun-dled conductors effectively, along with a method for connecting subconductors to im-prove experimental precision. The tests utilized laser displacement sensors and wireless posture sensors, considering the installation and data collection characteristics of the sensors. Through signal conversion, error correction, and other technical methods, sim-ultaneous measurement of in-plane, out-of-plane, and torsional vibration signals was achieved. The spatial galloping behavior, changing with wind speed, exhibits limited-amplitude and synchronous characteristics. The participation of different modes shows elliptical orbital motion in single-mode galloping and “8” shaped orbital motion in cou-pled-mode galloping. These results are consistent with previous theoretical research, offering a new approach to studying iced bundled conductors’ galloping.

Mind the Exit Pupil Gap: Revisiting the Intrinsics of a Standard Plenoptic Camera

Among the common applications of plenoptic cameras are depth reconstruction and post-shot refocusing. These require a calibration relating the camera-side light field to that of the scene. Numerous methods with this goal have been developed based on thin lens models for the plenoptic camera’s main lens and microlenses. Our work addresses the often-overlooked role of the main lens exit pupil in these models, specifically in the decoding process of standard plenoptic camera (SPC) images. We formally deduce the connection between the refocusing distance and the resampling parameter for the decoded light field and provide an analysis of the errors that arise when the exit pupil is not considered. In addition, previous work is revisited with respect to the exit pupil’s role, and all theoretical results are validated through a ray tracing-based simulation. With the public release of the evaluated SPC designs alongside our simulation and experimental data, we aim to contribute to a more accurate and nuanced understanding of plenoptic camera optics.

Interval parity relations design for fault diagnosis

SummaryThe problem of interval parity relations design for systems described by linear and nonlinear models under the external disturbances is considered. The problem is solved based on the reduced‐order model of the original system. The relations allowing designing interval parity relations insensitive or having minimal sensitivity to the disturbances are obtained. The obtained interval parity relations are used to solve the problem of fault diagnosis. Theoretical results are illustrated by example.

Defect-Induced All-Solid-State Frustrated Lewis Pair on Metal-Organic Monolayer Accelerating Photocatalytic CO2 Reduction with H2O Vapor.

Understanding the structure-performance relationships of a frustrated Lewis pair (FLP) at the atomic level is key to yielding high efficiency in activating chemically "inert" molecules into value-added products. A sound strategy was developed herein through incorporating oxygen defects into a Zr-based metal-organic layer (Zr-MOL-D) and employing Lewis basic proximal surface hydroxyls for the in situ formation of solid heterogeneous FLP (Zr4-δ-VO-Zr-OH). Zr-MOL-D exhibits a superior CO2 to CO conversion rate of 49.4 μmol g-1 h-1 in water vapor without any sacrificing agent or photosensitizer, which is about 12 times higher than that of pure MOL (Zr-MOL-P), with extreme stability even after being placed for half a year. Theoretical and experimental results reveal that the introduction of FLP converts the process of the crucial intermediate COOH* from an endothermic reaction to an exothermic spontaneous reaction. This work is expected to provide new prospects for developing efficient MOL-based photocatalysts in FLP chemistry through a sound defect-engineering strategy.

Modeling Studies of the Mechanism of Context-Dependent Bidirectional Movements of Kinesin-14 Motors

Kinesin-14s, a subfamily of the large superfamily of kinesin motor proteins, function mainly in spindle assembly and maintenance during mitosis and meiosis. KlpA from Aspergillus nidulans and GiKIN14a from Giardia intestinalis are two types of kinesin-14s. Available experimental results puzzlingly showed that while KlpA moves preferentially toward the minus end in microtubule-gliding setups and inside parallel microtubule overlaps, it moves preferentially toward the plus end on single microtubules. More puzzlingly, the insertion of an extra polypeptide linker in the central region of the neck stalk switches the motility direction of KlpA on single microtubules to the minus end. Prior experimental results showed that GiKIN14a moves preferentially toward the minus end on single microtubules in either tailless or full-length forms. The tail not only greatly enhances the processivity but also accelerates the ATPase rate and velocity of GiKIN14a. The insertion of an extra polypeptide linker in the central region of the neck stalk reduces the ATPase rate of GiKIN14a. However, the underlying mechanism of these puzzling dynamical features for KlpA and GiKIN14a is unclear. Here, to understand this mechanism, the dynamics of KlpA and GiKIN14a were studied theoretically on the basis of the proposed model, incorporating potential changes between the kinesin head and microtubule, as well as the potential between the tail and microtubule. The theoretical results quantitatively explain the available experimental results and provide predicted results. It was found that the elasticity of the neck stalk determines the directionality of KlpA on single microtubules and affects the ATPase rate and velocity of GiKIN14a on single microtubules.

Anti-plane waves in a liquid-loaded piezo-flexo-electric layered model with interface energy

The basic design of a Love wave (LW) bio-sensor contains the loading of a viscoelastic liquid on top of a layered structure with distinct viscoelastic properties. Changes in the characteristics of the propagating acoustic wave caused by biochemical interactions at the sensing area can be detected at the output Inter digital transducer (IDT). The propagation of the anti-plane (AP) wave is discussed in this work in a layered structure of piezo-flexo-electric (PFE) layer bonded with a PFE half-space having a soft reinforced layer at the interface. The free surface of the PFE layer is loaded with viscous liquid. The viscosity of the loaded liquid introduces losses and results in the damping of the wave. For the formulation of the problem with interface energy, the Gurtin–Murdoch approach is used. Using suitable conditions, a dispersion relation for propagating waves is derived in complex form. On separating the dispersion relation in real and non-real parts, the expressions relating the phase and damp velocities with wave number are derived. The obtained theoretical results are portrayed for the numerical data of PFE materials and distinct data of the interface layer. The obtained results are validated with pre-existing literature.

Alveoli-Inspired Carbon Cathodes with Interconnected Porous Structure and Asymmetric Coordinated Vanadium Sites for Superior Li-S Batteries.

Accelerating sulfur conversion catalysis to alleviate the shuttle effect has become a novel paradigm for effective Li-S batteries. Although nitrogen-coordinated metal single-atom (M-N4) catalysts have been investigated, further optimizing its utilization rate and catalytic activities is urgently needed for practical applications. Inspired by the natural alveoli tissue with interconnected structure and well-distributed enzyme catalytic sites on the wall for the simultaneously fast diffusion and in-situ catalytic conversion of substrates, here, we proposed the controllable synthesis of bioinspired carbon cathode with interconnected porous structure and asymmetric coordinated V-S1N3 sites for efficient and stable Li-S batteries. The enzyme-mimetic V-S1N3 shows asymmetric electronic distribution and high tunability, therefore enhancing in-situ polysulfide conversion activities. Experimental and theoretical results reveal that the high charge asymmetry degree and large atom radius of S in V-S1N3 result in sloping adsorption for polysulfide, thereby exhibiting low thermodynamic energy barriers and long-range stability (0.076% decay over 600 cycles).

Dynamics of HIV-1 and HTLV-1 Coinfection with both CTL and Antibody Responses

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type 1 (HTLV-1) coinfection models with simply an antibody response or a CTL response have been the subject of several recent investigations. Thus, the primary objective of this paper is to formulate and examine a mathematical framework for analyzing the intricate dynamics of coinfection between HIV-1 and HTLV-1. The model takes into account the role of antibody response against free HIV-1 particles and CTL response against HTLV-1-infected cells. We prove that the model is well-posed and it admits eight equilibria. The stability and existence of the equilibria are precisely controlled by eight threshold parameters ℜi, i = 1, 2, ..., 8. By formulating suitable Lyapunov functions and applying LaSalle's invariance principle, we show the global asymptotic stability for all equilibria. To demonstrate the theoretical results, we conduct numerical simulations. We look at how the antibody and CTL responses affect the dynamical behavior of HIV-1/HTLV-1 coinfection. Although the parameters of antibody and CTL responses have no effect on the basic reproduction ratio of HIV-1 single-infection (ℜ₁) and HTLV-1 single-infection (ℜ₂), it has been demonstrated that viral coinfection can be inhibited by immunological activation of antibody and CTL responses. This could potentially facilitate the advancement of therapeutic approaches for HIV-1 and HTLV-1, which have the capability to enhance the HIV-1-specific antibody and HTLV-1-specific CTL reactions.

A Data Sharing Model for Blockchain Trusted Sensor Leveraging Mimic Hash Mechanism

Blockchain, as a distributed trust database, has been widely applied in the field of trustworthy sharing of Internet of Things (IoT) sensor data. A single hash mechanism has achieved, to some extent, the trustworthy on-chain storage of blockchain sensor data, that is, the consistency of data on and off the chain. However, it still faces potential security risks such as collision attacks, short password attacks, and rainbow table attacks. To address this issue, this paper proposes a resiliently secure blockchain sensor data trustworthy sharing model based on a mimic hash mechanism. Specifically, in response to the security risks that may arise from the single hash mechanism, this study innovatively introduces a mimic hash mechanism and proposes two methods for constructing mimic hashes based on Verifiable Random Function (VRF) and Cyber Mimic Defense (CMD) in dedicated Wireless Sensor Networks (WSNs) and open public networks, respectively. Theoretical analysis and experimental results demonstrate that this model effectively solves the problem of trustworthy on-chain storage of sensor data in edge computing environments, enhancing the trustworthiness and security of the data on the chain.

Achieving Highly Stable Zn Metal Anodes at Low Temperature via Regulating Electrolyte Solvation Structure.

Zinc metal is an attractive anode material for rechargeable aqueous Zn-ion batteries (ZIBs). However, the dendrite growth, water-induced parasitic reactions and freezing problem of aqueous electrolyte at low temperatures are the major roadblocks that hinder the widely commercialization of ZIBs with Zn anodes. Herein, tetrahydrofuran (THF) is proposed as the electrolyte additive to improve the reversibility and stability of Zn anode. Theoretical calculation and experimental results reveal that the introduction of THF into the aqueous electrolyte can optimize the solvation structure and preferentially form solvated clusters with Zn2+, which can effectively alleviate the H2O-induced side reactions and protect Zn anode from being corrosion. While, THF molecules have stronger affinity for Zn2+ compared to H2O, which can greatly enhance the reversibility of Zn plating/stripping and suppress the formation of Zn dendrite. Moreover, THF can act as hydrogen bond acceptor to interact with H2O, which can greatly reduce the activity of free H2O in electrolyte and improve the low-temperature electrochemical performance of Zn anode. As a result, the Zn anodes demonstrate a high cyclic stability for 2800h at 27°C and over 4000h at -10°C at 1mA cm-2 with an areal capacity of 1 mAh cm-2. The full cell with NaV3O8∙1.5H2O cathode and Zn anode exhibits an excellent cyclic stability and rate capability at 27 and -10°C. This work is expected to provide a new approach to regulate the aqueous electrolyte and Zn anode interface chemistry for highly stable and reversible Zn anodes. This article is protected by copyright. All rights reserved.

Observer‐based distributed dynamic event‐triggered control of multi‐agent systems with adjustable interevent time

AbstractIn this paper, a novel dynamic event‐triggered control protocol for leader‐following problems of generic linear multi‐agent systems is proposed. Compared with the existing static event‐triggered strategy, the developed event‐triggered approach significantly reduces the utilization of communication resources while guaranteeing asymptotic consensus, and the interevent time is adjustable. Under this event scheduling mechanism, a synthesis approach combining controller and observer design is presented. The observer‐based control and event‐triggered rules are distributed, which only require local information of each agent to implement. The proposed methods incorporate model‐based estimation and auxiliary dynamic variables with a clock‐like behavior to prolong the interevent time as long as possible. The sufficient conditions for leader‐following consensus are established using linear matrix inequalities (LMIs) formulation to facilitate numerical computation. Comparative simulations in different scenarios demonstrate the validity of the proposed theoretical results.