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This article justifies a historically grounded method for reading Romantic aesthetics in mathematical terms, and argues that the application of this method: 1) helps us to reread Romantic texts that both do and do not address infinity explicitly, beginning with theories of the sublime; 2) helps to clarify certain aspects of the Romantic inheritance in later modern poetry; and 3) allows us to ground critical treatments of poetry and mathematics in an early nineteenth-century moment at which aesthetics and poetics participate in mathematical debates. The article identifies a century-long "crisis of infinity" during which the concept of infinity lacked a stable mathematical definition and, for that reason among others, generated heated discussion within the discourses of religion, philosophy, mathematics, and aesthetics. In this context, the article excavates models of infinity animating key intellectual resources for Romantic and Victorian poetry and then uses these models to illuminate famously enigmatic moments in the canonical poetries of both periods, taking William Wordsworth and Robert Browning as key examples.

We develop a model for contagion risks and optimal security investment in a directed network of interconnected agents with heterogeneous degrees, loss functions and security profiles. Our model generalizes much of contagion models in the literature; in particular the independent cascade model and the linear threshold model. We state various limit theorems on the final size of infected agents in the case of random networks with given vertex degrees for finite and infinite variance degree distributions. The results allow us to derive a resilience condition of the network to the infection of a large group of agents and quantify how contagion amplifies small shocks to the network. We show that when the degree distribution has infinite variance and, highly correlated in- and out-degrees, then even when agents have high thresholds, a sub-linear fraction of initially infected agents is enough to trigger the infection of a positive fraction. We also show how these results are sensitive to vertex and edge percolation (immunization). We then study the asymptotic Nash equilibrium and socially optimal security investment. In the asymptotic limit, agents' risk depends on all other agents' investment through an aggregate quantity, that we call network vulnerability. The limit theorems allow us to capture the impact of one class of agents' decision on the overall network vulnerability. Based on our results, the vulnerability is semi-analytic allowing for a tractable Nash equilibrium. We give sufficient conditions for investment in equilibrium to be monotone in the network vulnerability. When investment is monotone, we show that the (asymptotic) Nash equilibrium is unique. In the particular example of two types core-periphery agents, we exhibit a strong effect of the cost heterogeneity and in particular non-monotonous investment as a function of costs.

In most traditional machine learning algorithms, the training and testing datasets have identical distributions and feature spaces. However, these assumptions have not held in many real applications. Although transfer learning methods have been invented to fill this gap, they introduce new challenges as negative transfers (NTs). Most previous research considered NT a significant problem, but they pay less attention to solving it. This study will propose a transductive learning algorithm based on cellular learning automata (CLA) to alleviate the NT issue. Two famous learning automata (LA) entitled estimators are applied as estimator CLA in the proposed algorithms. A couple of new decision criteria called merit and and attitude parameters are introduced to CLA to limit NT. The proposed algorithms are applied to standard LA environments. The experiments show that the proposed algorithm leads to higher accuracy and less NT results.

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging method. The first algorithm allows one to transform the considered differential systems to the normal form of averaging. Here, we restricted the unperturbed term of the normal form of averaging to be identically zero. The second algorithm is used to derive the computational formulae of the averaged functions at any order. The third algorithm is based on the first two algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The proposed approach is implemented in Maple and its effectiveness is shown by several examples. Moreover, we report some incorrect results in published papers on the averaging method.

In this work, we design a distributed algorithm for time-varying convex optimization over networks with quantized communications. Each agent has its local time-varying objective function, while the agents need to cooperatively track the optimal solution trajectories of global time-varying functions. The distributed algorithm is motivated by the alternating direction method of multipliers, but the agents can only share quantization information through an undirected graph. To reduce the tracking error due to information loss in quantization, we apply the dynamic quantization scheme with a decaying scaling function. The tracking error is explicitly characterized with respect to the limit of the decaying scaling function in quantization. Furthermore, we are able to show that the algorithm could asymptotically track the optimal solution when time-varying functions converge, even with quantization information loss. Finally, the theoretical results are validated via numerical simulation.

The aim of the present paper is to compare the current design codes’ predictions for reinforced concrete (RC) T-beams with the alternative physical methods – namely, the compressive force path (CFP) method and artificial neural networks (ANNs). Therefore, two databases, for T-beams without stirrups and with stirrups, are developed using the available experimental studies. The comparative study on prediction (obtained from the American Concrete Institute and Eurocode 2, CFP and ANN models) shows that the predictions of the ANN model provide a closer fit to the experimental results; after ANN the predictions of the CFP method are close to the experimental results when compared with the counterpart physical model. Comparative studies are also conducted on the critical parameters for the behaviour of RC T-beams. Furthermore, a non-linear finite-element tool (i.e. Abaqus) is used to validate the prediction of the ANN and CFP model. The crack pattern from Abaqus exhibited the same mechanics, on which the CFP models are based.

The individual differences and the dynamic uncertain relationships among different electroencephalogram (EEG) regions are essential factors that limit EEG emotion recognition. To address these issues, in this paper, we propose a variational instance-adaptive graph method (V-IAG) that simultaneously captures the individual dependencies among different EEG electrodes and estimates the underlying uncertain information. Specifically, we employ two branches, i.e., instance-adaptive branch and variational branch, to construct the graph. Inspired by the attention mechanism, the instance-adaptive branch generates the graph based on the input so as to characterize the individual dependencies among EEG channels. The variational branch generates the probabilistic graph, which quantifies the uncertainties. We combine these two types of graphs to extract more discriminative features. To present more precise graph representation, we propose a new operation named the multi-level and multi-graph convolution operation, which aggregates the features of EEG channels from different frequencies with different graphs. Furthermore, we design the graph coarsening and employ the sparse constraint to obtain more robust features. We conduct extensive experiments on two widely-used EEG emotion recognition databases, i.e., SJTU emotion EEG dataset (SEED) and Multi-modal physiological emotion recognition dataset (MPED). The results demonstrate that the proposed model achieves the-state-of-the-art performance.

Knowledge graph embedding is an effective way to represent knowledge graph, which greatly enhance the performances on knowledge graph completion tasks, e.g. entity or relation prediction. For knowledge graph embedding models, designing a powerful loss framework is crucial to the discrimination between correct and incorrect triplets. Margin-based ranking loss is a commonly used negative sampling framework to make a suitable margin between the scores of positive and negative triples. However, this loss can not ensure ideal low scores for the positive triplets and high scores for the negative triplets, which is not beneficial for knowledge completion tasks. In this paper, we present a double limit scoring loss to separately set upper bound for correct triplets and lower bound for incorrect triplets, which provides more effective and flexible optimization for knowledge graph embedding. Upon the presented loss framework, we present several knowledge graph embedding models including TransE-SS, TransH-SS, TransD-SS, ProjE-SS and ComplEx-SS. The experimental results on link prediction and triplet classification show that our proposed models have the significant improvement compared to state-of-the-art baselines.

A simple necessary and sufficient condition ensuring that a real matrix of dimension 3 is similar to a Metzler matrix is exhibited. When this condition is satisfied, a construction of the transfer matrix is given. This construction is used to design an interval observer for a family of continuous-time systems. An example is provided with interval observer design for the so-called love dynamics in the case of limit cycles.

A user-centric location privacy trading framework, called ULPT, is constructed to facilitate location privacy trading between workers and the platform. Each worker can decide how much location privacy to disclose to the platform in an MCS task based on its own location privacy leakage budget $\xi$ . The higher $\xi$ is, the more privacy its reported location discloses. Accordingly, it receives higher payment from the platform as compensation. Besides, ULPT enables the platform to select a suitable set of winning workers to achieve desirable MCS service accuracy while taking into account its budget limit and worker privacy requirements. For this purpose, a heuristic algorithm is devised with a bounded optimality gap. As formally proved in this manuscript, ULPT guarantees a series of nice properties, including $\xi$ -privacy, $(\alpha, \beta)$ -accuracy, budget feasibility. Moreover, both rigorous theoretical analysis and extensive simulations are conducted to evaluate tradeoffs among these three.

Tensor singular value decomposition (t-SVD) has recently become increasingly popular for tensor recovery under partial and/or corrupted observations. However, the existing t -SVD-based methods neither make use of a rank prior nor provide an accurate rank estimation (RE), which would limit their recovery performance. From the practical perspective, the tensor RE problem is nontrivial and difficult to solve. In this article, we, therefore, aim to determine the correct rank of an intrinsic low-rank tensor from corrupted observations based on t-SVD and further improve recovery results with the estimated rank. Specifically, we first induce the equivalence of the tensor nuclear norm (TNN) of a tensor and its f -diagonal tensor. We then simultaneously minimize the reconstruction error and TNN of the f -diagonal tensor, leading to RE. Subsequently, we relax our model by removing the TNN regularizer to improve the recovery performance. Furthermore, we consider more general cases in the presence of missing data and/or gross corruptions by proposing robust tensor principal component analysis and robust tensor completion with RE. The robust methods can achieve successful recovery by refining the models with correct estimated ranks. Experimental results show that the proposed methods outperform the state-of-the-art methods with significant improvements.

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds on rates of convergence for parametric estimators in migration models. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible.

In this work, a parametric up-converter amplifier is introduced as a wideband impedance-matching network. Chu’s limit restricts the minimum Q-factor of unloaded small antennas. However, the practical bandwidth (BW) of small antennas is defined by their loaded Q-factor. By connecting a small antenna to an amplifier with a real input impedance that is several times greater than the radiation resistance of the antenna, we propose increasing the return loss, which leads to a reduction in the loaded Q-factor and an increase in the BW. In addition, a parametric amplifier is used because, in comparison with transistor amplifiers, it offers low-noise characteristics. The gain of the low-noise parametric amplifier compensates for the loss due to the imposed mismatch. Our simulation result shows BW improvements up to 32 times can be accomplished by trading 2 dB of noise figure (NF), compared to the 15 dB suggested by Chu’s limit for a lossy antenna. Accepted version

Edge caching can significantly improve the quality of wireless video services by deploying cache servers at network edges. Recently, video conversion and recommendation have been introduced to improve the caching performance at the edges. Specifically, they work to produce lower quality versions of videos via video converting (for the former) or provide alternative similar videos when requested videos are not available by using video recommendation (for the latter). However, existing work in this aspect has utilized these two techniques separately, which largely limit their capabilities in providing improved video services. In this article, we study how to jointly utilize these two techniques in edge caching for improved caching performance. The objective is to maximally reduce the video delivery delay while satisfying users’ requirements. We first formulate the optimal video caching problem in this case and derive its NP-hardness. We, then, propose an effective transcoding- and recommending-based caching algorithm (TRBA). The TRBA works in a greedy manner to iteratively buffer the most valuable video versions, one video version each time, until no more video version or cache space is available. We define the value of a video version as the reduced delivery delay if this version were buffered divided by the extra cache space required for its buffering. The computational complexity of TRBA is deduced as $O(|V|^3|Q|^3)$ , where $|V|$ and $|Q|$ represent the total number of videos and the number of versions per video, respectively. Numerical results demonstrate that, compared with existing caching algorithms, TRBA can significantly improve the caching performance.

Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a solution. However, classic improvement heuristics are all guided by hand-crafted rules which may limit their performance. In this paper, we propose a deep reinforcement learning framework to learn the improvement heuristics for routing problems. We design a self-attention based deep architecture as the policy network to guide the selection of next solution. We apply our method to two important routing problems, i.e. travelling salesman problem (TSP) and capacitated vehicle routing problem (CVRP). Experiments show that our method outperforms state-of-the-art deep learning based approaches. The learned policies are more effective than the traditional hand-crafted ones, and can be further enhanced by simple diversifying strategies. Moreover, the policies generalize well to different problem sizes, initial solutions and even real-world dataset., Comment: 10 pages, 4 figures

Few-shot learning aims at heuristically resolving new tasks with limited labeled data; most of the existing approaches are affected by knowledge learned from similar experiences. However, inter-class barriers and new samples insufficiency limit the transfer of knowledge. In this paper, we propose a novel mixture distribution graph network, in which the inter-class relation is explicitly modeled and propagated via graph generation. Owing to the weighted distribution features based on Gaussian Mixture Model, we take class diversity into consideration, thereby utilizing information precisely and efficiently. Equipped with Minimal Gated Units, the “memory" of similar tasks can be preserved and reused through episode training, which fills a gap in temporal characteristics and softens the impact of data insufficiency. Extensive trials are carried out based on the MiniImageNet and CIFAR-FS datasets. Results turn out that our method exceeds most state-of-the-art approaches, which shows the validity and universality of our method in few-shot learning.

We show that, on the Riemann hypothesis, $\limsup_{X\to\infty}I(X)/X^{2} \leq 0.8603$, where $I(X) = \int_X^{2X} (\psi(x)-x)^2\,dx.$ This proves (and improves on) a claim by Pintz from 1982. We also show unconditionally that $\frac{1}{5\,374}\leq I(X)/X^2 $ for sufficiently large $X$, and that the $I(X)/X^{2}$ has no limit as $X\rightarrow\infty$., Comment: 23 pages

This article studies the state estimation for probabilistic Boolean networks via observing output sequences. Detectability describes the ability of an observer to uniquely estimate system states. By defining the probability of an observed output sequence, a new concept called detectability measure is proposed. The detectability measure is defined as the limit of the sum of probabilities of all detectable output sequences when the length of output sequences goes to infinity, and it can be regarded as a quantitative assessment of state estimation. A stochastic state estimator is designed by defining a corresponding nondeterministic stochastic finite automaton, which combines the information of state estimation and probability of output sequences. The proposed concept of detectability measure further performs the quantitative analysis on detectability. Furthermore, by defining a Markov chain, the calculation of detectability measure is converted to the calculation of the sum of probabilities of certain specific states in Markov chain. Finally, numerical examples are given to illustrate the obtained theoretical results.

The absolute zeta function for a scheme X of finite type over Z satisfying a certain condition is defined as the limit as p → 1 of the zeta function of X ⊗ F p . In 2016, after calculating absolute zeta functions for a few specific schemes, Kurokawa suggested that an absolute zeta function for a general scheme of finite type over Z should have an infinite product structure which he called the absolute Euler product. In this article, formulating his suggestion using a torsion free Noetherian F 1 -scheme defined by Connes and Consani, we give a proof of his suggestion. Moreover, we show that each factor of the absolute Euler product is derived from the counting function of the F 1 -scheme.

In this paper, we study the phenomenon of concentration and the formation of delta shock wave in vanishing adiabatic exponent limit of Riemann solutions to the Aw–Rascle traffic model. It is proved that as the adiabatic exponent vanishes, the limit of solutions tends to a special delta-shock rather than the classical one to the zero pressure gas dynamics. In order to further study this problem, we consider a perturbed Aw–Rascle model and proceed to investigate the limits of solutions. We rigorously proved that, as the adiabatic exponent tends to one, any Riemann solution containing two shock waves tends to a delta-shock to the zero pressure gas dynamics in the distribution sense. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis.

Due to the data distribution discrepancy, fault diagnosis models, trained with labeled data in one scene, likely fails in classifying by unlabeled data acquired from the other scenes. Transfer learning is capable to generalize successful application trained in one scene to the fault diagnosis in the other scenes. However, the existing transfer methods do not pay much attention to reduce adaptively marginal and conditional distribution biases, and also ignore the degree of contribution between both biases and among network layers, which limit classification performance and generalization in reality. To overcome these weaknesses, we established a new fault diagnosis model, called subdomain adaptation transfer learning network (SATLN). Firstly, two convolutional building blocks were stacked to extract transferable features from raw data. Then, the pseudo label learning was amended to construct target subdomain of each class. Furthermore, a sub-domain adaptation was combined with domain adaptation to reduce both marginal and conditional distribution biases simultaneously. Finally, a dynamic weight term was applied for adaptive adjustment of the contributions from both discrepancies and each network layers. The SATLN method was tested with six transfer tasks. The results demonstrate the effectiveness and superiority of the SATLN in the cross-domain fault diagnosis field.

A delivery mix that includes delivery from stock and drop-shipping is of interest to many internet retailers. We consider a retailer serving a time- and price-sensitive market with two substitutable products that differ in the guaranteed delivery time and price, an express product (delivered from the stock) and a regular product (drop-shipped). In case of stockout, customers may switch from the express product to the regular product. We study how to differentiate the products in terms of delivery times and prices and how to determine the stock level to maximize the retailer's expected profit while satisfying service constraints. We solve different variants of the problem and derive insights into the optimal retailer's strategy. In addition, we study the impact of stockout-based substitution. This paper is the first to investigate time- and price-based differentiation along with inventory decisions for a retailer who relies on a hybrid distribution to satisfy a time- and price-sensitive demand subject to stockout-based substitution. When prices and stock are fixed, in addition to minimum and maximum time differentiations, a medium differentiation strategy may be optimal but depends on the stock level. When only prices are fixed, there exists a price differentiation limit below which a minimum time differentiation is optimal, and above which only the express product should be offered. For the general model, numerical experiments show that a higher stockout-based substitution leads to greater time differentiation (which is consistent with the results of previous models) and more stock. However, this would not impact the price differentiation.

Exploiting Bilevel Optimization Techniques to Disconnect Graphs into Small Components In order to limit the spread of possible viral attacks in a communication or social network, it is necessary to identify critical nodes, the protection of which disconnects the remaining unprotected graph into a bounded number of shores (subsets of vertices) of limited cardinality. In the article “'Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem”, Furini, Ljubic, Malaguti, and Paronuzzi provide a new bilevel interpretation of the associated capacitated vertex separator problem and model it as a two-player Stackelberg game in which the leader interdicts (protects) the vertices, and the follower solves a combinatorial optimization problem on the resulting graph. Thanks to this bilevel interpretation, the authors derive different families of strengthening inequalities and show that they can be separated in polynomial time. The ideas exploited in their framework can also be extended to other vertex/edge deletion/insertion problems or graph partitioning problems by modeling them as two-player Stackelberg games to be solved through bilevel optimization.

This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for generalized factor models, with slightly stronger conditions on the relative magnitude of N (number of subjects) and T (number of time periods). Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear, Logit, Probit, Tobit, Poisson and some other single-index nonlinear models. The probability density/mass function is allowed to vary across subjects and time, thus mixed models are also allowed for. For factor-augmented regressions, this paper establishes the limit distributions of the parameter estimates, the conditional mean, and the forecast when factors estimated from nonlinear/mixed data are used as proxies for the true factors.

In this paper, an integrated guidance and control approach is presented to improve the performance of the missile interception. The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping. In addition, physical constraints, which can affect the performance of the missile interception, such as acceleration limit, seeker’s look angle, and look angle rate constraints are considered. The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints, and the solution is obtained by a primal–dual interior point method. The performance of the proposed method is verified through several numerical examples.

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns giving the relative positions of the data points within a cluster. Since these patterns take only the ordinal structure of consecutive data points into account, the method is robust under monotone transformations and measurement errors. We verify the existence of the corresponding limit distributions in the framework of regularly varying time series, develop non-parametric estimators and show their asymptotic normality under appropriate mixing conditions. The performance of the estimators is demonstrated in a simulated example and a real data application to discharge data of the river Rhine., Deutsche Forschungsgemeinschaft, Projekt DEAL

In this paper, we highlight three issues that limit performance of machine learning on biomedical images, and tackle them through 3 case studies: 1) Interactive Machine Learning (IML): we show how IML can drastically improve exploration time and quality of direct volume rendering. 2) transfer learning: we show how transfer learning along with intelligent pre-processing can result in better Alzheimer's diagnosis using a much smaller training set 3) data imbalance: we show how our novel focal Tversky loss function can provide better segmentation results taking into account the imbalanced nature of segmentation datasets. The case studies are accompanied by in-depth analytical discussion of results with possible future directions.

The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a stochastic differential equation system. When the total activity of the network has an instantaneous effect on the network, in the average-excitatory case, a blow-up phenomenon occurs. This article is devoted to the theoretical study of the NNLIF model in the case where a delay in the effect of the total activity on the neurons is added. We first prove global-in-time existence and uniqueness of “strong” solutions, independently of the sign of the connectivity parameter, that is, for both cases: excitatory and inhibitory. Secondly, we prove some qualitative properties of solutions: asymptotic convergence to the stationary state for weak interconnections and a non-existence result for periodic solutions if the connectivity parameter is large enough. The proofs are mainly based on an appropriate change of variables to rewrite the NNLIF equation as a Stefan-like free boundary problem, constructions of universal super-solutions, the entropy dissipation method and Poincaré’s inequality.

We study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain., Deutsche Forschungsgemeinschaft, Projekt DEAL

The analysis of mechanically stabilised earthworks using geosynthetic reinforcements is typically addressed by means of a limit equilibrium or finite-element analysis. However, the design of the reinforcement layout and strength is generally specified based on design guidance or on experience. Limit analysis, and in particular discontinuity layout optimisation (DLO) presents an alternative for both the analysis and design of reinforced slopes. The current study presents a novel automated approach for determining the optimum layout of reinforcement for any given earthwork geometry. In this paper, a modified formulation of DLO termed ‘reinforcement layout and strength optimisation’ is presented that is able to find the minimum tensile strength of the reinforcing material and optimal layout required for the stability of the system for a given initial design domain. Examples are given for a slope stability problem and compared with conventional design guidance.

This paper examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure within which consensus can be achieved robustly despite the presence of uncertain and time-varying delays. We apply an Hinf-type small-gain analysis to multi-agent systems, which results in explicit lower bounds on the DCM for both undirected and directed graphs. The results provide sufficient conditions for robust consensus for all time-varying delays that may vary within the range. It is seen that the agent dynamics and the graph connectivity may fundamentally limit the range of tolerable delays. It is also found that the DCM can be increased beyond that achieved by P protocol by incorporating the delay variation rate in the design of the PD control protocol.

Timeliness is an emerging requirement for many Internet of Things (IoT) applications. In IoT networks, where a large-number of nodes are distributed, severe interference may incur during the transmission phase which causes age of information (AoI) degradation. It is therefore important to study the performance limit of AoI as well as how to achieve such limit. In this paper, we aim to optimize the AoI in random access Poisson networks. By taking into account the spatio-temporal interactions amongst the transmitters, an expression of the peak AoI is derived, based on explicit expressions of the optimal peak AoI and the corresponding optimal system parameters including the packet arrival rate and the channel access probability are further derived. It is shown that with a given packet arrival rate (resp. a given channel access probability), the optimal channel access probability (resp. the optimal packet arrival rate), is equal to one under a small node deployment density, and decrease monotonically as the spatial deployment density increases due to the severe interference caused by spatio-temproal coupling between transmitters. When joint tuning of the packet arrival rate and channel access probability is performed, the optimal channel access probability is always set to be one. Moreover, with the sole tuning of the channel access probability, it is found that the optimal peak AoI performance can be improved with a smaller packet arrival rate only when the node deployment density is high, which is contrast to the case of the sole tuning of the packet arrival rate, where a higher channel access probability always leads to better optimal peak AoI regardless of the node deployment density. In all the cases of optimal tuning of system parameters, the optimal peak AoI linearly grows with the node deployment density as opposed to an exponential growth with fixed system parameters.

Due to the excellent performance in complex systems modeling under small samples and uncertainty, Belief Rule Base (BRB) expert system has been widely applied in fault diagnosis. However, the fault diagnosis process for complex mechanical equipment normally needs multiple attributes, which can lead to the rule number explosion problem in BRB, and limit the efficiency and accuracy. To solve this problem, a novel Combination Belief Rule Base (C-BRB) model based on Directed Acyclic Graph (DAG) structure is proposed in this paper. By dispersing numerous attributes into the parallel structure composed of different sub-BRBs, C-BRB can effectively reduce the amount of calculation with acceptable result. At the same time, a path selection strategy considering the accuracy of child nodes is designed in C-BRB to obtain the most suitable sub-models. Finally, a fusion method based on Evidential Reasoning (ER) rule is used to combine the belief rules of C-BRB and generate the final results. To illustrate the effectiveness and reliability of the proposed method, a case study of fault diagnosis of rolling bearing is conducted, and the result is compared with other methods.

We consider an environment with m servers in parallel and n jobs. The n jobs have i.i.d. exponentially distributed processing requirements. The servers operate at different speeds and preemptions are allowed. The jobs have random release times that are not known in advance, but whenever a job is released, its due date is fixed and becomes known to the scheduler. We first consider three stochastic scheduling problems with three due date related objective functions and consider variations of the Earliest Due Date (EDD) rule, including the preemptive policy that at any point in time assigns the job with the Earliest Due Date to the Fastest Server (EDD-FS). Our optimality results turn out to be examples of stochastic scheduling problems that have relatively simple priority rules that are optimal while their deterministic counterparts do not allow such simple priority rules to be optimal. We furthermore extend our results to include a priority queueing model with m exponential servers that operate at different speeds and preemptions being allowed. The jobs arrive according to an arbitrary renewal process, and we assume that the utilization factor of the system is less than 1. Upon a job’s release the time difference between its due date and release time is set by the draw of a random variable from a given distribution. At a job’s release time, its due date is then immediately fixed and known while its actual processing time only becomes known upon its service completion. We show that for this priority queueing model the preemptive EDD-FS rule also minimizes the limit of several due date related objective functions as the number of jobs converges to infinity.

Advanced robotic applications have revived interest in identification of a high-precision dynamic model. In this paper, we propose an extended dynamic parameter set (EDS). The EDS breaks through the limitation that the base dynamic parameter set (BDS) needs a priori knowledge of the gravity direction for modeling. Moreover, we present a novel parameters identification technique (RSIH) which is a complete solution and can significantly mitigate negative effects of the measurement noise and outliers. Besides, an incremental learning technique combined with a compensation limit criterion is employed to compensate for unmodeled dynamics. Simulations and experiments demonstrate the EDS-based model can adapt to any installation angle of a base-plate, and confirm the RSIH technique outperforms the widely used identification techniques in industry and is equal to or even better than the state of the art physical feasibility technique in terms of identification precision and robustness. In addition, the modeling errors, especially the uncertainty of the friction model, can be greatly compensated.

Planning high-speed trajectories for UAVs in unknown environments requires algorithmic techniques that enable fast reaction times to guarantee safety as more information about the environment becomes available. The standard approaches that ensure safety by enforcing a "stop" condition in the free-known space can severely limit the speed of the vehicle, especially in situations where much of the world is unknown. Moreover, the ad-hoc time and interval allocation scheme usually imposed on the trajectory also leads to conservative and slower trajectories. This work proposes FASTER (Fast and Safe Trajectory Planner) to ensure safety without sacrificing speed. FASTER obtains high-speed trajectories by enabling the local planner to optimize in both the free-known and unknown spaces. Safety is ensured by always having a safe back-up trajectory in the free-known space. The MIQP formulation proposed also allows the solver to choose the trajectory interval allocation. FASTER is tested extensively in simulation and in real hardware, showing flights in unknown cluttered environments with velocities up to 7.8m/s, and experiments at the maximum speed of a skid-steer ground robot (2m/s)., This paper has been accepted for publication in IEEE Transactions on Robotics. arXiv admin note: text overlap with arXiv:1903.03558

The problems discussed in this paper are motivated by general ratio consensus algorithms, introduced by Kempe, Dobra, and Gehrke (2003) in a simple form as the push-sum algorithm, later extended by B\'en\'ezit et al. (2010) under the name weighted gossip algorithm. We consider a communication protocol described by a strictly stationary, ergodic, sequentially primitive sequence of non-negative matrices, applied iteratively to a pair of fixed initial vectors, the components of which are called values and weights defined at the nodes of a network. The subject of ratio consensus problems is to study the asymptotic properties of ratios of values and weights at each node, expecting convergence to the same limit for all nodes. The main results of the paper provide upper bounds for the rate of the almost sure exponential convergence in terms of the spectral gap associated with the given sequence of random matrices. It will be shown that these upper bounds are sharp. Our results complement previous results of Picci and Taylor (2013) and Iutzeler, Ciblat and Hachem (2013).

Surface Electromyography (sEMG) plays a key role in many applications such as control of Human-Machine Interfaces (HMI) and neuromusculoskeletal modeling. It has strongly nonlinear relations to joint kinematics and reflects the subjects’ intention in moving their limbs. Such relations have been traditionally examined by either integrated biomechanics and multi-body dynamics or gesture-based classification approaches. However, these methods have drawbacks that limit their usability. Different from them, joint kinematics can be continuously reconstructed from sEMG via estimation approaches, for instance, the Artificial Neural Networks (ANNs). The Comparison of different ANNs used in different studies is difficult, and in many cases, impossible. The current study focuses on fairly evaluating four types of ANN over the same dataset and conditions in proportional and simultaneous estimation of 15 hand joint angles from 10 sEMG signals. The presented ANNs are Feedforward, Cascade-Forward, Radial Basis Function (RBFNN), and Generalized Regression (GRNN). Each ANN is applied to its special parametric study. All the methods efficiently solved the regression problem of the complex multi-input multi-output bio-system. The RBFNN has the best performance over the others with a 79.80% mean correlation coefficient over all joints, and its accuracy reaches as high as 92.67% in some joints. Interestingly, the highest accuracy over individual joints is 93.46%, which is achieved via the GRNN. The good accuracy suggests that the proposed approaches can be used as alternatives to the previously adopted ones and can be employed effectively to synchronously control multi-degrees of freedom HMI and for general multi-joint kinematics estimation purposes.

Suppose that in a given planar circular region, there are some smart mobile evaders and we would like to find them using sweeping agents. We assume that each agent has a line sensor of length 2r. We propose procedures for designing cooperative sweeping processes that ensure the successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity that the sweeper swarm must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present results on the total search time as a function of the sweeping velocity of the swarm's agents given the initial conditions on the size of the search region and the maximal velocity of the evaders., arXiv admin note: text overlap with arXiv:1905.04006

We consider the evolution of the one-particle function in the weak-coupling limit in three space dimensions, obtained by truncating the BBGKY hierarchy under a propagation of chaos approximation. For this dynamics, we rigorously show the convergence to a solution of the Landau equation, keeping the full singularity of the Landau kernel. This resolves the issue arising from [10], where the singular region has been removed artificially. Since the singularity appears in the Landau equation due to the geometry of particle interactions, it is an intrinsic physical property of the weak-coupling limit which is crucial to the understanding of the transition from particle systems to the Landau equation., Comment: 30 pages

The kinetic description of relativistic plasmas in the presence of time-varying and spatially non-uniform electromagnetic fields is a fundamental theoretical issue both in astrophysics and plasma physics. This refers, in particular, to the treatment of collisionless and strongly-magnetized plasmas in the presence of intense radiation sources. In this paper the problem is investigated in the framework of a covariant gyrokinetic treatment for Vlasov-Maxwell equilibria. The existence of a new class of kinetic equilibria is pointed out, which occur for spatially-symmetric systems. These equilibria are shown to exist in the presence of non-uniform background EM fields and curved space-time. In the non-relativistic limit this feature permits the determination of kinetic equilibria even for plasmas in which particle energy is not conserved due to the occurrence of explicitly time-dependent EM fields. Finally, absolute stability criteria are established which apply in the case of infinitesimal symmetric perturbations that can be either externally or internally produced., Comment: 8 pages

In this paper, we propose to exploit the side-tuning framework for multimodal document classification. Side-tuning is a methodology for network adaptation recently introduced to solve some of the problems related to previous approaches. Thanks to this technique it is actually possible to overcome model rigidity and catastrophic forgetting of transfer learning by fine-tuning. The proposed solution uses off-the-shelf deep learning architectures leveraging the side-tuning framework to combine a base model with a tandem of two side networks. We show that side-tuning can be successfully employed also when different data sources are considered, e.g. text and images in document classification. The experimental results show that this approach pushes further the limit for document classification accuracy with respect to the state of the art., Comment: 2020 25th International Conference on Pattern Recognition (ICPR)

There is sustained and widespread interest in understanding the limit, if any, to the human lifespan. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social security systems. A central question is whether the endpoint of the underlying lifetime distribution is finite. Recent analyses of data on the oldest human lifetimes have led to competing claims about survival and to some controversy, due in part to incorrect statistical analysis. This paper discusses the particularities of such data, outlines correct ways of handling them and presents suitable models and methods for their analysis. We provide a critical assessment of some earlier work and illustrate the ideas through reanalysis of semi-supercentenarian lifetime data. Our analysis suggests that remaining life-length after age 109 is exponentially distributed, and that any upper limit lies well beyond the highest lifetime yet reliably recorded. Lower limits to 95% confidence intervals for the human lifespan are around 130 years, and point estimates typically indicate no upper limit at all., Comment: 30 pages, including Appendix

The proliferation of vehicle-to-vehicle (V2V) communication techniques has resulted in collaborative vehicle localization (CVL) approaches that localize a target vehicle by leveraging the state information of nearby vehicles. However, CVL approaches typically require a large search space to locate the real position of a target vehicle and assume small measurement errors of nearby vehicle information, which limit the efficiency and robustness of the existing methods. In this paper, we propose an efficient and error-tolerant CVL approach (referred to as ET-CVL) that increases localization efficiency and accuracy even in the case of large measurement errors of nearby vehicle information. Unlike the existing CVL approaches, our approach prunes the search space for the position of the target vehicle through a pruning-based strategy that considers the relative positions of nearby vehicles. To determine the position of the target vehicle from the search space, we propose a displacement-based selection method to reduce the influence of the measurement errors of nearby vehicle information. The localization accuracy and efficiency of the proposed approach are then evaluated using simulated GPS trajectories in a large road network in New York City. The experimental results show that the proposed approach achieves higher localization efficiency and greater accuracy even with large measurement errors compared with state-of-the-art CVL approaches.

This paper defends the use of quasi-experiments for causal estimation in economics against the widespread objection that quasi-experimental estimates lack external validity. The defence is that quasi-experimental replication of estimates can yield defeasible evidence for external validity. The paper then develops a different objection. The stable unit treatment value assumption (SUTVA), on which quasi-experiments rely, is argued to be implausible due to the influence of social interaction effects on economic outcomes. A more plausible stable marginal unit treatment value assumption (SMUTVA) is proposed, but it is demonstrated to severely limit the usefulness of quasi-experiments for economic policy evaluation.