In this article, we employ the construction of the time-marching Discontinuous Petrov-Galerkin (DPG) scheme we developed for linear problems to derive high-order multistage DPG methods for non-linear systems of ordinary differential equations. The methodology extends to abstract evolution equations in Banach spaces, including a class of nonlinear partial differential equations. We present three nested multistage methods: the hybrid Euler method and the two- and three-stage DPG methods. We employ a linearization of the problem as in exponential Rosenbrock methods, so we need to compute exponential actions of the Jacobian that change from time steps. The key point of our construction is that one of the stages can be post-processed from another without an extra exponential step. Therefore, the class of methods we introduce is computationally cheaper than the classical exponential Rosenbrock methods. We provide a full convergence proof to show that the methods are second, third, and fourth-order accurate, respectively. We test the convergence in time of our methods on a 2D + time semi-linear partial differential equation after a semidiscretization in space.
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The idea of next-generation ports has become more apparent in the last ten years in response to the challenge posed by the rising demand for efficiency and the ever-increasing volume of goods. In this new era of intelligent infrastructure and facilities, it is evident that cyber-security has recently received the most significant attention from the seaport and maritime authorities, and it is a primary concern on the agenda of most ports. Traditional security solutions can be applied to safeguard IoT and Cyber-Physical Systems (CPS) from harmful entities. Nevertheless, security researchers can only watch, examine, and learn about the behaviors of attackers if these solutions operate more transparently. Herein, honeypots are potential solutions since they offer valuable information about the attackers. It can be virtual or physical. Virtual honeypots must be more realistic to entice attackers, necessitating better high-fidelity. To this end, Digital Twin (DT) technology can be employed to increase the complexity and simulation fidelity of the honeypots. Seaports can be attacked from both their existing devices and external devices at the same time. Existing mechanisms are insufficient to detect external attacks; therefore, the current systems cannot handle attacks at the desired level. DT and honeypot technologies can be used together to tackle them. Consequently, we suggest a DT-assisted honeypot, called TwinPot, for external attacks in smart seaports. Moreover, we propose an intelligent attack detection mechanism to handle different attack types using DT for internal attacks. Finally, we build an extensive smart seaport dataset for internal and external attacks using the MANSIM tool and two existing datasets to test the performance of our system. We show that under simultaneous internal and external attacks on the system, our solution successfully detects internal and external attacks.
Recently efforts have been made by social media platforms as well as researchers to detect hateful or toxic language using large language models. However, none of these works aim to use explanation, additional context and victim community information in the detection process. We utilise different prompt variation, input information and evaluate large language models in zero shot setting (without adding any in-context examples). We select three large language models (GPT-3.5, text-davinci and Flan-T5) and three datasets - HateXplain, implicit hate and ToxicSpans. We find that on average including the target information in the pipeline improves the model performance substantially (~20-30%) over the baseline across the datasets. There is also a considerable effect of adding the rationales/explanations into the pipeline (~10-20%) over the baseline across the datasets. In addition, we further provide a typology of the error cases where these large language models fail to (i) classify and (ii) explain the reason for the decisions they take. Such vulnerable points automatically constitute 'jailbreak' prompts for these models and industry scale safeguard techniques need to be developed to make the models robust against such prompts.
For augmentation of the square-shaped image data of a convolutional neural network (CNN), we introduce a new method, in which the original images are mapped onto a disk with a conformal mapping, rotated around the center of this disk and mapped under such a M\"obius transformation that preserves the disk, and then mapped back onto their original square shape. This process does not result the loss of information caused by removing areas from near the edges of the original images unlike the typical transformations used in the data augmentation for a CNN. We offer here the formulas of all the mappings needed together with detailed instructions how to write a code for transforming the images. The new method is also tested with simulated data and, according the results, using this method to augment the training data of 10 images into 40 images decreases the amount of the error in the predictions by a CNN for a test set of 160 images in a statistically significant way (p-value=0.0360).
In this article, we focus on the error that is committed when computing the matrix logarithm using the Gauss--Legendre quadrature rules. These formulas can be interpreted as Pad\'e approximants of a suitable Gauss hypergeometric function. Empirical observation tells us that the convergence of these quadratures becomes slow when the matrix is not close to the identity matrix, thus suggesting the usage of an inverse scaling and squaring approach for obtaining a matrix with this property. The novelty of this work is the introduction of error estimates that can be used to select a priori both the number of Legendre points needed to obtain a given accuracy and the number of inverse scaling and squaring to be performed. We include some numerical experiments to show the reliability of the estimates introduced.
We propose an interpretation of multiparty sessions with asynchronous communication as Flow Event Structures. We introduce a new notion of global type for asynchronous multiparty sessions, ensuring the expected properties for sessions, including progress. Our global types, which reflect asynchrony more directly than standard global types and are more permissive, are themselves interpreted as Prime Event Structures. The main result is that the Event Structure interpretation of a session is equivalent, when the session is typable, to the Event Structure interpretation of its global type.
In this paper, I present three closed-form approximations of the two-sample Pearson Bayes factor. The techniques rely on some classical asymptotic results about gamma functions. These approximations permit simple closed-form calculation of the Pearson Bayes factor in cases where only the summary statistics are available (i.e., the t-score and degrees of freedom).
In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to approximate within a factor of $n^{1-\varepsilon}$ for any $\varepsilon > 0$. Due to this, investigating the complexity of Maximum Independent Set in various graph classes in hope of finding better tractability results is an active research direction. In $H$-free graphs, that is, graphs not containing a fixed graph $H$ as an induced subgraph, the problem is known to remain NP-hard and APX-hard whenever $H$ contains a cycle, a vertex of degree at least four, or two vertices of degree at least three in one connected component. For the remaining cases, where every component of $H$ is a path or a subdivided claw, the complexity of Maximum Independent Set remains widely open, with only a handful of polynomial-time solvability results for small graphs $H$ such as $P_5$, $P_6$, the claw, or the fork. We show that for every graph $H$ for which Maximum Independent Set is not known to be APX-hard and SUBEXP-hard in $H$-free graphs, the problem admits a quasi-polynomial time approximation scheme and a subexponential-time exact algorithm in this graph class. Our algorithm works also in the more general weighted setting, where the input graph is supplied with a weight function on vertices and we are maximizing the total weight of an independent set.
To overcome the computational bottleneck of various data perturbation procedures such as the bootstrap and cross validations, we propose the Generative Multiple-purpose Sampler (GMS), which constructs a generator function to produce solutions of weighted M-estimators from a set of given weights and tuning parameters. The GMS is implemented by a single optimization without having to repeatedly evaluate the minimizers of weighted losses, and is thus capable of significantly reducing the computational time. We demonstrate that the GMS framework enables the implementation of various statistical procedures that would be unfeasible in a conventional framework, such as the iterated bootstrap, bootstrapped cross-validation for penalized likelihood, bootstrapped empirical Bayes with nonparametric maximum likelihood, etc. To construct a computationally efficient generator function, we also propose a novel form of neural network called the \emph{weight multiplicative multilayer perceptron} to achieve fast convergence. Our numerical results demonstrate that the new neural network structure enjoys a few orders of magnitude speed advantage in comparison to the conventional one. An R package called GMS is provided, which runs under Pytorch to implement the proposed methods and allows the user to provide a customized loss function to tailor to their own models of interest.
The aim of this paper is to show the relationship that lies in the fact of a person being right or left handed, in their skateboarding stance. Starting from the null hypothesis that there is no relationship, the Pearson's X^2 with Yates correction tests, as well as its respective p-value will be used to test the hypothesis. It will also be calculated and analyzed the residuals, Cramer's V and the Risk and Odds Ratios, with their respective confidence intervals to know the intensity of the association.
In this paper, we focus on the self-supervised learning of visual correspondence using unlabeled videos in the wild. Our method simultaneously considers intra- and inter-video representation associations for reliable correspondence estimation. The intra-video learning transforms the image contents across frames within a single video via the frame pair-wise affinity. To obtain the discriminative representation for instance-level separation, we go beyond the intra-video analysis and construct the inter-video affinity to facilitate the contrastive transformation across different videos. By forcing the transformation consistency between intra- and inter-video levels, the fine-grained correspondence associations are well preserved and the instance-level feature discrimination is effectively reinforced. Our simple framework outperforms the recent self-supervised correspondence methods on a range of visual tasks including video object tracking (VOT), video object segmentation (VOS), pose keypoint tracking, etc. It is worth mentioning that our method also surpasses the fully-supervised affinity representation (e.g., ResNet) and performs competitively against the recent fully-supervised algorithms designed for the specific tasks (e.g., VOT and VOS).
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