Set Of Representations Research Articles

A new scalarization approach and applications in set optimization

In this paper, we introduce a new nonlinear scalarization function and apply it to investigate optimality conditions and scalar representations for minimal sets and set optimization problems with the set less order relation. First, we propose a new scalarization function for sets belonging to the power set of a normed space and discuss its properties. Next, we apply such properties to formulate sufficient and necessary optimality conditions for strictly minimal and weakly minimal sets. Finally, under suitable adjustments, we provide nonlinear scalarization functions and investigate scalar representations of strictly efficient solution and weakly efficient solution sets of the reference problems.

Flow Processing Optimization with Accelerated Flow Actions on High Speed Programmable Data Plane

With the development of network technology, next-generation networks must satisfy many new requirements for network functions and performance. The processing of overlong packet fields is one of the requirements and is also the basis for ID-based routing and content lookup, and packet field addition/deletion mechanisms. The current SDN switches do not provide good support for the processing of overlong fields. In this paper, we propose a series of optimization mechanisms for protocol-oblivious instructions, in which we address the problem of insufficient support for overlong data in existing SDN switches by extending the bit width of instructions and accelerating them using SIMD instruction sets. We also provide an intermediate representation of the protocol-oblivious instruction set to improve the efficiency of storing and reading instruction blocks, and further reduce the execution time of instruction blocks by preprocessing them. The experiments show that our approach improves the performance of overlong data processing by 56%. For instructions involving packet field addition and deletion, the improvement in performance reaches 455%. In normal forwarding scenarios, our solution reduces the packet forwarding latency by around 30%.

Recursive structures in involutive bases theory

We study characterisations of involutive bases using a recursion over the variables in the underlying polynomial ring and corresponding completion algorithms. Three key ingredients are (i) an old result by Janet recursively characterising Janet bases for which we provide a new and simpler proof, (ii) the Berkesch–Schreyer variant of Buchberger's algorithm and (iii) a tree representation of sets of terms also known as Janet trees. We start by extending Janet's result to a recursive criterion for minimal Janet bases leading to an algorithm to minimise any given Janet basis. We then extend Janet's result also to Janet-like bases as introduced by Gerdt and Blinkov. Next, we design a novel recursive completion algorithm for Janet bases. We study then the extension of these results to Pommaret bases. It yields a novel recursive characterisation of quasi-stability which we use for deterministically constructing “good” coordinates more efficiently than in previous works. A small modification leads to a novel deterministic algorithm for putting an ideal into Nœther position. Finally, we provide a general theory of involutive-like bases with special emphasis on Pommaret-like bases and study the syzygy theory of Janet-like and Pommaret-like bases.

ProFeatMap: a highly customizable tool for 2D feature representation of protein sets.

Studies of sets of proteins are a central point in biology. In particular, the application of omics in the last decades has generated lists of several hundreds or thousands of proteins or genes. However, these lists are often not inspected globally, possibly due to the lack of tools capable of simultaneously visualizing the feature architectures of a large number of proteins. Here, we present ProFeatMap, an intuitive Python-based website. For a given set of proteins, it allows to display features such as domains, repeats, disorder or post-translational modifications and their organization along the sequences, into a highly customizable 2D map. Starting from a user-defined protein list of UniProt accession codes, ProFeatMap extracts the most important annotated features available for each protein from one of the well-established databases such as Uniprot or InterPro, allocates shapes and colors, potentially depending on quantitative or qualitative data and sorts the protein list based on homologous feature content. The resulting publication-quality map allows even large protein families to be explored, and to classify them based on shared features. It can help to gain insights, for example, feature redundancy or feature pattern, that were previously overlooked. ProFeatMap is freely available on the web at: https://profeatmap.pythonanywhere.com/. Source code is freely accessible at https://github.com/profeatmap/ProFeatMap under the GPL license. Supplementary data are available at Bioinformatics Advances online.

Matrix Approaches for Covering-Based Multigranulation Fuzzy Rough Set Models

Multigranulation rough set theory is one of the most effective tools for data analysis and mining in multicriteria information systems. Six types of covering-based multigranulation fuzzy rough set (CMFRS) models have been constructed through fuzzy β -neighborhoods or multigranulation fuzzy measures. However, it is often time-consuming to compute these CMFRS models with a large fuzzy covering using set representation approaches. Hence, presenting novel methods to compute them quickly is our motivation for this paper. In this article, we study the matrix representations of CMFRS models to save time in data processing. Firstly, some new matrices and matrix operations are proposed. Then, matrix representations of optimistic CMFRSs are presented. Moreover, matrix approaches for computing pessimistic CMFRSs are also proposed. Finally, some experiments are proposed to illustrate the effectiveness of our approaches.

The complete mitochondrial genome of Dascyllus trimaculatus (Rüppell, 1829)

Damselfishes (family Pomacentridae) comprise approximately 400 species that play an important ecological role in temperate and coral reefs. Here, for the first time, we assemble and annotate the mitochondrial genome of Dascyllus trimaculatus, the three-spot dascyllus, a planktivorous damselfish that primarily recruits in anemones. The circular genome of D. trimaculatus is 16,967 bp in length and contains 13 protein-coding genes, 22 transfer RNA genes, two ribosomal RNA genes, and a control region. Gene arrangement and codon usage is similar to reported mitochondrial genomes of other damselfish genera, and a phylogenetic analysis of a set of damselfish representatives is consistent with known evolutionary analyses.

Cross-Class Bias Rectification for Point Cloud Few-Shot Segmentation

The point cloud is a densely distributed 3D (three-dimensional) data, and annotating the point cloud is a time-consuming and labor-intensive work. The existing semantics segmentation work adopts few-shot learning to reduce the dependence on labeling samples while improving the generalization of the model to new categories. Since point clouds are 3D structures with rich geometric features, even objects of the same category have feature differences that cannot be ignored. Therefore, a few samples (support set) used to train the model do not cover all the features of this category. There is a distribution difference between the support samples and the samples used to verify the model performance (query set). In this paper, we propose an efficient point cloud few-shot segmentation method based on prototypes for bias rectification. A prototype is a vector representation of a category in the metric space. To make the prototype representation of the support set closer to the query set features, we define a feature bias term and reduce the distribution distance between the two sets by fusing the support set features and the bias term. On this basis, we design a feature cross-reference module. By mining the co-occurring features of the support and query sets, it can generate a more representative prototype which captures the overall features of the point cloud. Extensive experiments on two challenging datasets demonstrate that our method outperforms the state-of-the-art method by an average of 3.31 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> in several N-way K-shot tasks, and achieves approximately 200 times faster reasoning speed. Our code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/964918993/2CBR</uri> .

Cubic Spherical Neutrosophic Sets

This paper introduces the concept of cubic spherical neutrosophic sets (CSNSs), a geometric representation of neutrosophic sets, as well as a specification of its operational principles. In CSNs, two aggregation operators are investigated. The shape of CSNSs represents the evaluation values of alternatives with respect to criteria in a MCDM strategy based on the two aggregation operators and cosine distance for CSNSs. The cosine distance between an alternative and the ideal alternative is used to rank them, and the best alternative(s) can be selected. A numerical example concludes by demonstrating the use of the suggested method.

Breaking Metanarratives in Tim O’Brien’s text: A Postmodern Analysis

The Vietnam War was a splitting conflict that caused significant social, political, and cultural upheaval in American society. Tim O’Brien’s work explores the personal experiences of soldiers who fought in the war, their inner lives, and the complexities of telling true stories about the war. This paper discusses O’Brien’s “How to Tell a True War Story” as a representation of a unique literary work set in the context of the Vietnam War. The paper argues that O’Brien’s narrative style departs from traditional metanarrative styles by emphasizing individual traumas and inner experiences, which transcends the question of factual accuracy. The paper utilizes Jean-Francois Lyotard’s theory of metanarratives in the postmodern era to explore how O’Brien’s narrative style subverts traditional narrative structures, creating an emphasis on individual emotions and experiences. The paper argues that O’Brien’s narrative style, which includes fragmentary narration, personification of items, and conscious expressions from the narrator’s perspective, authentically elaborates the obscurity and disorder of people’s inner world during wars. This narrative style provides a meaningful way for people to empathize and connect with the text, especially during times of uncertainty and despair such as the COVID-19 pandemic. O’Brien disrupts metanarratives, making readers doubt their own viewpoints and beliefs, and deconstructs the textures of power and authority. While his work is significant in subverting authoritative storytelling, the loss of belief in overarching narratives may lead to social unrest, political upheaval, and economic instability. The combination of the metanarrative and the postmodern subversive narration might be a possible solution.

Multi-Querying: A Subsequence Matching Approach to Support Multiple Queries

The widespread use of sensors has resulted in an unprecedented amount of time series data. Time series mining has experienced a particular surge of interest, among which, subsequence matching is one of the most primary problem that serves as a foundation for many time series data mining techniques, such as anomaly detection and classification. In literature there exist many works to study this problem. However, in many real applications, it is uneasy for users to accurately and clearly elaborate the query intuition with a single query sequence. Consequently, in this paper, we address this issue by allowing users to submit a small query set, instead of a single query. The multiple queries can embody the query intuition better. In particular, we first propose a novel probability-based representation of the query set. A common segmentation is generated which can approximate the queries well, in which each segment is described by some features. For each feature, the corresponding values of multiple queries are represented as a Gaussian distribution. Then, based on the representation, we design a novel distance function to measure the similarity of one subsequence to the multiple queries. Also, we propose a breadth-first search strategy to find out similar subsequences. We have conducted extensive experiments on both synthetic and real datasets, and the results verify the superiority of our approach.

Masked Embedding Modeling with Rapid Domain Adjustment for Few-Shot Image Classification.

In few-shot classification, performing well on a testing dataset is a challenging task due to the restricted amount of labelled data available and the unknown distribution. Many previously proposed techniques rely on prototypical representations of the support set in order to classify a query set. Although this approach works well with a large, in-domain support set, accuracy suffers when transitioning to an out-of-domain setting, especially when using small support sets. To address out-of-domain performance degradation with small support sets, we propose Masked Embedding Modeling for Few-Shot Learning (MEM-FS), a novel, self-supervised, generative technique that reinforces few-shot-classification accuracy for a prototypical backbone model. MEM-FS leverages the data completion capabilities of a masked autoencoder to expand a given embedded support set. To further increase out-of-domain performance, we also introduce Rapid Domain Adjustment (RDA), a novel, self-supervised process for quickly conditioning MEM-FS to a new domain. We show that masked support embeddings generated by MEM-FS+RDA can significantly improve backbone performance on both out-of-domain and in-domain datasets. Our experiments demonstrate that applying the proposed technique to an inductive classifier achieves state-of-the-art performance on mini-imagenet, the CVPR L2ID Classification Challenge, and a newly proposed dataset, IKEA-FS. We provide code for this work at https://github.com/Brikwerk/MEM-FS.

Development of a method for automatic construction of hierarchical structures of several collections of texts in the formalization of linguistic expert information

The paper discusses methods of forming special models for the representation of various sets of knowledge in various information systems. The work is devoted to the application of distributive semantics in the identification of significant combinations in one subject area (PRO) within the framework of the formalization of linguistic expert information (LEI). The paper applies an approach to the formalization of LEI based on a set of analytical methods, where linear algebra is used as models. This approach makes it possible to initialize the procedure for the automatic formation of hierarchical LEI architectures or dendrograms when identifying significant combinations of titles of several collections of texts. The scientific novelty lies in the proposed analytical approach using distributive semantics in identifying significant combinations of titles of several collections of texts, which allows for the analysis and processing of linguistic expert information. The paper aims to create conditions for the formalization of the LEI by applying distributive semantics when identifying significant combinations of titles of several collections. The ontology constructed in this work complements the search structure within the framework of the considered PRO and can be supplemented and developed in the future.

APS-Net: An Adaptive Point Set Network for Optical Remote-Sensing Object Detection

Oriented object detection in optical remote-sensing images has been a challenging task due to arbitrary orientations and densely packed distribution of objects. Specifically, most existing methods lack adaptivity when regressing objects with different shapes and orientations. Although the point set representation is relatively flexible, the initial distribution of the point set is fixed in advance. In addition, some models based on the point set cannot get high location precision of points, affecting the bounding box generation. In this letter, we propose an Adaptive Point Set Network (APS-Net) for optical remote-sensing object detection, including three improvements. First, we propose the initial distribution learner (IDL) to learn the optimal initial aspect ratio, which helps the point set fit the object’s shape well. Second, we design the uncertainty measurement module (UMM), which considers the uncertainty of point location to improve location precision. Third, we introduce the local outlier factor (LOF) in the loss to punish outlier points more reasonably. Extensive experiments demonstrate that our proposed model achieves state-of-the-art performance on three commonly used datasets (i.e., DOTA-v1.0, UCAS-AOD, and HRSC2016) in the remote-sensing field.

Optimized Point Set Representation for Oriented Object Detection in Remote-Sensing Images

Optimized Point Set Representation for Oriented Object Detection in Remote-Sensing Images

WSODet: A Weakly Supervised Oriented Detector for Aerial Object Detection

In contrast to natural objects, aerial targets are usually non-axis aligned with arbitrary orientations. However, mainstream Weakly Supervised Object Detection (WSOD) methods can only predict horizontal bounding boxes (HBB) from existing proposals generated by offline algorithms. To predict oriented bounding boxes (OBB) for aerial targets while testing images end-to-end without proposals, WSODet is designed leveraging on Layer-wise Relevance Propagation (LRP) and Point Set Representation (RepPoints). To be specific, based on the mainstream WSOD framework, Layer-wise Relevance Propagation on Multiple Instance Learning branch (MIL-LRP) is conducted to decrease the uncertainty and ambiguity of feature map. Then, a pseudo oriented label generation algorithm is designed to obtain OBB pseudo labels, which serve as supervision to train an Oriented RepPoint Net under the guidance of improved oriented loss function. During the test, input images are sent to oriented RepPoint branch to obtain OBB predictions without proposals. Extensive experiments on DIOR, NWPU VHR-10.v2 and HRSC2016 datasets demonstrate the effectiveness of our method to predict precise oriented aerial objects, achieving 22.2%, 46.5% and 43.3% mAP, respectively. Moreover, training jointly with oriented RepPoint branch boosts the results of original WSOD framework compared with existing WSOD methods even if there is no specific design for original structure.

Linguistic Hedge Based Constrained Representation of Interval Type-2 Fuzzy Sets

Linguistic Hedge Based Constrained Representation of Interval Type-2 Fuzzy Sets

Comedy and Plague in the Time of Covid: The BBC's Upstart Crow: Lockdown Christmas 1603

The BBC’s Upstart Crow, created and scripted by Ben Elton, is a British situation comedy loosely based on the life and career of the early modern dramatist William Shakespeare (1564-1616). Beginning in 2016, as part of worldwide commemorations of the 400th anniversary of the writer’s death, the show has gone on to provide viewers with a more irreverent take on this most well-known of playwrights for a total of three series thus far, repeatedly inviting favourable comparisons to the 1980s historical comedy series Blackadder (1983-9), on which Elton also previously worked. On 21 December 2020, however, a special episode of the sitcom aired which altered its tone and style considerably. The article first considers how the episode’s tone and representation of social isolation sets it apart from the show’s established formula. It then considers how this episode seeks to relate its viewers’ experience of the contemporary Covid-19 pandemic to the experience of plague in early modern England. Finally, the article explores how the episode takes inspiration from Shakespeare’s own life experiences and, more specifically, from his Jacobean tragedy Macbeth in order to construct a poignant reflection of the social isolation experienced by so many of the episode’s anticipated audiences over the previous year.

Bn−1-bundles on the flag variety, II

This paper is the sequel to “Bn−1-bundles on the flag variety, I”. We continue our study of the orbits of a Borel subgroup Bn−1 of Gn−1=GL(n−1) (resp. SO(n−1)) acting on the flag variety Bn of G=GL(n) (resp. SO(n)). We begin by using the results of the first paper to obtain a complete combinatorial model of the Bn−1-orbits on Bn in terms of partitions into lists. The model allows us to obtain explicit formulas for the number of orbits as well as the exponential generating functions for the sequences {|Bn−1﹨Bn|}n≥1. We then use the combinatorial description of the orbits to construct a canonical set of representatives of the orbits in terms of flags. These representatives allow us to understand an extended monoid action on Bn−1﹨Bn using simple roots of both gn−1 and g and show that the closure ordering on Bn−1﹨Bn is the standard ordering of Richardson and Springer.

Topology optimization of thermal cloaks in euclidean spaces and manifolds using an extended level set method

Thermal cloaks are devices designed to shield an object against thermal detection, which have attracted growing interest in research. This paper proposes to design thermal cloaks using the level-set-based shape and topology optimization in the context of pure heat conduction. The cloaking effect is achieved by optimizing the distribution of two bulk heat conductive materials to eliminate the temperature disturbance induced by the introduction of the insulator (cloaking region) into a homogeneous thermal conduction medium. The optimized thermal cloaks are free of high anisotropy and nonhomogeneity commonly seen in the popular transformation thermotics or scattering cancellation methods. Due to the clear boundary characteristic of the level set representation, no sophisticated filtering techniques are required to suppress the appearance of ”gray regions” as opposed to the density-based topology optimization methods. Considering the fact that the device components that need to be thermally cloaked, e.g., sensors, can take an arbitrary free-form shape, a conformal thermal cloak on the manifold is also topologically optimized using the extended level set method (X-LSM), which has not been reported in the literature. The structural boundary is evolved by solving the (modified) Hamilton-Jacobi equation. The feasibility and robustness of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through a number of 2D and 3D (solid and shell) numerical examples with different cloaking regions (circular, human-shaped, spherical, and curved circular). This work may shed light on further exploration of the thermal meta-devices in the heat flux manipulation regime.

Lingering Neural Representations of Past Task Features Adversely Affect Future Behavior.

During goal-directed behavior, humans purportedly form and retrieve so-called event files, conjunctive representations that link context-specific information about stimuli, their associated actions, and the expected action outcomes. The automatic formation, and later retrieval, of such conjunctive representations can substantially facilitate efficient action selection. However, recent behavioral work suggests that these event files may also adversely affect future behavior, especially when action requirements have changed between successive instances of the same task context (e.g., during task switching). Here, we directly tested this hypothesis with a recently developed method for measuring the strength of the neural representations of context-specific stimulus-action conjunctions (i.e., event files). Thirty-five male and female adult humans performed a task switching paradigm while undergoing EEG recordings. Replicating previous behavioral work, we found that changes in action requirements between two spaced repetitions of the same task incurred a significant reaction time cost. By combining multivariate pattern analysis and representational similarity analysis of the EEG recordings with linear mixed-effects modeling of trial-to-trial behavior, we then found that the magnitude of this behavioral cost was directly proportional to the strength of the conjunctive representation formed during the most recent previous exposure to the same task, that is, the most recent event file. This confirms that the formation of conjunctive representations of specific task contexts, stimuli, and actions in the brain can indeed adversely affect future behavior. Moreover, these findings demonstrate the potential of neural decoding of complex task set representations toward the prediction of behavior beyond the current trial.SIGNIFICANCE STATEMENT Understanding how the human brain organizes individual components of complex tasks is paramount for understanding higher-order cognition. During complex tasks, the brain forms conjunctive representations that link individual task features (contexts, stimuli, actions), which aids future performance of the same task. However, this can have adverse effects when the required sequence of actions within a task changes. We decoded conjunctive representations from electroencephalographic recordings during a task that included frequent changes to the rules determining the response. Indeed, stronger initial conjunctive representations predicted significant future response-time costs when task contexts repeated with changed response requirements. Showing that the formation of conjunctive task representations can have negative future effects generates novel insights into complex behavior and cognition, including task switching, planning, and problem solving.