Showing papers on "Disjoint sets published in 2022"

On the maximal number of disjoint circuits of a graph

Abstract: Throughout this paper Gg" will denote a graph with n vertices and k edges where circuits consisting of two edges and loops (i . e. circuits of one edge) are not permitted and G'" will denote a graph of n vertices and k edges where loops and circuits with two edges are permitted . v(G) (respectively v(G)) will denote the number of edges of G (respectively G) . If x,, x" . . ., x,, are some of the vertices of G, then (G-x, . . . -xk) will denote the graph which we obtain from G by omitting the vertices x,, . . ., x k and all the edges incident to them . By G(x,, . . ., x k ) we denote the subgraph of G spanned by the vertices x,, . . ., xk . The valency of a vertex x v (x) will denote the number of edges incident to it. (A loop is counted doubly.) The edge connecting x, and x, will be denoted by [x,, x,], edges will sometimes be denoted by e,, ez , . . . . (x,, x,, . . .xk ) will denote the circuit having the edges [x,, x,], . . ., [xk_,, .vk], [x k x,] . A set of edges is called independent if no two of them have a common vertex . A set of circuits will be called independent if no two of them have a common vertex . They will be called weakly independent if no two of them have a common edge . In a previous paper ERDŐS and GALLAI [l] proved that every

Decomposition, Condensation Defects, and Fusion

Abstract: In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher‐form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement that d‐dimensional quantum field theories with global (d−1)$(d-1)$ ‐form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non‐invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher‐form symmetries, which can be used to select individual universes in a decomposition.

BlindFL: Vertical Federated Machine Learning without Peeking into Your Data

Abstract: Due to the rising concerns on privacy protection, how to build machine learning (ML) models over different data sources with security guarantees is gaining more popularity. Vertical federated learning (VFL) describes such a case where ML models are built upon the private data of different participated parties that own disjoint features for the same set of instances, which fits many real-world collaborative tasks. Nevertheless, we find that existing solutions for VFL either support limited kinds of input features or suffer from potential data leakage during the federated execution. To this end, this paper aims to investigate both the functionality and security of ML modes in the VFL scenario. To be specific, we introduce BlindFL, a novel framework for VFL training and inference. First, to address the functionality of VFL models, we propose the federated source layers to unite the data from different parties. Various kinds of features can be supported efficiently by the federated source layers, including dense, sparse, numerical, and categorical features. Second, we carefully analyze the security during the federated execution and formalize the privacy requirements. Based on the analysis, we devise secure and accurate algorithm protocols, and further prove the security guarantees under the ideal-real simulation paradigm. Extensive experiments show that BlindFL supports diverse datasets and models efficiently whilst achieves robust privacy guarantees.

Optimal Scale Combination Selection Integrating Three-Way Decision With Hasse Diagram

Abstract: Multi-scale decision system (MDS) is an effective tool to describe hierarchical data in machine learning. Optimal scale combination (OSC) selection and attribute reduction are two key issues related to knowledge discovery in MDSs. However, searching for all OSCs may result in a combinatorial explosion, and the existing approaches typically incur excessive time consumption. In this study, searching for all OSCs is considered as an optimization problem with the scale space as the search space. Accordingly, a sequential three-way decision model of the scale space is established to reduce the search space by integrating three-way decision with the Hasse diagram. First, a novel scale combination is proposed to perform scale selection and attribute reduction simultaneously, and then an extended stepwise optimal scale selection (ESOSS) method is introduced to quickly search for a single local OSC on a subset of the scale space. Second, based on the obtained local OSCs, a sequential three-way decision model of the scale space is established to divide the search space into three pair-wise disjoint regions, namely the positive, negative, and boundary regions. The boundary region is regarded as a new search space, and it can be proved that a local OSC on the boundary region is also a global OSC. Therefore, all OSCs of a given MDS can be obtained by searching for the local OSCs on the boundary regions in a step-by-step manner. Finally, according to the properties of the Hasse diagram, a formula for calculating the maximal elements of a given boundary region is provided to alleviate space complexity. Accordingly, an efficient OSC selection algorithm is proposed to improve the efficiency of searching for all OSCs by reducing the search space. The experimental results demonstrate that the proposed method can significantly reduce computational time.

Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

Abstract: Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement and critical slowdown. We show that at high energies the particular form of the projectors causes the emergence of disjoint Krylov subspaces for open boundary conditions, with an exact quantum scar being embedded in each subspace, leading to slow growth of entanglement and localized dynamics for specific out-of-equilibrium initial states. Furthermore, focusing on infinite temperature, we unveil that spin transport is subdiffusive, which we corroborate by simulations of constrained stochastic cellular automaton circuits. Compared to dipole moment conserving systems, the deformed Motzkin chain appears to belong to a different universality class with distinct dynamical transport exponent and only polynomially many Krylov subspaces.

Flexible Body Partition-Based Adversarial Learning for Visible Infrared Person Re-Identification

Abstract: Person re-identification (Re-ID) aims to retrieve images of the same person across disjoint camera views. Most Re-ID studies focus on pedestrian images captured by visible cameras, without considering the infrared images obtained in the dark scenarios. Person retrieval between visible and infrared modalities is of great significance to public security. Current methods usually train a model to extract global feature descriptors and obtain discriminative representations for visible infrared person Re-ID (VI-REID). Nevertheless, they ignore the detailed information of heterogeneous pedestrian images, which affects the performance of Re-ID. In this article, we propose a flexible body partition (FBP) model-based adversarial learning method (FBP-AL) for VI-REID. To learn more fine-grained information, FBP model is exploited to automatically distinguish part representations according to the feature maps of pedestrian images. Specially, we design a modality classifier and introduce adversarial learning which attempts to discriminate features between visible and infrared modality. Adaptive weighting-based representation learning and threefold triplet loss-based metric learning compete with modality classification to obtain more effective modality-sharable features, thus shrinking the cross-modality gap and enhancing the feature discriminability. Extensive experimental results on two cross-modality person Re-ID data sets, i.e., SYSU-MM01 and RegDB, exhibit the superiority of the proposed method compared with the state-of-the-art solutions.

Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

Abstract: <abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

Convolutional relation network for facial expression recognition in the wild with few-shot learning

Abstract: Recent deep learning based facial expression recognition (FER) methods are mostly driven by the availability of large amount of training data. However, availability of such data is not always possible for FER in the wild where the infeasibility of obtaining sufficient training samples for each emotion category. Therefore, in this paper, we introduce the few-shot learning to construct a deep learning model named Convolutional Relation Network (CRN) for FER in the wild, which is learnt by exploiting a feature similarity comparison among the sufficient samples of the emotion categories to identify new classes with few samples. Specifically, our method learns a metric space in which classification can be performed by computing distances to capitalize on powerful discriminative ability of deep expression features to generalize the predictive power of the network. To achieve this, the features are constrained to maximize the distance between the features of different classes and discover the commonality of the same classes. Extensive experiments on three challenging in-the-wild datasets demonstrate that the proposed model significantly outperforms state-of-the-art methods.

Continuous Influence-Based Community Partition for Social Networks

Abstract: Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under LT model in social networks, which is a combinatorial optimization problem that divides the social network to disjoint $m$ communities. Our goal is to maximize the sum of influence propagation through maximizing it within each community. As the influence propagation function of community partition problem is supermodular under LT model, we use the method of Lov{$\acute{a}$}sz Extension to relax the target influence function and transfer our goal to maximize the relaxed function over a matroid polytope. Next, we propose a continuous greedy algorithm using the properties of the relaxed function to solve our problem, which needs to be discretized in concrete implementation. Then, random rounding technique is used to convert the fractional solution to integer solution. We present a theoretical analysis with $1-1/e$ approximation ratio for the proposed algorithms. Extensive experiments are conducted to evaluate the performance of the proposed continuous greedy algorithms on real-world online social networks datasets and the results demonstrate that continuous community partition method can improve influence spread and accuracy of the community partition effectively.

Deep Multimodal Transfer Learning for Cross-Modal Retrieval

Abstract: Cross-modal retrieval (CMR) enables flexible retrieval experience across different modalities (e.g., texts versus images), which maximally benefits us from the abundance of multimedia data. Existing deep CMR approaches commonly require a large amount of labeled data for training to achieve high performance. However, it is time-consuming and expensive to annotate the multimedia data manually. Thus, how to transfer valuable knowledge from existing annotated data to new data, especially from the known categories to new categories, becomes attractive for real-world applications. To achieve this end, we propose a deep multimodal transfer learning (DMTL) approach to transfer the knowledge from the previously labeled categories (source domain) to improve the retrieval performance on the unlabeled new categories (target domain). Specifically, we employ a joint learning paradigm to transfer knowledge by assigning a pseudolabel to each target sample. During training, the pseudolabel is iteratively updated and passed through our model in a self-supervised manner. At the same time, to reduce the domain discrepancy of different modalities, we construct multiple modality-specific neural networks to learn a shared semantic space for different modalities by enforcing the compactness of homoinstance samples and the scatters of heteroinstance samples. Our method is remarkably different from most of the existing transfer learning approaches. To be specific, previous works usually assume that the source domain and the target domain have the same label set. In contrast, our method considers a more challenging multimodal learning situation where the label sets of the two domains are different or even disjoint. Experimental studies on four widely used benchmarks validate the effectiveness of the proposed method in multimodal transfer learning and demonstrate its superior performance in CMR compared with 11 state-of-the-art methods.

Convolutional relation network for facial expression recognition in the wild with few-shot learning

Abstract: Recent deep learning based facial expression recognition (FER) methods are mostly driven by the availability of large amount of training data. However, availability of such data is not always possible for FER in the wild where the infeasibility of obtaining sufficient training samples for each emotion category. Therefore, in this paper, we introduce the few-shot learning to construct a deep learning model named Convolutional Relation Network (CRN) for FER in the wild, which is learnt by exploiting a feature similarity comparison among the sufficient samples of the emotion categories to identify new classes with few samples. Specifically, our method learns a metric space in which classification can be performed by computing distances to capitalize on powerful discriminative ability of deep expression features to generalize the predictive power of the network. To achieve this, the features are constrained to maximize the distance between the features of different classes and discover the commonality of the same classes. Extensive experiments on three challenging in-the-wild datasets demonstrate that the proposed model significantly outperforms state-of-the-art methods. • Recognize new emotion classes in the wild given only few examples from each. • Salient discriminative feature learning and emotion similarity learning. • Few-shot learning and transfer discriminative knowledge. • Divide the emotion database into independent disjoint training and testing set.

Holographic study of reflected entropy in anisotropic theories

Abstract: We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using this prescription, we study in detail the effect of anisotropy on reflected entropy and other holographic entanglement measures. In partic-ular, we study the discontinuous phase transition of this quantity for a symmetric configuration consisting of two disjoint strips. We find that in the specific regimes of the parameter space the critical separation is an increasing function of the anisotropy parameter and hence the correlation between the subregions becomes more pronounced. We carefully examine how these results are consistent with the behavior of other correlation measures including the mutual information. Finally, we show that the structure of the universal terms of entanglement entropy is corrected depending on the orientation of the entangling region with respect to the anisotropic direction.

StabMap: Mosaic single cell data integration using non-overlapping features

Abstract: Currently available single cell -omics technologies capture many unique features with different biological information content. Data integration aims to place cells, captured with different technologies, onto a common embedding to facilitate downstream analytical tasks. Current horizontal data integration techniques use a set of common features, thereby ignoring non-overlapping features and losing information. Here we introduce StabMap, a mosaic data integration technique that stabilises mapping of single cell data by exploiting the non-overlapping features. StabMap is a flexible approach that first infers a mosaic data topology, then projects all cells onto supervised or unsupervised reference coordinates by traversing shortest paths along the topology. We show that StabMap performs well in various simulation contexts, facilitates disjoint mosaic data integration, and enables the use of novel spatial gene expression features for mapping dissociated single cell data onto a spatial transcriptomic reference.

A ReMeDI for Microstructure Noise

Abstract: We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high‐frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes, and data frequencies.

Reliability modelling for linear and circular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e10155" altimg="si12.svg"><mml:mi>k</mml:mi></mml:math>-out-of-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e10160" altimg="si13.svg"><mml:mi>n</mml:mi></mml:math>: F systems with shared components

Abstract: Reliability analysis for k-out-of-n systems has received much attention in the field of reliability due to its practical importance. In this work, models for linear and circular k-out-of-n: F systems with shared components, consisting of m subsystems, are discussed. The finite Markov chain imbedding approach cannot be used directly to derive reliability of the considered systems because of the common area existing between adjacent subsystems. For this reason, we first derive the probability that the number of failed components is a given value in the m common areas. Then, all disjoint cases, each of which is regarded as a series system consisting of m subsystems with different initial state probability distributions, are obtained, with which the nith step transition rate matrix is calculated by using the Markov chain technique, for i=1,2,…,m. Finally, the reliability of the system is obtained by summing the reliabilities of all cases along with the finite Markov chain imbedding approach. Some numerical examples are presented to illustrate the efficiency of the proposed reliability evaluation method.

Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape

Abstract: Within the Kardar–Parisi–Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work [27] of Dauvergne, Ortmann, and Virág, this object was constructed and, upon a parabolic correction, shown to be the limit of one such model: Brownian last passage percolation. The limit object without parabolic correction, called the directed landscape, admits geodesic paths between any two space-time points (x,s) and (y,t) with s

Entanglement Negativity in Flat Holography

Abstract: We advance holographic constructions for the entanglement negativity of bipartite states in a class of $(1+1)-$dimensional Galilean conformal field theories dual to asymptotically flat three dimensional bulk geometries described by Einstein Gravity and Topologically Massive Gravity. The construction involves specific algebraic sums of the lengths of bulk extremal curves homologous to certain combinations of the intervals appropriate to such bipartite states. Our analysis exactly reproduces the corresponding replica technique results in the large central charge limit. We substantiate our construction through a semi classical analysis involving the geometric monodromy technique for the case of two disjoint intervals in such Galilean conformal field theories dual to bulk Einstein Gravity.

Signal Temporal Logic Task Decomposition via Convex Optimization

Abstract: In this letter we focus on the problem of decomposing a global Signal Temporal Logic formula (STL) assigned to a multi-agent system to local STL tasks when the team of agents is a-priori decomposed to disjoint sub-teams. The predicate functions associated to the local tasks are parameterized as hypercubes depending on the states of the agents in a given sub-team. The parameters of the functions are, then, found as part of the solution of a convex program that aims implicitly at maximizing the volume of the zero superlevel set of the corresponding predicate function. Two alternative definitions of the local STL tasks are proposed and the satisfaction of the global STL formula is proven when the conjunction of the local STL tasks is satisfied.

A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators

Abstract: <abstract><p>Given a bounded open set $ \Omega\subseteq{\mathbb{R}}^n $, we consider the eigenvalue problem for a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of $ \Omega $. We prove that the second eigenvalue $ \lambda_2(\Omega) $ is always strictly larger than the first eigenvalue $ \lambda_1(B) $ of a ball $ B $ with volume half of that of $ \Omega $. This bound is proven to be sharp, by comparing to the limit case in which $ \Omega $ consists of two equal balls far from each other. More precisely, differently from the local case, an optimal shape for the second eigenvalue problem does not exist, but a minimizing sequence is given by the union of two disjoint balls of half volume whose mutual distance tends to infinity.</p></abstract>