Optimal Bound Research Articles

A Novel Lightweight Grape Detection Method

This study proposes a novel lightweight grape detection method. First, the backbone network of our method is Uniformer, which captures long-range dependencies and further improves the feature extraction capability. Then, a Bi-directional Path Aggregation Network (BiPANet) is presented to fuse low-resolution feature maps with strong semantic information and high-resolution feature maps with detailed information. BiPANet is constructed by introducing a novel cross-layer feature enhancement strategy into the Path Aggregation Network, which fuses more feature information with a significant reduction in the number of parameters and computational complexity. To improve the localization accuracy of the optimal bounding boxes, a Reposition Non-Maximum Suppression (R-NMS) algorithm is further proposed in post-processing. The algorithm performs repositioning operations on the optimal bounding boxes by using the position information of the bounding boxes around the optimal bounding boxes. Experiments on the WGISD show that our method achieves 87.7% mAP, 88.6% precision, 78.3% recall, 83.1% F1 score, and 46 FPS. Compared with YOLOx, YOLOv4, YOLOv3, Faster R-CNN, SSD, and RetinaNet, the mAP of our method is increased by 0.8%, 1.7%, 3.5%, 21.4%, 2.5%, and 13.3%, respectively, and the FPS of our method is increased by 2, 8, 2, 26, 0, and 10, respectively. Similar conclusions can be obtained on another grape dataset. Encouraging experimental results show that our method can achieve better performance than other recognized detection methods in the grape detection tasks.

Mathematical Methods for IoT-Based Annotating Object Datasets with Bounding Boxes

Object datasets used in the construction of object detectors are typically annotated with horizontal or oriented bounding rectangles for IoT-based. The optimality of an annotation is obtained by fulfilling two conditions: (i) the rectangle covers the whole object and (ii) the area of the rectangle is minimal. Building a large-scale object dataset requires annotators with equal manual dexterity to carry out this tedious work. When an object is horizontal for IoT-based, it is easy for the annotator to reach the optimal bounding box within a reasonable time. However, if the object is oriented, the annotator needs additional time to decide whether the object will be annotated with a horizontal rectangle or an oriented rectangle for IoT-based. Moreover, in both cases, the final decision is not based on any objective argument, and the annotation is generally not optimal. In this study, we propose a new method of annotation by rectangles for IoT-based, called robust semi-automatic annotation, which combines speed and robustness. Our method has two phases. The first phase consists in inviting the annotator to click on the most relevant points located on the contour of the object. The outputs of the first phase are used by an algorithm to determine a rectangle enclosing these points. To carry out the second phase, we develop an algorithm called RANGE-MBR, which determines, from the selected points on the contour of the object, a rectangle enclosing these points in a linear time. The rectangle returned by RANGE-MBR always satisfies optimality condition (i). We prove that the optimality condition (ii) is always satisfied for objects with isotropic shapes. For objects with anisotropic shapes, we study the optimality condition (ii) by simulations. We show that the rectangle returned by RANGE-MBR is quasi-optimal for the condition (ii) and that its performance increases with dilated objects, which is the case for most of the objects appearing on images collected by aerial photography.

First stability eigenvalue of singular hypersurfaces with constant mean curvature in the unit sphere

In this paper, we study the first eigenvalue of the stability operator on an integral n n -varifold with constant mean curvature in the unit sphere S n + 1 \mathbb {S}^{n+1} . We find the optimal upper bound and prove a rigidity result characterizing the case when it is attained. This gives a new characterization for certain singular Clifford tori.

Triharmonic CMC Hypersurfaces in Space Forms with at Most 3 Distinct Principal Curvatures

A k-harmonic map is a critical point of the k-energy defined on the space of smooth maps between two Riemannian manifolds. In this paper, we prove that if $$M^{n} (n\ge 3)$$ is a CMC proper triharmonic hypersurface with at most three distinct principal curvatures in a space form $$\mathbb {R}^{n+1}(c)$$ , then M has constant scalar curvature. This supports the generalized Chen’s conjecture when $$c\le 0$$ . When $$c=1$$ , we give an optimal upper bound of the mean curvature H for a non-totally umbilical proper CMC k-harmonic hypersurface with constant scalar curvature in a sphere. As an application, we give the complete classification of the 3-dimensional complete proper CMC triharmonic hypersurfaces in $$\mathbb {S}^{4}$$ .

Bounds on shifted convolution sums for Hecke eigenforms

Shifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.

A task scheduling algorithm for cloud computing with resource reservation

Resource-reservation-based services have been provided where cloud resources are reserved for tasks within specific time intervals so as fully to exploit the benefits of cloud computing. Such a practice induces an additional decision for task allocation timing and a time index to resource status. Combined with the increasing scale of cloud computing, this increases the complexity of task scheduling in cloud computing. On the other hand, the quality and responsiveness of a task scheduling process should be pursued to meet the desired service features of the market. A task scheduling problem with time-dependent resource availability is formulated, and an heuristic algorithm that derives a high-quality solution to the problem within a very short time is designed to address these challenges. The performance of the algorithm in terms of its optimality and computation efficiency is demonstrated by comparison with the optimal bound found by a commercial optimization solver.

A new analysis of Galerkin Legendre spectral methods for coupled hyperbolic/parabolic system arising in unsteady MHD flow of Maxwell fluid and numerical simulation

In this paper, a high-order accurate numerical method for two-dimensional coupled hyperbolic and parabolic partial differential system arising in unsteady magnetohydrodynamics (MHD) flow of upper-convected Maxwell fluid is presented. We apply Galerkin-Legendre spectral method for discretizing spatial derivatives for MHD-M (MHD flow of Maxwell fluid) equations and then Crank-Nicolson scheme is used for time derivatives. Optimal a priori error bound is derived in the L2 and H1 norm for the semidiscrete formulation. We then proceed to discuss an instability mechanism in polynomial spectral methods and show that filtering suffices to ensure stability. Optimal error bound is derived between the semi-analytical solutions and filtered semi-analytical solutions. The results are illustrated by computational experiments. Furthermore, these results indicate that the proposed method is simple, accurate, efficient, and stable for solving various MHD-M and MHD flow problems or in general coupled hyperbolic-parabolic partial differential equations.

Effect of Contact Preference among Heterogeneous Individuals on Social Contagions

In social networks, individual heterogeneity is widely existed, and an individual often tends to contact more frequently with friends of similar status or opinion. It is worth noting that the contact preference characteristic among heterogeneous individuals will have a significant effect on social contagions. Thus, we propose a social contagion model which takes the heterogeneity of individual influence and contact preference into account, and make a theoretical analysis of the social spreading process by developing an edge-based compartmental theory. We find that the competition between simple contagion and complex contagion leads to the emergence of crossover phase transition phenomena when the influence of ordinary individuals is low: it changes from being hybrid to continuous, then to hybrid, and eventually to continuous phase transition with the increase of the contact probability of homogeneous individuals. However, it changes from being first-order to continuous phase transition when the influence strength of ordinary individuals is relatively high. In addition, there is an optimal value or range of contact probability of homogeneous individuals which maximizes the spreading size, and the optimal value or lower bound of the optimal range decreases with the increase of transmission probability. Our theoretical prediction results are in good agreement with the simulation results.

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

SummaryThis study focuses on the guaranteed cost control problem for interval type‐2 stochastic fuzzy coupled neural networks (NNs) elicited by the observer framework with Markov switching topology, external disturbances, and quantization effect. In particular, the guaranteed cost controller is developed with an upper bound of the guaranteed cost function and also ensures stability of the addressed networks. Also, the integration of lower and upper membership functions are incorporated to relax the stability condition of the networks. Notably, the randomness phenomena are incorporated by the agency of stochastic variables that satisfies the Bernoulli distribution characteristics. Specifically, the state feedback controller considered with quantization effect is designed through undirected communication graph subject to Markov switching topology. In consequence with Lyapunov–Krasovskii‐functional and algebraic graph theory, sufficient conditions are established to assure the stochastic stabilization of the NNs with some specified cost value. Explicitly, the optimal upper bound of the guaranteed cost function and the controller gain fluctuations of the state and the observer are effectuated through the developed conditions. Finally, the reduced conservatism and efficiency of the proposed analytical design are demonstrated through a numerical example.

An Optimal Bound on the Solution Sets of One-Variable Word Equations and its Consequences

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 2 January 2020Accepted: 17 September 2021Published online: 10 January 2022Keywordscombinatorics on words, word equations, systems of equationsAMS Subject Headings68R15Publication DataISSN (print): 0097-5397ISSN (online): 1095-7111Publisher: Society for Industrial and Applied MathematicsCODEN: smjcat

Finite 𝒟C-groups

Let G be a group and [Formula: see text]. G is said to be a [Formula: see text]-group if [Formula: see text] is a chain under set inclusion. In this paper, we prove that a finite [Formula: see text]-group is a semidirect product of a Sylow p-subgroup and an abelian [Formula: see text]-subgroup. For the case of G being a finite p-group, we obtain an optimal upper bound of [Formula: see text] for a [Formula: see text] p-group G. We also prove that a [Formula: see text] p-group is metabelian when [Formula: see text] and provide an example showing that a non-abelian [Formula: see text] p-group is not necessarily metabelian when [Formula: see text]. In particular, [Formula: see text] 2-groups are characterized.

Derangement model of ligand-receptor binding

Abstract We introduce a derangement model of ligand-receptor binding that allows us to quantitatively frame the question “How can ligands seek out and bind to their optimal receptor sites in a sea of other competing ligands and suboptimal receptor sites?” To answer the question, we first derive a formula to count the number of partial generalized derangements in a list, thus extending the derangement result of Gillis and Even. We then compute the general partition function for the ligand-receptor system and derive the equilibrium expressions for the average number of bound ligands and the average number of optimally bound ligands. A visual model of squares assembling onto a grid allows us to easily identify fully optimal bound states. Equilibrium simulations of the system reveal its extremes to be one of two types, qualitatively distinguished by whether optimal ligand-receptor binding is the dominant form of binding at all temperatures and quantitatively distinguished by the relative values of two critical temperatures. One of those system types (termed “search-limited,” as it was in previous work) does not exhibit kinetic traps and we thus infer that biomolecular systems where optimal ligand-receptor binding is functionally important are likely to be search-limited.

Several Optimal Bounds for Some Means Derived from the Lemniscatic Mean

Several Optimal Bounds for Some Means Derived from the Lemniscatic Mean

Operational matrix based set-membership method for fractional order systems parameter identification

In this paper, a new method is proposed to identify the coefficients and differentiation orders of fractional order systems with measurement noise. The proposed method combines the operational matrix method and the set-membership method. First, the block pulse functions operational matrix of the fractional differentiation is used to convert the fractional order system to an algebraic system. Then, the coefficients and differentiation orders are simultaneously estimated through a nest loop optimization process, where the optimal bounding ellipsoid set-membership algorithm is utilized to estimate the system’s coefficients and the orders are estimated with the interior-point method. The proposed method can accurately estimate the coefficients and differentiation orders of fractional order systems under any bounded measurement noise with less computational effort. Experimental results demonstrate the effectiveness of the proposed method.

Advances in parallel and distributed computing and its applications

Advances in parallel and distributed computing and its applications

Asymptotic properties of the OBE parameter estimation algorithm under diffuse initialization

The parameters estimation problem of autoregressive with exogenous inputs models is considered. Our approach is based on the study of the optimal bounding ellipsoid (OBE) recurrent algorithm properties. It is assumed that the shape matrix of the initial ellipsoid in the OBE algorithm is proportional to a large positive parameter. Asymptotic expansions of the relations that describe the OBE algorithm are obtained. The limit recursive algorithm (diffuse) not depending on a large parameter which may lead the OBE algorithm to a divergence is proposed and explored. The robust properties of the proposed algorithm are illustrated by a numerical example. By simulation, it is shown that it may provide better the tracking ability compared to the diffuse least-squares (RLS) algorithm and the diffuse RLS algorithm with the sliding window.

An Edgeworth Expansion for the Ratio of Two Functionals of Gaussian Fields and Optimal Berry–Esseen Bounds

This paper is concerned with the rate of convergence of the distribution of the sequence {Fn/Gn}, where Fn and Gn are each functionals of infinite-dimensional Gaussian fields. This form very frequently appears in the estimation problem of parameters occurring in Stochastic Differential Equations (SDEs) and Stochastic Partial Differential Equations (SPDEs). We develop a new technique to compute the exact rate of convergence on the Kolmogorov distance for the normal approximation of Fn/Gn. As a tool for our work, an Edgeworth expansion for the distribution of Fn/Gn, with an explicitly expressed remainder, will be developed, and this remainder term will be controlled to obtain an optimal bound. As an application, we provide an optimal Berry–Esseen bound of the Maximum Likelihood Estimator (MLE) of an unknown parameter appearing in SDEs and SPDEs.

Succinct Encoding of Binary Strings Representing Triangulations

We consider the problem of designing a succinct data structure for representing the connectivity of planar triangulations. The main result is a new succinct encoding achieving the information-theory optimal bound of 3.24 bits per vertex, while allowing efficient navigation. Our representation is based on the bijection of Poulalhon and Schaeffer (Algorithmica, 46(3):505–527, 2006) that defines a mapping between planar triangulations and a special class of spanning trees, called PS-trees. The proposed solution differs from previous approaches in that operations in planar triangulations are reduced to operations in particular parentheses sequences encoding PS-trees. Existing methods to handle balanced parentheses sequences have to be combined and extended to operate on such specific sequences, essentially for retrieving matching elements. The new encoding supports extracting the d neighbors of a query vertex in O(d) time and testing adjacency between two vertices in O(1) time. Additionally, we provide an implementation of our proposed data structure. In the experimental evaluation, our representation reaches up to 7.35 bits per vertex, improving the space usage of state-of-the-art implementations for planar embeddings.

Three regularization methods for identifying the initial value of homogeneous anomalous secondary diffusion equation

In this paper, the inverse problem of initial value identification for homogeneous anomalous diffusion equation with Riemann‐Liouville fractional derivative in time is studied. We prove that this kind of problem is ill‐posed. We analyze the optimal error bound of the problem under the source condition and apply the quasi‐boundary regularization method, fractional Landweber iterative regularization method, and Landweber iterative regularization method to solve this inverse problem. Based on the results of conditional stability, the error estimates between the exact solution and the regular solution are given under the priori and posteriori regularization parameter selection rules. Finally, three examples are given to illustrate the effectiveness and feasibility of these methods.

On the limitations of single-step drift and minorization in Markov chain convergence analysis

Over the last three decades, there has been a considerable effort within the applied probability community to develop techniques for bounding the convergence rates of general state space Markov chains. Most of these results assume the existence of drift and minorization (d&m) conditions. It has often been observed that convergence rate bounds based on single-step d&m tend to be overly conservative, especially in high-dimensional situations. This article builds a framework for studying this phenomenon. It is shown that any convergence rate bound based on a set of d&m conditions cannot do better than a certain unknown optimal bound. Strategies are designed to put bounds on the optimal bound itself, and this allows one to quantify the extent to which a d&m-based convergence rate bound can be sharp. The new theory is applied to several examples, including a Gaussian autoregressive process (whose true convergence rate is known), and a Metropolis adjusted Langevin algorithm. The results strongly suggest that convergence rate bounds based on single-step d&m conditions are quite inadequate in high-dimensional settings.