Strong Local Properties Research Articles

Local diagnosability of bipartite graphs with conditional faulty edges under Preparata, Metze and Chien’s model

Diagnosability of a multiprocessor system is an important research topic. The system or interconnection network has an underlying topology, which usually presented by a graph. In this paper, let G be a bipartite graph with δ ( G ) = δ and let there be at most two common neighbor vertices of any two vertices in G under the PMC model. We firstly study the diagnosability of G . We prove that G − F keeps the strong local diagnosability property even if it has the set F of ( δ − 2 ) faulty edges. Secondly, we study the diagnosability of G with conditional faulty edges. We prove that G − F keeps strong local diagnosability property even if it has the set F of ( 3 δ − 7 ) faulty edges, provided that each vertex of G − F is incident with at least two fault-free edges. Finally, we prove that G − F keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of G − F is incident with at least three fault-free edges.

Continuum models of directed polymers on disordered diamond fractals in the critical case

We construct and study a family of random continuum polymer measures Mr corresponding to limiting partition function laws recently derived in a weak-coupling regime for polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval [0,1] into a compact diamond fractal having Hausdorff dimension two, and there is a natural “uniform” probability measure, μ, over the space of directed paths, Γ. Realizations of the random path measures Mr exhibit strong localization properties in comparison to their subcritical counterparts in which the diamond fractal has dimension less than two. Whereas two paths p,q∈Γ sampled independently using the pure measure μ have only finitely many intersections with probability one, a realization of the disordered product measure Mr×Mr a.s. assigns positive weight to the set of pairs of paths (p,q) whose intersection sets are uncountable but of Hausdorff dimension zero. We give a more refined characterization of the size of these dimension-zero sets using generalized (logarithmic) Hausdorff measures. The law of the random measure Mr cannot be constructed as a subcritical Gaussian multiplicative chaos because the coupling strength to the Gaussian field would, in a formal sense, have to be infinite.

Bandgap and Wave Propagation Properties of 2D Curved and Chiral Hybrid Star‐Shaped Metamaterials

Designing artificial microstructural metamaterials that fulfill the single‐phase vibration dampening and lightweight twin goals is challenging and critical. 2D curved and chiral hybrid star‐shaped metamaterials (CCHSM) are proposed to perform vibration reduction filtering in the midfrequency region by combining the properties of chiral structure and concave structure. The generating process of the bandgap of in‐plane elastic waves, the properties of directional attenuation, and the flow direction of energy in the dispersion curve are examined using the modal shape, dispersion surface, and group velocity. In a specific frequency range, the equivalent medium parameters satisfy the conditions of negative refraction transverse and longitudinal waves, so the structure also has double‐negative characteristics. The filtering performance is validated using the CCHSM periodic plate structure and a finite‐element simulation of transmission loss. In addition, the correlation between wave attenuation characteristics and structural parameters is explored. The radius of the circular arc and the deflection angle of the connecting rod have a significant impact on the frequency range of the structural bandgap. The results show that the created simple‐configured, single‐phase lightweight acoustic metamaterials exhibit strong local resonance properties and double‐negative features.

Topological surface plasmon resonance in deep subwavelength structure

We propose a plasmonic topological junction structure that combines topological robustness and subwavelength localization properties. The proposed structure is a junction of two topologically distinguished metal-insulator-metal waveguide gratings. Assuming Au–SiO2–Au waveguide gratings, we theoretically demonstrate a plasmonic Jackiw-Rebbi-state resonance which has substantially small effective mode-field area in the order of 0.1 μm2 at 1560 nm wavelength and requires only 10 periods for fully sustaining the ideal resonance Q-factor of the infinitely large array. Therefore, our proposed approach provides an efficient scheme for creating various plasmonic leaky-mode resonance components that can take advantages of spectral robustness and strong localization properties.

Localization of light in 2D photonic Moiré superlattices

In this paper, monolayer photonic Moiré superlattices (PMSs) are constructed by superposing two periodic sublattices with square primitive cells and tunable twist angles. The sublattices are designed by interfering four umbrella-like beams. Light localization properties and physical flat-band effects of PMSs are studied by solving the Schrödinger equation in the periodic potentials. We have investigated the influence of interference angle and twist angle of sublattices on the localization of light and physical flat bands, and demonstrated that PMSs have physical flat bands and strong light localization properties when the twist angle is less than 5°, while the interference angle does not affect the flat-bands and localization properties. Our work provides a new research idea for manipulating spatial light fields and processing light information.

The Local Diagnosability of a Class of Cayley Graphs with Conditional Faulty Edges Under the PMC Model

Abstract The diagnosability of a multiprocessor system is of great significance in measuring the reliability and faulty tolerance of interconnection networks. In this paper, we firstly study the diagnosability of a class of Cayley graphs $Cay(H_n,S_n)$ under the PMC model. We prove that $Cay(H_n,S_n)-F$ keeps the strong local diagnosability property even if it has the set $F$ of $(m-2)$ faulty edges and $m-2$ is maximum number of faulty edges, where $m$ is the regular degree of $Cay(H_n,S_n)$. Secondly, we study the diagnosability of $Cay(H_n,S_n)$ with conditional faulty edges under the PMC model. We prove that $Cay(H_n,S_n)-F$ keeps strong local diagnosability property even if it has the set $F$ of $(3m-10)$ faulty edges, provided that each vertex of $Cay(H_n,S_n)-F$ is incident with at least two fault-free edges, where $3m-10$ is maximum number of faulty edges. Finally, we prove that $Cay(H_n,S_n)-F$ keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of $Cay(H_n,S_n)-F$ is incident with at least four fault-free edges.

The Local Diagnosability of Folded Hypercubes with Conditional Faulty Edges Under the PMC Model

The diagnosability of a multiprocessor system is of great significance in measuring the reliability and faulty tolerance of interconnection networks. In this paper, we firstly study the diagnosability of the [Formula: see text]-dimensional folded hypercube [Formula: see text] under the PMC model. We prove that [Formula: see text] keeps the strong local diagnosability property even if it has the set [Formula: see text] of [Formula: see text] faulty edges and [Formula: see text] is maximum number of faulty edges. Secondly, we study the diagnosability of [Formula: see text] [Formula: see text] and [Formula: see text] is odd) with conditional faulty edges under the PMC model. We prove that [Formula: see text] keeps strong local diagnosability property even if it has the set [Formula: see text] of [Formula: see text] faulty edges, provided that each vertex of [Formula: see text] is incident with at least two fault-free edges, where [Formula: see text] is maximum number of faulty edges. Finally, we prove that [Formula: see text] keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of [Formula: see text] is incident with at least three fault-free edges.

DA-SACOT: Domain adaptive-segmentation guided attention for correlation based object tracking

Object tracking relies on a recursive search technique around the previous target location, concurrently learning the target appearance in each frame. A failure in any frame causes a drift from its optimal target path. Thus, obtaining highly confident search regions is essential in each frame. Motivated by the strong localization property of segmented object masks, the proposed method introduces instance segmentation as an attention mechanism in object tracking framework. The core contribution of this paper is threefold: (i) a region proposal module (RPM) based on instance segmentation to focus on search proposals having a high probability of being the target, (ii) a target localization module (TLM) to localize the final target using a correlation filter and (iii) a domain adaptation technique in both RPM and TLM modules to incorporate target specific knowledge and strong discrimination ability. Extensive experimental evaluation on three benchmark datasets demonstrate a significant average gain of 2.47% in precision, 2.55% in AUC score and 2.15% in overlap score in comparison with recent competing trackers.

Conjugate Gradient Methods for Computing Weighted Analytic Center for Linear Matrix Inequalities Using Exact and Quadratic Interpolation Line Searches

We study the problem of computing the weighted analytic center for linear matrix inequality constraints. In this paper, we apply conjugate gradient (CG) methods to find the weighted analytic center. CG methods have low memory requirements and strong local and global convergence properties. The methods considered are the classical methods by Hestenes-Stiefel (HS), Fletcher and Reeves (FR), Polak and Ribiere (PR) and a relatively new method by Rivaie, Abashar, Mustafa and Ismail (RAMI). We compare performance of each method on random test problems by observing the number of iterations and time required by the method to find the weighted analytic center for each test problem. We use Newton’s method exact line search and Quadratic Interpolation inexact line search. Our numerical results show that PR is the best method, followed by HS, then RAMI, and then FR. However, PR and HS performed about the same with exact line search. The results also indicate that both line searches work well, but exact line search handles weights better than the inexact line search when some weight is relatively much larger than the other weights. We also find from our results that with Quadratic interpolation line search, FR is more susceptible to jamming phenomenon than both PR and HS.

Diagnosability of the Cayley Graph Generated by Complete Graph with Missing Edges under the MM$^{\ast }$ Model

Abstract Diagnosability of a multiprocessor system is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. Under the Maeng and Malek's (MM) model, to diagnose the system, a node sends the same task to two of its neighbors, and then compares their responses. The MM$^{*}$ is a special case of the MM model and each node must test all pairs of its adjacent nodes. In 2009, Chiang and Tan (Using node diagnosability to determine $t$-diagnosability under the comparison diagnosis (cd) model. IEEE Trans. Comput., 58, 251–259) proposed a new viewpoint for fault diagnosis of the system, namely, the node diagnosability. As a new topology structure of interconnection networks, the nest graph $CK_{n}$ has many good properties. In this paper, we study the local diagnosability of $CK_{n}$ and show it has the strong local diagnosability property even if there exist $(\frac{n(n-1)}{2}-2)$ missing edges in it under the MM$^{*}$ model, and the result is optimal with respect to the number of missing edges.

Diagnosability of expanded k-ary n-cubes with missing edges under the comparison model

ABSTRACTThe diagnosability of multiprocessor systems is an important research topic. In 2017, Wang et al. extended the k-ary n-cube and defined an expanded k-ary n-cube, which is a system topology structure with good properties. In this paper, we prove that the expanded k-ary n-cube has the strong local diagnosability property for and , and it keeps this strong property even if there exist missing edges in it under the comparison model.

A short note on strong local diagnosability property of exchanged hypercubes under the comparison model

The diagnosability of a multiprocessor system plays an important role. The system and an interconnection network have a underlying topology, which are usually presented by a graph. The exchanged hypercube has some good properties. In this paper, we study the diagnosis on under the comparison model. Following the concept of the local diagnosability, the strong local diagnosability property is discussed. This property describes the equivalence of the local diagnosability of a node and its degree. We prove that ( and s=1,t=2) has this property under the comparison model.

Diagnosability of Bubble-Sort Star Graphs with Missing Edges

The diagnosability of a multiprocessor system plays an important role. The bubble-sort star graph BSn has many good properties. In this paper, we study the diagnosis on BSn under the comparison model. Following the concept of the local diagnosability, the strong local diagnosability property is discussed. This property describes the equivalence of the local diagnosability of a node and its degree. We prove that BSn (n ≥ 5) has this property, and it keeps this strong property even if there exist (2n − 5) missing edges in it, and the result is optimal with respect to the number of missing edges.

A construction for difference sets with local properties

We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set A of n real numbers such that |A−A|=nlog23 and that every subset A′⊆A of size k satisfies |A′−A′|≥klog23. This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.

Diagnosability of arrangement graphs with missing edges under the MM* model

Diagnosability is an important parameter to measure the fault tolerance of interconnection networks. Arrangement graph is a generalisation of the star graphs, yet it is more flexible in its size than the star graphs. In this paper, we study the local diagnosability of , and show that it has the strong local diagnosability property even if there exist missing edges in it under the MM* model, and the result is optimal with respect to the number of missing edges.

Local diagnosability under the PMC model with application to matching composition networks

SummaryMatching composition network is a family of interconnection networks, including the BC network and the hyper Petersen network, etc. In this paper, we prove that the local diagnosability of an MCN can be obtained by adding one to that of the component with some structural restrictions. Additionally, we obtain a sufficient condition for verifying that an MCN with fault‐free edges (faulty edges, respectively) has strong local diagnostic properties. By applying these results, the BC network BCn and the hyper Petersen network HPn are nl‐diagnosable at each node belonging to them, for n ⩾ 3. These interconnection networks with fault‐free edges (faulty edges, respectively) possess the strong local diagnosability property.

Large scale index of multi-partitioned manifolds

Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a Hermitean bundle on M with connection. We define a coarse multi-partitioned index of the spin Dirac operator on M twisted by E . Our main result is the computation of this multi-partitioned index as the Fredholm index of the Dirac operator on the compact manifold N , twisted by the restriction of E to N . We establish the following main application: if the scalar curvature of M is bounded below by a positive constant everywhere (or even if this happens only on one of the quadrants defined by the partitioning hypersurfaces) then the multi-partitioned index vanishes. Consequently, the multi-partitioned index is an obstruction to uniformly positive scalar curvature on M . The proof of the multi-partitioned index theorem proceeds in two steps: first we establish a strong new localization property of the multi-partitioned index which is the main novelty of this note. This we establish even when we twist with an arbitrary Hilbert A -module bundle E (for an auxiliary C^* -algebra A ). This allows to reduce to the case where M is the product of N with Euclidean space of dimension q . For this special case, standard methods for the explicit calculation of the index in this product situation can be adapted to obtain the result.

Localization of quantum states and landscape functions

Eigenfunctions in inhomogeneous media can have strong localization properties. Filoche and Mayboroda showed that the function u u solving ( − Δ + V ) u = 1 (-\Delta + V)u = 1 controls the behavior of eigenfunctions ( − Δ + V ) ϕ = λ ϕ (-\Delta + V)\phi = \lambda \phi via the inequality \[ | ϕ ( x ) | ≤ λ u ( x ) ‖ ϕ ‖ L ∞ . |\phi (x)| \leq \lambda u(x) \|\phi \|_{L^{\infty }}. \] This inequality has proven to be remarkably effective in predicting localization and recently Arnold, David, Jerison, Mayboroda and Filoche connected 1 / u 1/u to decay properties of eigenfunctions. We aim to clarify properties of the landscape: the main ingredient is a localized variation estimate obtained from writing ϕ ( x ) \phi (x) as an average over Brownian motion ω ( ⋅ ) \omega (\cdot ) started in x x \[ ϕ ( x ) = E x ( ϕ ( ω ( t ) ) e λ t − ∫ 0 t V ( ω ( z ) ) d z ) . \phi (x) = \mathbb {E}_{x}\left (\phi (\omega (t)) e^{\lambda t-\int _{0}^{t}{V(\omega (z))dz}} \right ). \] This variation estimate will guarantee that ϕ \phi has to change at least by a factor of 2 in a small ball, which implicitly creates a landscape whose relationship with 1 / u 1/u we discuss.

A Globally Convergent LP-Newton Method

We develop a globally convergent algorithm based on the LP-Newton method, which has been recently proposed for solving constrained equations, possibly nonsmooth and possibly with nonisolated solutions. The new algorithm makes use of linesearch for the natural merit function and preserves the strong local convergence properties of the original LP-Newton scheme. We also present computational experiments on a set of generalized Nash equilibrium problems, and a comparison of our approach with the previous hybrid globalization employing the potential reduction method.

Improved Tampering Localization in Digital Image Forensics Based on Maximal Entropy Random Walk

In this paper we propose to use maximal entropy random walk on a graph for tampering localization in digital image forensics. Our approach serves as an additional post-processing step after conventional sliding-window analysis with a forensic detector. Strong localization property of this random walk will highlight important regions and attenuate the background - even for noisy response maps. Our evaluation shows that the proposed method can significantly outperform both the commonly used threshold-based decision, and the recently proposed optimization-based approach with a Markovian prior.