Low-Density Arrays of Circulant Matrices: Rank and Row-Redundancy Analysis, and Quasi-Cyclic LDPC Codes

This paper is concerned with general analysis on the rank and row-redundancy of an array of circulants whose null space defines a QC-LDPC code. Based on the Fourier transform and the properties of conjugacy classes and Hadamard products of matrices, we derive tight upper bounds on rank and row-redundancy for general array of circulants, which make it possible to consider row-redundancy in constructions of QC-LDPC codes to achieve better performance. We further investigate the rank of two types of construction of QC-LDPC codes: constructions based on Vandermonde Matrices and Latin Squares and give combinatorial expression of the exact rank in some specific cases, which demonstrates the tightness of the bound we derive. Moreover, several types of new construction of QC-LDPC codes with large row-redundancy are presented and analyzed.Comment: arXiv admin note: text overlap with arXiv:1004.118

Supereulerian Properties in Graphs and Hamiltonian Properties in Line Graphs

Following the trend initiated by Chvatal and Erdos, using the relation of independence number and connectivity as sufficient conditions for hamiltonicity of graphs, we characterize supereulerian graphs with small matching number, which implies a characterization of hamiltonian claw-free graph with small independence number.;We also investigate strongly spanning trailable graphs and their applications to hamiltonian connected line graphs characterizations for small strongly spanning trailable graphs and strongly spanning trailable graphs with short longest cycles are obtained. In particular, we have found a graph family F of reduced nonsupereulerian graphs such that for any graph G with kappa\u27(G) ≥ 2 and alpha\u27( G) ≤ 3, G is supereulerian if and only if the reduction of G is not in F..;We proved that any connected graph G with at most 12 vertices, at most one vertex of degree 2 and without vertices of degree 1 is either supereulerian or its reduction is one of six exceptional cases. This is applied to show that if a 3-edge-connected graph has the property that every pair of edges is joined by a longest path of length at most 8, then G is strongly spanning trailable if and only if G is not the wagner graph.;Using charge and discharge method, we prove that every 3-connected, essentially 10-connected line graph is hamiltonian connected. We also provide a unified treatment with short proofs for several former results by Fujisawa and Ota in [20], by Kaiser et al in [24], and by Pfender in [40]. New sufficient conditions for hamiltonian claw-free graphs are also obtained

CAT: Learning to Collaborate Channel and Spatial Attention from Multi-Information Fusion

Channel and spatial attention mechanism has proven to provide an evident performance boost of deep convolution neural networks (CNNs). Most existing methods focus on one or run them parallel (series), neglecting the collaboration between the two attentions. In order to better establish the feature interaction between the two types of attention, we propose a plug-and-play attention module, which we term "CAT"-activating the Collaboration between spatial and channel Attentions based on learned Traits. Specifically, we represent traits as trainable coefficients (i.e., colla-factors) to adaptively combine contributions of different attention modules to fit different image hierarchies and tasks better. Moreover, we propose the global entropy pooling (GEP) apart from global average pooling (GAP) and global maximum pooling (GMP) operators, an effective component in suppressing noise signals by measuring the information disorder of feature maps. We introduce a three-way pooling operation into attention modules and apply the adaptive mechanism to fuse their outcomes. Extensive experiments on MS COCO, Pascal-VOC, Cifar-100, and ImageNet show that our CAT outperforms existing state-of-the-art attention mechanisms in object detection, instance segmentation, and image classification. The model and code will be released soon.Comment: 8 pages, 5 figure

Attending Category Disentangled Global Context for Image Classification

In this paper, we propose a general framework for image classification using the attention mechanism and global context, which could incorporate with various network architectures to improve their performance. To investigate the capability of the global context, we compare four mathematical models and observe the global context encoded in the category disentangled conditional generative model could give more guidance as "know what is task irrelevant will also know what is relevant". Based on this observation, we define a novel Category Disentangled Global Context (CDGC) and devise a deep network to obtain it. By attending CDGC, the baseline networks could identify the objects of interest more accurately, thus improving the performance. We apply the framework to many different network architectures and compare with the state-of-the-art on four publicly available datasets. Extensive results validate the effectiveness and superiority of our approach. Code will be made public upon paper acceptance.Comment: Under revie

Computational design of steady 3D dissection puzzles

Dissection puzzles require assembling a common set of pieces into multiple distinct forms. Existing works focus on creating 2D dissection puzzles that form primitive or naturalistic shapes. Unlike 2D dissection puzzles that could be supported on a tabletop surface, 3D dissection puzzles are preferable to be steady by themselves for each assembly form. In this work, we aim at computationally designing steady 3D dissection puzzles. We address this challenging problem with three key contributions. First, we take two voxelized shapes as inputs and dissect them into a common set of puzzle pieces, during which we allow slightly modifying the input shapes, preferably on their internal volume, to preserve the external appearance. Second, we formulate a formal model of generalized interlocking for connecting pieces into a steady assembly using both their geometric arrangements and friction. Third, we modify the geometry of each dissected puzzle piece based on the formal model such that each assembly form is steady accordingly. We demonstrate the effectiveness of our approach on a wide variety of shapes, compare it with the state-of-the-art on 2D and 3D examples, and fabricate some of our designed puzzles to validate their steadiness

Align before Search: Aligning Ads Image to Text for Accurate Cross-Modal Sponsored Search

Cross-Modal sponsored search displays multi-modal advertisements (ads) when consumers look for desired products by natural language queries in search engines. Since multi-modal ads bring complementary details for query-ads matching, the ability to align ads-specific information in both images and texts is crucial for accurate and flexible sponsored search. Conventional research mainly studies from the view of modeling the implicit correlations between images and texts for query-ads matching, ignoring the alignment of detailed product information and resulting in suboptimal search performance.In this work, we propose a simple alignment network for explicitly mapping fine-grained visual parts in ads images to the corresponding text, which leverages the co-occurrence structure consistency between vision and language spaces without requiring expensive labeled training data. Moreover, we propose a novel model for cross-modal sponsored search that effectively conducts the cross-modal alignment and query-ads matching in two separate processes. In this way, the model matches the multi-modal input in the same language space, resulting in a superior performance with merely half of the training data. Our model outperforms the state-of-the-art models by 2.57% on a large commercial dataset. Besides sponsored search, our alignment method is applicable for general cross-modal search. We study a typical cross-modal retrieval task on the MSCOCO dataset, which achieves consistent performance improvement and proves the generalization ability of our method. Our code is available at https://github.com/Pter61/AlignCMSS