Counting Independent Sets and Colorings on Random Regular Bipartite Graphs

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every Delta-regular bipartite graph if Delta >= 53. In the weighted case, for all sufficiently large integers Delta and weight parameters lambda = Omega~ (1/(Delta)), we also obtain an FPTAS on almost every Delta-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all q >= 3 and sufficiently large integers Delta=Delta(q), there is an FPTAS to count the number of q-colorings on almost every Delta-regular bipartite graph

On the Complexity of #CSP^d

Counting CSP^d is the counting constraint satisfaction problem (#CSP in short) restricted to the instances where every variable occurs a multiple of d times. This paper revisits tractable structures in #CSP and gives a complexity classification theorem for #CSP^d with algebraic complex weights. The result unifies affine functions (stabilizer states in quantum information theory) and related variants such as the local affine functions, the discovery of which leads to all the recent progress on the complexity of Holant problems. The Holant is a framework that generalizes counting CSP. In the literature on Holant problems, weighted constraints are often expressed as tensors (vectors) such that projections and linear transformations help analyze the structure. This paper gives an example showing that different classes of tensors distinguished by these algebraic operations may share the same closure property under tensor product and contraction

[Withdrawn] How Do E-commerce Capabilities Influence Agricultural Firm Performance Gains? Theory and Empirical Evidence

Based on the resource-based view of the firm and from the perspective of organizational agility, thisstudybuilds a model of the factors affecting agricultural firm performance gains in the context of e-commerce and discusses the effects of e-commerce capabilities on firm performance gains. The empirical results show that market capitalizing agility and operational adjustment agility play important mediating roles in conveying positive influences of e-commerce capabilities’ dimensions on financialand non-financial performance gains. Specifically, managerial, analytical, and technical capabilities have different effects on market capitalizing agility and operational adjustment agility, with talent capability performing the most important role. Both market capitalizing agility and operational adjustment agility have positive impacts on financial and non-financial performance gains, respectively

The Complexity of Holant Problems over Boolean Domain with Non-Negative Weights

Holant problem is a general framework to study the computational complexity of counting problems. We prove a complexity dichotomy theorem for Holant problems over the Boolean domain with non-negative weights. It is the first complete Holant dichotomy where constraint functions are not necessarily symmetric. Holant problems are indeed read-twice #CSPs. Intuitively, some #CSPs that are #P-hard become tractable when restricted to read-twice instances. To capture them, we introduce the Block-rank-one condition. It turns out that the condition leads to a clear separation. If a function set F satisfies the condition, then F is of affine type or product type. Otherwise (a) Holant(F) is #P-hard; or (b) every function in F is a tensor product of functions of arity at most 2; or (c) F is transformable to a product type by some real orthogonal matrix. Holographic transformations play an important role in both the hardness proof and the characterization of tractability

How to Train Your Dragon: Tamed Warping Network for Semantic Video Segmentation

Real-time semantic segmentation on high-resolution videos is challenging due to the strict requirements of speed. Recent approaches have utilized the inter-frame continuity to reduce redundant computation by warping the feature maps across adjacent frames, greatly speeding up the inference phase. However, their accuracy drops significantly owing to the imprecise motion estimation and error accumulation. In this paper, we propose to introduce a simple and effective correction stage right after the warping stage to form a framework named Tamed Warping Network (TWNet), aiming to improve the accuracy and robustness of warping-based models. The experimental results on the Cityscapes dataset show that with the correction, the accuracy (mIoU) significantly increases from 67.3% to 71.6%, and the speed edges down from 65.5 FPS to 61.8 FPS. For non-rigid categories such as "human" and "object", the improvements of IoU are even higher than 18 percentage points