Sampling Lov\'asz Local Lemma For General Constraint Satisfaction Solutions In Near-Linear Time

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. The expected running time of our algorithm is near-linear in $n$ and a fixed polynomial in $\Delta$, where $n$ is the number of variables and $\Delta$ is the max degree of constraints. Previously, up to similar conditions, sampling algorithms with running time polynomial in both $n$ and $\Delta$, only existed for the almost atomic case, where each constraint is violated by a small number of forbidden local configurations. Our sampling approach departs from all previous fast algorithms for sampling LLL, which were based on Markov chains. A crucial step of our algorithm is a recursive marginal sampler that is of independent interests. Within a local lemma regime, this marginal sampler can draw a random value for a variable according to its marginal distribution, at a local cost independent of the size of the CSP

Structural investigation of eukaryotic cells: From the periphery to the interior by cryo-electron tomography

Cryo-electron tomography (cryo-ET) combines a close-to-life preservation of the cell with high-resolution three-dimensional (3D) imaging. This allows to study the molecular architecture of the cellular landscape and provides unprecedented views on biological processes and structures. In this review we mainly focus on the application of cryo-ET to visualize and structurally characterize eukaryotic cells - from the periphery to the cellular interior. We discuss strategies that can be employed to investigate the structure of challenging targets in their cellular environment as well as the application of complimentary approaches in conjunction with cryo-ET

To enlarge the travel markets from Shanghai to Turku (Shanghai CITS, Ltd.)

This paper is made in order to make thorough analysis in current Chinese travel markets and travel agencies, as well as the analysis on Turku’s travel markets, with which it can know the feasibility in enlarge the travel markets for CITS into Turku. In details, as the background information, the brief overview of history of China’s domestic travel agencies and a brief description of Shanghai CITS in terms of its business and management status are posed with the aim of getting enough supporting information. Further researches on background have been placed in the appendix, including the information of Chinese Oversea Travel Market, the information of Shanghai Travel Markets, More Information about CITS, and information of Turku Travel markets. As the preparation of marketing research on the above objective, theoretical structure about marketing and tourism are reviewed in terms of marketing mix theory, sustaining developments in tourism industry, brand marketing, and SWOT analysis. The research was mainly contained both secondary information and primary information, the secondary information is acquired mainly from domestic books and journals in writing for the introduction and analysis of Chinese and Turku’s travel markets, relative data will be collected within the range of the topic in supports the findings of primary information as well as the further analysis. Primary information is acquired from a semi-structured interview with on of the marketing manager in CITS, current working in Shanghai. And 9 questions will be posed in order to gather enough information for the CITS’ idea and desire in establishing abroad market. After the research multiple analyses including the SWOT analysis on the Shanghai and Turku’s travel markets, especially for the abroad touring market in Shanghai. Besides, the brand strategy in CITS is been researched, together with its marketing resource in planning, and the competition with other travel agencies. Conclusion and final findings will be focused in four aspects summarized from the above analysis, including the strengthening of macro-control in tourism market for Chinese Authorities, the establishment of sustainable tourism development concept, and the accelerate product development of tourism, the three aspects of analysis, in line with the suggestion for building strategic alliance with abroad hospitality companies and government and NGOs, will make the travel agencies have better performance in foreign traveling market, and as for CITS, the expansion in Turku will be much smoother than it supposed to be

Towards derandomising Markov chain Monte Carlo

We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC) algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of marginal distributions. For the latter task, we introduce a method called coupling towards the past that can, in logarithmic time, evaluate one or a constant number of variables from a stationary Markov chain state. Since there are at most logarithmic random choices, this leads to very simple derandomisation. We provide two applications of this framework, namely efficient deterministic approximate counting algorithms for hypergraph independent sets and hypergraph colourings, under local lemma type conditions matching, up to lower order factors, their state-of-the-art randomised counterparts.Comment: 57 page