FO-Definability of Shrub-Depth

Shrub-depth is a graph invariant often considered as an extension of tree-depth to dense graphs. We show that the model-checking problem of monadic second-order logic on a class of graphs of bounded shrub-depth can be decided by AC^0-circuits after a precomputation on the formula. This generalizes a similar result on graphs of bounded tree-depth [Y. Chen and J. Flum, 2018]. At the core of our proof is the definability in first-order logic of tree-models for graphs of bounded shrub-depth

Corporate Governance and Corporate Performance: Some Evidence from Newly Listed Firms on Chinese Stock Markets

This paper is concerned with some corporate governance issues related to newly listed firms in China based on a sample of 329 firms commencing listing on Shanghai Stock Exchange (SHSE) and Shenzhen Stock exchange (SZSE) during the period from 1998 to 2000. We first investigate the impact of ownership change due to stock market listing on corporate performance. We consider four aspects of corporate performance: profitability, sales, leverage and employee productivity. Our research results indicate that, on average, profitability, sales and employee productivity have improved from pre-listing to post-listing. We further investigate the impacts of state majority control, foreign ownership and regulation effects on corporate performance. Overall, this paper provides some new evidence on the listing effect, ownership structure and regulation effect on Chinese firms which will be valuable to the future reform of state owned enterprises in China.State owned enterprise, corporate governance, and corporate performance

The parameterized space complexity of model-checking bounded variable first-order logic

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-checking problem for queries with a bounded number of variables. For each bound on the quantifier alternation rank the problem becomes complete for the corresponding level of what we call the tree hierarchy, a hierarchy of parameterized complexity classes defined via space bounded alternating machines between parameterized logarithmic space and fixed-parameter tractable time. We observe that a parameterized logarithmic space model-checker for existential bounded variable queries would allow to improve Savitch's classical simulation of nondeterministic logarithmic space in deterministic space $O(\log^2n)$. Further, we define a highly space efficient model-checker for queries with a bounded number of variables and bounded quantifier alternation rank. We study its optimality under the assumption that Savitch's Theorem is optimal

The emergence of the fintech industry in China: An evolutionary economic geography perspective

Over the last decade, the global economy has rapidly becoming digited. Digital technologies have transformed the economy and society, affecting all sectors of activity around the world. Among them, the financial sector is one of the most digitalized sectors, and the term ‘fintech’ is coined to describe the digitalization of the financial sector. Although the global fintech landscape is currently geographically concentrated in the United States and Europe, the pace of China’s fintech development has been dramatically accelerated. However, it is quite surprising that there is hardly any study that investigates fintech in China from a subnational scale. To fill this gap, this dissertation conducts a city-level analysis of the emergence of the fintech industry in China. Theoretically, I position this dissertation within the broad literature on evolutionary economic geography (EEG), which has emerged as one of the main paradigms in economic geography. This dissertation aims to provide a comprehensive understanding of the emergence of the new industry in regions. Conventional wisdom in EEG posits that new industry in regions tends to grow out of technologically related pre-existing industries. However, this conventional understanding is somewhat technology-centric. In response, this dissertation extends the scholarly work from technology-centric to embrace the role of the demand-side market and institutional logic in the emergence of the new industry in regions. It proposes that not only supply-side technology but also demand-side market and institutional logics matter for the emergence of the new industry in regions. Moreover, this dissertation ascribes the underlying logic of how technology, market, and institutional logics matter to the agentic processes of asset modification, particularly redeploying pre-existing assets and creating new assets. In other words, the emergence of the new industry in regions results from relevant regional actors’ purposeful actions in terms of modifying technological, market, and institutional assets. Methodologically, there is a dualism in evolutionary economic geography research between qualitative and quantitative work. To seek a methodology integration, this dissertation proposes the mixed-method that is composed of four concrete approaches, namely the triangulation approach, the embedded approach, the sequential exploratory approach, and the sequential explanatory approach. Among these concrete approaches, the embedded approach is utilized in empirical work. The embedded approach in this dissertation refers to the embedding of the qualitative case study (which deals with the ‘how’ questions) into quantitative research (which deals with the ‘whether and to what extent’ questions). Empirically, this dissertation first examines the emergence of fintech industries in China’s cities based on the quantitative regression analysis (mainly dealing with the ‘whether and to what extent’ questions) and then zooms in on the city of Shenzhen, which is the largest fintech hub in southern China, based on the qualitative case study (mainly dealing with the ‘how’ questions). The findings are as follows. (1) Based on a unique dataset from 2003 – 2019, this dissertation provides a city-level analysis of the fintech industry in China. The econometric results show that fintech industries tend to emerge in cities that have more fintech-related technologies, particularly in the fields of finance, e-commerce, data sciences, and security. This confirms the principle of technological relatedness. Moreover, it finds a positive relationship between the development of the fintech industry and the demand for fintech services. To the best of my knowledge, this is the first systematic evidence of the significant positive role of the demand-side market in the emergence of the new industry in regions. (2) In order to uncover the underlying processes (the question of ‘how’) that lead to the above significantly positive effect, this dissertation resorts to the qualitative case study. The case study shows that the rise of Shenzhen’s fintech industry mainly grows out of Shenzhen’s pre-existing internet and financial industry. By systematically comparing the processes that internet and financial industry diversify into the fintech industry, it finds that the emergence of the fintech industry in Shenzhen result from internet and financial firms’ purposeful actions in terms of redeploying their pre-existing technologies, market, and institutional logics, as well as creating the new ones that are necessary for fintech but are missing for the internet or financial firms. In other words, it is the processes of asset modification, particularly redeploying pre-existing assets and creating new assets, that give rise to the birth of the fintech industry, leading to the positive relationships found in the quantitative regression analysis

Some Lower Bounds in Parameterized AC^0

We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical AC^0. Among others, we derive such a lower bound for all fpt-approximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the first lower bound, we prove a strong AC^0 version of the planted clique conjecture: AC^0-circuits asymptotically almost surely can not distinguish between a random graph and this graph with a randomly planted clique of any size <= n^xi (where 0 <= xi < 1)

Slicewise Definability in First-Order Logic with Bounded Quantifier Rank

For every natural number q let FO_q denote the class of sentences of first-order logic FO of quantifier rank at most q. If a graph property can be defined in FO_q, then it can be decided in time O(n^q). Thus, minimizing q has favorable algorithmic consequences. Many graph properties amount to the existence of a certain set of vertices of size k. Usually this can only be expressed by a sentence of quantifier rank at least k. We use the color coding method to demonstrate that some (hyper)graph problems can be defined in FO_q where q is independent of k. This property of a graph problem is equivalent to the question of whether the corresponding parameterized problem is in the class para-AC^0. It is crucial for our results that the FO-sentences have access to built-in addition and multiplication (and constants for an initial segment of natural numbers whose length depends only on k). It is known that then FO corresponds to the circuit complexity class uniform AC^0. We explore the connection between the quantifier rank of FO-sentences and the depth of AC^0-circuits, and prove that FO_q is strictly contained in FO_{q+1} for structures with built-in addition and multiplication

Switching of controlling mechanisms during the rapid solidification of a melt pool in additive manufacturing

Fusion-based metal additive manufacturing (AM) is a disruptive technology that can be employed to fabricate metallic component of near-net-shape with an unprecedented combination of superior properties. However, the interrelationship between AM processing and the resulting microstructures is still not well understood. This poses a grand challenge in controlling the development of microstructures during AM to achieve desired properties. Here we study the microstructure development of a single melt pool, the building block of AM-fabricated metallic component, using a phase-field model specifically developed for the rapid solidification of AM. It is found that during the rapid solidification of the melt pool, the solid-liquid interface is initially controlled by solute diffusion followed by a thermal diffusion-controlled stage with an undercooling larger than the freezing range. This switching of controlling mechanisms leads to the sudden changes in interfacial velocity, solute concentration, and temperature, which perfectly explains the formation of various heterogeneous microstructures observed in AM. By manipulating the processing conditions, the switching of controlling mechanisms can be controlled to form refined microstructures or layered structures for improved mechanical properties and resistance to cracking