On Structures of Large Rooted Graphs

A rooted graph is a pair (G,R), where G is a graph and R⊆V(G). There are two research topics in this thesis. One is about unavoidable substructures in sufficiently large rooted graphs. The other is about characterizations of rooted graphs excluding specific large graphs. The first topic of this thesis is motivated by Ramsey Theorem, which states that K_n and ¯(K_n ) are unavoidable induced subgraphs in every sufficiently large graph. It is also motivated by a classical result of Oporowski, Oxley, and Thomas, which determines unavoidable large 3-connected minors. We first determine unavoidable induced subgraphs, and unavoidable subgraphs in connected graphs with sufficiently many roots. We also extend this result to generalized rooted connected graphs. Secondly, we extend these results to rooted graphs of higher connectivity. In particular, we determine unavoidable subgraphs of sufficiently large rooted 2- connected graphs. Again, this result is extended to generalized rooted 2-connected graphs. The second topic of this dissertation is motivated by two results of Robertson and Seymour, let’s only talk about path and star. In the first result they established that graphs without a long path subgraph are precisely those that can be constructed using a specific operation within a bounded number of iterations, starting from the trivial graph. In the second result they showed that graphs without a large star minor are those that are subdivisions of graphs with bounded number vertices. We consider similar problems for path, star and comb. We have some theorems on characterizations of rooted connected graphs excluding a heavy path, a large (nicely) confined comb, a large (nicely) confined star, which are similar to those of Robertson and Seymour. Moreover, our results strengthen their related results

Cross-Domain Local Characteristic Enhanced Deepfake Video Detection

As ultra-realistic face forgery techniques emerge, deepfake detection has attracted increasing attention due to security concerns. Many detectors cannot achieve accurate results when detecting unseen manipulations despite excellent performance on known forgeries. In this paper, we are motivated by the observation that the discrepancies between real and fake videos are extremely subtle and localized, and inconsistencies or irregularities can exist in some critical facial regions across various information domains. To this end, we propose a novel pipeline, Cross-Domain Local Forensics (XDLF), for more general deepfake video detection. In the proposed pipeline, a specialized framework is presented to simultaneously exploit local forgery patterns from space, frequency, and time domains, thus learning cross-domain features to detect forgeries. Moreover, the framework leverages four high-level forgery-sensitive local regions of a human face to guide the model to enhance subtle artifacts and localize potential anomalies. Extensive experiments on several benchmark datasets demonstrate the impressive performance of our method, and we achieve superiority over several state-of-the-art methods on cross-dataset generalization. We also examined the factors that contribute to its performance through ablations, which suggests that exploiting cross-domain local characteristics is a noteworthy direction for developing more general deepfake detectors

On 4n4n-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras

For a class of neither pointed nor semisimple Hopf algebras $H_{4n}$ of dimension $4n$, it is shown that they are quasi-triangular, which universal $R$-matrices are described. The corresponding weak Hopf algebras $\mathfrak{w}H_{4n}$ and their representations are constructed. Finally, their duality and their Green rings are established by generators and relations explicitly. It turns out that the Green rings of the associated weak Hopf algebras are not commutative even if the Green rings of $H_{4n}$ are commutative.Comment: 18 page

Exploiting and integrating rich features for biological literature classification

<p>Abstract</p> <p>Background</p> <p>Efficient features play an important role in automated text classification, which definitely facilitates the access of large-scale data. In the bioscience field, biological structures and terminologies are described by a large number of features; domain dependent features would significantly improve the classification performance. How to effectively select and integrate different types of features to improve the biological literature classification performance is the major issue studied in this paper.</p> <p>Results</p> <p>To efficiently classify the biological literatures, we propose a novel feature value schema <it>TF</it>*<it>ML</it>, features covering from lower level domain independent “string feature” to higher level domain dependent “semantic template feature”, and proper integrations among the features. Compared to our previous approaches, the performance is improved in terms of <it>AUC</it> and <it>F-Score</it> by 11.5% and 8.8% respectively, and outperforms the best performance achieved in BioCreAtIvE 2006.</p> <p>Conclusions</p> <p>Different types of features possess different discriminative capabilities in literature classification; proper integration of domain independent and dependent features would significantly improve the performance and overcome the over-fitting on data distribution.</p

On finite-dimensional irreducible modules for the universal Askey-Wilson algebra

Let $\Delta_q$ be the universal Askey-Wilson algebra. If $q$ is not a root of unity, it is shown in the Huang's earlier paper that an $(n+1)$-dimensional irreducible $\Delta_q$-module is a quotient $V_n(a, b, c)$ of a $\Delta_q$-Verma module with ${\textbf{ Condition A: }} \; abc, a^{-1}bc, ab^{-1}c, abc^{-1} \notin \left \{q^{n-2i+1}| 1 \leq i \leq n\right \}.$ The aim of this paper is to discuss the structures of $(n+1)$-dimensional $\Delta_q$-modules $V_n(a, b, c)$ when the given triples $(a, b, c)$ do not satisfy Condition A

Effects of fracturing fluid composition and other factors on improving the oil imbibition recovery of shale reservoir

Imbibition is an important mechanism of shale reservoir development. In exploring the factors affecting the enhanced recovery of shale reservoirs by imbibition, laboratory spontaneous and forced imbibition experiments were conducted using outcrop cores of shale reservoirs. The effects of imbibition agent composition, fracture, and pressure on imbibition are obtained in this work based on imbibition recovery test findings and imbibition theory. Results show that the imbibition curve includes three stages, namely, imbibition, transition, and stability. Among the components of compound fracking fluid, surfactants have the greatest impact, whereas emulsifiers have the least impact. Complex crack structures and high-temperature environments can improve imbibition recovery. Pressure is inversely proportional to imbibition recovery in the highly stress-sensitive shale reservoir. In addition, the throughput time of the imbibition agent has an optimal value in the shale reservoir. After the huff-n-puff time exceeds the optimal value, the imbibition agent should be replaced to continuously improve the imbibition effect. The research results can serve as a basis for enhancing oil recovery through imbibition.Document Type: Original articleCited as: Li, S., Ye, Z., Wang, J., Tang, L., Lai, N. Effects of fracturing fluid composition and other factors on improving the oil imbibition recovery of shale reservoir. Capillarity, 2023, 9(3): 45-54. https://doi.org/10.46690/capi.2023.12.0