Intravoxel incoherent motion (IVIM) imaging is a magnetic resonance imaging (MRI) technique widely used in clinical applications for various organs. However, IVIM imaging at low b-values is a persistent problem. This paper aims to investigate in a systematic and detailed manner how the number of low b-values influences the estimation of IVIM parameters. To this end, diffusion-weighted (DW) data with different low b-values were simulated to get insight into the distributions of subsequent IVIM parameters. Then, in vivo DW data with different numbers of low b-values and different number of excitations (NEX) were acquired. Finally, least-squares (LSQ) and Bayesian shrinkage prior (BSP) fitting methods were implemented to estimate IVIM parameters. The influence of the number of low b-values on IVIM parameters was analyzed in terms of relative error (RE) and structural similarity (SSIM). The results showed that the influence of the number of low b-values on IVIM parameters is variable. LSQ is more dependent on the number of low b-values than BSP, but the latter is more sensitive to noise.

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a $\lambda$-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.

The essence of syndrome differentiation in Traditional Chinese Medicine (TCM) lies in dynamically filtering and associating symptoms to reach dialectical conclusions. However, while large language models (LLMs) have shown promise in various domains, they struggle to replicate the context-sensitive and exclusionary reasoning required for syndrome differentiation in TCM, primarily because they are typically trained on structured data that does not account for the complex and iterative reasoning process inherent in TCM. In this paper, we propose DiagX-DT, a novel diagnostic framework that integrates dialectical thinking with exclusion-based reasoning to enhance TCM diagnosis using LLMs. Our method first prompts the LLM to generate an initial answer along with a multi-step reasoning chain, while simultaneously extracting the initial probability distribution over candidate options from the model’s final output layer. Then, external structured TCM knowledge bases are utilized to iteratively exclude implausible choices based on treatment contradictions and diagnostic mismatches. After each exclusion, the remaining option set is used to recompute a normalized probability distribution. A recombination-evaluation module dynamically selects the top-scoring candidate under a confidence threshold mechanism to produce the final diagnosis. We evaluate DiagX-DT on three benchmark TCM choice diagnostic datasets, and experimental results demonstrate that our approach significantly improves diagnostic accuracy and robustness compared to standard LLM baselines.

In a regular ($d,k$)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the $(d,k)$-SAT problem for short. The regular exact 2-($d,k$)-SAT problem is that for a ($d,k$)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of $2n/k$ such that F is 2-exactly satisfiable. This paper introduces the ($d,k$)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point $d^{*}$ of the 2-($d,k$)-SAT instance with only positive literals. When $d<d^{*}$, the 2-($d,k$)-SAT instance can be satisfied with high probability. When $d>d^{*}$, the 2-($d,k$)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results.