Quantitative Robustness Analysis of Quantum Programs (Extended Version)

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called $\epsilon$-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

Digital village construction, human capital and the development of the rural older adult care service industry

BackgroundThe advancement of digital villages in China is shaped by the degree of human capital within the rural labor force, which not only restricts the potential of digital village but also influences the impact of digital empowerment on the progression of the rural older adult care service industry.Materials and methodsUsing panel data from 30 Chinese provinces between 2011 and 2020, we created benchmark and threshold regression models to investigate the influence of digital village construction on the development of the rural older adult care service industry and to delineate the threshold effects of human capital on it. We further scrutinized the correlation between the two systems, along with the factors that affect it, through a coupling coordination model.ResultsPreliminary, the baseline regression outcomes show that the digital village construction is conducive to the progression of the rural older adult care service industry (p < 0.05). Moreover, we identified a significant nonlinear threshold relationship between the digital village, human capital, and the advancement of the rural older adult care service industry (HUM1ST, p < 0.05; HUM2DT, p < 0.01; HUM3DT, p < 0.01). These results indicate that the digital technology’s effect on the development of the rural older adult care service industry is limited by the rural human capital level. Lastly, we found that higher levels of human capital enhance the coupling of the digital village with the rural older adult care service industry (p < 0.01), with the influence of per capita education level being the most pronounced (CoefHUM1 > CoefHUM2 > CoefHUM3).ConclusionThe digital village substantially empowers the rural older adult care service industry, with human capital exhibiting a significant threshold effect on this empowerment. Furthermore, variances in the level of human capital have a considerable impact on the integration of the digital village and the rural older adult care service industry

The expression and role of protein kinase C (PKC) epsilon in clear cell renal cell carcinoma

Protein kinase C epsilon (PKCε), an oncogene overexpressed in several human cancers, is involved in cell proliferation, migration, invasion, and survival. However, its roles in clear cell renal cell carcinoma (RCC) are unclear. This study aimed to investigate the functions of PKCε in RCC, especially in clear cell RCC, to determine the possibility of using it as a therapeutic target. By immunohistochemistry, we found that the expression of PKCε was up-regulated in RCCs and was associated with tumor Fuhrman grade and T stage in clear cell RCCs. Clone formation, wound healing, and Borden assays showed that down-regulating PKCε by RNA interference resulted in inhibition of the growth, migration, and invasion of clear cell RCC cell line 769P and, more importantly, sensitized cells to chemotherapeutic drugs as indicated by enhanced activity of caspase-3 in PKCε siRNA-transfected cells. These results indicate that the overexpression of PKCε is associated with an aggressive phenotype of clear cell RCC and may be a potential therapeutic target for this disease

Applications of Graph Theory and Logic in Computer Science

We study the CSP of unary expansions of directed graphs. When we expand the simple structure (Z,succ) with one unary predicate U , its CSP (Constraint Satisfaction Problem) may vary in complexity. We find some sufficient conditions for its tractability, prove bounds on its complexity, and then generalize our results to more complicated structures. We also give a Karp-equivalent characterization of CSP(Z, succ, U)’s. Next, fixing α ∈ (0, 1], we generalized the axiomatizations in [1] to the class of hereditarily linearly sparse Kn-free graphs, and made efforts towards connecting this with almost sure theories of Shelah-Spencer graphs, a type of random graphs, which may be of interest in theory of computer science. Then we study the constraint satisfaction problems of selected infinite relational structures. For α ∈ (0, 5/6], K_α := the class of hereditarily α-sparse graphs, M_α := the generic structure of K_α; K_{α,Kn−free}, M_{α,Kn−free}:= the Kn-free subclass and its generic structure respectively, we prove multiple structural properties of graphs presenting the Hrushovski-Fraïssé class K_{α,TF}, strongly indicating that this class should have a finite homomorphic presentation when α is close to 5/6 from below, which would imply NP-Completeness. More general results are explored along. We also study the complexity-theoretic implications of our findings on a relevant decision problem, namely the constraint satisfaction problem of the corresponding generic structure

Performance analysis of a modified zone-based hierarchical link state routing

Existing IEEE 802.11 provide minimal connectivity for wireless network, while a number of different routing protocols are proposed for wireless ad-hoc network connectivity in recent years. Traditional routing protocols are classified in two categories: proactive and reactive. More efficient routing protocols combine both features to minimize network overhead and transfer delay. In this work, a modified zone-based hierarchical link state routing protocol (MZHLS) is presented. In MZHLS, the network is divided into non-overlapping zones. Link state routing is performed on two levels: node level and zone level. MZHLSP is proactive at node level and reactive when destination node exists in different zones. Only zone ID and node ID of a destination are needed for routing and zone ID is found by searching specific zones, for example, periphery zones. Performance analysis of MZHLS is emphasized. To evaluate the performance of MZHLS, a simulation model of file transfer process is built in C programming language. Performance analysis of MZHLS focuses on transfer delay, overhead, throughput, buffer overflow, etc. The protocol's behavior and changes introduced by variations on some of the parameter settings and the mechanisms that makes up the protocol are examined. Simulation results show the parameter and mechanisms that have the greatest impact and the trade offs that exist between them