On n-fold L(j,k)-and circular L(j,k)-labelings of graphs

AbstractWe initiate research on the multiple distance 2 labeling of graphs in this paper.Let n,j,k be positive integers. An n-fold L(j,k)-labeling of a graph G is an assignment f of sets of nonnegative integers of order n to the vertices of G such that, for any two vertices u,v and any two integers a∈f(u), b∈f(v), |a−b|≥j if uv∈E(G), and |a−b|≥k if u and v are distance 2 apart. The span of f is the absolute difference between the maximum and minimum integers used by f. The n-fold L(j,k)-labeling number of G is the minimum span over all n-fold L(j,k)-labelings of G.Let n,j,k and m be positive integers. An n-fold circular m-L(j,k)-labeling of a graph G is an assignment f of subsets of {0,1,…,m−1} of order n to the vertices of G such that, for any two vertices u,v and any two integers a∈f(u), b∈f(v), min{|a−b|,m−|a−b|}≥j if uv∈E(G), and min{|a−b|,m−|a−b|}≥k if u and v are distance 2 apart. The minimum m such that G has an n-fold circular m-L(j,k)-labeling is called the n-fold circular L(j,k)-labeling number of G.We investigate the basic properties of n-fold L(j,k)-labelings and circular L(j,k)-labelings of graphs. The n-fold circular L(j,k)-labeling numbers of trees, and the hexagonal and p-dimensional square lattices are determined. The upper and lower bounds for the n-fold L(j,k)-labeling numbers of trees are obtained. In most cases, these bounds are attainable. In particular, when k=1 both the lower and the upper bounds are sharp. In many cases, the n-fold L(j,k)-labeling numbers of the hexagonal and p-dimensional square lattices are determined. In other cases, upper and lower bounds are provided. In particular, we obtain the exact values of the n-fold L(j,1)-labeling numbers of the hexagonal and p-dimensional square lattices

Asymptotic enumeration of some RNA secondary structures

AbstractIn this paper, we derive recursions of some RNA secondary structures with certain properties under two new representations. Furthermore, by making use of methods of asymptotic analysis and generating functions we present asymptotic enumeration of these RNA secondary structures

Towards Optimal Randomized Strategies in Adversarial Example Game

The vulnerability of deep neural network models to adversarial example attacks is a practical challenge in many artificial intelligence applications. A recent line of work shows that the use of randomization in adversarial training is the key to find optimal strategies against adversarial example attacks. However, in a fully randomized setting where both the defender and the attacker can use randomized strategies, there are no efficient algorithm for finding such an optimal strategy. To fill the gap, we propose the first algorithm of its kind, called FRAT, which models the problem with a new infinite-dimensional continuous-time flow on probability distribution spaces. FRAT maintains a lightweight mixture of models for the defender, with flexibility to efficiently update mixing weights and model parameters at each iteration. Furthermore, FRAT utilizes lightweight sampling subroutines to construct a random strategy for the attacker. We prove that the continuous-time limit of FRAT converges to a mixed Nash equilibria in a zero-sum game formed by a defender and an attacker. Experimental results also demonstrate the efficiency of FRAT on CIFAR-10 and CIFAR-100 datasets.Comment: Extended version of paper https://doi.org/10.1609/aaai.v37i9.26247 which appeared in AAAI 202

Peripheral Ulcerative Keratitis Associated with Autoimmune Disease: Pathogenesis and Treatment

Peripheral ulcerative keratitis (PUK) is type of crescent-shaped inflammatory damage that occurs in the limbal region of the cornea. PUK is always combined with an epithelial defect and the destruction of the peripheral corneal stroma. PUK may have a connection to systemic conditions, such as long-standing rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), Wegener granulomatosis (WG), relapsing polychondritis, classic polyarteritis nodosa and its variants, microscopic polyangiitis, and Churg-Strauss syndrome. However, the most common connection is with RA, which is also the focus of this review. The pathogenesis of PUK is still unclear. It is thought that circulating immune complexes and cytokines exert an important influence on the progression of this syndrome. Treatment is applied to inhibit certain aspects of PUK pathogenesis

Inhibition of Zymosan-Induced Inflammatory Factors Expression by ATRA Nanostructured Lipid Carriers

Purpose. The study aimed to evaluate the effect of all-trans retinoic acid-loaded nanostructured lipid carriers (ATRA-NLCs) on the zymosan-induced expression of the cytokines IL-4, IL-10, and IFN-γ and the matrix metalloproteinases/tissue inhibitor of metalloproteinases (MMPs/TIMPs) and TLR2 in rabbit corneal fibroblasts (RCFs). Methods. ATRA-NLCs were prepared by emulsification. RCFs were isolated and harvested after four to seven passages in monolayer culture. Cytokine release (IL-4, IL-10, and IFN-γ) induced by zymosan was analyzed by cytokine release assay, reverse transcription, and real-time polymerase chain reaction (RT-PCR) analysis detection. MMP-1, MMP-3, and MMP-13, TIMP-1 and TIMP-2, and TLR2 expression were analyzed by immunoblotting. Results. ATRA-NLCs were resistant to light and physically stable, and the average size of the ATRA-NLCs was 200 nm. ATRA-NLCs increased the zymosan-induced release of IL-4 and IL-10 and decreased the release of IFN-γ by RCFs. ATRA-NLCs decreased the levels of TLR2 and MMPs/TIMPs above. Conclusions. ATRA may be a potent anti-inflammatory agent for the therapy of fungal keratitis (FK)

Research on Maintenance Boundary Variation of Cascade Hydropower Units Based on Dynamic Programming-Progressive Optimization Algorithm

Hydropower, as a primary source of renewable energy, plays a crucial role in achieving the dualcarbon goal. Therefore, it is essential to optimize the maintenance schedule to ensure the smooth operation of hydropower units and explore the principles governing the boundaries of the maintenance window period, considering multiple realistic constraints. In this paper, we take the “3-reservoirs and 7-levels” hydropower station in the lower Yalong River Basin as a case study. We establish an optimal model with the objective of maximizing the generating output, considering the total generating capacity and output of each hydropower station under various constraints. Next, we calculate the number of repairable units based on the ten-day output for each scenario and compare the maintenance window period while analysing its changing pattern. Finally, a comprehensive maintenance plan was developed based on historical maintenance data and industry standards with considering the changing rules. Additionally, we provide suggestions based on these rules

Analysis of fine grained sand and shale sedimentary characteristics in estuary based on sediment dynamics

Due to the dual effects of fluvial and tides, the tidal sand bars in estuaries have complex sedimentary characteristics and complex internal structures, making them difficult to predict and describe. In this paper, the sedimentary dynamics numerical simulation method is used to establish a tidal-controlled estuary model. The effects of tidal range and sediment grain size on tidal sand bars are simulated. The length, width, and thickness of tidal sand bars, as well as the length and thickness of the internal shale layer, are also analyzed. The results show that in the environment of a tide-controlled estuary, the tidal range has a more significant effect on tidal sand bars compared to the sediment grain size under the specific conditions used in this study. The main effect of tidal range on tidal sand bars is that the greater the tidal range, the greater the length-to-width ratio of the sandbank, and the higher the degree of sandbank development. In a tidal-controlled estuary environment, the formation and distribution of shale layer structures are also affected by tides: the length of the shale layer increases as the tidal energy increases, but the changes in the thickness are not obvious. Numerical simulations of the development and distribution of the tidal sand bars and shale layers in estuaries based on sedimentary dynamics will provide a basis for the sedimentary evolution of tide-controlled estuaries and will provide guidance for the exploration and development of tidal estuaries

The roles of 13 major countries in 2000,2010, and 2021.

The roles of 13 major countries in 2000,2010, and 2021.</p