Proper Interval Research Articles

On non-superperfection of edge intersection graphs of paths

The routing and spectrum assignment problem in modern flexgrid elastic optical networks asks for assigning to given demands a route in an optical network and a channel within an optical frequency spectrum so that the channels of two demands are disjoint whenever their routes share a link in the optical network. This problem can be modeled in two phases: firstly, a selection of paths in the network and, secondly, an interval coloring problem in the edge intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all possible non-negative integral weights are called superperfect. Therefore, the occurrence of non-superperfect edge intersection graphs of routing paths can provoke the need of larger spectral resources. In this work, we examine the question which minimal non-superperfect graphs can occur in the edge intersection graphs of routing paths in different underlying networks: when the network is a path, a tree, a cycle, or a sparse planar graph with small maximum degree. We show that for any possible network (even if it is restricted to a path) the resulting edge intersection graphs are not necessarily superperfect. We close with a discussion of possible consequences and of some lines of future research.

An algorithm for the secure total domination problem in proper interval graphs

A subset S of vertices of G is a total dominating set if, for any vertex v, there is a vertex in S adjacent to v. A total dominating set S is a secure total dominating set if, for any vertex v∉S, there is a vertex u∈S such that uv is an edge and (S∖{u})∪{v} is also a total dominating set. In this paper, we design an O(m)-time algorithm for computing a minimum secure total dominating set in a proper interval graph, where m is the number of edges.

Graphs with at most two moplexes

AbstractA moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. The notion is known to be closely related to lexicographic searches in graphs as well as to asteroidal triples, and has been applied in several algorithms related to graph classes, such as interval graphs, claw‐free, and diamond‐free graphs. However, while every noncomplete graph has at least two moplexes, little is known about structural properties of graphs with a bounded number of moplexes. The study of these graphs is, in part, motivated by the parallel between moplexes in general graphs and simplicial modules in chordal graphs: unlike in the moplex setting, properties of chordal graphs with a bounded number of simplicial modules are well understood. For instance, chordal graphs having at most two simplicial modules are intervals. In this work, we initiate an investigation of ‐moplex graphs, which are defined as graphs containing at most moplexes. Of particular interest is the smallest nontrivial case , which forms a counterpart to the class of interval graphs. As our main structural result, we show that, when restricted to connected graphs, the class of 2‐moplex graphs is sandwiched between the classes of proper interval graphs and cocomparability graphs; moreover, both inclusions are tight for hereditary classes. From a complexity‐theoretic viewpoint, this leads to the natural question of whether the presence of at most two moplexes guarantees a sufficient amount of structure to efficiently solve problems that are known to be intractable on cocomparability graphs, but not on proper interval graphs. We develop new reductions that answer this question negatively for two prominent problems fitting this profile, namely, Graph Isomorphism and Max‐Cut. On the other hand, we prove that every connected 2‐moplex graph contains a Hamiltonian path, generalising the same property of connected proper interval graphs. Furthermore, for graphs with a higher number of moplexes, we lift the previously known result that graphs without asteroidal triples have at most two moplexes to the more general setting of larger asteroidal sets.

Weakly toll convexity and proper interval graphs

Weakly toll convexity and proper interval graphs

Investigate of unsimilar effect of longer rest interval in multiple sets by performing deload repetition training regimes to micro strength gain change on light weeks of weightlifters

Continuum zone repetition training strategies are one of repetition manipulation both multiple set and repetition zone periodization on weightlifters. The present study was aimed to strength level on weightlift exercise condition of weightlifting athletes, deload repetition resistance training regimes involved in proper rest interval and repetition range by performing multiple set and longer rest interval within different maximize performance on light weeks. The experimental study was conducted to 2 olympic, 1 national, 6 professional weightlifters participated on age (16-21 years) this study. With study maximize performance condition over 3 week resistance training finished to weightlifters. Priority experimental pre-test and post-test outcomes after resistance training showed significant different (p < .05) in dynamic strength to countermovement jump shrug (p = .035; d = 0.69; = 17.78%). However, significant different in low load repetition failure to overhead press (p = .007; d = 0.86; = 5.56%), high load repetition failure to bent-over row (p = .017; d = 1.14; = 8.00%), low and high load repetition failure to countermovement jump shrug (p = .017; d = 1.17; = 13.78% - p = .048; d = 0.73; = 5.44%), in localize endurance not significant performance level to resistance exercise performance. However, isometric strength detected to overhead press (p = .016; d = 1.30; = -0.72%), bent-over row (p = .012; d = 1.67; = -0.51%) and countermovement jump shrug (p = .004; d = 2.45; = -0.48%) in weightlifters. Unsimilar longer rest interval multiple set configuration suggested to maximize strength gain on short time deload repetition training regimes by manipulated repetition and set addition rest interval currently manipulation of weightlifters.

GCN-assisted attention-guided UNet for automated retinal OCT segmentation

With the increase in the aging population of many countries, the prevalence of neovascular age-related macular degeneration (nAMD) is expected to increase. Morphological parameters such as intraretinal fluid (IRF), subretinal fluid (SRF), subretinal hyperreflective material (SHRM), and pigment epithelium detachment (PED) of spectral-domain optical coherence tomography (SD-OCT) images are vital markers for proper treatment of nAMD, especially to get the information of treatment response to determine the proper treatment interval and switching of anti-vascular endothelial growth factor (VEGF) agents. For the precise evaluation of the change in nAMD lesions and patient-specific treatment, quantitative evaluation of the lesions in the OCT volume scans is necessary. However, manual segmentation requires many resources, and the number of studies of automatic segmentation is increasing rapidly. Improving automated segmentation performance in SD-OCT visual results requires long-range contextual inference of spatial information between retinal lesions and layers. This paper proposes a GAGUNet (graph convolution network (GCN)-assisted attention-guided UNet) model with a novel global reasoning module considering these points. The dataset used in the main experiment of this study underwent rigorous review by a retinal specialist from Konkuk University Hospital in Korea, contributing to both data preprocessing and validation to ensure a qualitative assessment. We conducted experiments on the RETOUCH dataset as well to demonstrate the scalability of the proposed model. Overall, our model demonstrates superior performance over the baseline models in both quantitative and qualitative evaluations.

Thinness and its variations on some graph families and coloring graphs of bounded thinness

Interval graphs and proper interval graphs are well known graph classes, for which several generalizations have been proposed in the literature. In this work, we study the (proper) thinness, and several variations, for the classes of cographs, crowns graphs and grid graphs. We provide the exact values for several variants of thinness (proper, independent, complete, precedence, and combinations of them) for the crown graphs CRn. For cographs, we prove that the precedence thinness can be determined in polynomial time. We also improve known bounds for the thinness of n × n grids GRn and m×n grids GRm,n, proving that n−1/3 ≤ thin(GRn) ≤ n+1/2. Regarding the precedence thinness, we prove that prec-thin(GRn,2) = n+1/2 and that n− 1 + 3/2 ≤ prec-thin(GRn) ≤ n− 1 2. As applications, we show that the k-coloring problem is NP-complete for precedence 2-thin graphs and for proper 2-thin graphs, when k is part of the input. On the positive side, it is polynomially solvable for precedence proper 2-thin graphs, given the order and partition.

Some new algorithmic results on co-secure domination in graphs

For a simple graph G=(V,E) without any isolated vertex, a co-secure dominating set S of G satisfies two properties, (i) S is a dominating set of G, (ii) for every vertex v∈S, there exists a vertex u∈V∖S such that uv∈E and (S∖{v})∪{u} is a dominating set of G. The minimum cardinality of a co-secure dominating set of G is called the co-secure domination number of G and is denoted by γcs(G). The Co-secure Domination problem is to find a co-secure dominating set of a graph G of cardinality γcs(G). The decision version of the problem is known to be NP-complete for bipartite, planar, and split graphs. On the other hand, it is also known that the Co-secure Domination problem is efficiently solvable for proper interval graphs and cographs.In an effort to reduce the complexity gap of the Co-secure Domination problem, in this paper, we work on various important graph classes. We show that the decision version of the problem remains NP-complete for doubly chordal graphs and for some subclasses of bipartite graphs, namely, chordal bipartite graphs, star-convex bipartite graphs, and comb-convex bipartite graphs. On the positive side, we give an efficient algorithm to compute the co-secure domination number of chain graphs, which is an important subclass of bipartite graphs. In addition, we show that the problem is linear-time solvable for bounded tree-width graphs and bounded clique-width graphs. Further, we establish that the computational complexity of this problem differs from that of the classical domination problem.

Shear-interference assisted deep-learning for enhancing spatially multiplexing capacity of free-space communication

The information capacity is a critical measure in free-space optical (FSO) communication. Traditional mode-multiplexing techniques employed in optical communication utilizing Laguerre-Gaussian beams (LGBs) necessitate proper topological charge interval to prevent mode-crosstalk. In this paper, we propose a novel approach that integrates deep learning (DL) into the LGB-based optical communication model, incorporating shearing interference techniques. This combination enables the FSO system to achieve the theoretical limit of capacity, resulting in a remarkable 300 % increase in information capacity compared to traditional techniques. Experimental results demonstrate that the constructed neural network attains a flawless pattern recognition accuracy of 100 %. Additionally, we evaluate various partially coherent light scenarios under the influence of beam decoherence. The results reveal that accurate discrimination of multiplexing patterns is maintained when the fringe contrast exceeds 0.43. Even at a degraded contrast level of 0.18, the recognition accuracy remains impressively high at 91.16 %. To demonstrate practicality, we successfully encode and transmit a cyan-magenta-yellow-black (CMYK) color image using the proposed system, achieving a low bit error rate of 7.5 × 10-5. These findings highlight the potential of DL-assisted mode-division multiplexing for future optical communication applications.

Algorithmic Aspects of Vertex-edge Domination in Some Graphs

Let \(G=(V,E)\) be a simple graph. A vertex \(v\in V(G)\) ve-dominates every edge \(uv\) incident to \(v\), as well as every edge adjacent to these incident edges. A set \(D\subseteq V(G)\) is a vertex-edge dominating set if every edge of \(E(G)\) is ve-dominated by a vertex of \(D.\) The MINIMUM VERTEX-EDGE DOMINATION problem is to find a vertex-edge dominating set of minimum cardinality. A linear time algorithm to find the minimum vertex-edge dominating set for proper interval graphs is proposed. The vertex-edge domination problem is proved to be APX-complete for bounded-free graphs and NP-Complete for Chordal bipartite and Undirected Path graphs.

Effect of perforated cracks on liquid water in microporous layers by lattice Boltzmann method

Microporous layer (MPL), as a critical constituent of the proton exchange membrane fuel cell (PEMFC), plays a key role in mass, heat, electron, and species transport. The cracks formed during the deposition process on the surface of MPL change the overall transport capacity and effect the output performance of PEMFC. In this study, a 2D Lattice Boltzmann Method (LBM) pseudopotential multicomponent model is used to investigate the effects of perforated cracks in MPL on distribution, pressure drop and flow state of liquid water. The simulation results show that Capillary number (Ca) of liquid water in perforated cracks is around two orders of magnitude higher than Ca in twisty pores. Perforated cracks in MPL can not only reduce capillary resistance but also convert liquid water from capillary fingering to viscous fingering essentially, thus enhancing the permeability of liquid water in the through-plane direction while reducing the invasion in the in-plane direction. In consideration of gas-liquid transportation and other structural characteristics of GDL, the proper interval between perforated cracks with width of 10 μm is 3–6 crack diameters. This study provides reference for the design of functional pore structure MPL and conducts guidance for further research on PEMFC.

Uptake and Distribution of Carbofuran and its Metabolites in Watermelon (Citrullus lanatus)

Carbofuran is toxic to humans and the environment, and its misuse in agriculture results in the violation of Maximum Residue Limits (MRL) for most crops. The use of carbofuran in Malaysia is to be banned effectively in May 2023. Limited data were published on the uptake and distribution of carbofuran and its metabolites for most crops. Therefore, a study was conducted to assess carbofuran residues in watermelon grown at the Agriculture Research Centre, Semongok. Carbofuran at 17 kg/ha and 34 kg/ha were applied to watermelon planted under the recommended agronomic practices. The plants were sampled at periodic intervals over 63 days after being treated with carbofuran. The carbofuran and their metabolites in the watermelon leaf, stem, and fruits were determined using a liquid chromatography equipped with a triple quadrupole mass spectrometer. The carbofuran residues were observed up to 35 days after application and reached below the quantification level (0.01 mg/kg) at 42 days after application. Residues were concentrated in the roots and stems for both treatments. About 80 to 90% of the carbofuran was metabolized to carbofuran-3-hydroxy in the watermelon leaves, and 50% in the stems. The highest residue level of carbofuran for application at 17 kg/ha was recorded on Day 9 for roots (0.192 mg/kg), Day 21 for leaves (0.057 mg/kg), and Day 5 for stems (0.134 mg/kg). At 34 kg/ha, the highest carbofuran residues concentrations were recorded on Day 5 for root (0.446 mg/kg) and stem (0.151 mg/kg), and Day 3 for leaves at 0.303 mg/kg. Traces of carbofuran residues were detected in the skin and flesh of the fruit. The carbofuran residue levels in watermelon fruit were below the established MRL of 0.01 mg/kg. Our findings suggest that a proper postharvest interval shall be observed.

Balancing graph Voronoi diagrams with one more vertex

AbstractLet be a graph with unit‐length edges and nonnegative costs assigned to its vertices. Given a list of pairwise different vertices , the prioritized Voronoi diagram of with respect to is the partition of in subsets so that, for every with , a vertex is in if and only if is a closest vertex to in and there is no closest vertex to in within the subset . For every with , the load of vertex equals the sum of the costs of all vertices in . The load of equals the maximum load of a vertex in . We study the problem of adding one more vertex at the end of in order to minimize the load. This problem occurs in the context of optimally locating a new service facility (e.g., a school or a hospital) while taking into account already existing facilities, and with the goal of minimizing the maximum congestion at a site. There is a brute‐force algorithm for solving this problem in time on ‐vertex ‐edge graphs. We prove a matching time lower bound–up to sub‐polynomial factors–for the special case where and , assuming the so called Hitting Set Conjecture of Abboud et al. On the positive side, we present simple linear‐time algorithms for this problem on cliques, paths and cycles, and almost linear‐time algorithms for trees, proper interval graphs and (assuming to be a constant) bounded‐treewidth graphs.

Enhanced Anticoagulation of Hierarchy Liquid Infused Surfaces in Blood Flow.

Liquid infused surfaces (LIS) hold remarkable potential in anticoagulation. However, liquid loss of LIS in the bloodstream remains a challenge toward its clinical application. Here, micronano hierarchy structures are obtained on the titanium alloy substrate by regulating the microspheres' distribution. When the gap between the microspheres is smaller than the diameter of the red blood cell (RBC), the LIS is more stable under the blood wash and presents a better anticoagulation performance. The proper interval is found to prevent the RBCs from entering the gap and remove the liquid on the surface. The retained thickness of the liquid film is measured by the atomic force microscopy (AFM) technique. The LIS is applied on the front guide vane of an artificial heart pump and exhibits significant improvement on anticoagulation in the blood circulation in vitro for 25 h. The techniques and findings can be used to optimize the anticoagulation performance of LIS-related biomedical implant devices.

Algorithms and hardness results for edge total domination problem in graphs

For a graph G=(V,E) without an isolated edge, a set D⊆E is an edge total dominating set of G if every edge e∈E is adjacent to at least one edge of D. The Minimum Edge Total Dominating Set problem is to compute a minimum cardinality edge total dominating set of G. It is known that the decision version of the problem is NP-complete for bipartite graphs, chordal graphs, and planar graphs. On the positive side, the problem is efficiently solvable for trees. In this paper, we further study the complexity of this problem in other graph classes. We design a linear-time algorithm to compute a minimum cardinality edge total dominating set in chain graphs, a subclass of bipartite graphs. We also propose linear-time algorithms for two subclasses of chordal graphs, namely, split graphs and proper interval graphs with no cut vertices. In addition, we show that the problem is APX-complete for graphs with maximum degree 3 and propose an approximation algorithm for the problem in k-regular graphs, where k≥4. We discuss the complexity difference between the Minimum Edge Dominating Set problem and Minimum Edge Total Dominating Set problem which seem to be closely related.

Optimal Fingerprinting with Estimating Equations

Abstract Climate change detection and attribution have played a central role in establishing the influence of human activities on climate. Optimal fingerprinting, a linear regression with errors in variables (EIVs), has been widely used in detection and attribution analyses of climate change. The method regresses observed climate variables on the expected climate responses to the external forcings, which are measured with EIVs. The reliability of the method depends critically on proper point and interval estimations of the regression coefficients. The confidence intervals constructed from the prevailing method, total least squares (TLS), have been reported to be too narrow to match their nominal confidence levels. We propose a novel framework to estimate the regression coefficients based on an efficient, bias-corrected estimating equations approach. The confidence intervals are constructed with a pseudo residual bootstrap variance estimator that takes advantage of the available control runs. Our regression coefficient estimator is unbiased, with a smaller variance than the TLS estimator. Our estimation of the sampling variability of the estimator has a low bias compared to that from TLS, which is substantially negatively biased. The resulting confidence intervals for the regression coefficients have coverage rates close to the nominal level, which ensures valid inferences in detection and attribution analyses. In applications to the annual mean near-surface air temperature at the global, continental, and subcontinental scales during 1951–2020, the proposed method led to shorter confidence intervals than those based on TLS in most of the analyses. Significance Statement Optimal fingerprinting is an important statistical tool for estimating human influences on the climate and for quantifying the associated uncertainty. Nonetheless, the estimators from the prevailing practice are not as optimal as believed, and their uncertainties are underestimated, both owing to the unreliable estimation of the optimal weight matrix that is critical to the method. Here we propose an estimation method based on the theory of estimating equations; to assess the uncertainty of the resulting estimator, we propose a pseudo bootstrap procedure. Through extensive numerical studies commonly used in statistical investigations, we demonstrate that the new estimator has a smaller mean-square error, and its uncertainty is estimated much closer to the true uncertainty than the prevailing total least squares method.

A characterization of unit interval bigraphs of open and closed intervals

Interval graphs are the intersection graphs of intervals on the real line. Unit interval graphs are interval graphs representable by intervals of unit length. Rautenbach and Szwarcfiter showed that the class of intersection graphs of the open and closed real intervals of unit length is a strict superclass of the class of unit interval graphs. They also characterized this class of graphs.An interval bigraph is a bipartite graph where to each vertex we can assign an interval so that vertices in the opposite partite sets are adjacent if and only if their intervals intersect. Analogously we show that the class of finite intersection bigraphs of open and closed intervals of unit length is a strict superclass of the class of unit interval bigraphs. We also characterize this class of bigraphs in terms of forbidden induced subgraphs and a suitable extension of proper interval bigraphs.

Drug adherence and treatment duration for denosumab and mortality risk among hip fracture patients.

Prescription of anti-osteoporotic medications (AOMs) after osteoporotic hip fracture may increase bone mineral density (BMD) and decrease mortality risk. However, few studies have been conducted on drug adherence and treatment duration for denosumab, a popular choice among AOMs. This study aimed to assess the impact of denosumab adherence and treatment duration on the mortality risk of hip fracture patients after surgery. We conducted a cohort study using nationwide population data from National Health Insurance Research Database (NHIRD) in Taiwan. Patients newly diagnosed with osteoporosis and hip fracture between 2008 and 2019 who used denosumab after surgery were included. We assessed drug adherence, treatment duration, and other parameters associated with patient outcomes. A total of 21,316 patients diagnosed with osteoporotic hip fractures were included. Compared with a > 7-month drug interval for denosumab, an interval of ≤ 7months led to lower all-cause mortality risk (hazard ratio (HR): 0.60, 95% confidence interval (CI): 0.57 ~ 0.64). Patients with denosumab treatment for over 1, 2, and 3years had lower all-cause mortality risk (HR&CI: 0.68 (0.64 ~ 0.73), 0.48 (0.43 ~ 0.53), 0.29 (0.26 ~ 0.33)) than those with treatment duration < 1year. Analysis after excluding short-term death yielded similar results. Analysis of causes of death also showed that good adherence and longer duration were associated with reduced mortality due to cancer and cardiovascular disease. Better drug adherence and longer duration of denosumab treatment are associated with lower all-cause mortality risk among hip fracture patients after surgery. Our study highlights the benefits of a proper time interval of denosumab administration. These findings provide important insight into management of osteoporotic hip fractures and may inform clinical practice and development of guidelines.

Correcting the algorithm for a minimum secure dominating set of proper interval graphs by Zou, Liu, Hsu and Wang

Correcting the algorithm for a minimum secure dominating set of proper interval graphs by Zou, Liu, Hsu and Wang

Intersection models and forbidden pattern characterizations for 2-thin and proper 2-thin graphs

The thinness of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many NP-complete problems can be solved in polynomial time for graphs with bounded thinness, given a suitable representation of the graph. Proper thinness is defined analogously, generalizing proper interval graphs, and a larger family of NP-complete problems are known to be polynomially solvable for graphs with bounded proper thinness.The complexity of recognizing 2-thin and proper 2-thin graphs is still open. In this work, we present characterizations of 2-thin and proper 2-thin graphs as intersection graphs of rectangles in the plane, as vertex intersection graphs of paths on a grid (VPG graphs), and by forbidden ordered patterns. We also prove that independent 2-thin graphs are exactly the interval bigraphs, and that proper independent 2-thin graphs are exactly the bipartite permutation graphs.Finally, we take a step towards placing the thinness and its variations in the landscape of width parameters, by upper bounding the proper thinness in terms of the bandwidth.