Minimum Span Research Articles

The (d, 1)-total labelling of Sierpi[formula omitted]ski-like graphs

A (d, 1)-total labelling of a simple graph G is an assignment of integers to V(G) ∪ E(G) such that any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers, and a vertex and an edge that are incident in G receive integers that differ by at least d in absolute value. The span of a (d, 1)-total labellingof G is the maximum difference between any two labels. The (d, 1)-total number of G, λdT(G), is the minimum span for which G is (d, 1)-total labelled. In this paper, the (d, 1)-total labellingof the Sierpin´ski graph S(n, k), Sierpin´ski gasket graph Sn, graphs S+(n,k) and S++(n,k) are studied, and all of λdT(S(n,k)),λdT(Sn),λdT(S+(n,k)) and λdT(S++(n,k)) for d ≥ k, are obtained.

What are they doing? And where? Tracking the Traffic as one of the instruments in an evidence-based redesign of a university library

During the last decade we have seen an increased focus on the future use of academic libraries, both in terms of their legitimacy and the use of the physical library space itself.
 Prior to a planned, major rebuilding of the Humanities and Social Sciences Library at the University of Oslo (HumSam library), a thorough study was required to establish the current use of the library space, as well as users’ wishes and needs for change.
 Several different methods were used to collect this data. One was the method Tracking the Traffic (TTT), developed by Tord Høivik. This is a purely quantitative method, where the users in the library are counted several times during the opening hours. This registration takes place over a set period, for example, at fixed hours every day over a minimum time span of two weeks. The activities of the users are also registered, but without talking to the user, so one can register that one user is reading a book or using a laptop, but not what kind of book or what the laptop is being used for. Other methods used were a user survey, different kinds of interview and photo documentation.
 This article aims at demonstrating how the use of the TTT method contributed when the HumSam library conducted studies to ensure an evidence-based renewal of the library. The experiences with this type of data collection are described, and a discussion of the methodology based on our experiences is presented. There are also examples for how this data affected the rebuilding and renewal of the HumSam library. The TTT method needs to be a part of a suite of methods to give an adequate profile of library use. Being a method based on observation, it is necessary to compliment it with other qualitative methods to fill in the picture of library users and to ensure library development soundly based on full evidence (Evidence-based Practice – EBP).
 Of course, the library staff had many pre-assumptions about the library use; however, documenting use in this way may lead to more accurate knowledge.
 When visiting the redesigned HumSam library today, the responses to the results of the TTT and the other studies mentioned in this article can be clearly seen. The most obvious are the number and variation of seating facilities, the number of group rooms and the reduced height and number of shelves for the physical collection. Scenes and special places for events have also been created, opening hours in exam periods have been increased and the library counters have a more inviting design than before.

Upper bound for radio [formula omitted]-chromatic number of graphs in connection with partition of vertex set

For a simple connected graph G=(V(G),E(G)) and a positive integer k with 1⩽k⩽diam(G), a radio k-coloring of G is a mapping f:V(G)→{0,1,2,…} such that |f(u)−f(v)|⩾k+1−d(u,v) holds for each pair of distinct vertices u and v of G, where diam(G) is the diameter of G and d(u,v) is the distance between u and v in G. The span of a radio k-coloring f is the number maxu∈V(G)f(u). The main aim of the radio k-coloring problem is to determine the minimum span of a radio k-coloring of G, denoted by rck(G). Due to NP-hardness of this problem, people are finding lower bounds for rck(.) for particular families of graphs or general graphs G. In this article, we concentrate on finding upper bounds of radio k-chromatic number for general graphs and in consequence a coloring scheme depending on a partition of the vertex set V(G). We apply these bounds to cycle graph Cn and hypercube Qn and show that it is sharp when k is close to the diameter of these graphs.

Radio Number for Generalized Petersen Graphs $P(n,2)$

Let G be a connected graph and d(μ, ω) be the distance between any two vertices of G. The diameter of G is denoted by diam(G) and is equal to max{d(μ, ω); μ, ω ∈ G}. The radio labeling (RL) for the graph G is an injective function F : V(G) → N U {0} such that for any pair of vertices μ and ω |F(μ) - F(ω)| ≥ diam(G) - d(μ, ω) + 1. The span of radio labeling is the largest number in F(V). The radio number of G, denoted by rn(G) is the minimum span over all radio labeling of G. In this paper, we determine radio number for the generalized Petersen graphs, P(n, 2), n = 4k +2. Further the lower bound of radio number for P(n, 2) when n = 4k is determined.

Detectability of Repeated Airborne Laser Scanning for Mountain Landslide Monitoring

Multi-temporal airborne laser scanning (ALS) surveys have become a prime consideration for detecting landslide movements and evaluating landslide risk in mountain areas. The minimum elevation change (or detectability) that can be detected by repeated ALS surveys has become a critical threshold for landslide researchers and engineers to decide if ALS is a capable tool for detecting targeted landslides and arranging the minimum time span between two scans if ALS is a choice. The National Center for Airborne Laser Mapping (NCALM) at the University of Houston conducted three repeated ALS surveys at the Slumgullion landslide site in Colorado, U.S. over one week in July of 2015. These repeated ALS surveys provide valuable datasets for evaluating the vertical detectability of multi-temporal ALS surveys in a typical mountain area. According to this study, the difference of digital elevation models (DDEM) derived from ALS has the ability of detecting a minimum elevation change of 5 cm over flatter and moderately rugged terrain areas (slope < 20 degrees) and a minimum of a 10-cm elevation change over rugged terrain areas (20 degrees < slope < 40 degrees). However, the DDEM values over highly rugged terrain areas (slope > 40 degrees), such as cliff and landslide scarps, should be interpolated with caution. Global Navigation Satellite Systems (GNSS) and Terrestrial Laser Scanning (TLS) surveys were also performed at the middle portion of the landslide area for assessing the accuracy of ALS datasets. The accuracy of ALS varies from approximately one decimeter (~10 cm) to one foot (~30 cm) depending on the roughness of terrain surface and vegetation coverage (point density). The detectability and accuracy estimates of ALS measurements obtained from the case study could be used as a reference for estimating the performance of modern ALS in mountain areas with similar topography and vegetation coverage.

L(j, k)-labeling Number of Cactus Graph

For j ≤ k, the L(j,k) -labelling problem arose from code assignment problem of computer wireless networks. That is, let j, k and m be positive numbers, an m-L(j, k) -labelling of a graph G is a mapping f: V(G) → [0, m] such that | f (u) - f (v) |≥ j if d (u, v) = 1, and | f (u) - f (v) |≥ k if d (u,v) = 2. The span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j, k) -labelling number of G, denoted by λjk (G), is the minimum span over all L( j, k)-labellings of G. In this paper, we introduce the L(j, k )- labelling numbers of Cactus graph for any positive real numbers j, k with j ≤ k.

L(j, k)-labeling Number of Generalized Petersen Graph

For j ≤ k, the L(j,k) -labeling arose from code assignment problem in the computer wireless network. For positive real numbers j and k, an L(j, k) -labeling f of G is an assignment of numbers to vertices of G such that | f (u)- f (v)|≥ j if u, v are adjacent, and | f(u)-f(v)|≥ k if u, v are distance two apart. The span of f is the maximum difference among the numbers assigned by f. The L(j, k) -labeling number of G, denoted by λjk (G), is the minimum span over all L(j,k) -labeling of G . The generalized Petersen graph, denoted by G(n,k), is a graph with vertex set {u0,u1,…,un-1,v0,v1,…,vn-1} and edge set{(u.,u.+1), (ui,vi.), (vi,vi+k): i = 0,•••,n-1}, where subscripts are to be taken modulo n and k ≤ [n/2]. In this paper, the author determines the L(j,k) -labeling numbers of generalized Petersen graphs G(n,1), G(n,2) and G(n, n/2), where n is even and 2j < k.

NOAA’s national water level observation network (NWLON)

ABSTRACTThe National Oceanographic and Atmospheric Administration National Water Level Observation Network (NWLON) is the foundation of a comprehensive system for observing, communicating, and assessing the impact of changing water levels nationwide. The network also measures other oceanographic parameters in addition to water levels, including meteorological parameters. Although initially established to support navigation, NWLON is a ‘go to’ source for data and products to support coastal community decision making. Real-time water level information available 24/7 is critical to emergency managers and planners monitoring changing water levels and contributes to NOAA’s forecast model for tsunami and storm surge warnings. This article also discusses the role of NWLON in terms of addressing emerging observational needs around emergency management, tracking changes in sea level rise through persistent changes in high tide flooding, establishing new regional sea level scenarios and projections, and restoring tidally influenced habitats. Sea level trends have been computed at 142 water level stations using a minimum span of 30 years of observations at each location. Coupling present trends with projected future scenarios supports decisions that will remain relevant into the future.

Unsupervised cluster analyses of character networks in fiction: Community structure and centrality

We present an integrated approach to cluster and visualize character networks in fiction with the aid of computational and statistical methods. An unsupervised clustering algorithm, minimum span clustering (MSC), was applied to cluster fictional characters at various characteristic resolutions based on their activities in the novel. As a demonstration, we study the character network in Dream of the Red Chamber, the greatest novel in Chinese literature. The character network of the novel is found to exhibit properties of scale-free and small-world networks. Based on unsupervised cluster analyses, we construct and visualize the community structure of the network, and find a three-tiered structure of core, secondary, and peripheral characters. By treating the network as a weighted graph, we further analyze the centralities of characters to determine their importance in the network, and find that betweenness centrality, as a measure of characters’ control over the flow of the narrative, is differentiated from other centrality measures for Dream of the Red Chamber. We believe that these analytic methods provide beneficial tools for applications such as autonomous novel writing.

Distance two labellings for 8-regular grid

ABSTRACTAn -labelling of a graph is a function f on V such that if and if . The span of f is the difference between the maximum and the minimum of f. The -labelling number of G is the minimum span over all -labellings of G. Calamoneri et al. [New bounds for the number of regular grids, Int. J. Mobile Netw. Design Innovat. 1 (2006), pp. 92–101] found lower bounds and upper bounds of for all h and k when and G is the 8-regular grid . In this paper, we obtain lower bounds and upper bounds of when h<k. Also we improve the result of Calamoneri when .

Anthropogenic calling sites boost the sound amplitude of advertisement calls produced by a tropical cricket

Acoustic signals are widely used as sexual displays to attract mates. The choice of display site can strongly influence the male call characteristics and their attractiveness to females. Males can improve the conspicuousness of their signals by increasing sound amplitude and expanding their broadcast area thereby reaching more potential mating partners and influencing female choice. Insects possess a rather limited degree of signal plasticity. To increase the intensity of their calls, insects have been known to manipulate and engineer their display locations. Mole crickets, for example, build burrows that are shaped like horns, designing the burrow such that its resonance closely matches that of their call frequency, thereby boosting sound amplitude. Tree crickets manipulate plant leaves, using them as baffles for optimal sound radiation. In this study, we show for the first time that an insect species can enhance its advertisement calls by using novel, anthropogenic environments as singing sites. During this study, the tropical cricket Anurogryllus muticus was frequently found singing beside the walls of houses, on concrete stairs or in storm drains. These locations significantly increased the sound amplitude of its calls, by an average of 13 and 7 dB SPL, respectively, as measured above and in front of the singing animals compared to the sound amplitude measured in their natural grassland habitat. To evaluate the effect of calling site choice on the male's life span, we conducted a 35-day population survey using the mark and recapture method. Our results revealed that those males that called in grassland habitat without occupying burrows had the shortest minimum life spans.

PELABELAN L(d,2,1) PADA OPERASI KOMPLEMEN DAN KORONA GRAF LINTASAN DAN SIKLUS

Let be a graph with vertices and edges. An labeling of graph is a function of such that the following condition for where denoted the on distance of two vertices and and for . A number is called the span of labeling, if is the largest label vertex of labeling. Notation states that the smallest span of all labeling on a graph . An injective labeling is called and a minimum span of all labeling denoted by . A graph which has labeling is called the graph. In this paper we study of such labeling by considering complement of path and cycle. The result showed that complement of path has , for and , for and complement of the cycle has for and , for and corona of two paths has . Therefor, the complement of paths the complement of cycle , and corona of two path are graph.

Complete formulations of polytopes related to extensions of assignment matrices

Let k,n denote two positive integers and consider the family of the polytopes defined as the convex hull of pairs of the form (Y,h) where Y is a 0/1-matrix with k rows, n columns, containing exactly one nonzero coefficient per column, and where h stands for the smallest index of a nonzero row of Y.These polytopes and some variants naturally emerge in formulations of different classical combinatorial optimization problems such as minimum makespan scheduling and minimum span frequency assignment.In this paper, we provide complete formulations for these polytopes and show the associated separation problem can be solved in polynomial time. The complete formulations in the original space of variables generally contain an exponential number of inequalities. Alternative extended compact formulations are also presented.

Protograph-Based Interleavers for Punctured Turbo Codes

A method to design efficient puncture-constrained interleavers for turbo codes (TCs) is introduced. Resulting TCs profit from a joint optimization of puncturing pattern and interleaver to achieve an improved error rate performance. First, the puncturing pattern is selected based on the constituent code Hamming distance spectrum and on the TC extrinsic information exchange under uniform interleaving. Then, the interleaver function is defined via a layered design process taking account of several design criteria, such as minimum span, correlation girth, and puncturing constraints. We show that applying interleaving with a periodic cross connection pattern that can be assimilated to a protograph improves error-correction performance when compared to the state-of-the-art TCs. An application example is elaborated and compared with the long-term evolution standard: a significant gain in performance can be observed. An additional benefit of the proposed technique resides in the important reduction of the search space for the different interleaver parameters.

&lt;i&gt;L&lt;/i&gt;(2, 1)-labeling of the Cartesian and strong product of two directed cycles

The frequency assignment problem (FAP) is the assignment of frequencies to television and radio transmitters subject to restrictions imposed by the distance between transmitters. One of the graph theoretical models of FAP which is well elaborated is the concept of distance constrained labeling of graphs. Let $G = (V, E)$ be a graph. For two vertices $u$ and $v$ of $G$, we denote $d(u, v)$ the distance between $u$ and $v$. An $L(2, 1)$-labeling for $G$ is a function $f: V → \{0, 1, ···\}$ such that $|f(u)-f(v)| ≥ 1$ if $d(u, v) = 2$ and $|f(u)-f(v)| ≥ 2$ if $d(u, v) = 1$. The span of $f$ is the difference between the largest and the smallest number of $f(V)$. The $λ$-number for $G$, denoted by $λ(G)$, is the minimum span over all $L(2, 1)$-labelings of $G$. In this paper, we study the $λ$-number of the Cartesian and strong product of two directed cycles. We show that for $m, n ≥ 4$ the $λ$-number of $\overrightarrow{C_m} \Box \overrightarrow{C_n}$ is between 4 and 5. We also establish the $λ$-number of $\overrightarrow{{{C}_{m}}}\boxtimes \overrightarrow{{{C}_{n}}}$ for $m ≤ 10$ and prove that the $λ$-number of the strong product of cycles $\overrightarrow{{{C}_{m}}}\boxtimes \overrightarrow{{{C}_{n}}}$ is between 6 and 8 for $m, n ≥ 48$.

&lt;i&gt;L&lt;/i&gt;(&lt;i&gt;d&lt;/i&gt;,1)-labellings of generalised Petersen graphs

An interesting graph distance constrained labelling problem can model the frequency channel assignment problem as well as code assignment in computer networks. The frequency assignment problem asks for assigning frequencies to transmitters in a broadcasting network with the aim of avoiding undesired interference. One of the graph theoretical models of The frequency assignment problem is the concept of distance constrained labelling of graphs. Let u and v be vertices of a graph G = (V (G),E(G)) and d(u, v) be the distance between u and v in G. For an integer d ≥ 0, an L(d, 1)-labelling of G is a function f : V (G) → {0, 1, · · · } such that for every u, v ϵ V (G), |f(u) – f(v)| ≥ d if d(u, v) = 1 and |f(u) – f(v)| ≥ 1 if d(u, v) = 2. The span of f is the difference between the largest and the smallest numbers in f(V (G)). The λd,1-number of G is the minimum span over all L(d, 1)-labellings of G. For natural numbers n and k, where n > 2k, a generalised Petersen graph P(n, k) is obtained by letting its vertex set be {u1, u2, · · · , un} υ {v1, v2, · · · , vn} and its edge set be the union of uiui+1, uivi, vivi+k over 1 ≤ i ≤ n, where subscripts are reduced modulo n. In this paper, we show the λd,1-numbers of the generalised Petersen graphs P(n, k) for n ≥ 5.

L(2,1)-Edge-Labelings of the Edge-Path-Replacement of a Graph

Two edges [Formula: see text] and [Formula: see text] in a graph [Formula: see text] are said to be adjacent if they have a vertex in common, and distance two apart if they are nonadjacent but both are adjacent to a common edge. An [Formula: see text]-edge-labeling of a graph [Formula: see text] is an assignment of nonnegative integers, called labels, to the edges of [Formula: see text] such that the difference between labels of any two adjacent edges is at least [Formula: see text], and the labels of any two edges that are distance two apart are different. The span of an [Formula: see text]-edge-labeling of a graph [Formula: see text] is the difference between the maximum and minimum labels. The minimum span over all [Formula: see text]-edge-labelings of a graph [Formula: see text] is called the [Formula: see text]-edge-labeling number of [Formula: see text], denoted by [Formula: see text]. For [Formula: see text], the edge-path-replacement of a graph [Formula: see text], denoted by [Formula: see text], is a graph obtained by replacing each edge of [Formula: see text] with a path [Formula: see text] on [Formula: see text] vertices. This paper investigates the [Formula: see text]-edge-labeling number of the edge-path-replacement [Formula: see text] of a graph [Formula: see text] for [Formula: see text]. We get the following main results: [Formula: see text] Let [Formula: see text] be a graph with maximum degree [Formula: see text] and [Formula: see text] be an integer not less than [Formula: see text], then [Formula: see text] if [Formula: see text] is odd, and otherwise [Formula: see text]. [Formula: see text] Let [Formula: see text] be a graph with maximum degree [Formula: see text]. Then [Formula: see text] when [Formula: see text] is even, and [Formula: see text] when [Formula: see text] is odd.

&lt;i&gt;L&lt;/i&gt;(&lt;i&gt;d&lt;/i&gt;,1)-labellings of generalised Petersen graphs

An interesting graph distance constrained labelling problem can model the frequency channel assignment problem as well as code assignment in computer networks. The frequency assignment problem asks for assigning frequencies to transmitters in a broadcasting network with the aim of avoiding undesired interference. One of the graph theoretical models of The frequency assignment problem is the concept of distance constrained labelling of graphs. Let u and v be vertices of a graph G = (V (G),E(G)) and d(u, v) be the distance between u and v in G. For an integer d ≥ 0, an L(d, 1)-labelling of G is a function f : V (G) → {0, 1, · · · } such that for every u, v ϵ V (G), |f(u) – f(v)| ≥ d if d(u, v) = 1 and |f(u) – f(v)| ≥ 1 if d(u, v) = 2. The span of f is the difference between the largest and the smallest numbers in f(V (G)). The λd,1-number of G is the minimum span over all L(d, 1)-labellings of G. For natural numbers n and k, where n > 2k, a generalised Petersen graph P(n, k) is obtained by letting its vertex set be {u1, u2, · · · , un} υ {v1, v2, · · · , vn} and its edge set be the union of uiui+1, uivi, vivi+k over 1 ≤ i ≤ n, where subscripts are reduced modulo n. In this paper, we show the λd,1-numbers of the generalised Petersen graphs P(n, k) for n ≥ 5.

Occurrence of CPPopt Values in Uncorrelated ICP and ABP Time Series.

Optimal cerebral perfusion pressure (CPPopt) is a concept that uses the pressure reactivity (PRx)-CPP relationship over a given period to find a value of CPP at which PRx shows best autoregulation. It has been proposed that this relationship be modelled by a U-shaped curve, where the minimum is interpreted as being the CPP value that corresponds to the strongest autoregulation. Owing to the nature of the calculation and the signals involved in it, the occurrence of CPPopt curves generated by non-physiological variations of intracranial pressure (ICP) and arterial blood pressure (ABP), termed here "false positives", is possible. Such random occurrences would artificially increase the yield of CPPopt values and decrease the reliability of the methodology.In this work, we studied the probability of the random occurrence of false-positives and we compared the effect of the parameters used for CPPopt calculation on this probability. To simulate the occurrence of false-positives, uncorrelated ICP and ABP time series were generated by destroying the relationship between the waves in real recordings. The CPPopt algorithm was then applied to these new series and the number of false-positives was counted for different values of the algorithm's parameters. The percentage of CPPopt curves generated from uncorrelated data was demonstrated to be 11.5%. This value can be minimised by tuning some of the calculation parameters, such as increasing the calculation window and increasing the minimum PRx span accepted on the curve.

Longer observation time increases adenoma detection in the proximal colon - a prospective study.

Background and study aims Longer observation times are associated with increased adenoma detection rates (ADR) in the entire colon. However, adenomas in the proximal colon are at risk of being missed during colonoscopy. The aim of this study was to investigate the impact of observation time on detection of adenomatous polyps in the proximal colon. Patients and methods This was a prospective study at a university hospital in Germany. Colonoscopies were conducted using magnetic endoscope imaging (MEI) in order to determine the exact position of the scope. Exact observation times spent for the detection of polyps in the proximal and distal colon segments were assessed. The primary outcome was adenoma detection in the proximal colon. ROC curves were generated in order to test the correlation between observation time and adenoma detection. Logistic regression analysis was used to check for interfering factors. Results A total 480 procedures with 538 polyps were available for analysis. The overall adenoma detection rate was 38.5 %. ADR in the proximal colon was 28.0 %. There was a significant association between observation time in the proximal colon and the detection of proximal adenomas ( P < 0.001). The impact of the time factor on ADR was stronger in the proximal compared to the distal colon ( P = 0.030). A net period of 4 min 7 sec was found to be the minimum time span for sufficient adenoma detection in the proximal colon. Conclusion Observation time is significant in terms of adenoma detection in the proximal colon. The impact of observation time on ADR is stronger in the proximal compared to the distal colon. In the proximal colon a minimum time span of 4 minutes should be spent in order to ensure adequate adenoma detection.