Search results for: vertex enumeration

Authors: Sammani Danwawu Abdullahi

Abstract:

Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration

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Authors: Ying Wang, Haiyan Xie, Aoming Zhang

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The degree distance of a graph is a graph invariant that is more sensitive than the Wiener index. In this paper, we calculate the vertex degree distances of one vertex union of the cycle and the star, and the degree distance of one vertex union of the cycle and the star. These results lay a foundation for further study on the extreme value of the vertex degree distances, and the distribution of the vertices with the extreme value in one vertex union of the cycle and the star.

Keywords: degree distance, vertex-degree-distance, one vertex union of a cycle and a star, graph

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Authors: Ezgi Kaya, A. Dilek Maden

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A topological index is a number related to graph which is invariant under graph isomorphism. In theoretical chemistry, molecular structure descriptors (also called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds. Let G be a graph with n vertices and m edges. For a given edge uv, the quantity nu(e) denotes the number of vertices closer to u than v, the quantity nv(e) is defined analogously. The vertex PI index defined as the sum of the nu(e) and nv(e). Here the sum is taken over all edges of G. The energy of a graph is defined as the sum of the eigenvalues of adjacency matrix of G and the Laplacian energy of a graph is defined as the sum of the absolute value of difference of laplacian eigenvalues and average degree of G. In theoretical chemistry, the π-electron energy of a conjugated carbon molecule, computed using the Hückel theory, coincides with the energy. Hence results on graph energy assume special significance. The Laplacian matrix of a graph G weighted by the vertex PI weighting is the Laplacian vertex PI matrix and the Laplacian vertex PI eigenvalues of a connected graph G are the eigenvalues of its Laplacian vertex PI matrix. In this study, Laplacian vertex PI energy of a graph is defined of G. We also give some bounds for the Laplacian vertex PI energy of graphs in terms of vertex PI index, the sum of the squares of entries in the Laplacian vertex PI matrix and the absolute value of the determinant of the Laplacian vertex PI matrix.

Keywords: energy, Laplacian energy, laplacian vertex PI eigenvalues, Laplacian vertex PI energy, vertex PI index

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Authors: Khidir R. Sharaf, Didar A. Ali

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The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: graph theory, graph spectra, nullity of graphs, statistic

Procedia PDF Downloads 199

Authors: Soner Nandappa D., Ahmed Mohammed Naji

Abstract:

In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

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Authors: Shaowei Sun

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Let G be a graph with vertex set V(G)={v_1,v_2,...,v_n} and edge set E(G). For any vertex v belong to V(G), let d_v denote the degree of v. The normalized Laplacian matrix of the graph G is the matrix where the non-diagonal (i,j)-th entry is -1/(d_id_j) when vertex i is adjacent to vertex j and 0 when they are not adjacent, and the diagonal (i,i)-th entry is the di. In this paper, we discuss some bounds on the largest and the second smallest normalized Laplacian eigenvalue of trees and graphs. As following, we found some new bounds on the second smallest normalized Laplacian eigenvalue of tree T in terms of graph parameters. Moreover, we use Sage to give some conjectures on the second largest and the third smallest normalized eigenvalues of graph.

Keywords: graph, normalized Laplacian eigenvalues, normalized Laplacian matrix, tree

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Authors: Thomas Odaker, Dieter Kranzlmueller, Jens Volkert

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We present an approach to triangle mesh simplification designed to be executed on the GPU. We use a quadric error metric to calculate an error value for each vertex of the mesh and order all vertices based on this value. This step is followed by the parallel removal of a number of vertices with the lowest calculated error values. To allow for the parallel removal of multiple vertices we use a set of per-vertex boundaries that prevent mesh foldovers even when simplification operations are performed on neighbouring vertices. We execute multiple iterations of the calculation of the vertex errors, ordering of the error values and removal of vertices until either a desired number of vertices remains in the mesh or a minimum error value is reached. This parallel approach is used to speed up the simplification process while maintaining mesh topology and avoiding foldovers at every step of the simplification.

Keywords: computer graphics, half edge collapse, mesh simplification, precomputed simplification, topology preserving

Procedia PDF Downloads 327

Authors: Saieed Akbari, Yousef Bagheri, Amir Hossein Ghodrati, Sima Saadat Akhtar

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Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.

Keywords: eigenvalues, energy, line graphs, matching number

Procedia PDF Downloads 195

Authors: Saif Akram, E. Rathakrishnan

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The mixing promoting efficiency of two identical sharp and truncated vertex triangular tabs offering geometrical blockage of 2.5% each, placed at the exit of a Mach 1.5 elliptic nozzle was studied experimentally. The effectiveness of both the tabs in enhancing the mixing of jets with the ambient air are determined by measuring the Pitot pressure along the jet axis and the jet spread in both the minor and major axes of the elliptic nozzle, covering marginally overexpanded to moderately underexpanded levels at the nozzle exit. The results reveal that both the tabs enhance mixing characteristics of the uncontrolled elliptic jet when placed at minor axis. A core length reduction of 67% is achieved at NPR 3 which is the overexpanded state. Similarly, the core length is reduced by about 67%, 50% and 57% at NPRs of 4, 5 and 6 (underexpanded states) respectively. However, unlike the considerable increment in mixing promoting efficiency by the use of truncated vertex tabs for axisymmetric jets, the effect is not much pronounced for the case of supersonic elliptic jets. The CPD plots for both the cases almost overlap, especially when tabs are placed at minor axis, at all the pressure conditions. While, when the tabs are used at major axis, in the case of overexpanded condition, the sharp vertex triangular tabs act as a better mixing enhancer for the supersonic elliptic jets. For the jet controlled with truncated vertex triangular tabs, the core length reductions are of the same order as those for the sharp vertex triangular tabs. The jet mixing is hardly influenced by the tip effect in case of supersonic elliptic jet.

Keywords: elliptic jet, tabs, truncated, triangular

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Authors: Chanon Promsakon, Sayan Panma

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Let S be a finite semigroup, A a subset of S and f an endomorphism on S. The endo-Cayley digraph of a semigroup S corresponding to a connecting set A and an endomorphism f, denoted by endo − Cayf (S, A) is a digraph whose vertex set is S and a vertex u is adjacent to a vertex v if and only if v = f(u)a for some a ∈ A. A digraph D is called undirected if any edge uv in D, there exists an edge vu in D. We consider the undirectedness of an endo-Cayley of a cyclic group of order prime, Zp. In this work, we investigate conditions for connecting sets and endomorphisms to make endo-Cayley digraphs of cyclic groups of order primes be undirected. Moreover, we give some conditions for an undirected endo-Cayley of cycle group of any order.

Keywords: endo-Cayley graph, undirected digraphs, cyclic groups, endomorphism

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Authors: Souad Slimani, Sylvain Gravier, Simon Schmidt

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Recently, several vertex identifying notions were introduced (identifying coloring, lid-coloring,...); these notions were inspired by identifying codes. All of them, as well as original identifying code, is based on separating two vertices according to some conditions on their closed neighborhood. Therefore, twins can not be identified. So most of known results focus on twin-free graph. Here, we show how twins can modify optimal value of vertex-identifying parameters for identifying coloring and locally identifying coloring.

Keywords: identifying coloring, locally identifying coloring, twins, separating

Procedia PDF Downloads 111

Authors: J. C. Valenzuela-Tripodoro, P. Álvarez-Ruíz, M. A. Mateos-Camacho, M. Cera

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In 2004, it was introduced the concept of Roman domination in graphs. This concept was initially inspired and related to the defensive strategy of the Roman Empire. An undefended place is a city so that no legions are established on it, whereas a strong place is a city in which two legions are deployed. This situation may be modeled by labeling the vertices of a finite simple graph with labels {0, 1, 2}, satisfying the condition that any 0-vertex must be adjacent to, at least, a 2-vertex. Roman domination in graphs is a variant of classic domination. Clearly, the main aim is to obtain such labeling of the vertices of the graph with minimum cost, that is to say, having minimum weight (sum of all vertex labels). Formally, a function f: V (G) → {0, 1, 2} is a Roman dominating function (RDF) in the graph G = (V, E) if f(u) = 0 implies that f(v) = 2 for, at least, a vertex v which is adjacent to u. The weight of an RDF is the positive integer w(f)= ∑_(v∈V)▒〖f(v)〗. The Roman domination number, γ_R (G), is the minimum weight among all the Roman dominating functions? Obviously, the set of vertices with a positive label under an RDF f is a dominating set in the graph, and hence γ(G)≤γ_R (G). In this work, we start the study of a generalization of RDF in which we consider that any undefended place should be defended from a sudden attack by, at least, k legions. These legions can be deployed in the city or in any of its neighbours. A function f: V → {0, 1, . . . , k + 1} such that f(N[u]) ≥ k + |AN(u)| for all vertex u with f(u) < k, where AN(u) represents the set of active neighbours (i.e., with a positive label) of vertex u, is called a [k]-multiple Roman dominating functions and it is denoted by [k]-MRDF. The minimum weight of a [k]-MRDF in the graph G is the [k]-multiple Roman domination number ([k]-MRDN) of G, denoted by γ_[kR] (G). First, we prove that the [k]-multiple Roman domination decision problem is NP-complete even when restricted to bipartite and chordal graphs. A problem that had been resolved for other variants and wanted to be generalized. We know the difficulty of calculating the exact value of the [k]-MRD number, even for families of particular graphs. Here, we present several upper and lower bounds for the [k]-MRD number that permits us to estimate it with as much precision as possible. Finally, some graphs with the exact value of this parameter are characterized.

Keywords: multiple roman domination function, decision problem np-complete, bounds, exact values

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Authors: Yu Chen, Seong-Jin Kim, Jaehoon Chung

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High throughput cells counting and sizing are often required for biomedical applications. Here we report design, fabrication and validating of a micro-machined Coulter counter device with multiple-channel to realize such application for low cost. Multiple vertical through-holes were fabricated on a silicon chip, combined with the PDMS micro-fluidics channel that serves as the sensing channel. In order to avoid the crosstalk introduced by the electrical connection, instead of measuring the current passing through, the potential of each channel is monitored, thus the high throughput is possible. A peak of the output potential can be captured when the cell/particle is passing through the microhole. The device was validated by counting and sizing the polystyrene beads with diameter of 6 μm, 10 μm and 15 μm. With the sampling frequency to be set at 100 kHz, up to 5000 counts/sec for each channel can be realized. The counting and enumeration of MCF7 cancer cells are also demonstrated.

Keywords: Coulter counter, cell enumeration, high through-put, cell sizing

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Authors: Mohammad Hossain Mohammadi, Saif Al Ameri, Sana Ziaei, Jinane Mounsef

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Automated enumeration of the number of hand fingers is widely used in several motion gaming and distance control applications, and is discussed in several published papers as a starting block for hand recognition systems. The automated finger enumeration technique should not only be accurate, but also must have a fast response for a moving-picture input. The high performance of video in motion games or distance control will inhibit the program’s overall speed, for image processing software such as Matlab need to produce results at high computation speeds. Since an automated finger enumeration with minimum error and processing time is desired, a comparative study between two finger enumeration techniques is presented and analyzed in this paper. In the pre-processing stage, various image processing functions were applied on a real-time video input to obtain the final cleaned auto-cropped image of the hand to be used for the two techniques. The first technique uses the known morphological tool of skeletonization to count the number of skeleton’s endpoints for fingers. The second technique uses a radial distance method to enumerate the number of fingers in order to obtain a one dimensional hand representation. For both discussed methods, the different steps of the algorithms are explained. Then, a comparative study analyzes the accuracy and speed of both techniques. Through experimental testing in different background conditions, it was observed that the radial distance method was more accurate and responsive to a real-time video input compared to the skeletonization method. All test results were generated in Matlab and were based on displaying a human hand for three different orientations on top of a plain color background. Finally, the limitations surrounding the enumeration techniques are presented.

Keywords: comparative study, hand recognition, fingertip detection, skeletonization, radial distance, Matlab

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Authors: Wongsakorn Charoenpanitseri

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The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: total colorings, the total chromatic number, 3-degenerated, CLAW-FREE

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Authors: E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell

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We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails.

Keywords: Hamilton cycle decision problem, computational complexity theory, graph theory, theoretical computer science

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Authors: T. Mokhele, O. Mutanga, F. Ahmed

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South Africa is one of the few countries that have stopped using the same Enumeration Areas (EAs) for census enumeration and dissemination. The advantage of this change is that confidentiality issue could be addressed for census dissemination as the design of geographic unit for collection is mainly to ensure that this unit is covered by one enumerator. The objective of this paper was to evaluate the performance of automated zone design output areas against non-zone design developed geographies using the 2001 census data, and 2011 census to some extent, as the main input. The comparison of the Automated Zone-design Tool (AZTool) census output areas with the Small Area Layers (SALs) and SubPlaces based on confidentiality limit, population distribution, and degree of homogeneity, as well as shape compactness, was undertaken. Further, SPSS was employed for validation of the AZTool output results. The results showed that AZTool developed output areas out-perform the existing official SAL and SubPlaces with regard to minimum population threshold, population distribution and to some extent to homogeneity. Therefore, it was concluded that AZTool program provides a new alternative to the creation of optimised census output areas for dissemination of population census data in South Africa.

Keywords: AZTool, enumeration areas, small areal layers, South Africa

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Authors: Sarchil H. Qader, Andrew Harfoot, Mathias Kuepie, Sabrina Juran, Attila Lazar, Andrew J. Tatem

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The need for high-quality, reliable, and timely population data, including demographic information, to support the achievement of the sustainable development goals (SDGs) in all countries was recognized by the United Nations' 2030 Agenda for sustainable development. However, many low and middle-income countries lack reliable and recent census data. To achieve reliable and accurate census and survey outputs, up-to-date census enumeration areas and digital national sampling frames are critical. Census enumeration areas (EAs) are the smallest geographic units for collection, disseminating, and analyzing census data and are often used as a national sampling frame to serve various socio-economic surveys. Even for countries that are wealthy and stable, creating and updating EAs is a difficult yet crucial step in preparing for a national census. Such a process is commonly done manually, either by digitizing small geographic units on high-resolution satellite imagery or walking the boundaries of units, both of which are extremely expensive. We have developed a user-friendly tool that could be employed to generate draft EA boundaries automatically. The tool is based on high-resolution gridded population and settlement datasets, GPS household locations, building footprints and uses publicly available natural, man-made and administrative boundaries. Initial outputs were produced in Burkina Faso, Paraguay, Somalia, Togo, Niger, Guinea, and Zimbabwe. The results indicate that the EAs are in line with international standards, including boundaries that are easily identifiable and follow ground features, have no overlaps, are compact and free of pockets and disjoints, and the boundaries are nested within administrative boundaries.

Keywords: enumeration areas, national sampling frame, gridded population data, preEA tool

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Authors: Analen Malnegro, Gina Malacas

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Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.

Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number

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Authors: Nuttawoot Nupo, Sayan Panma

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A semigroup S is said to be a left (right) zero semigroup if S satisfies the equation xy=x (xy=y) for all x,y in S. In addition, the semigroup S is called a left (right) group if S is isomorphic to the direct product of a group and a left (right) zero semigroup. The Cayley digraph Cay(S,A) of a semigroup S with a connection set A is defined to be a digraph with the vertex set S and the arc set E(Cay(S,A))={(x,xa) | x∈S, a∈A} where A is any subset of S. All sets in this research are assumed to be finite. Let D be a digraph together with a vertex set V and an arc set E. Let u and v be two different vertices in V and I a nonempty subset of V. The vertices u and v are said to be independent if (u,v)∉E and (v,u)∉E. The set I is called an independent set of D if any two different vertices in I are independent. The independence number of D is the maximum cardinality of an independent set of D. Moreover, the vertices u and v are said to be path independent if there is no dipath from u to v and there is no dipath from v to u. The set I is called a path independent set of D if any two different vertices in I are path independent. The path independence number of D is the maximum cardinality of a path independent set of D. In this research, we describe a lower bound and an upper bound of the independence number of Cayley digraphs of left groups and right groups. Some examples corresponding to those bounds are illustrated here. Furthermore, the exact value of the path independence number of Cayley digraphs of left groups and right groups are also presented.

Keywords: Cayley digraphs, independence number, left groups, path independence number, right groups

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Authors: Shaikah Alsubayae, Gianluigi Casse, Carlos Chavez, Jon Taylor, Alan Taylor, Mohammad Alsulimane

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Ensuring accurate radiotherapy with carbon therapy requires precise monitoring of radiation dose distribution within the patient's body. This monitoring is essential for targeted tumor treatment, minimizing harm to healthy tissues, and improving treatment effectiveness while lowering side effects. In our investigation, we employed a methodological approach to monitor secondary proton doses in carbon therapy using Monte Carlo simulations. Initially, Geant4 simulations were utilized to extract the initial positions of secondary particles formed during interactions between carbon ions and water. These particles included protons, gamma rays, alpha particles, neutrons, and tritons. Subsequently, we studied the relationship between the carbon ion beam and these secondary particles. Interaction Vertex Imaging (IVI) is valuable for monitoring dose distribution in carbon therapy. It provides details about the positions and amounts of secondary particles, particularly protons. The IVI method depends on charged particles produced during ion fragmentation to gather information about the range by reconstructing particle trajectories back to their point of origin, referred to as the vertex. In our simulations regarding carbon ion therapy, we observed a strong correlation between some secondary particles and the range of carbon ions. However, challenges arose due to the target's unique elongated geometry, which hindered the straightforward transmission of forward-generated protons. Consequently, the limited protons that emerged mostly originated from points close to the target entrance. The trajectories of fragments (protons) were approximated as straight lines, and a beam back-projection algorithm, using recorded interaction positions in Si detectors, was developed to reconstruct vertices. The analysis revealed a correlation between the reconstructed and actual positions.

Keywords: radiotherapy, carbon therapy, monitoring of radiation dose, interaction vertex imaging

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Authors: E. Accomando, L. Delle Rose, S. Moretti, E. Olaiya, C. Shepherd-Themistocleous

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Heavy sterile neutrinos are almost ubiquitous in the class of Beyond Standard Model scenarios aimed at addressing the puzzle that emerged from the discovery of neutrino flavour oscillations, hence the need to explain their masses. In particular, they are necessary in a U(1)’ enlarged Standard Model (SM). We show that these heavy neutrinos can be rather long-lived producing distinctive displaced vertices and tracks. Indeed, depending on the actual decay length, they can decay inside a Large Hadron Collider (LHC) detector far from the main interaction point and can be identified in the inner tracking system or the muon chambers, emulated here through the Compact Muon Solenoid (CMS) detector parameters. Among the possible production modes of such heavy neutrino, we focus on their pair production mechanism in the SM Higgs decay, eventually yielding displaced lepton signatures following the heavy neutrino decays into weak gauge bosons. By employing well-established triggers available for the CMS detector and using the data collected by the end of the LHC Run 2, these signatures would prove to be accessible with negligibly small background. Finally, we highlight the importance that the exploitation of new triggers, specifically, displaced tri-lepton ones, could have for this displaced vertex search.

Keywords: beyond the standard model, displaced vertex, Higgs physics, neutrino physics

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Authors: E. Yazıcı, H. Sundu, E. Veli Veliev

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In order to understand the nature of strong interactions and QCD vacuum, investigation of the meson coupling constants have an important role. The knowledge on the temperature dependence of the form factors is very important for the interpretation of heavy-ion collision experiments. Also, more accurate determination of these coupling constants plays a crucial role in understanding of the hadronic decays. With the increasing of CM energies of the experiments, researches on meson interactions have become one of the more interesting problems of hadronic physics. In this study, we analyze the temperature dependence of the strong form factor of the BcBcJ/ψ vertex using the three point QCD sum rules method. Here, we assume that with replacing the vacuum condensates and also the continuum threshold by their thermal version, the sum rules for the observables remain valid. In calculations, we take into account the additional operators, which appear in the Wilson expansion at finite temperature. We also investigated the momentum dependence of the form factor at T = 0, fit it into an analytic function, and extrapolate into the deep time-like region in order to obtain a strong coupling constant of the vertex. Our results are consistent with the results existing in the literature.

Keywords: QCD sum rules, thermal QCD, heavy mesons, strong coupling constants

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Authors: Shaikah Alsubayae, Gianluigi Casse, Carlos Chavez, Jon Taylor, Alan Taylor, Mohammad Alsulimane

Abstract:

Achieving precise radiotherapy through carbon therapy necessitates the accurate monitoring of radiation dose distribution within the patient's body. This process is pivotal for targeted tumor treatment, minimizing harm to healthy tissues, and enhancing overall treatment effectiveness while reducing the risk of side effects. In our investigation, we adopted a methodological approach to monitor secondary proton doses in carbon therapy using Monte Carlo (MC) simulations. Initially, Geant4 simulations were employed to extract the initial positions of secondary particles generated during interactions between carbon ions and water, including protons, gamma rays, alpha particles, neutrons, and tritons. Subsequently, we explored the relationship between the carbon ion beam and these secondary particles. Interaction vertex imaging (IVI) proves valuable for monitoring dose distribution during carbon therapy, providing information about secondary particle locations and abundances, particularly protons. The IVI method relies on charged particles produced during ion fragmentation to gather range information by reconstructing particle trajectories back to their point of origin, known as the vertex. In the context of carbon ion therapy, our simulation results indicated a strong correlation between some secondary particles and the range of carbon ions. However, challenges arose due to the unique elongated geometry of the target, hindering the straightforward transmission of forward-generated protons. Consequently, the limited protons that did emerge predominantly originated from points close to the target entrance. Fragment (protons) trajectories were approximated as straight lines, and a beam back-projection algorithm, utilizing interaction positions recorded in Si detectors, was developed to reconstruct vertices. The analysis revealed a correlation between the reconstructed and actual positions.

Keywords: radiotherapy, carbon therapy, monitor secondary proton doses, interaction vertex imaging

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Authors: Richa Sharma, Uma Nahar, Sadhna Sharma, Indu Verma

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Counteracting the deadly pathogen Mycobacterium tuberculosis (M. tb) effectively is still a global challenge. Scrutinizing alternative weapons like antimicrobial peptides to strengthen existing tuberculosis artillery is urgently required. Considering the antimycobacterial potential of Human Beta Defensin 1 (HBD-1) along with isoniazid, the present study was designed to explore the ability of HBD-1 to act against active and dormant M. tb. HBD-1 was screened in silico using antimicrobial peptide prediction servers to identify its short antimicrobial motif. The activity of both HBD-1 and its selected motif (Pep B) was determined at different concentrations against actively growing M. tb in vitro and ex vivo in monocyte derived macrophages (MDMs). Log phase M. tb was grown along with HBD-1 and Pep B for 7 days. M. tb infected MDMs were treated with HBD-1 and Pep B for 72 hours. Thereafter, colony forming unit (CFU) enumeration was performed to determine activity of both peptides against actively growing in vitro and intracellular M. tb. The dormant M. tb models were prepared by following two approaches and treated with different concentrations of HBD-1 and Pep B. Firstly, 20-22 days old M. tbH37Rv was grown in potassium deficient Sauton media for 35 days. The presence of dormant bacilli was confirmed by Nile red staining. Dormant bacilli were further treated with rifampicin, isoniazid, HBD-1 and its motif for 7 days. The effect of both peptides on latent bacilli was assessed by colony forming units (CFU) and most probable number (MPN) enumeration. Secondly, human PBMC granuloma model was prepared by infecting PBMCs seeded on collagen matrix with M. tb(MOI 0.1) for 10 days. Histopathology was done to confirm granuloma formation. The granuloma thus formed was incubated for 72 hours with rifampicin, HBD-1 and Pep B individually. Difference in bacillary load was determined by CFU enumeration. The minimum inhibitory concentrations of HBD-1 and Pep B restricting growth of mycobacteria in vitro were 2μg/ml and 20μg/ml respectively. The intracellular mycobacterial load was reduced significantly by HBD-1 and Pep B at 1μg/ml and 5μg/ml respectively. Nile red positive bacterial population, high MPN/ low CFU count and tolerance to isoniazid, confirmed the formation of potassium deficienybaseddormancy model. HBD-1 (8μg/ml) showed 96% and 99% killing and Pep B (40μg/ml) lowered dormant bacillary load by 68.89% and 92.49% based on CFU and MPN enumeration respectively. Further, H&E stained aggregates of macrophages and lymphocytes, acid fast bacilli surrounded by cellular aggregates and rifampicin resistance, indicated the formation of human granuloma dormancy model. HBD-1 (8μg/ml) led to 81.3% reduction in CFU whereas its motif Pep B (40μg/ml) showed only 54.66% decrease in bacterial load inside granuloma. Thus, the present study indicated that HBD-1 and its motif are effective antimicrobial players against both actively growing and dormant M. tb. They should be further explored to tap their potential to design a powerful weapon for combating tuberculosis.

Keywords: antimicrobial peptides, dormant, human beta defensin 1, tuberculosis

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Authors: Masoud Karimi

Abstract:

‎Let R be a commutative ring‎. ‎The regular digraph of ideals of R, which is denoted by‎ Γ(R)‎, ‎is a digraph whose vertex-set is the set of all ‎non-‎trivial ideals of R and‎, ‎for every‎ two distinct vertices I and J‎, ‎there is an arc from I to J‎, ‎whenever I contains‎ a non-zero-divisor on J. In this article, ‎we ‎show ‎that an indecomposable ‎Noetherian ring ‎‎‎R ‎is ‎Artinian ‎local ‎if ‎and ‎only ‎if Z(I)=Z(R) ‎for ‎every ‎non-nilpotent ‎ideal ‎‎‎I‎. ‎Then ‎we ‎conclude ‎that ‎‎the ‎girth ‎of‎ Γ(R)‎ ‎is ‎not ‎equal ‎to ‎four.

Keywords: commutative ring‎, ‎girth‎, regular digraph‎, zero-divisor

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Authors: Bin Sheng, Changhong Lu

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Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

Procedia PDF Downloads 203

Authors: Chin-Chia Jane

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In a transportation network, travel time refers to the transmission time from source node to destination node, whereas reliability refers to the probability of a successful connection from source node to destination node. With an increasing emphasis on quality of service (QoS), both performance indexes are significant in the design and analysis of transportation systems. In this work, we extend the well-known flow network model for transportation networks so that travel time and reliability are integrated into the QoS measurement simultaneously. In the extended model, in addition to the general arc capacities, each intermediate node has a time weight which is the travel time for per unit of commodity going through the node. Meanwhile, arcs and nodes are treated as binary random variables that switch between operation and failure with associated probabilities. For pre-specified travel time limitation and demand requirement, the QoS of a transportation network is the probability that source can successfully transport the demand requirement to destination while the total transmission time is under the travel time limitation. This work is pioneering, since existing literatures that evaluate travel time reliability via a single optimization path, the proposed QoS focuses the performance of the whole network system. To compute the QoS of transportation networks, we first transfer the extended network model into an equivalent min-cost max-flow network model. In the transferred network, each arc has a new travel time weight which takes value 0. Each intermediate node is replaced by two nodes u and v, and an arc directed from u to v. The newly generated nodes u and v are perfect nodes. The new direct arc has three weights: travel time, capacity, and operation probability. Then the universal set of state vectors is recursively decomposed into disjoint subsets of reliable, unreliable, and stochastic vectors until no stochastic vector is left. The decomposition is made possible by applying existing efficient min-cost max-flow algorithm. Because the reliable subsets are disjoint, QoS can be obtained directly by summing the probabilities of these reliable subsets. Computational experiments are conducted on a benchmark network which has 11 nodes and 21 arcs. Five travel time limitations and five demand requirements are set to compute the QoS value. To make a comparison, we test the exhaustive complete enumeration method. Computational results reveal the proposed algorithm is much more efficient than the complete enumeration method. In this work, a transportation network is analyzed by an extended flow network model where each arc has a fixed capacity, each intermediate node has a time weight, and both arcs and nodes are independent binary random variables. The quality of service of the transportation network is an integration of customer demands, travel time, and the probability of connection. We present a decomposition algorithm to compute the QoS efficiently. Computational experiments conducted on a prototype network show that the proposed algorithm is superior to existing complete enumeration methods.

Keywords: quality of service, reliability, transportation network, travel time

Procedia PDF Downloads 191

Authors: Vivek B. Ravindran, Aravind Surapaneni, Rebecca Traub, Sarvesh K. Soni, Andrew S. Ball

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Parasitic diseases have a devastating, long-term impact on human health and welfare. More than two billion people are infected with soil-transmitted helminths (STHs), including the roundworms (Ascaris), hookworms (Necator and Ancylostoma) and whipworm (Trichuris) with majority occurring in the tropical and subtropical regions of the world. Despite its low prevalence in developed countries, the removal of STHs from wastewater remains crucial to allow the safe use of sludge or recycled water in agriculture. Conventional methods such as incubation and optical microscopy are cumbersome; consequently, the results drastically vary from person-to-person observing the ova (eggs) under microscope. Although PCR-based methods are an alternative to conventional techniques, it lacks the ability to distinguish between viable and non-viable helminth ova. As a result, wastewater treatment industries are in major need for radically new and innovative tools to detect and quantify STHs eggs with precision, accuracy and being cost-effective. In our study, we focus on the following novel and innovative techniques: -Recombinase polymerase amplification and Surface enhanced Raman spectroscopy (RPA-SERS) based detection of helminth ova. -Use of metal nanoparticles and their relative nanozyme activity. -Colorimetric detection, differentiation and enumeration of genera of helminth ova using hydrolytic enzymes (chitinase and lipase). -Propidium monoazide (PMA)-qPCR to detect viable helminth ova. -Modified assay to recover and enumerate helminth eggs from fresh raw sewage. -Transcriptome analysis of ascaris ova in fresh raw sewage. The aforementioned techniques have the potential to replace current conventional and molecular methods thereby producing a standard protocol for the determination and enumeration of helminth ova in sewage sludge.

Keywords: colorimetry, helminth, PMA-QPCR, nanoparticles, RPA, viable

Procedia PDF Downloads 263

Authors: Dongqin Cheng

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The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.

Keywords: interconnection network, balanced hypercube, Hamiltonian cycle, prescribed edges

Procedia PDF Downloads 171