Combinatorial Characteristics Research Articles

Identification of Pathogen and Host‐Response Markers Correlated With Periodontal Disease

Periodontitis is the major cause of tooth loss in adults and is linked to systemic illnesses, such as cardiovascular disease and stroke. The development of rapid point-of-care (POC) chairside diagnostics has the potential for the early detection of periodontal infection and progression to identify incipient disease and reduce health care costs. However, validation of effective diagnostics requires the identification and verification of biomarkers correlated with disease progression. This clinical study sought to determine the ability of putative host- and microbially derived biomarkers to identify periodontal disease status from whole saliva and plaque biofilm. One hundred human subjects were equally recruited into a healthy/gingivitis group or a periodontitis population. Whole saliva was collected from all subjects and analyzed using antibody arrays to measure the levels of multiple proinflammatory cytokines and bone resorptive/turnover markers. Salivary biomarker data were correlated to comprehensive clinical, radiographic, and microbial plaque biofilm levels measured by quantitative polymerase chain reaction (qPCR) for the generation of models for periodontal disease identification. Significantly elevated levels of matrix metalloproteinase (MMP)-8 and -9 were found in subjects with advanced periodontitis with Random Forest importance scores of 7.1 and 5.1, respectively. The generation of receiver operating characteristic curves demonstrated that permutations of salivary biomarkers and pathogen biofilm values augmented the prediction of disease category. Multiple combinations of salivary biomarkers (especially MMP-8 and -9 and osteoprotegerin) combined with red-complex anaerobic periodontal pathogens (such as Porphyromonas gingivalis or Treponema denticola) provided highly accurate predictions of periodontal disease category. Elevated salivary MMP-8 and T. denticola biofilm levels displayed robust combinatorial characteristics in predicting periodontal disease severity (area under the curve = 0.88; odds ratio = 24.6; 95% confidence interval: 5.2 to 116.5). Using qPCR and sensitive immunoassays, we identified host- and bacterially derived biomarkers correlated with periodontal disease. This approach offers significant potential for the discovery of biomarker signatures useful in the development of rapid POC chairside diagnostics for oral and systemic diseases. Studies are ongoing to apply this approach to the longitudinal predictions of disease activity.

Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane

Abstract We consider finite systems of straight lines in the Euclidean plane 𝐑2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains determined by a given finite line-system in 𝐑2 is presented and it is shown that this estimate is precise in a certain sense.

Multiplicative inequalities for the L 1 norm: Applications in analysis and number theory

The paper is devoted to multiplicative lower estimates for the L 1 norm and their applications in analysis and number theory. Multiplicative inequalities of the following three types are considered: martingale (for the Haar system), complex trigonometric (for exponential sums), and real trigonometric. A new method for obtaining sharp bounds for the integral norm of trigonometric and power series is proposed; this method uses the number-theoretic and combinatorial characteristics of the spectrum. Applications of the method (both in H 1 and L 1) to an important class of power density spectra, including [n α] with 1 ≤ α < ∞, are developed. A new combinatorial theorem is proved that makes it possible to estimate the arithmetic characteristics of spectra under fairly general assumptions.

Topological characteristics of random triangulated surfaces

AbstractWe consider the topological characteristics of orientable surfaces generated by randomly gluing n triangles together. Our results are most conveniently expressed in terms of a parameter h = n / 2 + χ, where χ is the Euler characteristic of the surface. Simulations and results for similar models suggest that Ex [h] = log(3n) + γ + o(1) and Var [h] = log(3n) + γ ‐ π2 / 6 + o(1). We prove that Ex [h] = log n + O(1) and Var [h] = O(log n). We also derive results concerning a number of other topological invariants and combinatorial characteristics of these random surfaces. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006

On the Maximum Noninteger Polyhedron Vertices of the Three-index Axial Assignment Problem

Consideration was given to the maximum noninteger polyhedron vertices in the three-index axial assignment problem of the order n, that is, vertices with 3n - 2 fractional components. New types of these vertices were specified and their combinatorial characteristics studied.

Heuristic concentration for the p-median: an example demonstrating how and why it works

We map certain combinatorial aspects of the p-median problem and explore their effects on the efficacy of a common (1-opt) interchange heuristic and of heuristic concentration (HC) for the problem's solution. Although the problem's combinatorial characteristics exist in abstract space, its data exist in two-dimensional space and are therefore mappable. By simultaneously analysing the problem's patterns in geographic space and its combinatorial characteristics in abstract space, we provide new insight into what demand node configurations cause problems for the interchange heuristic and how HC overcomes these problems. Scope and purpose Location-allocation (LA) models simultaneously locate facilities and allocate demand points to them. They have extensive applications in both the public and private sectors (Rosing, Hodgson, JORBEL: Belgian Journal of Operations Research and Statistics 36 (1997) 75). The p-median, which minimizes the average demand-facility distance is the most widely used LA model. The p-median model is np hard and its data sets are frequently extremely large, requiring heuristic solutions. As the size of the data set grows, the quality of solutions from the most commonly used heuristic, that of Tietz and Bart (Operations Research 16 (1968) 955) deteriorate (Rosing, Environment and Planning 24 (1997) 59). HC (Rosing, ReVelle, European Journal of Operational Research 97 (1997) 75), a method concentrates and builds upon the good elements of suboptimal heuristic solutions, has been shown to produce excellent solutions for large data sets (Rosing, ReVelle, Rolland, Schilling, Current, European Journal of Operational Research 104 (1998) 93). The purpose of this paper is to demonstrate how and why HC improves upon the results of a 1-opt interchange heuristic. The method used is a node by node examination of good solutions and their geography.

Search heuristics for operation sequencing in process planning

The operation-sequencing problem in process planning is considered to produce a part with the objective of minimizing the sum of machine, setup and tool change costs. In general, the problem has combinatorial characteristics and complex precedence relations, which makes the problem difficult to solve. Six local search heuristics have been developed based on simulated annealing and tabu search to obtain good solutions for practical-sized problems within a reasonable amount of computation time. Application of the algorithms is illustrated using an example part. Also, computational experiments were done on randomly generated problems and the results show that the tabu search-based algorithms are better than the simulated annealing-based algorithms on overall average. In particular, one of the tabu search algorithms suggested here gave optimal solutions for most small-sized test problems within very short computation times.

Branch and fathoming algorithms for operation sequencing in process planning

This paper focuses on the operation sequencing problem in process planning, which is the problem of determining the sequence of operations required for producing a part with the objective of minimizing the sum of machine, set-up and tool change costs. In general, operation sequencing in process planning has been a difficult optimization problem, since it has combinatorial characteristics and complex precedence relations. This paper first suggests a precedence-directed graph to describe the precedence relations among operations with a compact form. Then, using the directed graph, the authors develop optimal and heuristic branch and fathoming algorithms that can give optimal and near optimal solutions respectively. Application of the two algorithms is illustrated using an example part. Also, to show the performance of the suggested algorithms, computational experiments were done on randomly generated problems and the results show that the heuristic algorithm gives optimal solutions for all the generated problems with much shorter computation time.

The average sensitivity of square-freeness

We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain an asymptotic formula, having a linear main term, for the average sensitivity of the Boolean function deciding whether a given integer is square-free. This result allows us to derive a quadratic lower bound for the formula size complexity of testing square-free numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximate polynomial representations of this function.

A Subpath Ejection Method for the Vehicle Routing Problem

Generically, ejection chains are methods conceived to allow solution transformations to be efficiently carried out by modifying a variable number of their components at each step of a local search algorithm. We consider a subpath ejection chain method for the vehicle routing problem (VRP) under capacity and route length restrictions. The method undertakes the identification of a substructure named the flower reference structure which, besides coordinating moves during an ejection chain construction, allows the creation of neighborhood structures with interesting combinatorial characteristics. Specifically, we base the method on a fundamental property of creating alternating paths and cycles during an ejection chain construction. A new algorithm based on a Tabu search framework is proposed, and computational results on a set of academic and real-world problems indicate that the algorithm may be a good alternative to the best heuristic algorithms for the VRP.

Lattice Animals and Self-Organized Criticality

The paper considers one model of SOC close to BTW and slider blocks models. In addition, it introduces an additional time parameter and imposes special restrictions on the avalanche geometrical structure. The generalization and modification of the avalanche's concept allows us to apply H. Weyl's theorem in the dynamical system theory so as to obtain the strong and exact results in this area. We introduce some combinatorial characteristic of clusters and use it as a tool for estimating the frequency of the avalanches. The results obtained give the asymptotically exact expressions for the asymptotical frequency as well as two special types of such extended avalanches. In some special cases, they reduce the determination of the frequency of the avalanches to combinatorial enumerative problem for lattice animals on the d-dimensional torus. The other two results are related to the one-dimensional model and establish the connection between the SOC and the theory of number partitions.

Learning reliably and with one-sided error

Reliable and probably useful learning, proposed by Rivest and Sloan, is a variant of probably approximately correct learning. In this model the hypothesis must never misclassify an instance but is allowed to answer “I don't know” with a low probability. We derive upper and lower bounds for the sample complexity of reliable and probably useful learning in terms of the combinatorial characteristics of the concept class to be learned. This is done by reducing reliable and probably useful learning to learning with one-sided error. The bounds also hold for a slightly weaker model that allows the learner to output with a low probability a hypothesis that makes misclassifications. We see that in these models learning with one oracle is more difficult than learning with two oracles. Our results imply that monotone Boolean conjunctions or disjunctions cannot be learned reliably and probably usefully from a polynomial number of examples. Rectangles in ℝ n forn ≥ 2 cannot be learned from any finite number of examples.

Green's relations on the strong endomorphism monoid of a graph

Combinatorial characteristics of Green's relations on the monoid of strong endomorphisms of graphs are explored. As an application, a short proof of the fact thats End(G) is regular is given.

On the Euler characteristic of finite unions of convex sets

The Euler characteristic plays an important role in many subjects of discrete and continuous mathematics. For noncompact spaces, its homological definition, being a homotopy invariant, seems not as important as its role for compact spaces. However, its combinatorial definition, as a finitely additive measure, proves to be more applicable in the study of singular spaces such as semialgebraic sets, finitely subanalytic sets, etc. We introduce an interesting integral by means of which the combinatorial Euler characteristic can be defined without the necessity of decomposition and extension as in the traditional treatment for polyhedra and finite unions of compact convex sets. Since finite unions of closed convex sets cannot be obtained by cutting convex sets as in the polyhedral case, a separate treatment of the Euler characteristic for functions generated by indicator functions of closed convex sets and relatively open convex sets is necessary, and this forms the content of this paper.

Some combinatorial aspects of parallel algorithm design for matrix multiplication

Some combinatorial characteristics of matrix multiplication on regular two-dimensional arrays are studied. From the studies, the authors are able to design many efficient varieties of the cylindrical array and the two-layered mesh array for matrix multiplication. To design a cylindrical array for matrix multiplication, a systematic design procedure is proposed. In this design procedure, Latin square (a special type of matrix) plays an important role. To design a two-layered mesh array, it is found that there is a transformation procedure to transform a cylindrical array to a two-layered mesh array.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Chemical graph theory. IV. On the cyclic polynomial

AbstractThe definition of the cyclic polynomial of conjugated hydrocarbons is offered. The combinatorial characteristics of this polynomial are investigated. The most important property of the cyclic polynomial is that it can be used for enumeration of conjugated circuits.

Some topological and graphical aspects of phase contours

Using the topological properties of phase contours, the phase contour diagram of a function in the complex plane is reduced to the simpler form of a bichromatic multigraph, which contains all the combinatorial characteristics regarding links between zeros and singularities of the function. It is found that the saddle points of the phase play an essential role in any such qualitative global description of the function, as can be anticipated from Morse theory. In the case of the scattering amplitude, constraints from symmetries, periodicity, or unitarity are seen to yield simplifications with interesting results concerning factorization and asymptotic behavior.

Disassembly Sequence Analysis ForEnvironmentally Conscious Design And Manufacturing

Environmentally conscious design and manufacturing (ECDM) is becoming a very important issue in the manufacturing community. Adequate product reuse and recycling can greatly reduce waste generation, thus increasing product environmental compatibility. Design for disassembly analysis is a building block of the ECDM system. It is able to design or redesign products so that a higher percentage of the component parts can be reused or recycled. In this study, an economic model of disassembly analysis is formulated and integrated with an object oriented product model. Due to the nonlinear and combinatorial characteristics of the problem, a simulated annealing algorithm is employed to find the economically optimal sequences that yield the maximum return value, and to advise where the disassembly operation should stop. It shows the potential of analyzing the environmental friendliness of material selection, assembly configuration, and fastening methods. The proposed method is illustrated with a water pump assembly example.

Organization and Information Handling in Task Groups

Organizational factors in information handling in task-oriented groups have been studied recently at M.I.T. Laboratory groups were given very simple information-collection tasks under rigidly controlled conditions and the communication recorded completely. Decisions were restricted to choices of message destination and the influence of various imposed communication nets on the adequacy of group performance analysed. A technique of group-action quantization was used, which made possible a well-defined measure of group efficiency and an easily understood group goal. Experimental results show that an equiprobable random assumption is a poor model even for initial behavior. Centralized nets are shown to learn to do as well as the net permits fairly rapidly but to be characterized by high minimum-action. A net designed to give the lowest average action for task completion with random message-destination choices is shown to be essentially incapable of achieving its limiting minimum. Another similar net with a higher random average and a favorable minimum is shown to learn its minimum readily. Differences among the results for different nets are found to be explained in terms of a concept of “locally rational behavior” and the combinatorial characteristics of the nets. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.