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Journal articles on the topic 'The non-intersecting paths'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Boyacı, Arman, Tınaz Ekim, Mordechai Shalom, and Shmuel Zaks. "Graphs of edge-intersecting and non-splitting paths." Theoretical Computer Science 629 (May 2016): 40–50. http://dx.doi.org/10.1016/j.tcs.2015.10.004.

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2

Borodin, Alexei, Ivan Corwin, and Daniel Remenik. "Multiplicative functionals on ensembles of non-intersecting paths." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, no. 1 (February 2015): 28–58. http://dx.doi.org/10.1214/13-aihp579.

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3

Johansson, Kurt. "Non-intersecting paths, random tilings and random matrices." Probability Theory and Related Fields 123, no. 2 (June 1, 2002): 225–80. http://dx.doi.org/10.1007/s004400100187.

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4

Delvaux, Steven. "Non-Intersecting Squared Bessel Paths at a Hard-Edge Tacnode." Communications in Mathematical Physics 324, no. 3 (October 12, 2013): 715–66. http://dx.doi.org/10.1007/s00220-013-1815-x.

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5

Price, Phillip N. "Pollutant tomography using integrated concentration data from non-intersecting optical paths." Atmospheric Environment 33, no. 2 (January 1999): 275–80. http://dx.doi.org/10.1016/s1352-2310(98)00159-9.

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6

Forrester, Peter J., and Eric M. Rains. "Symmetrized Models of Last Passage Percolation and Non-Intersecting Lattice Paths." Journal of Statistical Physics 129, no. 5-6 (September 21, 2007): 833–55. http://dx.doi.org/10.1007/s10955-007-9413-y.

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7

Kuijlaars, A. B. J., A. Martínez-Finkelshtein, and F. Wielonsky. "Non-Intersecting Squared Bessel Paths: Critical Time and Double Scaling Limit." Communications in Mathematical Physics 308, no. 1 (September 6, 2011): 227–79. http://dx.doi.org/10.1007/s00220-011-1322-x.

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8

Delvaux, Steven, Arno B. J. Kuijlaars, Pablo Román, and Lun Zhang. "Non-intersecting squared Bessel paths with one positive starting and ending point." Journal d'Analyse Mathématique 118, no. 1 (October 2012): 105–59. http://dx.doi.org/10.1007/s11854-012-0031-5.

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9

CHANDRA, ANUJ, and RAMI MELHEM. "RECONFIGURATION IN FAULT-TOLERANT 3D MESHES." Parallel Processing Letters 05, no. 03 (September 1995): 387–99. http://dx.doi.org/10.1142/s0129626495000369.

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The [Formula: see text] track model for fault tolerant 2D processor arrays is extended to 3D mesh architectures. Non-intersecting, continuous, straight and non-near miss compensation paths are considered. It is shown that when six directions in the 3D mesh are allowed for compensation paths, then switches with 13 states are needed to preserve the 3D mesh topology after faults. The number of switch states reduces to 7 if only 3 directions are allowed for compensation paths. It is also shown that switch reconfiguration after faults is local in the sense that the state of each switch is uniquely determined by the states of the 2 processors connected to it.

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10

Kuijlaars, A. B. J., A. Martínez-Finkelshtein, and F. Wielonsky. "Non-Intersecting Squared Bessel Paths and Multiple Orthogonal Polynomials for Modified Bessel Weights." Communications in Mathematical Physics 286, no. 1 (October 29, 2008): 217–75. http://dx.doi.org/10.1007/s00220-008-0652-9.

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11

Brak, R., and J. W. Essam. "Return polynomials for non-intersecting paths above a surface on the directed square lattice." Journal of Physics A: Mathematical and General 34, no. 49 (December 5, 2001): 10763–82. http://dx.doi.org/10.1088/0305-4470/34/49/303.

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12

Delvaux, Steven, and Bálint Vető. "The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths." Random Matrices: Theory and Applications 04, no. 02 (April 2015): 1550008. http://dx.doi.org/10.1142/s2010326315500082.

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A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches the hard edge, a limiting critical process is described in the neighborhood of the touching point which we call the hard edge tacnode process. We derive its correlation kernel in an explicit new form which involves Airy type functions and operators that act on the direct sum of L2(ℝ+) and a finite-dimensional space. As the starting points of the squared Bessel paths are set to 0, a cusp in the boundary appears. The limiting process is described near the cusp and it is called the hard edge Pearcey process. We compute its multi-time correlation kernel which extends the existing formulas for the single-time kernel. Our pre-asymptotic correlation kernel involves the ratio of two Toeplitz determinants which are rewritten using a Borodin–Okounkov type formula.

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13

Nichols, Len M. "Government Intervention in Health Care Markets is Practical, Necessary, and Morally Sound." Journal of Law, Medicine & Ethics 40, no. 3 (2012): 547–57. http://dx.doi.org/10.1111/j.1748-720x.2012.00688.x.

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The intensity of the opposition to health reform in the United States continues to shock and perplex proponents of the Patient Protection and Affordable Care Act (PPACA). The emotion (“Abort Obama”) and the apocalyptic rhetoric (“Save our Country, Protect our Liberty, Repeal Obamacare”), render civil and evidence-based debate over the implications and alternatives to specific provisions in the law difficult if not problematic. The public debate has largely barreled down two non-parallel yet non-intersecting paths: opponents focus on their fear of government expansion in the future if PPACA is implemented now, while proponents focus on the urgency and specifics of our health care market problems and the limited number of tools we have to address them. Frustration on both sides has led opponents to deny the seriousness of our health system’s problems and proponents to ignore the risk of governmental overreach. These non-intersecting lines of argument are not moving us closer to a desired and necessary resolution.

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14

Boyacı, Arman, Tınaz Ekim, Mordechai Shalom, and Shmuel Zaks. "Graphs of edge-intersecting non-splitting paths in a tree: Representations of holes—Part I." Discrete Applied Mathematics 215 (December 2016): 47–60. http://dx.doi.org/10.1016/j.dam.2015.07.024.

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15

Kuijlaars, A. B. J., and P. Román. "Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths." Journal of Approximation Theory 162, no. 11 (November 2010): 2048–77. http://dx.doi.org/10.1016/j.jat.2010.06.003.

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16

GÖRKE, ROBERT, CHAN-SU SHIN, and ALEXANDER WOLFF. "CONSTRUCTING THE CITY VORONOI DIAGRAM FASTER." International Journal of Computational Geometry & Applications 18, no. 04 (August 2008): 275–94. http://dx.doi.org/10.1142/s0218195908002623.

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Given a set P of n point sites in the plane, the city Voronoi diagram subdivides the plane into the Voronoi regions of the sites, with respect to the city metric. This metric is induced by quickest paths according to the Manhattan metric and an accelerating transportation network that consists of c non-intersecting axis-parallel line segments. We describe an algorithm that constructs the city Voronoi diagram (including quickest path information) using O((c+n) polylog (c+n)) time and storage by means of a wavefront expansion. For [Formula: see text] our algorithm is faster than an algorithm by Aichholzer et al., which takes O(n log n + c2 log c) time.

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17

Lin, Chao, Yu Wang, Yanan Hu, and Yongquan Yu. "Compound transmission principle analysis of eccentric curve-face gear pair with curvilinear-shaped teeth based on tooth contact analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 8 (December 23, 2021): 4026–37. http://dx.doi.org/10.1177/09544062211047075.

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A new type of compound transmission gear pair was put forward, called eccentric curve-face gear pair with curvilinear-shaped teeth. It could realize reciprocating motion of the gear shaft when the intersecting shafts achieve transferring motion and power through its unique tooth profile. The compound transmission principle of this gear pair was fully established based on the profile-closure process of axial direction and meshing process of the end face. The tooth surfaces of the eccentric curve-face gear and non-circular gear were generated. The contact paths of different teeth were obtained, and the compound transmission principle of eccentric curve-face gear pair with curvilinear-shaped teeth was verified by tooth contact analysis. By analyzing the mechanical characteristics of time-varying contact points, the changing rule of contact force was studied, and the compound transmission principle of the gear pair was further revealed from mechanics. Moreover, the experimental platform for transmission of eccentric curve-face gear pair with curvilinear-shaped teeth was set up to measure the motion law and contact area, and the correctness of the analysis results was verified.

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18

Makarovskikh, Tatiana, and Anatoly Panyukov. "Special Type Routing Problems in Plane Graphs." Mathematics 10, no. 5 (March 2, 2022): 795. http://dx.doi.org/10.3390/math10050795.

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We considered routing problems for plane graphs to solve control problems of cutting machines in the industry. According to the cutting plan, we form its homeomorphic image in the form of a plane graph G. We determine the appropriate type of route for the given graph: OE-route represents an ordered sequence of chains satisfying the requirement that the part of the route that is not passed does not intersect the interior of its passed part, AOE-chain represents OE-chain consecutive edges which are incident to vertex v and they are neighbours in the cyclic order O±(v), NOE-route represents the non-intersecting OE-route, PPOE-route represents the Pierce Point NOE-route with allowable pierce points that are start points of OE-chains forming this route. We analyse the solvability of the listed routing problems in graph G. We developed the polynomial algorithms for obtaining listed routes with the minimum number of covering paths and the minimum length of transitions between the ending of the current path and the beginning of the next path. The solutions proposed in the article can improve the quality of technological preparation of cutting processes in CAD/CAM systems.

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19

Monterrubio, Carlos. "Tourism and male homosexual identities: directions for sociocultural research." Tourism Review 74, no. 5 (November 4, 2019): 1058–69. http://dx.doi.org/10.1108/tr-08-2017-0125.

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Purpose This paper aims to offer a critical review of the existing research on the relationships between tourism and male homosexual identities and, based on a sociocultural perspective, suggestions for specific directions in future research. Design/methodology/approach The analysis is based on a review of the literature that focuses on two independent yet intersecting topics: tourism and homosexuality and identity formation processes. Findings Specific directions for future research are offered regarding the role that tourism plays in homosexual identity development. The proposed paths for future research include the tangible contributions of tourism to the stages of homosexual tourists’ identity development and the (re)construction, negotiation and globalisation of homosexual and queer identities through tourists’ cultural interactions. Two further suggested directions are the significance of tourism for non-Western homosexual tourists and tourism’s impacts on local homosexual identities. Research limitations/implications This study is based solely on the existing literature on male homosexuality and mostly on studies published in English. Originality/value The research included a critical analysis of the commonly assumed significance of tourism in homosexual identity formation. The results provide directions for future empirical research and calls for a solid theoretical foundation that allows researchers to demonstrate, understand and explain how tourism contributes to gay and queer identities.

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20

Тetiana Kresan, Serhiy Pylypaka, Iryna Hryshchenko, Tetiana Fedoryna, and Yaroslav Kremets. "CONGRUENT AXOIDS OF NON-CIRCULAR CONICAL WHEELS FORMED BY ARCS OF THE LOXODROME." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 99 (December 17, 2020): 110–23. http://dx.doi.org/10.32347/0131-579x.2020.99.110-123.

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If two linear surfaces move one after another without sliding, then they can be considered as axoids of a solid body that performs a corresponding motion in space. If the axoids are cylindrical surfaces, then the study of their rolling can be replaced by the study of the rolling of centroids - curves of the orthogonal cross section of these cylindrical surfaces. Usually the rolling of a moving centroid on a stationary one is considered. However, there are cases when centroids roll one after another, while rotating around fixed centers. Examples of round centroids are circles, non-round - congruent ellipses, in which the centers of rotation are foci. In both cases, the center-to-center distance is constant. The point of contact of the circles is located at the center distance and is stationary during their rotation, and for ellipses it "floats" on this segment. In the article [1] the congruent centroids formed by symmetric arcs of a logarithmic spiral are considered. The centers of rotation of the centroid are the poles of the spirals. A characteristic feature of logarithmic spirals is that they intersect all radius vectors emanating from the pole at a constant angle. For a sphere, the prototype of a logarithmic spiral is a loxodrome, which crosses all the meridians at a constant angle and twists around the pole of the sphere. The paper hypothesizes that closed spherical curves formed from arcs of loxodrome, like centroids from arcs of a logarithmic spiral on a plane, can also roll around axes intersecting in the center of the sphere. If these closed curves are connected by rectilinear segments with the center of the sphere, then two cones are formed - axoids of non- circular conical wheels. This hypothesis is based on the fact that with an infinite increase in the radius of the sphere, its surface around the pole turns into a plane, and the meridians - in straight lines emanating from the pole. Accordingly, the loxodrome is transformed into a logarithmic spiral. The article shows that the hypothesis is confirmed. Axoids of non- circular wheels are built in it, the axes of which intersect at right angles. The expression of the arc length of the loxodrome is found and it is shown that when the conical axoids rotate at appropriate angles around their axes, the contact curves pass straight paths. This means that the rolling of the axis occurs without sliding.

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21

Baker, Phillip, Jennifer Lacy-Nichols, Owain Williams, and Ronald Labonté. "The Political Economy of Healthy and Sustainable Food Systems: An Introduction to a Special Issue." International Journal of Health Policy and Management 10, no. 12 (November 14, 2021): 734–44. http://dx.doi.org/10.34172/ijhpm.2021.156.

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Today’s food systems are contributing to multiple intersecting health and ecological crises. Many are now calling for transformative, or even radical, food systems change. Our starting assumption in this Special Issue is the broad claim that the transformative changes being called for in a global food system in crisis cannot – and ultimately will not – be achieved without intense scrutiny of and changes in the underlying political economies that drive today’s food systems. The aim is to draw from diverse disciplinary perspectives to critically evaluate the political economy of food systems, understand key challenges, and inform new thinking and action. We received 19 contributions covering a diversity of country contexts and perspectives, and revealing inter-connected challenges and opportunities for realising the transformation agenda. We find that a number of important changes in food governance and power relations have occurred in recent decades, with a displacement of power in four directions. First, upwards as globalization has given rise to more complex and globally integrated food systems governed increasingly by transnational food corporations (TFCs) and international financial actors. Second, downwards as urbanization and decentralization of authority in many countries gives cities and sub-national actors more prominence in food governance. Third, outwards with a greater role for corporate and civil society actors facilitated by an expansion of food industry power, and increasing preferences for market-orientated and multi-stakeholder forms of governance. Finally, power has also shifted inwards as markets have become increasingly concentrated through corporate strategies to gain market power within and across food supply chain segments. The transformation of food systems will ultimately require greater scrutiny of these challenges. Technical ‘problem-solving’ and overly-circumscribed policy approaches that depoliticise food systems challenges, are insufficient to generate the change we need, within the narrow time-frame we have. While there will be many paths to transformation, rights-based and commoning approaches hold great promise, based on principles of participation, accountability and non-discrimination, alongside coalition building and social mobilization, including social movements grounded in food sovereignty and agroecology.

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22

Kenyon, Richard W., and David B. Wilson. "Critical resonance in the non-intersecting lattice path model." Probability Theory and Related Fields 130, no. 3 (August 20, 2004): 289–318. http://dx.doi.org/10.1007/s00440-003-0293-z.

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23

Liu, Yan, Jiang Liu, and Xincheng Tian. "An approach to the path planning of intersecting pipes weld seam with the welding robot based on non-ideal models." Robotics and Computer-Integrated Manufacturing 55 (February 2019): 96–108. http://dx.doi.org/10.1016/j.rcim.2018.07.010.

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24

MAHESHWARI, ANIL, and JÖRG-RÜDIGER SACK. "SIMPLE OPTIMAL ALGORITHMS FOR RECTILINEAR LINK PATH AND POLYGON SEPARATION PROBLEMS." Parallel Processing Letters 09, no. 01 (March 1999): 31–42. http://dx.doi.org/10.1142/s0129626499000062.

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The link metric, defined on a constrained region R of the plane, sets the distance between a pair of points in R to equal the minimum number of line segments or links needed to construct a path in R between the point pair. The minimum rectilinear link path problem considered here is to compute a rectilinear path consisting of the minimum number of links between two points in R, when R is inside an n-sided rectilinear simple polygon. In this paper we present optimal sequential and parallel algorithms to compute a minimum rectilinear link path in a trapezoided region R. Our parallel algorithm requires O( log n) time using a total of O(n) operations. The complexity of our algorithm matches that of the algorithm of McDonald and Peters [19]. By exploiting the dual structure of the trapezoidation of R, we obtain a conceptually simple and easy to implement algorithm. As applications of our techniques we provide an optimal solution to the minimum nested polygon problem and the minimum polygon separation problem. The minimum nested polygon problem asks for finding a rectilinear polygon, with minimum number of sides, that is nested between two given rectilinear polygons one of which is contained in the other. The minimum polygon separation problem asks for computing a minimum number of orthogonal lines and line segments that separate two given non-intersecting simple rectilinear polygons. All parallel algorithms are deterministic, designed to run on the exclusive read exclusive write parallel random access machine (EREW PRAM), and are optimal.

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25

Nguyen, Gia Bao, and Daniel Remenik. "Extreme statistics of non-intersecting Brownian paths." Electronic Journal of Probability 22 (2017). http://dx.doi.org/10.1214/17-ejp119.

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26

Ciucu, Mihai. "A Short Conceptual Proof of Narayana's Path-Counting Formula." Electronic Journal of Combinatorics 23, no. 4 (October 14, 2016). http://dx.doi.org/10.37236/6131.

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27

Bosio, Frédéric, and Marc A. A. Van Leeuwen. "A Bijection Proving the Aztec Diamond Theorem by Combing Lattice Paths." Electronic Journal of Combinatorics 20, no. 4 (November 29, 2013). http://dx.doi.org/10.37236/2809.

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We give a bijective proof of the Aztec diamond theorem, stating that there are $2^{n(n+1)/2}$ domino tilings of the Aztec diamond of order $n$. The proof in fact establishes a similar result for non-intersecting families of $n+1$ Schröder paths, with horizontal, diagonal or vertical steps, linking the grid points of two adjacent sides of an $n\times n$ square grid; these families are well known to be in bijection with tilings of the Aztec diamond. Our bijection is produced by an invertible "combing'' algorithm, operating on families of paths without non-intersection condition, but instead with the requirement that any vertical steps come at the end of a path, and which are clearly $2^{n(n+1)/2}$ in number; it transforms them into non-intersecting families.

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28

Cook II, D., and Uwe Nagel. "Signed Lozenge Tilings." Electronic Journal of Combinatorics 24, no. 1 (January 20, 2017). http://dx.doi.org/10.37236/5579.

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It is well-known that plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in bijection. In this work we consider regions that are more general than hexagons. They are obtained by further removing upward-pointing triangles. We call the resulting shapes triangular regions. We establish signed versions of the latter three bijections for triangular regions. We first investigate the tileability of triangular regions by lozenges. Then we use perfect matchings and families of non-intersecting lattice paths to define two signs of a lozenge tiling. Using a new method that we call resolution of a puncture, we show that the two signs are in fact equivalent. As a consequence, we obtain the equality of determinants, up to sign, that enumerate signed perfect matchings and signed families of lattice paths of a triangular region, respectively. We also describe triangular regions, for which the signed enumerations agree with the unsigned enumerations.

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29

Brak, R., and J. W. Essam. "Bicoloured Dyck Paths and the Contact Polynomial for $n$ Non-Intersecting Paths in a Half-Plane Lattice." Electronic Journal of Combinatorics 10, no. 1 (September 12, 2003). http://dx.doi.org/10.37236/1728.

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In this paper configurations of $n$ non-intersecting lattice paths which begin and end on the line $y=0$ and are excluded from the region below this line are considered. Such configurations are called Hankel $n-$paths and their contact polynomial is defined by $\hat{Z}^{\cal{H}}_{2r}(n;\kappa)\equiv \sum_{c= 1}^{r+1} |{\cal H}_{2r}^{(n)}(c)|\kappa^c$ where ${\cal H}_{2r}^{(n)}(c)$ is the set of Hankel $n$-paths which make $c$ intersections with the line $y=0$ the lowest of which has length $2r$. These configurations may also be described as parallel Dyck paths. It is found that replacing $\kappa$ by the length generating function for Dyck paths, $\kappa(\omega) \equiv \sum_{r=0}^\infty C_r \omega^r$, where $C_r$ is the $r^{th}$ Catalan number, results in a remarkable simplification of the coefficients of the contact polynomial. In particular it is shown that the polynomial for configurations of a single Dyck path has the expansion $\hat{Z}^{\cal{H}}_{2r}(1;\kappa(\omega)) = \sum_{b=0}^\infty C_{r+b}\omega^b$. This result is derived using a bijection between bi-coloured Dyck paths and plain Dyck paths. A bi-coloured Dyck path is a Dyck path in which each edge is coloured either red or blue with the constraint that the colour can only change at a contact with the line $y=0$. For $n>1$, the coefficient of $\omega^b$ in $\hat{Z}^{\cal{W}}_{2r}(n;\kappa(\omega))$ is expressed as a determinant of Catalan numbers which has a combinatorial interpretation in terms of a modified class of $n$ non-intersecting Dyck paths. The determinant satisfies a recurrence relation which leads to the proof of a product form for the coefficients in the $\omega$ expansion of the contact polynomial.

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30

Eu, Sen-Peng, and Tung-Shan Fu. "A Simple Proof of the Aztec Diamond Theorem." Electronic Journal of Combinatorics 12, no. 1 (April 20, 2005). http://dx.doi.org/10.37236/1915.

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Based on a bijection between domino tilings of an Aztec diamond and non-intersecting lattice paths, a simple proof of the Aztec diamond theorem is given by means of Hankel determinants of the large and small Schröder numbers.

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31

Dai, Dan, and Luming Yao. "The distribution function for the maximal height of N non-intersecting Bessel paths." Ramanujan Journal, April 20, 2022. http://dx.doi.org/10.1007/s11139-022-00567-3.

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32

Francesco, Philippe Di. "The Solution of the $A_r$ T-System for Arbitrary Boundary." Electronic Journal of Combinatorics 17, no. 1 (June 14, 2010). http://dx.doi.org/10.37236/361.

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We present an explicit solution of the $A_r$ $T$-system for arbitrary boundary conditions. For each boundary, this is done by constructing a network, i.e. a graph with positively weighted edges, and the solution is expressed as the partition function for a family of non-intersecting paths on the network. This proves in particular the positive Laurent property, namely that the solutions are all Laurent polynomials of the initial data with non-negative integer coefficients.

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33

Bouvel, Mathilde, Veronica Guerrini, and Simone Rinaldi. "Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings, 28th... (April 22, 2020). http://dx.doi.org/10.46298/dmtcs.6357.

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International audience We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes (called slicings) which grow according to these succession rules. We also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, and a new Schröder subset of Baxter permutations.

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34

Lai, Tri. "A Generalization of Aztec Diamond Theorem, Part I." Electronic Journal of Combinatorics 21, no. 1 (March 10, 2014). http://dx.doi.org/10.37236/3691.

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We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagonals drawn in. By proving that the number of tilings of the new regions is given by a power 2, we generalize both Aztec diamond theorem and Douglas' theorem. The proof extends an idea of Eu and Fu for Aztec diamonds, by using a bijection between domino tilings and non-intersecting Schröder paths, then applying Lindström-Gessel-Viennot methodology.

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35

Francesco, Philippe Di, and Rinat Kedem. "Positivity of the T-System Cluster Algebra." Electronic Journal of Combinatorics 16, no. 1 (November 24, 2009). http://dx.doi.org/10.37236/229.

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We give the path model solution for the cluster algebra variables of the $T$-system of type $A_r$ with generic boundary conditions. The solutions are partition functions of (strongly) non-intersecting paths on weighted graphs. The graphs are the same as those constructed for the $Q$-system in our earlier work, and depend on the seed or initial data in terms of which the solutions are given. The weights are "time-dependent" where "time" is the extra parameter which distinguishes the $T$-system from the $Q$-system, usually identified as the spectral parameter in the context of representation theory. The path model is alternatively described on a graph with non-commutative weights, and cluster mutations are interpreted as non-commutative continued fraction rearrangements. As a consequence, the solution is a positive Laurent polynomial of the seed data.

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36

Vichitkunakorn, Panupong. "Solutions to the T-Systems with Principal Coefficients." Electronic Journal of Combinatorics 23, no. 2 (June 10, 2016). http://dx.doi.org/10.37236/5698.

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The $A_\infty$ T-system, also called the octahedron recurrence, is a dynamical recurrence relation. It can be realized as mutation in a coefficient-free cluster algebra (Kedem 2008, Di Francesco and Kedem 2009). We define T-systems with principal coefficients from cluster algebra aspect, and give combinatorial solutions with respect to any valid initial condition in terms of partition functions of perfect matchings, non-intersecting paths and networks. This also provides a solution to other systems with various choices of coefficients on T-systems including Speyer's octahedron recurrence (Speyer 2007), generalized lambda-determinants (Di Francesco 2013) and (higher) pentagram maps (Schwartz 1992, Ovsienko et al. 2010, Glick 2011, Gekhtman et al. 2016).

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37

Beaton, Nicholas R., Mathilde Bouvel, Veronica Guerrini, and Simone Rinaldi. "Slicings of Parallelogram Polyominoes: Catalan, Schröder, Baxter, and Other Sequences." Electronic Journal of Combinatorics 26, no. 3 (July 19, 2019). http://dx.doi.org/10.37236/7375.

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We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, a new Schröder subset of Baxter permutations, and a new Schröder subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the $m$-skinny slicings and the $m$-row-restricted slicings, for $m \in \mathbb{N}$. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any $m$.

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38

"Ultrasonic measurement of internal temperature distribution." Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 320, no. 1554 (November 26, 1986): 341–61. http://dx.doi.org/10.1098/rsta.1986.0123.

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Implementation of advanced materials processing strategies are presently hampered by a lack of adequate process-control sensors. For the processing of basic materials, such as steel and aluminium, an internal temperature-distribution sensor is needed. For these metals, the velocity of ultrasound is well known to be a strong function of temperature. We have therefore explored the feasibility of precisely measuring the velocity-temperature relation for a particular steel grade and using this to convert an ultrasonic-velocity distribution (tomogram) for a hot steel body to an internal temperature distribution. To overcome the usual need in conventional tomography for many thousands of path-integral measurements along intersecting ray paths, a priori heat-flow information has been incorporated into the reconstruction algorithms. As a result, for uniformly cooling bodies with the simple geometries usually encountered (e.g. circular, square or rectangular cross sections), the number of measurements can be reduced from many thousands to as few as three to five. Initial experiments on austenitic steel samples of cylindrical and square cross section by using non-contact ultrasonic techniques have shown that this approach yields acceptable temperature profiles at temperatures of up to 750 °C.

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Amer, Ahmad, and Fotis P. Kopsaftopoulos. "Statistical guided-waves-based structural health monitoring via stochastic non-parametric time series models." Structural Health Monitoring, June 19, 2021, 147592172110245. http://dx.doi.org/10.1177/14759217211024527.

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Damage detection in active-sensing, guided-waves-based structural health monitoring (SHM) has evolved through multiple eras of development during the past decades. Nevertheless, there still exist a number of challenges facing the current state-of-the-art approaches, both in the industry as well as in research and development, including low damage sensitivity, lack of robustness to uncertainties, need for user-defined thresholds, and non-uniform response across a sensor network. In this work, a novel statistical framework is proposed for active-sensing SHM based on the use of ultrasonic guided waves. This framework is based on stochastic non-parametric time series models and their corresponding statistical properties in order to readily provide healthy confidence bounds and enable accurate and robust damage detection via the use of appropriate statistical decision-making tests. Three such methods and corresponding statistical quantities (test statistics) along with decision-making schemes are formulated and experimentally assessed via the use of three coupons with different levels of complexity: an Al plate with a growing notch, a carbon fiber-reinforced plastic (CFRP) plate with added weights to simulate local damage, and the CFRP panel used in the Open Guided Waves project, all fitted with piezoelectric transducers under a pitch-catch configuration. The performance of the proposed methods is compared to that of state-of-the-art time-domain damage indices (DIs). The results demonstrate the increased detection sensitivity and robustness of the proposed methods, with better tracking capability of damage evolution compared to conventional approaches, even for damage-non-intersecting actuator–sensor paths. In particular, the Z statistic emerges as the best damage detection metric compared to conventional DIs, as well as the other proposed statistics. Overall, the proposed statistics in this study promise greater damage sensitivity across different components, with enhanced robustness to uncertainties, as well as user-friendly application.

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Eğecioğlu, Ömer, Timothy Redmond, and Charles Ryavec. "From a Polynomial Riemann Hypothesis to Alternating Sign Matrices." Electronic Journal of Combinatorics 8, no. 1 (October 24, 2001). http://dx.doi.org/10.37236/1580.

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This paper begins with a brief discussion of a class of polynomial Riemann hypotheses, which leads to the consideration of sequences of orthogonal polynomials and 3-term recursions. The discussion further leads to higher order polynomial recursions, including 4-term recursions where orthogonality is lost. Nevertheless, we show that classical results on the nature of zeros of real orthogonal polynomials (i. e., that the zeros of $p_n$ are real and those of $p_{n+1}$ interleave those of $p_n$) may be extended to polynomial sequences satisfying certain 4-term recursions. We identify specific polynomial sequences satisfying higher order recursions that should also satisfy this classical result. As with the 3-term recursions, the 4-term recursions give rise naturally to a linear functional. In the case of 3-term recursions the zeros fall nicely into place when it is known that the functional is positive, but in the case of our 4-term recursions, we show that the functional can be positive even when there are non-real zeros among some of the polynomials. It is interesting, however, that for our 4-term recursions positivity is guaranteed when a certain real parameter $C$ satisfies $C\ge 3$, and this is exactly the condition of our result that guarantees the zeros have the aforementioned interleaving property. We conjecture the condition $C\ge 3$ is also necessary. Next we used a classical determinant criterion to find exactly when the associated linear functional is positive, and we found that the Hankel determinants $\Delta_n$ formed from the sequence of moments of the functional when $C = 3$ give rise to the initial values of the integer sequence $1, 3, 26, 646, 45885, \cdots,$ of Alternating Sign Matrices (ASMs) with vertical symmetry. This spurred an intense interest in these moments, and we give 9 diverse characterizations of this sequence of moments. We then specify these Hankel determinants as Macdonald-type integrals. We also provide an an infinite class of integer sequences, each sequence of which gives the Hankel determinants $\Delta_n$ of the moments. Finally we show that certain $n$-tuples of non-intersecting lattice paths are evaluated by a related class of special Hankel determinants. This class includes the $\Delta_n$. At the same time, ASMs with vertical symmetry can readily be identified with certain $n$-tuples of osculating paths. These two lattice path models appear as a natural bridge from the ASMs with vertical symmetry to Hankel determinants.

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Veryard, Lewis, Hani Hagras, Andrew Starkey, Anthony Conway, and Gilbert Owusu. "NNIR: N-Non-Intersecting-Routing Algorithm for Multi-Path Resilient Routing in Telecommunications Applications." International Journal of Computational Intelligence Systems, 2020. http://dx.doi.org/10.2991/ijcis.d.200313.001.

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Che, Li, and F. J. Kang. "Automatic global path generation for large-scale 3D scene exploration." International Journal of Modeling, Simulation, and Scientific Computing, December 22, 2020, 2050050. http://dx.doi.org/10.1142/s1793962320500506.

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Large-scale virtual scene exploration is still a challenging task. The novice users can easily get distracted and disorientated, which results in being lost in space. Assisted camera control technology is the most effective solution for virtual environment exploration problems which requires viewpoint computation and path planning. In this paper, a novel approach for large-scale virtual scene based on viewpoint scoring is proposed. First, the scene was adaptively divided into several meaningful and easily analyzed subregions according to the optimal view distance criterion. Second, a novel viewpoint scoring method based on visual perception and information entropy fusion was developed for optimal viewpoint determination and greedy N-Bestviewpoint selection algorithm was utilized for visual perceptibility calculation. Then evolutionary programming approach for the Traveling Salesman problem was applied for intra-subregion and inter-subregion exploring path optimization. Finally, the Cubic Hermite Curve was introduced to smoothen the inflection point on the exploration path. The experimental results demonstrate that the proposed method can effectively generate an automatic smooth, informative, aesthetic and non-intersecting path, with the characteristics of good exploring comfort, strong immersion and high scene information perception.

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