Relevant bibliographies by topics / Lattice path

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Lattice path'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Lattice path"

1

Friedman, Jane, Ira Gessel, and Doron Zeilberger. "Talmudic lattice path counting." Journal of Combinatorial Theory, Series A 68, no. 1 (October 1994): 215–17. http://dx.doi.org/10.1016/0097-3165(94)90100-7.

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BRLEK, S., G. LABELLE, and A. LACASSE. "PROPERTIES OF THE CONTOUR PATH OF DISCRETE SETS." International Journal of Foundations of Computer Science 17, no. 03 (June 2006): 543–56. http://dx.doi.org/10.1142/s012905410600398x.

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We consider paths in the square lattice and use a valuation called the winding number in order to exhibit some combinatorial properties on these paths. As a corollary, we obtain a characteristic property of non-crossing closed paths, generalizing in this way a result of Daurat and Nivat (2003) on the boundary properties of polyominoes concerning salient and reentrant points. Moreover we obtain a similar result for hexagonal lattices and show that there is no other regular lattice having that property.
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Maier, Robert S., and Robert S. Bernard. "Accuracy of the Lattice-Boltzmann Method." International Journal of Modern Physics C 08, no. 04 (August 1997): 747–52. http://dx.doi.org/10.1142/s0129183197000631.

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The accuracy of the lattice-Boltzmann method (LBM) is moderated by several factors, including Mach number, spatial resolution, boundary conditions, and the lattice mean free path. Results obtained with 3D lattices suggest that the accuracy of certain two-dimensional (2D) flows, such as Poiseuille and Couette flow, persist even when the mean free path between collisions is large, but that of the 3D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3D low-Reynolds-number flow. The influence of boundary representations on LBM accuracy is captured by the proposed index, when the accuracy of the prescribed boundary conditions is consistent with that of LBM.
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Chen, Yu, Jinguo You, Benyuan Zou, Guoyu Gan, Ting Zhang, and Lianyin Jia. "Exploring Structural Characteristics of Lattices in Real World." Complexity 2020 (January 21, 2020): 1–11. http://dx.doi.org/10.1155/2020/1250106.

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There are two important models for data analysis and knowledge system: data cube lattices and concept lattices. They both essentially have lattice structures, which are actually irregular in our real world. However, their structural characteristics and relationship are not yet clear. To the best of our knowledge, no work has paid enough attention to this challenging issue from the perspective of graph data, in spite of the importance of structures in lattice data. In this paper, we first tackle the structural statistics of lattice data from three aspects: the degree distribution, clustering coefficient, and average path length. We demonstrated by various datasets that data cube lattices and concept lattices share similarities underlying their topology, which are, in general, different from random networks and complex networks. Specifically, lattice data follow the Poisson distribution and have smaller clustering coefficient and greater average path length. We further discuss and explain these characteristics intrinsically by building the analytical model and the generating mechanism.
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Callan, David, and Kenneth Bernstein. "A Lattice Path Equality: 11106." American Mathematical Monthly 113, no. 7 (August 1, 2006): 656. http://dx.doi.org/10.2307/27642018.

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Quesney, Alexandre. "The relative lattice path operad." Algebraic & Geometric Topology 18, no. 3 (April 3, 2018): 1753–98. http://dx.doi.org/10.2140/agt.2018.18.1753.

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Wagner, Carl G. "The Carlitz lattice path polynomials." Discrete Mathematics 222, no. 1-3 (July 2000): 291–98. http://dx.doi.org/10.1016/s0012-365x(00)00058-3.

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Bonin, Joseph E., and Anna de Mier. "Lattice path matroids: Structural properties." European Journal of Combinatorics 27, no. 5 (July 2006): 701–38. http://dx.doi.org/10.1016/j.ejc.2005.01.008.

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Deutsch, Emeric, David Callan, M. Beck, D. Beckwith, W. Bohm, R. F. McCoart, and GCHQ Problems Group. "Another Type of Lattice Path: 10658." American Mathematical Monthly 107, no. 4 (April 2000): 368. http://dx.doi.org/10.2307/2589192.

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Delucchi, Emanuele, and Martin Dlugosch. "Bergman Complexes of Lattice Path Matroids." SIAM Journal on Discrete Mathematics 29, no. 4 (January 2015): 1916–30. http://dx.doi.org/10.1137/130944242.

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Dissertations / Theses on the topic "Lattice path"

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Böhm, Walter. "Lattice path counting and the theory of queues." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2008. http://epub.wu.ac.at/1086/1/document.pdf.

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In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (author´s abstract)
Series: Research Report Series / Department of Statistics and Mathematics
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Katzenbeisser, Walter, and Wolfgang Panny. "Some further Results on the Height of Lattice Path." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1990. http://epub.wu.ac.at/878/1/document.pdf.

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This paper deals with the joint and conditional distributions concerning the maximum of random walk paths and the number of times this maximum is achieved. This joint distribution was studied first by Dwass [1967]. Based on his result, the correlation and some conditional moments are derived. The main contributions are however asymptotic expansions concerning the conditional distribution and conditional moments. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
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Liou, Ching-Pin. "The lattice approaches for pricing path-dependent mortgage-related products." Case Western Reserve University School of Graduate Studies / OhioLINK, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=case1057678646.

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Melczer, Stephen. "Analytic Combinatorics in Several Variables : Effective Asymptotics and Lattice Path Enumeration." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN013/document.

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La combinatoire analytique étudie le comportement asymptotique des suites à travers les propriétés analytiques de leurs fonctions génératrices. Ce domaine a conduit au développement d’outils profonds et puissants avec de nombreuses applications. Au delà de la théorie univariée désormais classique, des travaux récents en combinatoire analytique en plusieurs variables (ACSV) ont montré comment calculer le comportement asymptotique d’une grande classe de fonctions différentiellement finies:les diagonales de fractions rationnelles. Cette thèse examine les méthodes de l’ACSV du point de vue du calcul formel, développe des algorithmes rigoureux et donne les premiers résultats de complexité dans ce domaine sous des hypothèses très faibles. En outre, cette thèse donne plusieurs nouvelles applications de l’ACSV à l’énumération des marches sur des réseaux restreintes à certaines régions: elle apporte la preuve de plusieurs conjectures ouvertes sur les comportements asymptotiques de telles marches,et une étude détaillée de modèles de marche sur des réseaux avec des étapes pondérées
The field of analytic combinatorics, which studies the asymptotic behaviour ofsequences through analytic properties of their generating functions, has led to thedevelopment of deep and powerful tools with applications across mathematics and thenatural sciences. In addition to the now classical univariate theory, recent work in thestudy of analytic combinatorics in several variables (ACSV) has shown how to deriveasymptotics for the coefficients of certain D-finite functions represented by diagonals ofmultivariate rational functions. This thesis examines the methods of ACSV from acomputer algebra viewpoint, developing rigorous algorithms and giving the firstcomplexity results in this area under conditions which are broadly satisfied.Furthermore, this thesis gives several new applications of ACSV to the enumeration oflattice walks restricted to certain regions. In addition to proving several openconjectures on the asymptotics of such walks, a detailed study of lattice walk modelswith weighted steps is undertaken
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Mori, Yuto. "Path optimization with neural network for sign problem in quantum field theories." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263466.

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Allen, Emily. "Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/366.

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The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation. This dissertation is dedicated to this open problem. In Chapter 1 we review known results on T (m,n) and their q-analog polynomials. In Chapter 2 we give a weighted interpretation for T(m,n) in terms of 2-Motzkin paths of length m+n2 and a reformulation of this interpretation in terms of Dyck paths. We then convert our weighted interpretation into a conventional combinatorial interpretation for m = 1,2. At the beginning of Chapter 2, we prove our weighted interpretation for T(m,n) by induction. In the final section of Chapter 2 we present a constructive combinatorial proof of this result based on rooted plane trees. In Chapter 3 we introduce two q-analog super Catalan numbers. We also define the q-Ballot number and provide its combinatorial interpretation. Using our q-Ballot number, we give an identity for one of the q-analog super Catalan numbers and use it to interpret a q-analog super Catalan number in the case m= 2. In Chapter 4 we review problems left open and discuss their difficulties. This includes the unimodality of some of the q-analog polynomials and the conventional combinatorial interpretation of the super Catalan numbers and their q-analogs for higher values of m.
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NAKAI, Wakako, Tomoki NAKANISHI, and 知樹 中西. "Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type C_n." Researchers of the Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine, 2007. http://hdl.handle.net/2237/8557.

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Valgushev, Semen [Verfasser], and Pavel [Akademischer Betreuer] Buividovich. "Non-perturbative lattice approaches to complex path integrals: from non-perturbative saddle points to real-time physics of chiral media / Semen Valgushev ; Betreuer: Pavel Buividovich." Regensburg : Universitätsbibliothek Regensburg, 2018. http://d-nb.info/1172970637/34.

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Krutz, Nicholas J. "On the Path-Dependent Microstructure Evolution of an Advanced Powder Metallurgy Nickel-base Superalloy During Heat Treatment." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1606949447780975.

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Böhm, Walter, and Kurt Hornik. "A Kolmogorov-Smirnov Test for r Samples." WU Vienna University of Economics and Business, 2010. http://epub.wu.ac.at/2960/1/Report105.pdf.

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We consider the problem of testing whether r (>=2) samples are drawn from the same continuous distribution F(x). The test statistic we will study in some detail is defined as the maximum of the circular differences of the empirical distribution functions, a generalization of the classical 2-sample Kolmogorov-Smirnov test to r (>=2) independent samples. For the case of equal sample sizes we derive the exact null distribution by counting lattice paths confined to stay in the scaled alcove $\mathcal{A}_r$ of the affine Weyl group $A_{r-1}$. This is done using a generalization of the classical reflection principle. By a standard diffusion scaling we derive also the asymptotic distribution of the test statistic in terms of a multivariate Dirichlet series. When the sample sizes are not equal the reflection principle no longer works, but we are able to establish a weak convergence result even in this case showing that by a proper rescaling a test statistic based on a linear transformation of the circular differences of the empirical distribution functions has the same asymptotic distribution as the test statistic in the case of equal sample sizes.
Series: Research Report Series / Department of Statistics and Mathematics
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Books on the topic "Lattice path"

1

Andrews, George E., Christian Krattenthaler, and Alan Krinik, eds. Lattice Path Combinatorics and Applications. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1.

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Albeverio, Sergio. The statistical mechanics of quantum lattice systems: A path integral approach. Zurich: European Mathematical Society, 2009.

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The statistical mechanics of quantum lattice systems: A path integral approach. Zurich: European Mathematical Society, 2009.

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Autumn College on Techniques in Many-Body Problems (1987 Lahore, Pakistan). Path integral method, lattice gauge theory and critical phenomena: Lahore, October 31-November 17, 1987. Edited by Shaukat A. Singapore: World Scientific, 1989.

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Ault, Shaun, and Charles Kicey. Counting Lattice Paths Using Fourier Methods. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26696-7.

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Krattenthaler, C. The major counting of nonintersecting lattice paths and generating functions for tableaux. Providence, RI: American Mathematical Society, 1995.

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Andrews, George E. Lattice Path Combinatorics and Applications. Springer, 2019.

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G, Mohanty S., and Conference on Lattice Path Combinatorics and Applications, (3nd : 1994 : University of Delhi, India), eds. Lattice path combinatorics and applications. Amsterdam: Elsevier, 1996.

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G, Mohanty S., and Conference on Lattice Path Combinatorics and Applications, (2nd : 1990 : Hamilton, Canada), eds. Lattice path combinatorics and applications. Amsterdam: North-Holland, 1993.

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Chekhov, Leonid. Two-dimensional quantum gravity. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.30.

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This article discusses the connection between large N matrix models and critical phenomena on lattices with fluctuating geometry, with particular emphasis on the solvable models of 2D lattice quantum gravity and how they are related to matrix models. It first provides an overview of the continuum world sheet theory and the Liouville gravity before deriving the Knizhnik-Polyakov-Zamolodchikov scaling relation. It then describes the simplest model of 2D gravity and the corresponding matrix model, along with the vertex/height integrable models on planar graphs and their mapping to matrix models. It also considers the discretization of the path integral over metrics, the solution of pure lattice gravity using the one-matrix model, the construction of the Ising model coupled to 2D gravity discretized on planar graphs, the O(n) loop model, the six-vertex model, the q-state Potts model, and solid-on-solid and ADE matrix models.
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Book chapters on the topic "Lattice path"

1

Pan, Ran, and Jeffrey B. Remmel. "Paired Patterns in Lattice Paths." In Lattice Path Combinatorics and Applications, 382–418. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_17.

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Haghighi, Aliakbar Montazer, and Sri Gopal Mohanty. "Professor Lajos Takács: A Tribute." In Lattice Path Combinatorics and Applications, 1–28. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_1.

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Cori, Robert, Enrica Duchi, Veronica Guerrini, and Simone Rinaldi. "Families of Parking Functions Counted by the Schröder and Baxter Numbers." In Lattice Path Combinatorics and Applications, 194–225. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_10.

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Dilcher, Karl, and Larry Ericksen. "Some Tilings, Colorings and Lattice Paths via Stern Polynomials." In Lattice Path Combinatorics and Applications, 226–49. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_11.

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Haglund, James, Jeffrey B. Remmel, and Meesue Yoo. "p-Rook Numbers and Cycle Counting in $$C_p \wr S_n$$ C p ≀ S n." In Lattice Path Combinatorics and Applications, 250–82. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_12.

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Kyriakoussis, Andreas, and Malvina Vamvakari. "Asymptotic Behaviour of Certain q-Poisson, q-Binomial and Negative q-Binomial Distributions." In Lattice Path Combinatorics and Applications, 283–306. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_13.

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Margolius, Barbara. "Asymptotic Estimates for Queueing Systems with Time-Varying Periodic Transition Rates." In Lattice Path Combinatorics and Applications, 307–26. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_14.

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Mercankosk, Guven, and Gopalan M. Nair. "A Combinatorial Analysis of the M/M $$^{[m]}$$ [ m ] /1 Queue." In Lattice Path Combinatorics and Applications, 327–42. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_15.

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Morrow, Gregory J. "Laws Relating Runs, Long Runs, and Steps in Gambler’s Ruin, with Persistence in Two Strata." In Lattice Path Combinatorics and Applications, 343–81. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_16.

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Takács, Lajos. "The Distribution of the Local Time of Brownian Motion with Drift." In Lattice Path Combinatorics and Applications, 29–42. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_2.

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Conference papers on the topic "Lattice path"

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Mishna, Marni. "Algorithmic Approaches for Lattice Path Combinatorics." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3087604.3087664.

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LEE, F. X. "PATH INTEGRALS IN LATTICE QUANTUM CHROMODYNAMICS." In Proceedings of the 9th International Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812837271_0050.

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Gao, Shanzhen, and Keh-Hsun Chen. "Unsolved Lattice Path Problems in Computational Science." In 2017 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2017. http://dx.doi.org/10.1109/csci.2017.31.

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Giusti, Leonardo, and Michele Della Morte. "Glueball masses from ratios of path integrals." In XXIX International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0308.

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Takeda, Shinji. "Tensor network approach to real-time path integral." In 37th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2019. http://dx.doi.org/10.22323/1.363.0033.

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Gao, Shanzhen, and Keh-Hsun Chen. "Unsolved Lattice Path Problems in Computational Science II." In 2018 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2018. http://dx.doi.org/10.1109/csci46756.2018.00048.

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Pothan, Sivakumar, J. L. Nandagopal, and Gopinath Selvaraj. "Path planning using state lattice for autonomous vehicle." In 2017 International Conference on Technological Advancements in Power and Energy (TAP Energy). IEEE, 2017. http://dx.doi.org/10.1109/tapenergy.2017.8397363.

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Butzke, Jonathan, Krishna Sapkota, Kush Prasad, Brian MacAllister, and Maxim Likhachev. "State lattice with controllers: Augmenting lattice-based path planning with controller-based motion primitives." In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014). IEEE, 2014. http://dx.doi.org/10.1109/iros.2014.6942570.

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Wagner, M., and Frieder Lenz. "The pseudoparticle approach for solving path integrals in gauge theories." In XXIIIrd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2005. http://dx.doi.org/10.22323/1.020.0315.

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Pavlovsky, Oleg, Aleksandr Ivanov, and Alexander Novoselov. "Path Integral Monte-Carlo method for relativistic quantum systems." In The 32nd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.214.0056.

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