Relevant bibliographies by topics / Log-concavity

Academic literature on the topic 'Log-concavity'

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Published: 18 May 2024

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Journal articles on the topic "Log-concavity"

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Saumard, Adrien, and Jon A. Wellner. "Log-concavity and strong log-concavity: A review." Statistics Surveys 8 (2014): 45–114. http://dx.doi.org/10.1214/14-ss107.

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Llamas, Aurora, and José Martínez-Bernal. "Nested Log-Concavity." Communications in Algebra 38, no. 5 (April 26, 2010): 1968–81. http://dx.doi.org/10.1080/00927870902950662.

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Finner, H., and M. Roters. "Distribution functions and log-concavity." Communications in Statistics - Theory and Methods 22, no. 8 (January 1993): 2381–96. http://dx.doi.org/10.1080/03610929308831156.

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Wang, Yi. "Linear transformations preserving log-concavity." Linear Algebra and its Applications 359, no. 1-3 (January 2003): 161–67. http://dx.doi.org/10.1016/s0024-3795(02)00438-x.

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Lin, Yi, and Álvaro Pelayo. "Log-concavity and symplectic flows." Mathematical Research Letters 22, no. 2 (2015): 501–27. http://dx.doi.org/10.4310/mrl.2015.v22.n2.a9.

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Wang, Yi, and Yeong-Nan Yeh. "Log-concavity and LC-positivity." Journal of Combinatorial Theory, Series A 114, no. 2 (February 2007): 195–210. http://dx.doi.org/10.1016/j.jcta.2006.02.001.

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Kahn, J., and M. Neiman. "Negative correlation and log-concavity." Random Structures & Algorithms 37, no. 3 (November 30, 2009): 367–88. http://dx.doi.org/10.1002/rsa.20292.

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Shaked, Moshe, and J. George Shanthikumar. "Characterization of Some First Passage Times Using Log-Concavity and Log-Convexity as Aging Notions." Probability in the Engineering and Informational Sciences 1, no. 3 (July 1987): 279–91. http://dx.doi.org/10.1017/s026996480000005x.

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An interpretation of log-concavity and log-convexity as aging notions is given in this paper. It imitates a stochastic ordering characterization of the NBU (new better than used) and the NWU (new worse than used) notions but stochastic ordering is now replaced by the likelihood ratio ordering. The new characterization of log-concavity and log-convexity sheds new light on these properties and enables one to obtain intuitively simple proofs of the log-convexity and log-concavity of some first passage times of interest in branching processes and in reliability theory.
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Johnson, Oliver, Ioannis Kontoyiannis, and Mokshay Madiman. "Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures." Discrete Applied Mathematics 161, no. 9 (June 2013): 1232–50. http://dx.doi.org/10.1016/j.dam.2011.08.025.

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Karp, D., and S. M. Sitnik. "Log-convexity and log-concavity of hypergeometric-like functions." Journal of Mathematical Analysis and Applications 364, no. 2 (April 2010): 384–94. http://dx.doi.org/10.1016/j.jmaa.2009.10.057.

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Dissertations / Theses on the topic "Log-concavity"

1

Vecchi, Lorenzo. "On the log-concavity of the characteristic polynomial of a matroid." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20797/.

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In this dissertation we address a long-standing conjecture, due to Heron, Rota and Welsh on the log-concavity of the characteristic polynomial of a matroid. After decades of attempts and a series of partial results, the conjecture was fully solved in 2018 by Adiprasito, Huh and Katz, using combinatorial analogues of several results in Algebraic Geometry concerning a particular cohomology ring called Chow ring. In February 2020, a new, simpler proof was announced by Braden, Huh, Matherne, Proudfoot and Wang. This dissertation is conceived to be a self-contained guide to support the reader in understanding these two papers, providing also the necessary background, a wide horizon ranging from Hodge Theory to Combinatorics to Toric Geometry. Moreover, we provide concrete and nontrivial examples of computations of Chow rings, of which we feel current literature is still lacking.
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Nance, Anthony Charles. "On the independence numbers for the cycle matroid of a wheel: Unimodality and bounds supporting log-concavity /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu148794501561837.

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Bizeul, Pierre. "Stochastic methods in convexity." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS731.

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Cette thèse s'inscrit dans le cadre des probabilités en grande dimension, en particulier sous hypothèse de convexité. Dans une première partie, on étudie le comportement des l'entropie et de l'information de Fisher vis à vis des convolutions de vecteurs log-concave. Ensuite, à l'aide de la localisation stochastique, une technique récente qui a notamment servi à la quasi résolution de la conjecture KLS, nous établissons des résultats nouveaux sur la fonction de concentration des mesures log-concave, et leur constante de log-sobolev. La dernière partie est consacrée à l'étude de grands systèmes linéaires aléatoires pour lesquels un phénomène de type cut-off est démontré
This thesis deals with high-dimensionnal phenomena arising under convexity assumptions. In a first part, we study the behavior of the entropy and information with respect to convolutions of log-concave vectors. Then, using stochastic localization, a very recent technique which led to an almost resolution of the KLS conjecture, we establish new results regarding the concentration fucntion of log-concave probabilities, and their log-Sobolev constant. Finally, the last chapter is devoted to the study of large random linear systems, for which a cut-off phenomenon is established
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Neiman, Michael. "Negative correlation and log-concavity." 2009. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051389.

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Chen, Shih-Yan, and 陳世晏. "Unimodality and Log-concavity of Independence Polynomials ofVery Well-covered Graphs and Topological Properties ofSome Interconnection Networks." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/12356328450125953702.

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博士
中原大學
應用數學研究所
99
There are two main parts in this dissertation. In the first part, we study “Unimodality and log-concavity of independence polynomials of very well-covered graphs”. We show that the independence polynomial I(G*;x) of G* is unimodal for any graph G* whose skeleton G has the stability number α(G)<=8. In addition, we show that the independence polynomial of K*2,n is log-concave with a unique mode. In the second part, we investigate “Topological properties of some interconnection networks”. Using the structures of dual-cubes introduced by Li and Peng, we introduce a new interconnection work, called dual-cube extensive networks (DCEN). Furthermore, we study some topological properties of DCEN. More precisely, we show that DCEN(G) preserves some nice properties of G such as the hamiltonian connectivity, globally 3*-connectivity, and edge-pancyclicity, and also discuss the fault-tolerant hamiltonian property of DCEN(G). In addition, we investigate the 4-fault-tolerant hamiltonicity of circular graphs G(n,4) and the existence of mutually independent hamiltonian cycles of alternating group graphs AGn.
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Guo, Yi-Xuan, and 郭易軒. "Log-concavity of independence polynomials of the very well-covered graphs generated from the complete bipartite graphs Kt,n." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/84442710530380984473.

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Abstract:
碩士
中原大學
應用數學研究所
99
A well-covered graph is a graph in which all maximal stable/independent sets have the same cardinality. Let sk denote the number of stable sets of cardinality k in graph G, and α(G) be the size of a maximum stable set. A well-covered graph G with no isolated vertices is called very well-covered if |G| = 2α(G). The independence polynomial of G is defined by I(G; x) = Σα(G) k=0 skxk, and I(G; x) is log-concave if s2k ≥ sk+1sk¡1 holds for 1 ≤ k ≤ α(G)−1. Given an arbitrary graph G, G¤ is the graph obtained from G by appending a single pendant edge to each vertex of G. It is easy to see that G¤ is very well-covered. In 2004, Levit and Mandrescu [17] proved that the independence polynomial of K¤1,n is log-concave. In 2010, the same result for K¤2,n is proved by Chen and Wang [8]. In this thesis, we find the independence polynomials I(K¤t,n; x) of K¤t,n for all positive integers t ≤ n and show that I(K¤t,n; x) is log-concave for any t with 3 ≤ t ≤ 5.
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Book chapters on the topic "Log-concavity"

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Asai, Nobuhiro, Izumi Kubo, and Hui-Hsiung Kuo. "Bell Numbers, Log-Concavity, and Log-Convexity." In Recent Developments in Infinite-Dimensional Analysis and Quantum Probability, 79–87. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0842-6_4.

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Wellner, Jon A. "Strong Log-concavity is Preserved by Convolution." In High Dimensional Probability VI, 95–102. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0490-5_7.

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García-Marco, Ignacio, Pascal Koiran, and Sébastien Tavenas. "Log-Concavity and Lower Bounds for Arithmetic Circuits." In Mathematical Foundations of Computer Science 2015, 361–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48054-0_30.

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Mező, István. "Unimodality, log-concavity, and log-convexity." In Combinatorics and Number Theory of Counting Sequences, 105–21. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9781315122656-4.

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"Log-Concavity and Unimodality." In Information and Exponential Families, 93–102. Chichester, UK: John Wiley & Sons, Ltd, 2014. http://dx.doi.org/10.1002/9781118857281.ch6.

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"Unimodality, Log-concavity, Real-rootedness And Beyond." In Handbook of Enumerative Combinatorics, 461–508. Chapman and Hall/CRC, 2015. http://dx.doi.org/10.1201/b18255-13.

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"Convexity and Log-Concavity Related Moment and Probability Inequalities." In Mathematics in Science and Engineering, 339–59. Elsevier, 1992. http://dx.doi.org/10.1016/s0076-5392(08)62825-8.

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Conference papers on the topic "Log-concavity"

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Ahmita, Moussa, Hacène Belbachir, and Takao Komatsu. "Preserving log-concavity and generalized triangles." In DIOPHANTINE ANALYSIS AND RELATED FIELDS—2010: DARF—2010. AIP, 2010. http://dx.doi.org/10.1063/1.3478183.

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Sun, Yin, and Shidong Zhou. "Tight Bounds of the Generalized Marcum Q-Function Based on Log-Concavity." In IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference. IEEE, 2008. http://dx.doi.org/10.1109/glocom.2008.ecp.226.

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