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A New Perspective for Risk Management: A Study of the Design of Generic Technology with a Matroid Model in C-K Theory [chapter]

Pascal Le Masson, Benoit Weil, Olga Kokshagina
2014 Principia Designae - Pre-Design, Design, and Post-Design  
We show (2)that the design of this generic technology depends on the structure of the unknown, ie the structure of the space generated by the concept of risk-free alternative. (3) We identify new strategies  ...  It consists in making the optimal choice between given possible decisions and probable states of nature. In this paper we extend this model to include a design capacity to deal with risk situations.  ...  Let's analyse the Wald statistical decision-making model (derived from decision theory), one of the most general models of decision-making under uncertainty.  ... 
doi:10.1007/978-4-431-54403-6_13 fatcat:uvarn6rv5nfifmdrzdslxkrlje

Less is more: Selecting informative and diverse subsets with balancing constraints [article]

Srikumar Ramalingam, Daniel Glasner, Kaushal Patel, Raviteja Vemulapalli, Sadeep Jayasumana, Sanjiv Kumar
2021 arXiv   pre-print
In addition to these measures, we show that balancing constraints on predicted class labels and decision boundaries are beneficial.  ...  We propose a novel formulation of these constraints using matroids, an algebraic structure that generalizes linear independence in vector spaces, and present an efficient greedy algorithm with constant  ...  Note that the intersection of two matroids is not a matroid in general.  ... 
arXiv:2104.12835v2 fatcat:ytcdgiepzreerkaj64hwofgcbq

Quantum Speedup and Limitations on Matroid Property Problems [article]

Xiaowei Huang, Jingquan Luo, Lvzhou Li
2022 arXiv   pre-print
It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats, hyperplanes) of a matroid, and for the decision problem  ...  In addition, for the paving matroid decision problem, a lower bound Ω(√(n⌊ n/2⌋/n)) on the query complexity is obtained, and an O(√(n⌊ n/2⌋)) quantum algorithm is presented.  ...  For any r-set A ⊆ V , let A 1 r,n be the matroid on V with bases all r-set except A. Similarly, when n is even, let A 2 r,n be the matroid on V with bases all r-set except A and V − A.  ... 
arXiv:2111.12900v2 fatcat:2i5cgcieyran7l55fxg5257nj4

Online auctions and generalized secretary problems

Moshe Babaioff, Nicole Immorlica, David Kempe, Robert Kleinberg
2008 ACM SIGecom Exchanges  
We present generalized secretary problems as a framework for online auctions. Elements, such as potential employees or customers, arrive one by one online.  ...  Many natural online auction scenarios can be cast as generalized secretary problems, by imposing natural restrictions on the feasible sets.  ...  Matroids relate to secretary problems in a very natural way.  ... 
doi:10.1145/1399589.1399596 fatcat:etnzuqvfo5abzjx5gspy5jrnfy

Monadic second-order model-checking on decomposable matroids [article]

Yann Strozecki
2011 arXiv   pre-print
A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids.  ...  We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded branch-width, by reduction to monadic second-order formulas on trees.  ...  I am also very grateful to Brice Minaud and Pierre Clairambault for discussions we had respectively about matroid representations and categories.  ... 
arXiv:0908.4499v2 fatcat:zslper2a7bftbhigjrk4uv6zqy

Recent advances on the matroid secretary problem

Michael Dinitz
2013 ACM SIGACT News  
A matroid M = (E, I) is an ordered pair consisting of a finite set E and a collection I of subsets (called the independent sets) of E satisfying the following three conditions: 1. ∅ ∈ I, 2.  ...  In this column I will introduce and motivate this problem, and give a survey of some of the exciting work that has been done on it over the past 6 years.  ...  Alternative Models Since [BIK07] , much of the work on the matroid secretary problem on general matroids falls into two categories: getting stronger upper bounds by weakening the adversary or allowing  ... 
doi:10.1145/2491533.2491557 fatcat:yfft66mjpzb2lhyszq5x3cpwyy

Trees, grids, and MSO decidability: From graphs to matroids

Petr Hliněný, Detlef Seese
2006 Theoretical Computer Science  
(Matroids can be viewed as a wide generalization of graphs, and they seem to capture some second order properties in a more suitable way than graphs themselves, cf. the recent development in matroid structure  ...  It is one of the main goals of this article to prove a variant of this conjecture for matroids representable over a finite field.  ...  Courcelle, the organizer of the workshop on "Logic and Graph Transformations" at the ICGT 2004 conference, for inviting us to present our research results there.  ... 
doi:10.1016/j.tcs.2005.10.006 fatcat:dtsh4w7hs5dbtkz6nyqjef3cp4

Monadic second-order model-checking on decomposable matroids

Yann Strozecki
2011 Discrete Applied Mathematics  
A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids.  ...  We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded branch-width, by reduction to monadic second-order formulas on trees.  ...  I am also very grateful to Brice Minaud and Pierre Clairambault for early discussions on matroids and pushout and to my advisor Arnaud Durand for his support and help while writing this article.  ... 
doi:10.1016/j.dam.2011.02.005 fatcat:33f6zing5zg4jnuqy4arvae47a

Qualitative reasoning with directional relations

D. Wolter, J.H. Lee
2010 Artificial Intelligence  
QSR has two primary goals: providing a symbolic model for human common-sense level of reasoning and providing efficient means for reasoning.  ...  Acknowledgements The authors thank Till Mossakowski and Arne Kreutzmann for commenting on a draft of this paper. We also thank our reviewers for helping us to improve the paper.  ...  The calculus assumes all points to be in general position, i.e., no three different points are positioned on the same line.  ... 
doi:10.1016/j.artint.2010.09.004 fatcat:dvanosnzg5evllebwfck6w6zq4

A one-way array algorithm for matroid scheduling

Matthias F. M. Stallmann
1991 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures - SPAA '91  
The greedy algorithm is a standard paradigm for solving matroid optimization problems on sequential computers.  ...  A k ey feature of the algorithm is its use of matroid contraction.  ...  What has been described is a generic one-way array algorithm for matroid problems that is analogous to the greedy algorithm in the sequential model.  ... 
doi:10.1145/113379.113411 dblp:conf/spaa/Stallmann91 fatcat:h4x5w2wa2vg3zaksywmodjuv3u

Diversity maximization under matroid constraints

Zeinab Abbassi, Vahab S. Mirrokni, Mayur Thakur
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
We model the latter approach as a (partition) matroid constraint, and study diversity maximization problems under matroid constraints.  ...  Our algorithms are based on computing a set of cluster centers, where clusters are formed around them.  ...  For example, notions of diversity has been suggested based on presenting decision trees to users [6] . Also computing diverse query results for online shopping has been studied in [23] .  ... 
doi:10.1145/2487575.2487636 dblp:conf/kdd/AbbassiMT13 fatcat:vxjten2qibcdblwww3b64qwfze

On the Generation of Oriented Matroids

J. Bokowski, A. Guedes de Oliveira
2000 Discrete & Computational Geometry  
We provide a multiple purpose algorithm for generating oriented matroids.  ...  Our algorithm is interesting in its own right as a tool for many investigations in which oriented matroids play a key role.  ...  We wish to thank in addition Boris Bokowski for all his advice in getting the computations done on various computers.  ... 
doi:10.1007/s004540010027 fatcat:2ekirxbuufaqbpgfb4noyigxwm

First order convergence of matroids

František Kardoš, Daniel Král', Anita Liebenau, Lukáš Mach
2017 European journal of combinatorics (Print)  
The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures.  ...  We establish the matroid counterpart of this result: every first order convergent sequence of matroids with bounded branch-depth representable over a fixed finite field has a limit modeling, i.e., there  ...  Matroids with rank three We now construct a sequence of matroids of rank three, each representable over the field of rationals, that has no limit modeling.  ... 
doi:10.1016/j.ejc.2016.08.005 fatcat:i5kvbbg7vvfibmi4ytzsls55yu

First order convergence of matroids [article]

Frantisek Kardos and Daniel Kral and Anita Liebenau and Lukas Mach
2016 arXiv   pre-print
The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures.  ...  We establish the matroid counterpart of this result: every first order convergent sequence of matroids with bounded branch-depth representable over a fixed finite field has a limit modeling, i.e., there  ...  Matroids with rank three We now construct a sequence of matroids of rank three, each representable over the field of rationals, that has no limit modeling.  ... 
arXiv:1501.06518v3 fatcat:ufrczsvzzbbs3lqvzzrndfeukm

Approximation Techniques in Symbolic Circuit Analysis [chapter]

Francisco V. Fernández, Carlos Sánchez-López, Rafael Castro-López, Elisenda Roca-Moreno
2012 Design of Analog Circuits through Symbolic Analysis  
This chapter reviews the different existing techniques for symbolic expression simplification, classifying them into three categories according to the step at which the simplification is performed: on  ...  Therefore, either if the symbolic expressions are used for gaining insight into circuit operation or for repetitive computer-based evaluations, simplification becomes mandatory.  ...  Most efficient analysis techniques are based on the two-graph method, which more recently have been modeled as matroid intersection problems, and on determinant decision diagrams.  ... 
doi:10.2174/978160805095611201010173 fatcat:vyzpua7tpzamvexteaqnedxvfi
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