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Leave-One-Out Cross-Validation Based Model Selection Criteria for Weighted LS-SVMs

G.C. Cawley
2006 The 2006 IEEE International Joint Conference on Neural Network Proceedings  
The best entry based on these methods was ranked in joint first place in the WCCI-2006 performance prediction challenge, demonstrating the effectiveness of this approach.  ...  While the model parameters of many kernel learning methods are given by the solution of a convex optimisation problem, the selection of good values for the kernel and regularisation parameters, i.e. model  ...  ACKNOWLEDGEMENTS The author would like to thank the organisers of the WCCI-2006 performance prediction challenge, the anonymous reviewers for their helpful comments and Nicola Talbot for her help in typesetting  ... 
doi:10.1109/ijcnn.2006.246634 dblp:conf/ijcnn/Cawley06 fatcat:yb224dsmobc6hnmsab7u5qqxpm

Quadratization and Roof Duality of Markov Logic Networks

Roderick Sebastiaan De Nijs, Christian Landsiedel, Dirk Wollherr, Martin Buss
2016 The Journal of Artificial Intelligence Research  
This article discusses the quadratization of Markov Logic Networks, which enables efficient approximate MAP computation by means of maximum flows.  ...  The procedure relies on a pseudo-Boolean representation of the model, and allows handling models of any order.  ...  Study (www.tum-ias.de), funded by the German Excellence Initiative.  ... 
doi:10.1613/jair.5023 fatcat:y6jk5vzr6fa6vfmp6vww2niv74

On lower bounds of second-order nonlinearities of cubic bent functions constructed by concatenating Gold functions

Ruchi Gode, Sugata Gangopadhyay
2011 International Journal of Computer Mathematics  
For r > 2 there is no efficient algorithm to compute rth-order nonlinearity of a Boolean function.  ...  The best known asymptotic upper bound on nl r (f ) found in [8] which is as follows: The first-order nonlinearity of a Boolean function on n variables can be computed by using fast Walsh transform in time  ...  The Propositions 1 and 2 are applicable for computation of the lower bounds of the second order nonlinearities of cubic Boolean functions.  ... 
doi:10.1080/00207160.2011.587874 fatcat:aewckrktubhplpvbcx2uudbkvq

Classification of Balanced Quadratic Functions

Lauren De Meyer, Begül Bilgin
2019 IACR Transactions on Symmetric Cryptology  
Due to their simplicity, quadratic vectorial Boolean functions are preferred when efficient implementations for a variety of applications are of concern.  ...  Our algorithm enables for the first time a complete classification of 6-bit quadratic permutations as well as all balanced quadratic functions for n ≤ 6.  ...  Acknowledgments The authors thank Dusan Bozilov for the insights into his algorithm and Prof. Vincent Rijmen for fruitful discussion and helpful comments.  ... 
doi:10.13154/tosc.v2019.i2.169-192 dblp:journals/tosc/MeyerB19 fatcat:db2jrsneerapxmbnjumwkla62a

Classification of Balanced Quadratic Functions

Lauren De Meyer, Begül Bilgin
2019 IACR Transactions on Symmetric Cryptology  
Due to their simplicity, quadratic vectorial Boolean functions are preferred when efficient implementations for a variety of applications are of concern.  ...  Our algorithm enables for the first time a complete classification of 6-bit quadratic permutations as well as all balanced quadratic functions for n ≤ 6.  ...  Acknowledgments The authors thank Dusan Bozilov for the insights into his algorithm and Prof. Vincent Rijmen for fruitful discussion and helpful comments.  ... 
doi:10.46586/tosc.v2019.i2.169-192 fatcat:miobcecw3jcnvpz4pgnpcunkhi

On Second-Order Nonlinearities of Two Classes of Cubic Boolean Functions [chapter]

Deep Singh, Maheshanand Bhaintwal
2013 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
In this paper, we obtain lower bounds of second-order nonlinearities of two classes of highly nonlinear cubic Boolean functions of the form f (x) = tr n 1 (λx 2 2r +2 r+1 +1 ), λ ∈ F2n \ {0}, for n = 3r  ...  The higher order nonlinearity of a Boolean function is a cryptographic criterion, which plays an important role in the design of secure block ciphers and stream ciphers.  ...  The work of the first author is supported by NBHM (DAE), INDIA.  ... 
doi:10.1007/978-3-642-37949-9_49 fatcat:uz5ktkvm3jgcxn4vvgr4mg6qy4

Generalized roof duality

Fredrik Kahl, Petter Strandmark
2012 Discrete Applied Mathematics  
We show how submodular relaxations can efficiently be constructed in order to compute the generalized roof dual bound for general cubic and quartic pseudo-boolean functions.  ...  The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems.  ...  Acknowledgments This work has been funded by the Swedish Foundation for Strategic Research (FFL and VINST) and by the European Research Council (GlobalVision grant no. 209480).  ... 
doi:10.1016/j.dam.2012.06.009 fatcat:fbax76dbebc2rgejoiglgeqaim

Quadratic relation of S-box and its application to the linear attack of full round DES [chapter]

Takeshi Shimoyama, Toshinobu Kaneko
1998 Lecture Notes in Computer Science  
In this paper, we derive 7 quadratic relations over GF (2) from the input and output bits of the S-boxes of DES. We apply one of those to an improved linear attack of full round DES.  ...  We describe an improved algorithm by combining the non-linear approximation method proposed by Knudsen and Robshaw, and the multiple approximation method proposed by Kaliski and Robshaw.  ...  Table 1 shows the number of quadratic and cubic polynomials in the reduced Gröbner basis of the Boolean algebraic relations of S-boxes as derived above with respect to the degree reverse lexicographic  ... 
doi:10.1007/bfb0055729 fatcat:3ha6kga26nhljooodaamgfioza

Walsh functions as surrogate model for pseudo-boolean optimization problems

Florian Leprêtre, Sébastien Verel, Cyril Fonlupt, Virginie Marion
2019 Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO '19  
We finally highlight how Walsh surrogates may outperform the state-of-the-art surrogate models for pseudo-boolean functions.  ...  We conduct our experiments on a benchmark of combinatorial structures and demonstrate the accuracy, and the optimization efficiency of the proposed model.  ...  ACKNOWLEDGMENTS Experiments presented in this paper were carried out using the CALCULCO computing platform, supported by SCOSI / ULCO (Service COmmun du Système d'Information de l'Université du Littoral  ... 
doi:10.1145/3321707.3321800 dblp:conf/gecco/LepretreVFM19 fatcat:qfxaglxn3fhfzjgnnv6tvdxyyi

Resource efficient gadgets for compiling adiabatic quantum optimization problems

Ryan Babbush, Bryan O'Gorman, Alán Aspuru-Guzik
2013 Annalen der Physik  
In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian.  ...  We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian.  ...  Greedy algorithm for choosing which ancilla bits to use with each cubic term in reducing a cubic pseudo-Boolean to a quadratic one.  ... 
doi:10.1002/andp.201300120 fatcat:losyjxjgnjbbhlwezlcsso23i4

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata [article]

Luca Mariot, Martina Saletta, Alberto Leporati, Luca Manzoni
2021 arXiv   pre-print
An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim  ...  We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial  ...  Thus, the Walsh transform can be used to compute the nonlinearity of a Boolean function f , which is defined as the minimum Hamming distance of (the truth table of) f from the set of all affine functions  ... 
arXiv:2111.13248v1 fatcat:5geqlgjhwjd2deaopvi6gfifwa

More on zeros and approximation of the Ising partition function

Alexander Barvinok, Nicholas Barvinok
2021 Forum of Mathematics, Sigma  
We consider the problem of computing the partition function $\sum _x e^{f(x)}$ , where $f: \{-1, 1\}^n \longrightarrow {\mathbb R}$ is a quadratic or cubic polynomial on the Boolean cube $\{-1, 1\}^n$  ...  In the case of a quadratic polynomial f, we show that the partition function can be approximated within relative error $0 < \epsilon < 1$ in quasi-polynomial $n^{O(\ln n - \ln \epsilon )}$ time if the  ...  Conflict of Interest: None. Financial support: The research of the first author was partially supported by NSF Grant DMS 1855428.  ... 
doi:10.1017/fms.2021.40 fatcat:it4d2qivtfbk3nwhdc5wyn2one

Periodic Fourier representation of Boolean functions [article]

Ryuhei Mori
2019 arXiv   pre-print
Second, we show that the periodic Fourier sparsity is at least 2^deg_F_2(f)-1, which means that NMQC_⊕ efficiently computes a Boolean function f if and only if F_2-degree of f is small.  ...  The minimum number of non-zero coefficients in the above representation, which we call the periodic Fourier sparsity, is equal to the required number of qubits for the exact computation of f by NMQC_⊕.  ...  Since these Boolean functions cannot be approximated by low F 2 -degree polynomial [23] , we can expect that these Boolean functions cannot be computed efficiently by NMQC ⊕ even with bounded error.  ... 
arXiv:1803.09947v3 fatcat:ryswf2p6ufgczmg2dyviodtzt4

Parallel and efficient Boolean on polygonal solids

Hanli Zhao, Charlie C. L. Wang, Yong Chen, Xiaogang Jin
2011 The Visual Computer  
We present a novel framework which can efficiently evaluate approximate Boolean set operations for B-rep models by highly parallel algorithms.  ...  This is achieved by taking axis-aligned surfels of Layered Depth Images (LDI) as a bridge and performing Boolean operations on the structured points.  ...  Acknowledgements The work was partially supported by  ... 
doi:10.1007/s00371-011-0571-1 fatcat:codadsonpfgvxl3pd7mx2xl7ju

Complexity of Discrete Energy Minimization Problems [article]

Mengtian Li, Alexander Shekhovtsov, Daniel Huber
2016 arXiv   pre-print
This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations.  ...  Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding  ...  We use the method of [24] to transform the cubic Boolean problem into a quadratic one, with polynomially many additional variables, which is an instance of QPBO. 4.  ... 
arXiv:1607.08905v1 fatcat:k5xddu3xvndnziljktxo5p4mpe
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