761 research outputs found
Finding efficient nonlinear functions by means of genetic programming
7th International Conference, KES 2003. Proceedings, Part I. Oxford, UK, September 3-5, 2003The design of highly nonlinear functions is relevant for a number of different applications, ranging from database hashing to message authentication. But, apart from useful, it is quite a challenging task. In this work, we propose the use of genetic programming for finding functions that optimize a particular nonlinear criteria, the avalanche effect, using only very efficient operations, so that the resulting functions are extremely efficient both in hardware and in software.Supported by the Spanish Ministerio de Ciencia y Tecnologia research project
TIC2002-04498-C05-4Publicad
Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
We introduce the problem of constructing weighted complex projective
2-designs from the union of a family of orthonormal bases. If the weight
remains constant across elements of the same basis, then such designs can be
interpreted as generalizations of complete sets of mutually unbiased bases,
being equivalent whenever the design is composed of d+1 bases in dimension d.
We show that, for the purpose of quantum state determination, these designs
specify an optimal collection of orthogonal measurements. Using highly
nonlinear functions on abelian groups, we construct explicit examples from d+2
orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10,
and 12, for example, where no complete sets of mutually unbiased bases have
thus far been found.Comment: 28 pages, to appear in J. Math. Phy
A Hedged Monte Carlo Approach to Real Option Pricing
In this work we are concerned with valuing optionalities associated to invest
or to delay investment in a project when the available information provided to
the manager comes from simulated data of cash flows under historical (or
subjective) measure in a possibly incomplete market. Our approach is suitable
also to incorporating subjective views from management or market experts and to
stochastic investment costs. It is based on the Hedged Monte Carlo strategy
proposed by Potters et al (2001) where options are priced simultaneously with
the determination of the corresponding hedging. The approach is particularly
well-suited to the evaluation of commodity related projects whereby the
availability of pricing formulae is very rare, the scenario simulations are
usually available only in the historical measure, and the cash flows can be
highly nonlinear functions of the prices.Comment: 25 pages, 14 figure
A Note on Cyclic Codes from APN Functions
Cyclic codes, as linear block error-correcting codes in coding theory, play a
vital role and have wide applications. Ding in \cite{D} constructed a number of
classes of cyclic codes from almost perfect nonlinear (APN) functions and
planar functions over finite fields and presented ten open problems on cyclic
codes from highly nonlinear functions. In this paper, we consider two open
problems involving the inverse APN functions and the Dobbertin
APN function . From the calculation of
linear spans and the minimal polynomials of two sequences generated by these
two classes of APN functions, the dimensions of the corresponding cyclic codes
are determined and lower bounds on the minimum weight of these cyclic codes are
presented. Actually, we present a framework for the minimal polynomial and
linear span of the sequence defined by ,
where is a primitive element in . These techniques can also be
applied into other open problems in \cite{D}
Integrated Inference and Learning of Neural Factors in Structural Support Vector Machines
Tackling pattern recognition problems in areas such as computer vision,
bioinformatics, speech or text recognition is often done best by taking into
account task-specific statistical relations between output variables. In
structured prediction, this internal structure is used to predict multiple
outputs simultaneously, leading to more accurate and coherent predictions.
Structural support vector machines (SSVMs) are nonprobabilistic models that
optimize a joint input-output function through margin-based learning. Because
SSVMs generally disregard the interplay between unary and interaction factors
during the training phase, final parameters are suboptimal. Moreover, its
factors are often restricted to linear combinations of input features, limiting
its generalization power. To improve prediction accuracy, this paper proposes:
(i) Joint inference and learning by integration of back-propagation and
loss-augmented inference in SSVM subgradient descent; (ii) Extending SSVM
factors to neural networks that form highly nonlinear functions of input
features. Image segmentation benchmark results demonstrate improvements over
conventional SSVM training methods in terms of accuracy, highlighting the
feasibility of end-to-end SSVM training with neural factors
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