From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum simulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. No other book incorporates all these fields, which have arisen in the past 20 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

/pdf/discrete-choice-methods-with-simulation-l1x4cghjtt.pdf

Discrete Choice Methods with Simulation

Grid search and manual search are the most widely used strategies for hyper-parameter optimization. This paper shows empirically and theoretically that randomly chosen trials are more efficient for hyper-parameter optimization than trials on a grid. Empirical evidence comes from a comparison with a large previous study that used grid search and manual search to configure neural networks and deep belief networks. Compared with neural networks configured by a pure grid search, we find that random search over the same domain is able to find models that are as good or better within a small fraction of the computation time. Granting random search the same computational budget, random search finds better models by effectively searching a larger, less promising configuration space. Compared with deep belief networks configured by a thoughtful combination of manual search and grid search, purely random search over the same 32-dimensional configuration space found statistically equal performance on four of seven data sets, and superior performance on one of seven. A Gaussian process analysis of the function from hyper-parameters to validation set performance reveals that for most data sets only a few of the hyper-parameters really matter, but that different hyper-parameters are important on different data sets. This phenomenon makes grid search a poor choice for configuring algorithms for new data sets. Our analysis casts some light on why recent "High Throughput" methods achieve surprising success--they appear to search through a large number of hyper-parameters because most hyper-parameters do not matter much. We anticipate that growing interest in large hierarchical models will place an increasing burden on techniques for hyper-parameter optimization; this work shows that random search is a natural baseline against which to judge progress in the development of adaptive (sequential) hyper-parameter optimization algorithms.

/pdf/random-search-for-hyper-parameter-optimization-20f67sngfv.pdf

Random search for hyper-parameter optimization

Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example

/pdf/the-design-and-analysis-of-computer-experiments-1kfo89lyf2.pdf

The design and analysis of computer experiments

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

where the supremum is extended over all subintervals J of [0, 1]s with one vertex at the origin. For a sequence S of points x1, x2, . . . in [0, 1] s, the star discrepancy of the first N terms of S is defined as D∗ N (S) = D ∗ N (x1, . . . , xN ). We say that S is a low-discrepancy sequence if D N (S) = O(N (logN)) for all N ≥ 2. This is conjectured to be the least possible order of magnitude of the star discrepancy that can be obtained, and the conjecture has been proved for s = 1 by Schmidt [21] (see also [8, Section 2.2]). Currently, the most powerful methods of constructing low-discrepancy sequences are built on the theory of (t, s)-sequences which was developed by Niederreiter [11] on the basis of earlier work by Sobol’ [24] and Faure [3]. We refer to the monographs [13, Chapter 4] and [20, Chapter 8] as well as to the recent survey article [14] for general background on this theory. The fact that, for any integers s ≥ 1 and b ≥ 2, there exists a (t, s)-sequence in base b for some integer t ≥ 0 was first shown by Niederreiter [12]. The star discrepancy of a (t, s)-sequence S in base b satisfies the following bound (see [11] and [13, Chapter 4]): D N (S) ≤ Cb(s, t)N (logN) +O(N(logN)) for all N ≥ 2,

https://www.impan.pl/shop/publication/transaction/download/product/82094?download.pdf

A new construction of (t, s)-sequences and some improved bounds on their quality parameter

Given a modulus m>2 and a multiplier X relatively prime to m, a sequence ^O'^i > • • • °f integers in the least residue system mod m is generated by the recursion yn+1 ~ \yn (mod m) for n = 0, 1, . . . , where the initial value y0 is relatively prime to m. The sequence x0, xx, . . . in the interval [0, 1), defined by xn = yn/m for n = 0, 1, . . . , is then a sequence of pseudo-random numbers generated by the linear congruential method. The sequence is periodic, with the least period r being the exponent to which X belongs mod m. For fixed s > 2, consider the s-tuples xn = {xn9 xn+ x, . . . , xn+s_x), n = 0, 1, . . . . We determine the empirical distribution of the s-tuples x0 , x1? . . . and compare it with the uniform distribution on [0, l]. The original sequence x0,xl9 . . .of linear congruential pseudo-random numbers passes the serial test (for the given value of s) if the deviation between these two distributions is small. To measure this deviation, we introduce the quantity

/pdf/statistical-independence-of-linear-congruential-pseudo-3jm9vt52wc.pdf

Statistical independence of linear congruential pseudo-random numbers

Let Gq be the group of permutations of the finite field Fq of odd order q that can be represented by polynomials of the form ax(q+1)/2 + bx with a, b ∈ Fq It is shown that Gq is isomorphic to the regular wreath product of two cyclic groups The structure of Gq can also be described in terms of cyclic, dicyclic, and dihedral groups It also turns out that Gq is isomorphic to the dymmetry group of a regular complex polygon

/pdf/the-structure-of-a-group-of-permutation-polynomials-548h3iqga3.pdf

Harald Niederreiter

Papers

A new construction of (t, s)-sequences and some improved bounds on their quality parameter

Statistical independence of linear congruential pseudo-random numbers

The structure of a group of permutation polynomials

Successive minima profile, lattice profile, and joint linear complexity profile of pseudorandom multisequences

Function Fields with Many Rational Places