Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Multiphase experiments with at least one later laboratory phase. I. orthogonal designs

The paper provides a systematic approach to designing the laboratory phase of a multiphase experiment, taking into account previous phases. General principles are outlined for experiments in which orthogonal designs can be employed. Multiphase experiments occur widely, although their multiphase nature is often not recognized. The need to randomize the material produced from the first phase in the laboratory phase is emphasized. Factor-allocation diagrams are used to depict the randomizations in a design and the use of skeleton analysis-of-variance (ANOVA) tables to evaluate their properties discussed. The methods are illustrated using a scenario and a case study. A basis for categorizing designs is suggested. This article has supplementary material online.

Accelerometer based performance assessment of basic routines in classical ballet

Classical ballet requires dancers to exercise significant muscle control and strength both while stationary and when moving. Following the Royal Academy of Dance (RAD) syllabus, 8 male and 27 female dancers (aged 20.2 + 1.9 yr) in a fulltime university undergraduate dance training program were asked to stand in first position for 10 seconds and then perform 10 repeats of a demi-plié exercise to a counted rhythm. Accelerometer records from the wrist, sacrum, knee and ankle were compared with the numerical scores from a professional dance instructor. The sacrum mounted sensor detected lateral tilts of the torso in dances with lower scores (Spearman’s rank correlation coefficient r = -0.64, p < 0.005). The RMS acceleration amplitude of wrist mounted sensor was linearly correlated to the movement scores (Spearman’s rank correlation coefficient r = 0.63, p < 0.005). The application of sacrum and wrist mounted sensors for biofeedback during dance training is a realistic, low cost option.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Ideal threshold schemes from orthogonal arrays

The work investigates the design of ideal threshold secret sharing in the context of cheating prevention. We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme. To prevent cheating, defining matrices should be nonlinear so both the cheaters and honest participants have the same chance of guessing of the valid secret. The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.

An orchestral audience: Classical music and continued patterns of distinction

This paper considers the key findings of a year-long collaborative research project focusing on the audience of the London Symphony Orchestra and their introduction of a new mobile telephone (‘app’) ticketing system. A mixed-method approach was employed, utilizing focus groups and questionnaires with over 80 participants, to research a sample group of university students. This research develops our understanding of classical music audiences, and highlights the continued individualistic, middle-class, and exclusionary culture of classical music attendance and patterns of behaviours. The research also suggests that a mobile phone app does prove a useful mechanism for selling discounted tickets, but shows little indication of being a useful means of expanding this audience beyond its traditional demographic.

Sealing the leak on classical NTRU signatures

Initial attempts to obtain lattice based signatures were closely related to reducing a vector modulo the fundamental parallelepiped of a secret basis (like GGH [9], or NTRUSign [12]). This approach leaked some information on the secret, namely the shape of the parallelepiped, which has been exploited on practical attacks [24]. NTRUSign was an extremely efficient scheme, and thus there has been a noticeable interest on developing countermeasures to the attacks, but with little success [6]. In [8] Gentry, Peikert and Vaikuntanathan proposed a randomized version of Babai’s nearest plane algorithm such that the distribution of a reduced vector modulo a secret parallelepiped only depended on the size of the base used. Using this algorithm and generating large, close to uniform, public keys they managed to get provably secure GGH-like lattice-based signatures. Recently, Stehlé and Steinfeld obtained a provably secure scheme very close to NTRUSign [26] (from a theoretical point of view). In this paper we present an alternative approach to seal the leak of NTRUSign. Instead of modifying the lattices and algorithms used, we do a classic leaky NTRUSign signature and hide it with gaussian noise using techniques present in Lyubashevky’s signatures. Our main contributions are thus a set of strong NTRUSign parameters, obtained by taking into account latest known attacks against the scheme, a statistical way to hide the leaky NTRU signature so that this particular instantiation of CVP-based signature scheme becomes zero-knowledge and secure against forgeries, based on the worst-case hardness of the O~(N1.5)-Shortest Independent Vector Problem over NTRU lattices. Finally, we give a set of concrete parameters to gauge the efficiency of the obtained signature scheme.

λ-orthogonal pericyclic macromolecular photoligation

A photochemical strategy enabling λ-orthogonal reactions is introduced to construct macromolecular architectures and to encode variable functional groups with site-selective precision into a single molecule by the choice of wavelength. λ-Orthogonal pericyclic reactions proceed independently of one another by the selection of functional groups that absorb light of specific wavelengths. The power of the new concept is shown by a one-pot reaction of equimolar quantities of maleimide with two polymers carrying different maleimide-reactive endgroups, that is, a photoactive diene (photoenol) and a nitrile imine (tetrazole). Under selective irradiation at λ=310–350 nm, any maleimide (or activated ene) end-capped compound reacts exclusively with the photoenol functional polymer. After complete conversion of the photoenol, subsequent irradiation at λ=270–310 nm activates the reaction of the tetrazole group with functional enes. The versatility of the approach is shown by λ-orthogonal click reactions of complex maleimides, functional enes, and polymers to the central polymer scaffold.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Serum levels of soluble receptor for advanced glycation end products and of S100 proteins are associated with inflammatory, autoantibody, and classical risk markers of joint and vascular damage in rheumatoid arthritis

Introduction: The receptor for advanced glycation end products (RAGE) is a member of the immunoglobulin superfamily of cell surface receptor molecules. High concentrations of three of its putative proinflammatory ligands, S100A8/A9 complex (calprotectin), S100A8, and S100A12, are found in rheumatoid arthritis (RA) serum and synovial fluid. In contrast, soluble RAGE (sRAGE) may prevent proinflammatory effects by acting as a decoy. This study evaluated the serum levels of S100A9, S100A8, S100A12 and sRAGE in RA patients, to determine their relationship to inflammation and joint and vascular damage. Methods: Serum sRAGE, S100A9, S100A8 and S100A12 levels from 138 patients with established RA and 44 healthy controls were measured by ELISA and compared by unpaired t test. In RA patients, associations with disease activity and severity variables were analyzed by simple and multiple linear regressions. Results: Serum S100A9, S100A8 and S100A12 levels were correlated in RA patients. S100A9 levels were associated with body mass index (BMI), and with serum levels of S100A8 and S100A12. S100A8 levels were associated with serum levels of S100A9, presence of anti-citrullinated peptide antibodies (ACPA), and rheumatoid factor (RF). S100A12 levels were associated with presence of ACPA, history of diabetes, and serum S100A9 levels. sRAGE levels were negatively associated with serum levels of C-reactive protein (CRP) and high-density lipoprotein (HDL), history of vasculitis, and the presence of the RAGE 82Ser polymorphism. Conclusions: sRAGE and S100 proteins were associated not just with RA inflammation and autoantibody production, but also with classical vascular risk factors for end-organ damage. Consistent with its role as a RAGE decoy molecule, sRAGE had the opposite effects to S100 proteins in that S100 proteins were associated with autoantibodies and vascular risk, whereas sRAGE was associated with protection against joint and vascular damage. These data suggest that RAGE activity influences co-development of joint and vascular disease in rheumatoid arthritis patients.

Difference covering arrays and pseudo-orthogonal Latin squares

A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146.

Eliciting and encoding expert knowledge on variable selection into classical or Bayesian species distribution models

The quality of species distribution models (SDMs) relies to a large degree on the quality of the input data, from bioclimatic indices to environmental and habitat descriptors (Austin, 2002). Recent reviews of SDM techniques, have sought to optimize predictive performance e.g. Elith et al., 2006. In general SDMs employ one of three approaches to variable selection. The simplest approach relies on the expert to select the variables, as in environmental niche models Nix, 1986 or a generalized linear model without variable selection (Miller and Franklin, 2002). A second approach explicitly incorporates variable selection into model fitting, which allows examination of particular combinations of variables. Examples include generalized linear or additive models with variable selection (Hastie et al. 2002); or classification trees with complexity or model based pruning (Breiman et al., 1984, Zeileis, 2008). A third approach uses model averaging, to summarize the overall contribution of a variable, without considering particular combinations. Examples include neural networks, boosted or bagged regression trees and Maximum Entropy as compared in Elith et al. 2006. Typically, users of SDMs will either consider a small number of variable sets, via the first approach, or else supply all of the candidate variables (often numbering more than a hundred) to the second or third approaches. Bayesian SDMs exist, with several methods for eliciting and encoding priors on model parameters (see review in Low Choy et al. 2010). However few methods have been published for informative variable selection; one example is Bayesian trees (O’Leary 2008). Here we report an elicitation protocol that helps makes explicit a priori expert judgements on the quality of candidate variables. This protocol can be flexibly applied to any of the three approaches to variable selection, described above, Bayesian or otherwise. We demonstrate how this information can be obtained then used to guide variable selection in classical or machine learning SDMs, or to define priors within Bayesian SDMs.