Arithmetical properties of Multiple Ramanujan sums

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page

Sums of products of Ramanujan sums

The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1,..., g_r$ are polynomials with integer coefficients. A modified orthogonality relation of the Ramanujan sums is also derived.Comment: 13 pages, revise

Polarizing Double Negation Translations

Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the polarization of the formul{\ae}{} and adapt those translation to the different connectives and quantifiers. We show that the embedding results still hold, using a customized version of the focused classical sequent calculus. We also prove the latter equivalent to more usual versions of the sequent calculus. This polarization process allows lighter embeddings, and sheds some light on the relationship between intuitionistic and classical connectives

A Smirnov-Bickel-Rosenblatt theorem for compactly-supported wavelets

In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the supremum norm of the variance term is asymptotically distributed as a Gumbel random variable. In the following, we prove a version of this result for estimators using compactly-supported wavelets, a popular tool in nonparametric statistics. Our result relies on an assumption on the nature of the wavelet, which must be verified by provably-good numerical approximations. We verify our assumption for Daubechies wavelets and symlets, with N = 6, ..., 20 vanishing moments; larger values of N, and other wavelet bases, are easily checked, and we conjecture that our assumption holds also in those cases

Could Large CP Violation Be Detected at Colliders?

We argue that CP--violation effects below a few tenths of a percent are probably undetectable at hadron and electron colliders. Thus only operators whose contributions interfere with tree--level Standard Model amplitudes are detectable. We list these operators for Standard Model external particles and some two and three body final state reactions that could show detectable effects. These could test electroweak baryogenesis scenarios.Comment: 11pp, LaTeX, UM--TH--92--27(massaged to make TeX output cleaner), no picture

On hyperovals of polar spaces

We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon E-3 has up to isomorphism a unique full embedding into the dual polar space DH(5, 4)

Repetition suppression and memory for faces is reduced in adults with autism spectrum conditions

Autism spectrum conditions (ASC) are associated with a number of atypicalities in face processing, including difficulties in face memory. However, the neural mechanisms underlying this difficulty are unclear. In neurotypical individuals, repeated presentation of the same face is associated with a reduction in activity, known as repetition suppression (RS), in the fusiform face area (FFA). However, to date, no studies have investigated RS to faces in individuals with ASC, or the relationship between RS and face memory. Here, we measured RS to faces and geometric shapes in individuals with a clinical diagnosis of an ASC and in age and IQ matched controls. Relative to controls, the ASC group showed reduced RS to faces in bilateral FFA and reduced performance on a standardized test of face memory. By contrast, RS to shapes in object-selective regions and object memory did not differ between groups. Individual variation in face memory performance was positively correlated with RS in regions of left parietal and prefrontal cortex. These findings suggest difficulties in face memory in ASC may be a consequence of differences in the way faces are stored and/or maintained across a network of regions involved in both visual perception and shortterm/ working memory

Dynamically Warped Theory Space and Collective Supersymmetry Breaking

We study deconstructed gauge theories in which a warp factor emerges dynamically and naturally. We present nonsupersymmetric models in which the potential for the link fields has translational invariance, broken only by boundary effects that trigger an exponential profile of vacuum expectation values. The spectrum of physical states deviates exponentially from that of the continuum for large masses; we discuss the effects of such exponential towers on gauge coupling unification. We also present a supersymmetric example in which a warp factor is driven by Fayet-Iliopoulos terms. The model is peculiar in that it possesses a global supersymmetry that remains unbroken despite nonvanishing D-terms. Inclusion of gravity and/or additional messenger fields leads to the collective breaking of supersymmetry and to unusual phenomenology.Comment: 28 pages LaTeX, JHEP format, 7 eps figures (v2: reference added

Phase transitions in BaTiO3_3 from first principles

We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultra-soft pseudopotential calculations. This approach is applied to BaTiO$_3$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder vs.\ displacive character of the transitions and the roles played by different interactions are discussed.Comment: 13 page