Dualities in CHL-Models

We define a very general class of CHL-models associated with any string theory (bosonic or supersymmetric) compactified on an internal CFT C x T^d. We take the orbifold by a pair (g,\delta), where g is a (possibly non-geometric) symmetry of C and \delta is a translation along T^d. We analyze the T-dualities of these models and show that in general they contain Atkin-Lehner type symmetries. This generalizes our previous work on N=4 CHL-models based on heterotic string theory on T^6 or type II on K3 x T^2, as well as the `monstrous' CHL-models based on a compactification of heterotic string theory on the Frenkel-Lepowsky-Meurman CFT V^{\natural}.Comment: 18 page

Time-frequency methods for coherent spectroscopy

Time-frequency decomposition techniques, borrowed from the signal-processing field, have been adapted and applied to the analysis of 2D oscillating signals. While the Fourier-analysis techniques available so far are able to interpret the information content of the oscillating signal only in terms of its frequency components, the time-frequency transforms (TFT) proposed in this work can instead provide simultaneously frequency and time resolution, unveiling the dynamics of the relevant beating components, and supplying a valuable help in their interpretation. In order to fully exploit the potentiality of this method, several TFTs have been tested in the analysis of sample 2D data. Possible artifacts and sources of misinterpretation have been identified and discussed

The Singular Locus of the Theta Divisor and Quadrics through a Canonical Curve

A section K on a genus g canonical curve C is identified as the key tool to prove new results on the geometry of the singular locus Theta_s of the theta divisor. The K divisor is characterized by the condition of linear dependence of a set of quadrics containing C and naturally associated to a degree g effective divisor on C. K counts the number of intersections of special varieties on the Jacobian torus defined in terms of Theta_s. It also identifies sections of line bundles on the moduli space of algebraic curves, closely related to the Mumford isomorphism, whose zero loci characterize special varieties in the framework of the Andreotti-Mayer approach to the Schottky problem, a result which also reproduces the only previously known case g=4. This new approach, based on the combinatorics of determinantal relations for two-fold products of holomorphic abelian differentials, sheds light on basic structures, and leads to the explicit expressions, in terms of theta functions, of the canonical basis of the abelian holomorphic differentials and of the constant defining the Mumford form. Furthermore, the metric on the moduli space of canonical curves, induced by the Siegel metric, which is shown to be equivalent to the Kodaira-Spencer map of the square of the Bergman reproducing kernel, is explicitly expressed in terms of the Riemann period matrix only, a result previously known for the trivial cases g=2 and g=3. Finally, the induced Siegel volume form is expressed in terms of the Mumford form.Comment: 88+1 page

Vector-Valued Modular Forms from the Mumford Form, Schottky-Igusa Form, Product of Thetanullwerte and the Amazing Klein Formula

Vector-valued Siegel modular forms are the natural generalization of the classical elliptic modular forms as seen by studying the cohomology of the universal abelian variety. We show that for g>=4, a new class of vector-valued modular forms, defined on the Teichmuller space, naturally appears from the Mumford forms, a question directly related to the Schottky problem. In this framework we show that the discriminant of the quadric associated to the complex curves of genus 4 is proportional to the square root of the products of Thetanullwerte \chi_{68}, which is a proof of the recently rediscovered Klein `amazing formula'. Furthermore, it turns out that the coefficients of such a quadric are derivatives of the Schottky-Igusa form evaluated at the Jacobian locus, implying new theta relations involving the latter, \chi_{68} and the theta series corresponding to the even unimodular lattices E_8\oplus E_8 and D_{16}^+. We also find, for g=4, a functional relation between the singular component of the theta divisor and the Riemann period matrix.Comment: 17 pages. Final version in Proc. Amer. Math. So

Higher genus partition functions of meromorphic conformal field theories

It is shown that the higher genus vacuum amplitudes of a meromorphic conformal field theory determine the affine symmetry of the theory uniquely, and we give arguments that suggest that also the representation content with respect to this affine symmetry is specified, up to automorphisms of the finite Lie algebra. We illustrate our findings with the self-dual theories at c=16 and c=24; in particular, we give an elementary argument that shows that the vacuum amplitudes of the E_8\times E_8 theory and the Spin(32)/Z_2 theory differ at genus g=5. The fact that the discrepancy only arises at rather high genus is a consequence of the modular properties of higher genus amplitudes at small central charges. In fact, we show that for c\leq 24 the genus one partition function specifies already the partition functions up to g\leq 4 uniquely. Finally we explain how our results generalise to non-meromorphic conformal field theories.Comment: 43 pages, 7 figure

Branching Asymptotics on Manifolds with Edge

We study pseudo-differential operators on a wedge with continuous and variable discrete branching asymptotics.Comment: 54 pages, 1 figure

Tailoring Targeted Therapy to Individual Patients: Lessons to be Learnt from the Development of Mitomycin C

The modern era of targeted therapeutics offers the potential to tailor therapy to individual patients whose tumours express a specific target. Previous attempts to forecast tumour response to conventional chemotherapeutics based on similar principles have however been disappointing. Mitomycin C (MMC), for example, is a bioreductive drug that requires metabolic activation by cellular reductases for activity. The enzyme NAD(P)H:Quinone oxidoreductase-1 (NQO1) can reduce MMC to DNA damaging species but attempts to establish the relationship between tumour response to MMC and NQO1 expression have generated conflicting reports of good and poor correlations. Several other reductases are known to activate MMC. This, in conjunction with the fact that various physiological and biochemical factors influence therapeutic response, suggests that the mechanism of action of MMC is too complex to allow tumour response to be predicted on the basis of a single enzyme. Alternative approaches using more complex biological and pharmacological systems that reflect the spectrum of reductases present within the tumour have been developed and it remains to be seen whether or not the predictive value of these approaches is enhanced. With regards to targeted therapeutics, the experience with MMC suggests that prediction of tumour response based on analysis of a single target may be too simplistic. Multiple mechanisms of action and the influence of tumour microenvironment on cell biology and drug delivery are likely to influence the final outcome of therapy. The challenge for the future progression of this field is to develop assays that reflect the overall biological and pharmacological processes involved in drug activation whilst retaining the simplicity and robustness required for routine chemosensitivity testing in a clinical setting

Old and new approaches to marketing. The quest of their epistemological roots

In recent years the marketing discipline faced a considerable increase in the number of approaches. Some of the new "labels" are probably just new names advertised to sell old products. But some may contain significant new issues that need to be identified and discussed. Do these new marketing denominations (viral, retro, vintage, postmodern, judo, tribal, buzz, and many more) identify distinctions on subjects being studied, without particular methodological implications, or rather, do new labels and new subjects imply orientations that start from different epistemological premises and involve different research methodologies? This paper try to investigate if the proliferation of labels related to alleged new methods of marketing analysis actually implies a distinctions of subjects being studied and different epistemological premises.marketing trends, marketing epistemology

On symmetries of N=(4,4) sigma models on T^4

Motivated by an analogous result for K3 models, we classify all groups of symmetries of non-linear sigma models on a torus T^4 that preserve the N=(4,4) superconformal algebra. The resulting symmetry groups are isomorphic to certain subgroups of the Weyl group of E8, that plays a role similar to the Conway group for the case of K3 models. Our analysis heavily relies on the triality automorphism of the T-duality group SO(4,4,Z). As a byproduct of our results, we discover new explicit descriptions of K3 models as asymmetric orbifolds of torus CFTs.Comment: 42 pages; minor changes, references added; version accepted for publicatio