Non-Beiter ternary cyclotomic polynomials with an optimally large set of coefficients

Let l>=1 be an arbitrary odd integer and p,q and r primes. We show that there exist infinitely many ternary cyclotomic polynomials \Phi_{pqr}(x) with l^2+3l+5<= p<q<r such that the set of coefficients of each of them consists of the p integers in the interval [-(p-l-2)/2,(p+l+2)/2]. It is known that no larger coefficient range is possible. The Beiter conjecture states that the cyclotomic coefficients a_{pqr}(k) of \Phi_{pqr} satisfy |a_{pqr}(k)|<= (p+1)/2 and thus the above family contradicts the Beiter conjecture. The two already known families of ternary cyclotomic polynomials with an optimally large set of coefficients (found by G. Bachman) satisfy the Beiter conjecture.Comment: 20 pages, 7 Table

Quantitative measurement of permeabilization of living cells by terahertz attenuated total reflection

International audienceUsing Attenuated Total Reflection imaging technique in the terahertz domain, we demonstrate non-invasive, non-staining real time measurements of cytoplasm leakage during permeabilization of epithelial cells by saponin. The terahertz signal is mostly sensitive to the intracellular protein concentration in the cells, in a very good agreement with standard bicinchoninic acid protein measurements. It opens the way to in situ real time dynamics of protein content and permeabilization in live cells

On the decomposition of finite-valued streaming string transducers

We prove the following decomposition theorem: every 1-register streaming string transducer that associates a uniformly bounded number of outputs with each input can be effectively decomposed as a finite union of functional 1-register streaming string transducers. This theorem relies on a combinatorial result by Kortelainen concerning word equations with iterated factors. Our result implies the decidability of the equivalence problem for the considered class of transducers. This can be seen as a first step towards proving a more general decomposition theorem for streaming string transducers with multiple registers

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page

Nonstandard Drinfeld-Sokolov reduction

Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0), where the $d_i$ are $\Z$-gradations of a loop algebra \A and \Lambda\in \A is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the $d_1$-grade zero part of \A into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil

Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling

We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement

The Singularity Problem for Space-Times with Torsion

The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their definition of geodesics only involves the Christoffel connection, though studying theories with torsion. We propose a preliminary definition of singularities which is based on timelike or null geodesic incompleteness, even though for theories with torsion the paths of particles are not geodesics. The study of the geodesic equation for cosmological models with torsion shows that the definition has a physical relevance. It can also be motivated, as done in the literature, remarking that the causal structure of a space-time with torsion does not get changed with respect to general relativity. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychaudhuri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Hawking's theorem can be generalized, provided the torsion tensor obeys some conditions. Thus our result can also be interpreted as a no-singularity theorem if these additional conditions are not satisfied. In other words, it turns out that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity. Our work is to be compared with previous papers in the literature. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy momentum tensor,Comment: 17 pages, plain-tex, published in Nuovo Cimento B, volume 105, pages 75-90, year 199

Quantum projection filter for a highly nonlinear model in cavity QED

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.Comment: 19 pages, 6 figures. A version with high quality images can be found at http://minty.caltech.edu/papers.ph