Implications of an arithmetical symmetry of the commutant for modular invariants

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3)_k, we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants.Comment: 17 pages, plain TeX, DIAS-STP-92-2

Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.Comment: 16 pp, plain te

Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality

We show that the generating functions of avalanche observables in SOC models exhibits a Lee-Yang phenomenon. This establishes a new link between the classical theory of critical phenomena and SOC. A scaling theory of the Lee-Yang zeroes is proposed including finite sampling effects.Comment: 33 pages, 19 figures, submitte

On the Classification of Diagonal Coset Modular Invariants

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all positive integer level $k$, and $su(2)_k\oplus su(2)_\ell/su(2)_{k+\ell}$ for all $k$ and infinitely many $\ell$ (in fact, for each $k$ a positive density of $\ell$). Of all these classifications, only that for $su(2)_k\oplus su(2)_1/su(2)_{k+1}$ had been known. Our lists include many new invariants.Comment: 24 pp (plain tex

A 12.5 GHz-Spaced Optical Frequency Comb Spanning >400 nm for near-Infrared Astronomical Spectrograph Calibration

A 12.5 GHz-spaced optical frequency comb locked to a Global Positioning disciplined oscillator for near-IR spectrograph calibration is presented. The comb is generated via filtering a 250 MHz-spaced comb. Subsequency nonlinear broadening of the 12.5 GHz comb extends the wavelength range to cover 1380 nm to 1820 nm, providing complete coverage over the H-band transmission widow of Earth's atmosphere. Finite suppression of spurious sidemodes, optical linewidth and instability of the comb have been examined to estmiate potential wavelength biases in spectrograph calibration. Sidemode suppression varies between 20 db and 45 dB, and the optical linewidth is ~350 kHz at 1550 nm. The comb frequency uncertainty is bounded by +/- 30 kHz (corresponding to a radial velocity of +/- 5 cm/s), limited by the Global Positioning System disciplined oscillator reference. These results indicate this comb can readily support radial velocity measurements below 1 m/s in the near-IR.Comment: 16 pages, 12 figures, new file fixes some readability problems on Mac

The approach to thermal equilibrium in quantized chaotic systems

We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables, assuming that the system is in a definite (but arbitrary) pure quantum state. We induce a probability distribution for the expectation values by treating the zero of time as a uniformly distributed random variable. We show explicitly that if an observable has a nonequilibrium expectation value at some particular moment, then it is overwhelmingly likely to move towards equilibrium, both forwards and backwards in time. For deviations from equilibrium that are not much larger than a typical quantum or thermal fluctuation, we find that the time dependence of the move towards equilibrium is given by the Kubo correlation function, in agreement with Onsager's postulate. These results are independent of the details of the system's quantum state.Comment: 15 pages, no figures; some arguments are clarified in the revised versio

An investigation of the apparent breast cancer epidemic in France: screening and incidence trends in birth cohorts

<p>Abstract</p> <p>Background</p> <p>Official descriptive data from France showed a strong increase in breast-cancer incidence between 1980 to 2005 without a corresponding change in breast-cancer mortality. This study quantifies the part of incidence increase due to secular changes in risk factor exposure and in overdiagnosis due to organised or opportunistic screening. Overdiagnosis was defined as non progressive tumours diagnosed as cancer at histology or progressive cancer that would remain asymptomatic until time of death for another cause.</p> <p>Methods</p> <p>Comparison between age-matched cohorts from 1980 to 2005. All women residing in France and born 1911-1915, 1926-1930 and 1941-1945 are included. Sources are official data sets and published French reports on screening by mammography, age and time specific breast-cancer incidence and mortality, hormone replacement therapy, alcohol and obesity. Outcome measures include breast-cancer incidence differences adjusted for changes in risk factor distributions between pairs of age-matched cohorts who had experienced different levels of screening intensity.</p> <p>Results</p> <p>There was an 8-fold increase in the number of mammography machines operating in France between 1980 and 2000. Opportunistic and organised screening increased over time. In comparison to age-matched cohorts born 15 years earlier, recent cohorts had adjusted incidence proportion over 11 years that were 76% higher [95% confidence limits (CL) 67%, 85%] for women aged 50 to 64 years and 23% higher [95% CL 15%, 31%] for women aged 65 to 79 years. Given that mortality did not change correspondingly, this increase in adjusted 11 year incidence proportion was considered as an estimate of overdiagnosis.</p> <p>Conclusions</p> <p>Breast cancer may be overdiagnosed because screening increases diagnosis of slowly progressing non-life threatening cancer and increases misdiagnosis among women without progressive cancer. We suggest that these effects could largely explain the reported "epidemic" of breast cancer in France. Better predictive classification of tumours is needed in order to avoid unnecessary cancer diagnoses and subsequent procedures.</p