Exponential Hierarchy From Spacetime Variable String Vacua

It is shown that non-supersymmetric spacetime varying string vacua can lead to an exponential hierarchy between the electroweak and the gravitational scales. The hierarchy is naturally generated by a string coupling of O(1).Comment: 22 pages, Latex, 2 figure

On Relativistic Brane Probes in Singular Spacetimes

We study the relativistic dynamics of brane probes in singular warped spacetimes and establish limits for such analysis. The behavior of the semiclassical brane probe wave functions implies that unitarity boundary conditions can be imposed at the singularity.Comment: 9 pages, 1 figure, typos corrected and references adde

The effect of additive noise on dynamical hysteresis

We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure

On Semi-Periods

The periods of the three-form on a Calabi-Yau manifold are found as solutions of the Picard-Fuchs equations; however, the toric varietal method leads to a generalized hypergeometric system of equations which has more solutions than just the periods. This same extended set of equations can be derived from symmetry considerations. Semi-periods are solutions of this extended system. They are obtained by integration of the three-form over chains; these chains can be used to construct cycles which, when integrated over, give periods. In simple examples we are able to obtain the complete set of solutions for the extended system. We also conjecture that a certain modification of the method will generate the full space of solutions in general.Comment: 18 pages, plain TeX. Revised derivation of $\Delta^*$ system of equations; version to appear in Nuclear Physics

Expand+Functional selection and systematic analysis of intronic splicing elements identify active sequence motifs and associated splicing factors

Despite the critical role of pre-mRNA splicing in generating proteomic diversity and regulating gene expression, the sequence composition and function of intronic splicing regulatory elements (ISREs) have not been well elucidated. Here, we employed a high-throughput in vivo Screening PLatform for Intronic Control Elements (SPLICE) to identify 125 unique ISRE sequences from a random nucleotide library in human cells. Bioinformatic analyses reveal consensus motifs that resemble splicing regulatory elements and binding sites for characterized splicing factors and that are enriched in the introns of naturally occurring spliced genes, supporting their biological relevance. In vivo characterization, including an RNAi silencing study, demonstrate that ISRE sequences can exhibit combinatorial regulatory activity and that multiple trans-acting factors are involved in the regulatory effect of a single ISRE. Our work provides an initial examination into the sequence characteristics and function of ISREs, providing an important contribution to the splicing code

On Periods for String Compactifications

Motivated by recent developments in the computation of periods for string compactifications with $c=9$, we develop a complementary method which also produces a convenient basis for related calculations. The models are realized as Calabi--Yau hypersurfaces in weighted projective spaces of dimension four or as Landau-Ginzburg vacua. The calculation reproduces known results and also allows a treatment of Landau--Ginzburg orbifolds with more than five fields.Comment: HUPAPP-93/6, IASSNS-HEP-93/80, UTTG-27-93. 21 pages,harvma

Universality of residence-time distributions in non-adiabatic stochastic resonance

We present mathematically rigorous expressions for the residence-time and first-passage-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distributions are close to periodically modulated exponential ones. Remarkably, the periodic modulations are governed by universal functions, depending on a single parameter related to the forcing period. The behaviour of the distributions and their moments is analysed, in particular in the low- and high-frequency limits.Comment: 8 pages, 1 figure New version includes distinction between first-passage-time and residence-time distribution

Mechanics of universal horizons

Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or Einstein-{\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.Comment: Minor clarifications. References update

Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main idea is to show that for sufficiently small noise intensity and slow time dependence, the vast majority of paths remain in small space-time sets, typically in the neighbourhood of potential wells. The size of these sets often has a power-law dependence on the small parameters, with universal exponents. The overall probability of exceptional paths is exponentially small, with an exponent also showing power-law behaviour. The results cover time spans up to the maximal Kramers time of the system. We apply our method to three phenomena characteristic for bistable systems: stochastic resonance, dynamical hysteresis and bifurcation delay, where it yields precise bounds on transition probabilities, and the distribution of hysteresis areas and first-exit times. We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure