Simple threshold rules solve explore/exploit trade‐offs in a resource accumulation search task

How, and how well, do people switch between exploration and exploitation to search for and accumulate resources? We study the decision processes underlying such exploration/exploitation trade‐offs using a novel card selection task that captures the common situation of searching among multiple resources (e.g., jobs) that can be exploited without depleting. With experience, participants learn to switch appropriately between exploration and exploitation and approach optimal performance. We model participants' behavior on this task with random, threshold, and sampling strategies, and find that a linear decreasing threshold rule best fits participants' results. Further evidence that participants use decreasing threshold‐based strategies comes from reaction time differences between exploration and exploitation; however, participants themselves report non‐decreasing thresholds. Decreasing threshold strategies that “front‐load” exploration and switch quickly to exploitation are particularly effective in resource accumulation tasks, in contrast to optimal stopping problems like the Secretary Problem requiring longer exploration

A Field Range Bound for General Single-Field Inflation

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models. This shows that non-trivial dynamics can't evade the Lyth bound. We also present a weaker, but completely universal bound that holds whenever the Null Energy Condition (NEC) is satisfied at horizon crossing.Comment: 16 page

Kinetics of the long-range spherical model

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo

Desensitizing Inflation from the Planck Scale

A new mechanism to control Planck-scale corrections to the inflationary eta parameter is proposed. A common approach to the eta problem is to impose a shift symmetry on the inflaton field. However, this symmetry has to remain unbroken by Planck-scale effects, which is a rather strong requirement on possible ultraviolet completions of the theory. In this paper, we show that the breaking of the shift symmetry by Planck-scale corrections can be systematically suppressed if the inflaton field interacts with a conformal sector. The inflaton then receives an anomalous dimension in the conformal field theory, which leads to sequestering of all dangerous high-energy corrections. We analyze a number of models where the mechanism can be seen in action. In our most detailed example we compute the exact anomalous dimensions via a-maximization and show that the eta problem can be solved using only weakly-coupled physics.Comment: 34 pages, 3 figures

Ageing without detailed balance: local scale invariance applied to two exactly solvable models

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass Transition" held in Luxemburg in September 05. Published versio

High power 405 nm diode laser fiber-coupled single-mode system with high long-term stability

Fiber-coupled 405 nm diode laser systems are rarely used with fiber output powers higher than 50 mW. A quick degradation of fiber-coupled high power modules with wavelengths in the lower range of the visible spectrum is known for several years. Meanwhile, the typical power of single-mode diode lasers around 400 nm is in the order of 100 to 300 mW, leading to single-mode fiber core power densities in the 1 MW/cm² range. This is three magnitudes of order below the known threshold for optical damage. Our profound investigations on the influence of 405 nm laser light irradiation of single-mode fibers found the growth of periodic surface structures in the form of ripples responsible for the power loss. The ripples are found on the proximal and distal fiber end surfaces, negatively impacting power transmission and beam quality, respectively. Important parameters in the generation of the surface structures are power density, surface roughness and polarization direction. A fiber-coupled high-power 405 nm diode laser system with a high long-term stability will be introduced and described

D3-brane Potentials from Fluxes in AdS/CFT

We give a comprehensive treatment of the scalar potential for a D3-brane in a warped conifold region of a compactification with stabilized moduli. By studying general ultraviolet perturbations in supergravity, we systematically incorporate `compactification effects' sourced by supersymmetry breaking in the compact space. Significant contributions to the D3-brane potential, including the leading term in the infrared, arise from imaginary anti-self-dual (IASD) fluxes. For an arbitrary Calabi-Yau cone, we determine the most general IASD fluxes in terms of scalar harmonics, then compute the resulting D3-brane potential. Specializing to the conifold, we identify the operator dual to each mode of flux, and for chiral operators we confirm that the potential computed in the gauge theory matches the gravity result. The effects of four-dimensional curvature, including the leading D3-brane mass term, arise directly from the ten-dimensional equations of motion. Furthermore, we show that gaugino condensation on D7-branes provides a local source for IASD flux. This flux precisely encodes the nonperturbative contributions to the D3-brane potential, yielding a promising ten-dimensional representation of four-dimensional nonperturbative effects. Our result encompasses all significant contributions to the D3-brane potential discussed in the literature, and does so in the single coherent framework of ten-dimensional supergravity. Moreover, we identify new terms with irrational scaling dimensions that were inaccessible in prior works. By decoupling gravity in a noncompact configuration, then systematically reincorporating compactification effects as ultraviolet perturbations, we have provided an approach in which Planck-suppressed contributions to the D3-brane effective action can be computed.Comment: 70 page