Fast optimization algorithms and the cosmological constant

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order $10^{-120}$ in a randomly generated $10^9$-dimensional ADK landscape.Comment: 19 pages, 5 figure

Behavior of Complex Knots in Single DNA Molecules

We used optical tweezers to tie individual DNA molecules in knots. Although these knots become highly localized under tension, they remain surprisingly mobile and undergo thermal diffusion with classical random walk statistics. The diffusion constants of knots with different complexities correlate with theoretical calculations of knot sizes. We show that this correlation can be explained by a simple hydrodynamical model of "self-reptation" of the knot along a polymer

GUANIDINIUM COMPOUNDS

The present application provides , inter alia , chemical com pounds useful as synthesis intermediates , said compounds comprising one or more guanidinium moieties and a hyper valent iodine atom . Methods for making these compounds are also provided

RADIOIODINATED COMPOUNDS

This disclosure relates to reagents and methods useful in the synthesis of aryl iodines ,for example , in the preparation of iodine labeled radiotracers . The reagents and methods provided herein may be used to access a broad range of compounds , including aromatic compounds , heteroaromatic compounds , amino acids , nucleotides , and synthetic com pounds

RADIOIODINATED COMPOUNDS

This disclosure relates to reagents and methods useful in the synthesis of aryl iodines ,for example , in the preparation of iodine labeled radiotracers . The reagents and methods provided herein may be used to access a broad range of compounds , including aromatic compounds , heteroaromatic compounds , amino acids , nucleotides , and synthetic com pounds

Algebraic structures for adjoint-symmetries and symmetries of partial differential equations

Symmetries of a partial differential equation (PDE) can be defined as the solutions of the linearization (Frechet derivative) equation holding on the space of solutions to the PDE, and they are well-known to comprise a linear space having the structure of a Lie algebra. Solutions of the adjoint linearization equation holding on the space of solutions to the PDE are called adjoint-symmetries. Their algebraic structure for general PDE systems is studied herein. This is motivated by the correspondence between variational symmetries and conservation laws arising from Noether's theorem, which has a well-known generalization to non-variational PDEs, where symmetries are replaced by adjoint-symmetries, and variational symmetries are replaced by multipliers (adjoint-symmetries satisfying a certain Euler-Lagrange condition). Several main results are obtained. Symmetries are shown to have three different linear actions on the linear space of adjoint-symmetries. These linear actions are used to construct bilinear adjoint-symmetry brackets, one of which is like a pull-back of the symmetry commutator bracket and has the properties of a Lie bracket. In the case of variational PDEs, adjoint-symmetries coincide with symmetries, and the linear actions themselves constitute new bilinear symmetry brackets which differ from the commutator bracket when acting on non-variational symmetries. Several examples of nonlinear PDEs are used to illustrate all of the results.Comment: 32 pages; minor change

The limited capacity of visual temporal integration in cats

It has been long known that prolonging stimulus duration may increase the perceived brightness of a visual stimulus. The interaction between intensity and duration generally follows a rule, such as that described in Bloch\u27s law. This visual temporal integration relationship has been identified in human subjects and in non-human primates. However, although auditory temporal integration has been extensively studied in the cat, visual temporal integration has not. Therefore, the goal of this study was to examine visual temporal integration in the cat. We trained five cats to respond when a brief luminance change was detected in a fixation dot. After training, we measured the success rate of detecting the luminance change with varying durations at threshold, subthreshold, and suprathreshold luminance levels. Psychometric functions showed that prolonging stimulus duration improved task performance, more noticeably for stimuli below 100 ms than beyond. Most psychometric functions were better fit to an exponential model than to a linear model. The gradually saturated performance observed here, as in previous studies, can be explained by the leaky integrator hypothesis, that is, temporal integration is only valid below a critical duration. Overall, we developed a task whereby visual temporal integration was successfully demonstrated in the cat. The effect of stimulus duration on detection success rate displayed a pattern generally consistent with previous human and non-human primate findings on visual temporal integration