Scarring Effects on Tunneling in Chaotic Double-Well Potentials

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period {$2\pi\hbar$} in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-{$\hbar$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.Comment: 22 pages, including 11 figure

Eigenstate Structure in Graphs and Disordered Lattices

We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected from random matrix theory, even though the spectral statistics are in agreement with random matrix predictions. Instead, analytical calculations based on short-time semiclassical behavior correctly describe the eigenstate structure.Comment: 4 pages, including 2 figure

On the Disambiguation of Weighted Automata

We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its correctness. The algorithm is not applicable to all weighted automata but we prove sufficient conditions for its applicability in the case of the tropical semiring by introducing the *weak twins property*. In particular, the algorithm can be used with all acyclic weighted automata, relevant to applications. While disambiguation can sometimes be achieved using determinization, our disambiguation algorithm in some cases can return a result that is exponentially smaller than any equivalent deterministic automaton. We also present some empirical evidence of the space benefits of disambiguation over determinization in speech recognition and machine translation applications

Supersymmetry on a Spatial Lattice

We construct a variety of supersymmetric gauge theories on a spatial lattice, including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at the desired continuum limit in these examples.Comment: Version 3: Text brought in line with published version (extended discussion of orbifolding

Insects as a Source of Phenolic Compounds and Potential Health Benefits

The use of insects in traditional medicine and unveiling the chemical structure of the bright pigments in butterfly wings led to the discovery of bioactive phenolic compounds in the insect bodies. These metabolites have been found not only due to the insect absorption and metabolisation of the plant-derived phenolic present in their diet, but also from the ability of insects to synthesise phenolic compounds de novo through the sclerotisation process. Plant phenolics are secondary metabolites involved in the protection of tissues against UV radiation, herbivores, and pathogens, as well as pigmentation of fruits and flowers. These bioactive compounds exhibit antioxidant, anti-inflammatory, anticancer, and antimicrobial activities, demonstrated through in vitro and in vivo studies. This bioactive potential is thought to occur due to their chemical characteristics that allow them to stabilise reactive oxygen species (ROS), chelate prooxidant metal ions, interact with key enzymes and signal cascades involved in biological pathways. Bioactivity of plant phenolics and both in vitro, in vivo studies, suggest that the dietary compounds absorbed by the insect maintain their chemical and bioactive properties. Further characterisation of the phenolic composition in edible insects and evaluation of their bioactive capacity as well as their bioavailability, could result in discovering additional health benefits of entomophagy apart from macro-nutritional (e.g. protein) content

Phenomenology of the Littlest Higgs with T-Parity

Little Higgs models offer an interesting approach to weakly coupled electroweak symmetry breaking without fine tuning. The original little Higgs models were plagued by strong constraints from electroweak precision data which required a fine tuning to be reintroduced. An economical solution to this problem is to introduce a discrete symmetry (analogous to R-parity of SUSY) called T-parity. T-parity not only eliminates most constraints from electroweak precision data, but it also leads to a promising dark matter candidate. In this paper we investigate the dark matter candidate in the littlest Higgs model with T-parity. We find bounds on the symmetry breaking scale f as a function of the Higgs mass by calculating the relic density. We begin the study of the LHC phenomenology of the littlest Higgs model with T-parity. We find that the model offers an interesting collider signature that has a generic missing energy signal which could "fake" SUSY at the LHC. We also investigate the properties of the heavy partner of the top quark which is common to all littlest Higgs models, and how its properties are modified with the introduction of T-parity. We include an appendix with a list of Feynman rules specific to the littlest Higgs with T-parity to facilitate further study.Comment: 32 pages, 8 figures; dark matter bounds revised; comphep model files made publicly available at http://www.lns.cornell.edu/public/theory/tparity

Rapid encoding of task regularities in the human hippocampus guides sensorimotor timing

The brain encodes the statistical regularities of the environment in a task-specific yet flexible and generalizable format. Here, we seek to understand this process by bridging two parallel lines of research, one centered on sensorimotor timing, and the other on cognitive mapping in the hippocampal system. By combining functional magnetic resonance imaging (fMRI) with a fast-paced time-to-contact (TTC) estimation task, we found that the hippocampus signaled behavioral feedback received in each trial as well as performance improvements across trials along with reward-processing regions. Critically, it signaled performance improvements independent from the tested intervals, and its activity accounted for the trial-wise regression-to-the-mean biases in TTC estimation. This is in line with the idea that the hippocampus supports the rapid encoding of temporal context even on short time scales in a behavior-dependent manner. Our results emphasize the central role of the hippocampus in statistical learning and position it at the core of a brain-wide network updating sensorimotor representations in real time for flexible behavior

Nucleon-Nucleon Scattering under Spin-Isospin Reversal in Large-N_c QCD

The spin-flavor structure of certain nucleon-nucleon scattering observables derived from the large N_c limit of QCD in the kinematical regime where time-dependent mean-field theory is valid is discussed. In previous work, this regime was taken to be where the external momentum was of order N_c which precluded the study of differential cross sections in elastic scattering. Here it is shown that the regime extends down to order N_c^{1/2} which includes the higher end of the elastic regime. The prediction is that in the large N_c limit, observables describable via mean-field theory are unchanged when the spin and isospin of either nucleon are both flipped. This prediction is tested for proton-proton and neutron-proton elastic scattering data and found to fail badly. We argue that this failure can be traced to a lack of a clear separation of scales between momentum of order N_c^{1/2} and N_c^1 when N_c is as small as three. The situation is compounded by an anomalously low particle production threshold due to approximate chiral symmetry.Comment: 5 pages, 1 figur

Collective Quartics from Simple Groups

This article classifies Little Higgs models that have collective quartic couplings. There are two classes of collective quartics: Special Cosets and Special Quartics. After taking into account dangerous singlets, the smallest Special Coset models are SU(5)/SO(5) and SU(6)/Sp(6). The smallest Special Quartic model is SU(5)/SU(3) x SU(2) x U(1) and has not previously been considered as a candidate Little Higgs model.Comment: 22 pages, 2 figure