Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Measurement of quantum weak values of photon polarization

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S-1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.

Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation

Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this approach can overcome decoherence effects. Our numerical study shows that nonlinearity of weak strength could be useful for macroscopic entanglement generation and quantum gate operations in the presence of decoherence. We suggest specific values for real experiments based on our analysis. Our discussion shows that the generation of macroscopic entanglement using this approach is within the reach of current technology.

Strong and weak lifespan extension: What is most feasible and likely?

Recent advances in biomedical science indicate that it may eventually be possible to intervene in the biological process of human ageing. This paper overviews the current state of the science of lifespan extension and promising future directions. It is uncertain whether 'strong' lifespan extension - the extension of human life beyond the maximum 122 years so far observed - will become a reality. It is more likely that cumulative effects of numerous scientific and biomedical advances in the treatment of common disease will produce 'weak' lifespan extension - the extension of average life expectancy. The practical application of molecular, genetic and nanomaterials research may also lead to advances in life expectancy. It is not too early to begin to consider the policy implications of either form of lifespan extension.

Quantum computation using weak nonlinearities: Robustness against decoherence

We investigate decoherence effects in the recently suggested quantum-computation scheme using weak nonlinearities, strong probe coherent fields, detection, and feedforward methods. It is shown that in the weak-nonlinearity-based quantum gates, decoherence in nonlinear media can be made arbitrarily small simply by using arbitrarily strong probe fields, if photon-number-resolving detection is used. On the contrary, we find that homodyne detection with feedforward is not appropriate for this scheme because in this case decoherence rapidly increases as the probe field gets larger.

Language against the odds, or rather not:the weak central coherence hypothesis and language

EV is a child with a talent for learning language combined with Asperger syndrome. EV’s talent is evident in the unusual circumstances of her acquisition of both her first (Bulgarian) and second (German) languages and the unique patterns of both receptive and expressive language (in both the L1 and L2), in which she shows subtle dissociations in competence and performance consistent with an uneven cognitive profile of skills and abilities. We argue that this case provides support for theories of language learning and usage that require more general underlying cognitive mechanisms and skills. One such account, the Weak Central Coherence (WCC) hypothesis of autism, provides a plausible framework for the interpretation of the simultaneous co-occurrence of EV’s particular pattern of cognitive strengths and weaknesses. Furthermore, we show that specific features of the uneven cognitive profile of Asperger syndrome can help explain the observed language talent displayed by EV. Thus, rather than demonstrating a case where language learning takes place despite the presence of deficits, EV’s case illustrates how a pattern of strengths within this profile can specifically promote language learning.

Interocular transfer of spatial adaptation is weak at low spatial frequencies

Adapting one eye to a high contrast grating reduces sensitivity to similar target gratings shown to the same eye, and also to those shown to the opposite eye. According to the textbook account, interocular transfer (IOT) of adaptation is around 60% of the within-eye effect. However, most previous studies on this were limited to using high spatial frequencies, sustained presentation, and criterion-dependent methods for assessing threshold. Here, we measure IOT across a wide range of spatiotemporal frequencies, using a criterion-free 2AFC method. We find little or no IOT at low spatial frequencies, consistent with other recent observations. At higher spatial frequencies, IOT was present, but weaker than previously reported (around 35%, on average, at 8c/deg). Across all conditions, monocular adaptation raised thresholds by around a factor of 2, and observers showed normal binocular summation, demonstrating that they were not binocularly compromised. These findings prompt a reassessment of our understanding of the binocular architecture implied by interocular adaptation. In particular, the output of monocular channels may be available to perceptual decision making at low spatial frequencies.