The A-decomposability of the Singer construction

Let $R_s M$ denote the Singer construction on an unstable module $M$ over the Steenrod algebra $A$ at the prime two; $R_s M$ is canonically a subobject of $P_s\otimes M$, where $P_s$ is the polynomial algebra on s generators of degree one. Passage to $A$-indecomposables gives the natural transformation $R_s M \rightarrow F \otimes_A (P_s \otimes M)$, which identifies with the dual of the composition of the Singer transfer and the Lannes-Zarati homomorphism. The main result of the paper proves the weak generalized algebraic spherical class conjecture, which was proposed by the first named author. Namely, this morphism is trivial on elements of positive degree when s>2. The condition s>2 is necessary, as exhibited by the spherical classes of Hopf invariant one and those of Kervaire invariant one.Comment: v2 15 pages. Minor revision. v3 17 pages, revision following referee's recommendations. Accepted for publication J. Al

B→a1(1260)a1(1260)B \to a_1(1260) a_1(1260) and b1(1235)b1(1235)b_1(1235) b_1(1235) decays in the perturbative QCD approach

In this work, we study six tree-dominated $B \to a_1(1260) a_1(1260)$ and $b_1(1235) b_1(1235)$ decays in the perturbative QCD(pQCD) approach, where $a_1$($b_1$) is a $^3P_1$($^1P_1$) axial-vector meson. Based on the perturbative calculations and phenomenological analysis, we find that: (a) the CP-averaged branching ratio of $B^0 \to a_1^+ a_1^-$ decay in the pQCD approach is $54.7 \times 10^{-6}$, which agrees well with the current data and the predictions given in the QCD factorization approach within errors; (b) the numerical results for the decay rates of other five channels are found to be in the order of $10^{-6} \sim 10^{-5}$, which could be accessed at B factories and Large Hadron Collider(LHC) experiments; (c) other physical observables such as polarization fractions and direct CP-violating asymmetries are also investigated with the pQCD approach in the present work and the predictions can be confronted with the relevant experiments in the near future; (d) the different phenomenologies shown between $B \to a_1 a_1$ and $B \to b_1 b_1$ decays are expected to be tested by the ongoing LHC and forthcoming Super-B experiments, which could shed light on the typical QCD dynamics involved in these decay modes, as well as in $^3P_1$ meson $a_1$ and $^1P_1$ meson $b_1$.Comment: 1 figure, 27 pages, references added, improved version. Accepted for publication in Phys. Rev.

Time-varying Huygens' meta-devices for parametric waves

Huygens' metasurfaces have demonstrated almost arbitrary control over the shape of a scattered beam, however, its spatial profile is typically fixed at fabrication time. Dynamic reconfiguration of this beam profile with tunable elements remains challenging, due to the need to maintain the Huygens' condition across the tuning range. In this work, we experimentally demonstrate that a time-varying metadevice which performs frequency conversion can steer transmitted or reflected beams in an almost arbitrary manner, with fully dynamic control. Our time-varying Huygens' metadevice is made of both electric and magnetic meta-atoms with independently controlled modulation, and the phase of this modulation is imprinted on the scattered parametric waves, controlling their shapes and directions. We develop a theory which shows how the scattering directionality, phase and conversion efficiency of sidebands can be manipulated almost arbitrarily. We demonstrate novel effects including all-angle beam steering and frequency-multiplexed functionalities at microwave frequencies around 4 GHz, using varactor diodes as tunable elements. We believe that the concept can be extended to other frequency bands, enabling metasurfaces with arbitrary phase pattern that can be dynamically tuned over the complete 2\pi range

Multistability in nonlinear left-handed transmission lines

Employing a nonlinear left-handed transmission line as a model system, we demonstrate experimentally the multi-stability phenomena predicted theoretically for microstructured left-handed metamaterials with a nonlinear response. We show that the bistability is associated with the period doubling which at higher power may result in chaotic dynamics of the transmission line

Rotational tuning of interaction in metamaterials

We experimentally observe the tuning of metamaterials through the relative rotation of the elements about their common axis. In contrast to previous results we observe a crossing of resonances, where the symmetric and anti-symmetric modes become degenerate. We associate this effect with an interplay between the magnetic and electric near-field interactions and verify this by calculations based on the interaction energy between resonators

The role of Uncertainty in Categorical Perception Utilizing Statistical Learning in Robots

At the heart of statistical learning lies the concept of uncertainty. Similarly, embodied agents such as robots and animals must likewise address uncertainty, as sensation is always only a partial reflection of reality. This thesis addresses the role that uncertainty can play in a central building block of intelligence: categorization. Cognitive agents are able to perform tasks like categorical perception through physical interaction (active categorical perception; ACP), or passively at a distance (distal categorical perception; DCP). It is possible that the former scaffolds the learning of the latter. However, it is unclear whether DCP indeed scaffolds ACP in humans and animals, nor how a robot could be trained to likewise learn DCP from ACP. Here we demonstrate a method for doing so which involves uncertainty: robots perform ACP when uncertain and DCP when certain. Furthermore, we demonstrate that robots trained in such a manner are more competent at categorizing novel objects than robots trained to categorize in other ways. This suggests that such a mechanism would also be useful for humans and animals, suggesting that they may be employing some version of this mechanism