On weighted norm inequalities for the Carleson and Walsh-Carleson operators

We prove $L^p(w)$ bounds for the Carleson operator ${\mathcal C}$, its lacunary version $\mathcal C_{lac}$, and its analogue for the Walsh series \W in terms of the $A_q$ constants $[w]_{A_q}$ for $1\le q\le p$. In particular, we show that, exactly as for the Hilbert transform, $\|{\mathcal C}\|_{L^p(w)}$ is bounded linearly by $[w]_{A_q}$ for $1\le q<p$. We also obtain $L^p(w)$ bounds in terms of $[w]_{A_p}$, whose sharpness is related to certain conjectures (for instance, of Konyagin \cite{K2}) on pointwise convergence of Fourier series for functions near $L^1$. Our approach works in the general context of maximally modulated Calder\'on-Zygmund operators.Comment: A major revision of arXiv: 1310.3352. In particular, the main result is proved under a different assumption, and applications to the lacunary Carleson operator and to the Walsh-Carleson operator are give

Patterns of variability in early life traits of a Mediterranean coastal fish

Spawning dates and pelagic larval duration (PLD) are early life traits (ELT) crucial for understanding life cycles, properly assessing patterns of connectivity and gathering indications about patchiness or homogeneity of larval pools. Considering that little attention has been paid to spatial variability in these traits, we investigated variability of ELT from the analysis of otolith microstructure in the common two-banded sea bream Diplodus vulgaris. In the southwestern Adriatic Sea, along ~200 km of coast (∼1° in latitude, 41.2° to 40.2°N), variability of ELT was assessed at multiple spatial scales. Overall, PLD (ranging from 25 to 61 d) and spawning dates (October 2009 to February 2010) showed significant variability at small scales (i.e. &lt;6 km), but not at larger scales. These outcomes suggest patchiness of the larval pool at small spatial scales. Multiple causal processes underlying the observed variability are discussed, along with the need to properly consider spatial variability in ELT, for example when delineating patterns of connectivity. Copyright © 2013 Inter-Research

Attachment styles as predictors of Facebook-related jealousy and surveillance in romantic relationships

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsFacebook has become ubiquitous over the past five years, yet few studies have examined its role within romantic relationships. In two studies, we tested attachment anxiety and avoidance as predictors of Facebook-related jealousy and surveillance (i.e., checking a romantic partner’s Facebook page). Study 1 found that anxiety was positively associated, and avoidance negatively associated, with Facebook jealousy and surveillance. The association of anxiety with Facebook jealousy was mediated in part by lower trust. Study 2 replicated this finding, and daily diary results further showed that over a one-week period, anxiety was positively associated, and avoidance negatively associated, with Facebook surveillance. The association of anxiety with greater surveillance was mediated in part by daily experiences of jealousy

Minimal Super Technicolor

We introduce novel extensions of the Standard Model featuring a supersymmetric technicolor sector. First we consider N=4 Super Yang-Mills which breaks to N=1 via the electroweak (EW) interactions and coupling to the MSSM. This is a well defined, economical and calculable extension of the SM involving the smallest number of fields. It constitutes an explicit example of a natural supersymmetric conformal extension of the Standard Model featuring a well defined connection to string theory. It allows to interpolate, depending on how we break the underlying supersymmetry, between unparticle physics and Minimal Walking Technicolor. As a second alternative we consider other N =1 extensions of the Minimal Walking Technicolor model. The new models allow all the standard model matter fields to acquire a mass.Comment: Improved version demonstrating that this extension is phenomenologically viable. No Landau pole exists in the theory to two loops level. This is the first theory showing that supersymmetry can solve the flavor problem when coupled to low energy technicolo

Topological Classification of Crystalline Insulators with Point Group Symmetry

We show that in crystalline insulators point group symmetry alone gives rise to a topological classification based on the quantization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is quantized and can only take three inequivalent values. Therefore, a Z3 topological classification exists. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on BN substrate as a possible candidate to realize the Z3 topological states. To complete our analysis we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry conserved topological phases and also elucidate topological properties of graphene like systems