Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Axion Protection from Flavor

The QCD axion fails to solve the strong CP problem unless all explicit PQ violating, Planck-suppressed, dimension n<10 operators are forbidden or have exponentially small coefficients. We show that all theories with a QCD axion contain an irreducible source of explicit PQ violation which is proportional to the determinant of the Yukawa interaction matrix of colored fermions. Generically, this contribution is of low operator dimension and will drastically destabilize the axion potential, so its suppression is a necessary condition for solving the strong CP problem. We propose a mechanism whereby the PQ symmetry is kept exact up to n=12 with the help of the very same flavor symmetries which generate the hierarchical quark masses and mixings of the SM. This "axion flavor protection" is straightforwardly realized in theories which employ radiative fermion mass generation and grand unification. A universal feature of this construction is that the heavy quark Yukawa couplings are generated at the PQ breaking scale.Comment: 16 pages, 2 figure

Vertical Field Effect Transistor based on Graphene-WS2 Heterostructures for flexible and transparent electronics

The celebrated electronic properties of graphene have opened way for materials just one-atom-thick to be used in the post-silicon electronic era. An important milestone was the creation of heterostructures based on graphene and other two-dimensional (2D) crystals, which can be assembled in 3D stacks with atomic layer precision. These layered structures have already led to a range of fascinating physical phenomena, and also have been used in demonstrating a prototype field effect tunnelling transistor - a candidate for post-CMOS technology. The range of possible materials which could be incorporated into such stacks is very large. Indeed, there are many other materials where layers are linked by weak van der Waals forces, which can be exfoliated and combined together to create novel highly-tailored heterostructures. Here we describe a new generation of field effect vertical tunnelling transistors where 2D tungsten disulphide serves as an atomically thin barrier between two layers of either mechanically exfoliated or CVD-grown graphene. Our devices have unprecedented current modulation exceeding one million at room temperature and can also operate on transparent and flexible substrates

Application of Graphene within Optoelectronic Devices and Transistors

Scientists are always yearning for new and exciting ways to unlock graphene's true potential. However, recent reports suggest this two-dimensional material may harbor some unique properties, making it a viable candidate for use in optoelectronic and semiconducting devices. Whereas on one hand, graphene is highly transparent due to its atomic thickness, the material does exhibit a strong interaction with photons. This has clear advantages over existing materials used in photonic devices such as Indium-based compounds. Moreover, the material can be used to 'trap' light and alter the incident wavelength, forming the basis of the plasmonic devices. We also highlight upon graphene's nonlinear optical response to an applied electric field, and the phenomenon of saturable absorption. Within the context of logical devices, graphene has no discernible band-gap. Therefore, generating one will be of utmost importance. Amongst many others, some existing methods to open this band-gap include chemical doping, deformation of the honeycomb structure, or the use of carbon nanotubes (CNTs). We shall also discuss various designs of transistors, including those which incorporate CNTs, and others which exploit the idea of quantum tunneling. A key advantage of the CNT transistor is that ballistic transport occurs throughout the CNT channel, with short channel effects being minimized. We shall also discuss recent developments of the graphene tunneling transistor, with emphasis being placed upon its operational mechanism. Finally, we provide perspective for incorporating graphene within high frequency devices, which do not require a pre-defined band-gap.Comment: Due to be published in "Current Topics in Applied Spectroscopy and the Science of Nanomaterials" - Springer (Fall 2014). (17 pages, 19 figures

Tolerability and Safety Profile of Cariprazine in Treating Psychotic Disorders, Bipolar Disorder and Major Depressive Disorder: A Systematic Review with Meta-Analysis of Randomized Controlled Trials

BACKGROUND: Cariprazine is a novel antipsychotic agent recently approved for treating schizophrenia and bipolar mania in the USA. The sample sizes of published randomized controlled trials (RCTs) of the drug are small; previous meta-analyses included few RCTs and did not specifically investigate the tolerability/safety profile of cariprazine. OBJECTIVE: Our objective was to conduct a meta-analysis of published RCTs to systematically review the tolerability and safety of cariprazine versus placebo. METHODS: We searched the clinical trial registers (the metaRegister of controlled trials, ClinicalTrials.gov and the World Health Organization International Clinical Trials Registry Platform) and electronic databases (PubMed, Embase, PsycINFO and Cochrane library) up to June 2016 to identify phase II/III RCTs of cariprazine in patients with schizophrenia, bipolar disorder or major depressive disorder. We conducted a meta-analysis to investigate outcomes, including risks of discontinuation due to adverse events (AEs), extrapyramidal side effects (EPS) or related events, metabolic syndrome and cardiovascular-related events. RESULTS: We included nine RCTs, with a total of 4324 subjects. The risk of discontinuation due to AEs for cariprazine was similar to that for placebo (risk ratio [RR] 1.13, 95 % confidence interval [CI] 0.77-1.66). Cariprazine was associated with higher risks of EPS-related events than was placebo, including risk of akathisia (RR 3.92, 95 % CI 2.83-5.43), tremor (RR 2.41, 95 % CI 1.53-3.79) and restlessness (RR 2.17, 95 % CI 1.38-3.40). The cariprazine treatment group was more likely to have clinically significant weight gain (RR 1.68, 95 % CI 1.12-2.52). No statistically significant differences in results were found in other metabolic parameters or cardiovascular-related events. CONCLUSION: There was a statistically significant higher risk of EPS-related AEs and a slight increase in mean body weight with cariprazine. There were no statistically significant effects on prolactin level or cardiovascular parameters. EPSs were the main short-term adverse reactions reported in the limited number of patients studied. Further clinical and post-marketing pharmacovigilance studies are needed to investigate the long-term safety of cariprazine

Neutrino masses from new generations

We reconsider the possibility that Majorana masses for the three known neutrinos are generated radiatively by the presence of a fourth generation and one right-handed neutrino with Yukawa couplings and a Majorana mass term. We find that the observed light neutrino mass hierarchy is not compatible with low energy universality bounds in this minimal scenario, but all present data can be accommodated with five generations and two right-handed neutrinos. Within this framework, we explore the parameter space regions which are currently allowed and could lead to observable effects in neutrinoless double beta decay, $\mu - e$ conversion in nuclei and $\mu \rightarrow e \gamma$ experiments. We also discuss the detection prospects at LHC.Comment: 28 pages, 4 figures. Version to be published. Some typos corrected. Improved figures 3 and

P-odd and CP-odd Four-Quark Contributions to Neutron EDM

In a class of beyond-standard-model theories, CP-odd observables, such as the neutron electric dipole moment, receive significant contributions from flavor-neutral P-odd and CP-odd four-quark operators. However, considerable uncertainties exist in the hadronic matrix elements of these operators strongly affecting the experimental constraints on CP-violating parameters in the theories. Here we study their hadronic matrix elements in combined chiral perturbation theory and nucleon models. We first classify the operators in chiral representations and present the leading-order QCD evolutions. We then match the four-quark operators to the corresponding ones in chiral hadronic theory, finding symmetry relations among the matrix elements. Although this makes lattice QCD calculations feasible, we choose to estimate the non-perturbative matching coefficients in simple quark models. We finally compare the results for the neutron electric dipole moment and P-odd and CP-odd pion-nucleon couplings with the previous studies using naive factorization and QCD sum rules. Our study shall provide valuable insights on the present hadronic physics uncertainties in these observables.Comment: 40 pages, 7 figures. This is the final version. A discussion of the uncertainty of the calculation is adde