Fixed point theorems for metric spaces with a conical geodesic bicombing

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a 1-Lipschitz barycenter construction and an existence result for invariant Radon probability measures. Furthermore, we construct a bounded complete Busemann space that admits an isometry without fixed points.Comment: 19 page

Almost minimal orthogonal projections

The projection constant $\Pi(E):=\Pi(E, \ell_\infty)$ of a finite-dimensional Banach space $E\subset\ell_\infty$ is by definition the smallest norm of a linear projection of $\ell_\infty$ onto $E$. Fix $n\geq 1$ and denote by $\Pi_n$ the maximal value of $\Pi(\cdot)$ amongst $n$-dimensional real Banach spaces. We prove for every $\varepsilon >0$ that there exist an integer $d\geq 1$ and an $n$-dimensional subspace $E\subset\ell_1^d$ such that $\Pi_n \leq \Pi(E, \ell_1^d) +2 \varepsilon$ and the orthogonal projection $P\colon \ell_1^d\to E$ is almost minimal in the sense that $\lVert P \rVert \leq \Pi(E, \ell_1^d)+\varepsilon$. As a consequence of our main result, we obtain a formula relating $\Pi_n$ to smallest absolute value row-sums of orthogonal projection matrices of rank $n$.Comment: final versio

The Higgs sector of the minimal SUSY B−LB-L model

I review the Higgs sector of the $U(1)_{B-L}$ extension of the minimal supersymmetric standard model (MSSM). I will show that the gauge kinetic mixing plays a crucial role in the Higgs phenomenology. Two light bosons are present, a MSSM-like one and a $B-L$-like one, that mix at one loop solely due to the gauge mixing. After briefly looking at constraints from flavour observables, new decay channels involving right-handed (s)neutrinos are presented. Finally, it will be reviewed how model features pertaining to the gauge extension affect the model phenomenology, concerning the existence of R-Parity-conserving minima at loop level and the Higgs-to-diphoton coupling.Comment: 10 pages, 17 figures, 2 tables. v2, to appear in "Supersymmetry beyond the NMSSM". Shortened model description, added a section concerning the R-parity conservation, typos corrected. arXiv admin note: text overlap with arXiv:1112.4600 by other author

The future of bioethanol

Yeasts have been domesticated by mankind before horses. After the mastering of alcoholic fermentation for centuries, yeasts have become the protagonist of one of the most important biotechnological industries worldwide: the production of bioethanol. This chapter will initially present some important challenges to be overcome in this industry, both in first and second generation biofuel production. Then, it will briefly revisit some advances obtained in recent years. Finally, it will present and discuss some opportunities, in the scope of metabolic engineering and synthetic biology, that will likely be present in the future of bioethanol

Liquidity, term spreads and monetary policy

We propose a model that delivers endogenous variations in term spreads driven primarily by banks' portfolio decision and their appetite to bear the risk of maturity transformation. We first show that fluctuations of the future profitability of banks' portfolios affect their ability to cover for any liquidity shortage and hence influence the premium they require to carry maturity risk. During a boom, profitability is increasing and thus spreads are low, while during a recession profitability is decreasing and spreads are high, in accordance with the cyclical properties of term spreads in the data. Second, we use the model to look at monetary policy and show that allowing banks to sell long-term assets to the central bank after a liquidity shock leads to a sharp decrease in long-term rates and term spreads. Such interventions have significant impact on long-term investment, decreasing the amplitude of output responses after a liquidity shock. The short-term rate does not need to be decreased as much and inflation turns out to be much higher than if no QE interventions were implemented. Finally, we provide macro and micro-econometric evidence for the U.S. confirming the importance of expected financial business profitability in the determination of term spread fluctuations

Bethe Ansaetze for GKP strings

Studying the scattering of excitations around a dynamical background has a long history in the context of integrable models. The Gubser-Klebanov-Polyakov string solution provides such a background for the string/gauge correspondence. Taking the conjectured all-loop asymptotic equations for the AdS_4/CFT_3 correspondence as the starting point, we derive the S-matrix and a set of spectral equations for the lowest-lying excitations. We find that these equations resemble closely the analogous equations for AdS_5/CFT_4, which are also discussed in this paper. At large values of the coupling constant we show that they reproduce the Bethe equations proposed to describe the spectrum of the low-energy limit of the AdS_4xCP^3 sigma model.Comment: 60 pages, 5 figure