The space of solutions to the Hessian one equation in the finitely punctured plane

We construct the space of solutions to the elliptic Monge-Ampere equation det(D^2 u)=1 in the plane R^2 with n points removed. We show that, modulo equiaffine transformations and for n>1, this space can be seen as an open subset of R^{3n-4}, where the coordinates are described by the conformal equivalence classes of once punctured bounded domains in the complex plane of connectivity n-1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampere equation, and generalizes a theorem by K. Jorgens.Comment: 14 pages, 3 figure

Cesaro mean distribution of group automata starting from measures with summable decay

Consider a finite Abelian group (G,+), with |G|=p^r, p a prime number, and F: G^N -> G^N the cellular automaton given by {F(x)}_n= A x_n + B x_{n+1} for any n in N, where A and B are integers relatively primes to p. We prove that if P is a translation invariant probability measure on G^Z determining a chain with complete connections and summable decay of correlations, then for any w= (w_i:i<0) the Cesaro mean distribution of the time iterates of the automaton with initial distribution P_w --the law P conditioned to w on the left of the origin-- converges to the uniform product measure on G^N. The proof uses a regeneration representation of P

War and Economics: Spanish Civil War Finances Revisited

This paper reviews how the Spanish civil war was financed. We present new evidence to show that the two combatant parties, the Republican government and the Franco administration followed similar financial strategies. In both cases money creation, rather than new taxes or the issue of debt, was the main mechanism used to cover the expenses of the war. We argue, contrary to the established knowledge, that both sides consumed a similar amount of domestic and foreign resources. We also argue that the Spanish Republic did not lose the war because of a lack of means. International factors, such as the Non-Intervention agreement promoted by France and Great Britain, and the military setbacks of the Republican army during the first year of the war, were decisive for Franco’s victory in 1939.Spain, civil war, financial resources

Adjusting for bias introduced by instrumental variable estimation in the Cox Proportional Hazards Model

Instrumental variable (IV) methods are widely used for estimating average treatment effects in the presence of unmeasured confounders. However, the capability of existing IV procedures, and most notably the two-stage residual inclusion (2SRI) procedure recommended for use in nonlinear contexts, to account for unmeasured confounders in the Cox proportional hazard model is unclear. We show that instrumenting an endogenous treatment induces an unmeasured covariate, referred to as an individual frailty in survival analysis parlance, which if not accounted for leads to bias. We propose a new procedure that augments 2SRI with an individual frailty and prove that it is consistent under certain conditions. The finite sample-size behavior is studied across a broad set of conditions via Monte Carlo simulations. Finally, the proposed methodology is used to estimate the average effect of carotid endarterectomy versus carotid artery stenting on the mortality of patients suffering from carotid artery disease. Results suggest that the 2SRI-frailty estimator generally reduces the bias of both point and interval estimators compared to traditional 2SRI.Comment: 27 pages, 8 figures, 4 table

Confined photon modes with triangular symmetry in hexagonal microcavities in 2D photonic Crystals

We present theoretical and experimental studies of the size and thickness dependencies of the optical emission spectra from microcavities with hexagonal shape in films of two-dimensional photonic crystal. A semiclassical plane-wave model, which takes into account the electrodynamic properties of quasi-2D planar photonic microcavity, is developed to predict the eigenfrequencies of the confined photon modes as a function of both the hexagon-cavity size and the film thickness. Modes with two different symmetries, triangular and hexagonal, are critically analyzed. It is shown that the model of confined photon modes with triangular symmetry gives a better agreement between the predicted eigenmodes and the observed resonances.Comment: 14 pages, 6 figure

Caustics, catastrophes, and symmetries in curved beams

In this paper, a meaningful classification of optical caustic beams in two dimensions is presented. It is demonstrated that the phase symmetry of the beam's angular spectrum governs the optical catastrophe, which describes the wave properties of ray singularities, for cusp (symmetric phase) and fold (antisymmetric phase) caustics. In contrast to the established idea, the caustic classification arises from the phase symmetry rather than from the phase power, thus breaking the commonly accepted concept that fold and cusp caustics are related to the Airy and Pearcey functions, respectively. Nevertheless, the role played by the spectral phase power is to control the degree of caustic curvature. These findings provide straightforward engineering of caustic beams by addressing the spectral phase into a spatial light modulator or glass plate.Fil: Vaveliuk, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - la Plata. Centro de Investigaciones Opticas. Provincia de Buenos Aires. Gobernación. Comision de Invest.científicas. Centro de Investigaciones Opticas. Universidad Nacional de la Plata. Centro de Investigaciones Opticas; ArgentinaFil: Lencina, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - la Plata. Centro de Investigaciones Opticas. Provincia de Buenos Aires. Gobernación. Comision de Invest.científicas. Centro de Investigaciones Opticas. Universidad Nacional de la Plata. Centro de Investigaciones Opticas; ArgentinaFil: Rodrigo, Jose A.. Universidad Complutense de Madrid; EspañaFil: Martinez Matos, Oscar. Universidad Complutense de Madrid; Españ

First report of Paelopatides (Synallactida, Synallactidae) for the SW Atlantic, with description of a new species from the deep-sea off Argentina

The present study describes a new species, Paelopatides shumel n. sp., from Argentinian deep-sea waters. This is the first report of the order Synallactida for Argentina, the fifth for southern hemisphere and the deepest report for the Argentinian holothuroid fauna (almost 3000 m). The species has up to 330 mm length, light brown color and around 19 pairs of dorsal appendages. The ventral side has one ventral ambulacra, with two rows of tube feet. Ossicles are present in dorsal appendages, tube feet, tentacles and body wall near the anus, and are mainly crosses, tables and rods-shaped. The depth at which P. shumel n. sp. has been found is occupied by the North Atlantic Deep Water current. This association with North Atlantic waters could be related with the occurrence of members of Paelopatides in the North Atlantic.Fil: Martinez, Mariano Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Solís Marín, Francisco A.. Universidad Nacional Autónoma de México; MéxicoFil: Penchaszadeh, Pablo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentin

Parsimonious Argument Annotations for Hate Speech Counter-narratives

We present an enrichment of the Hateval corpus of hate speech tweets (Basile et. al 2019) aimed to facilitate automated counter-narrative generation. Comparably to previous work (Chung et. al. 2019), manually written counter-narratives are associated to tweets. However, this information alone seems insufficient to obtain satisfactory language models for counter-narrative generation. That is why we have also annotated tweets with argumentative information based on Wagemanns (2016), that we believe can help in building convincing and effective counter-narratives for hate speech against particular groups. We discuss adequacies and difficulties of this annotation process and present several baselines for automatic detection of the annotated elements. Preliminary results show that automatic annotators perform close to human annotators to detect some aspects of argumentation, while others only reach low or moderate level of inter-annotator agreement