The Kinematic Algebras from the Scattering Equations

We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant.Comment: 23 pages, 4 figure

Enriching Information to Prevent Bank Runs

Sequential service in the banking sector, as modeled by Diamondand Dybvig (1983), is a barrier to full insurance and potential source offinancial fragility against which deposit insurance is infeasible (Wallace,1988). In this paper, we pursue a different perspective, viewingthe sequence of contacts as opportunities to extract informationthrough a larger message space with commitment to richer promises.As we show, if preferences satisfy a separating property then the desiredelimination of dominated strategies (Green and Lin, 2003) occurseven when shocks are correlated. In this manner the sequential servicepromotes stability.

The Tenure Game: Building Up Academic Habits

Why do some academics continue to be productive after receiving tenure? This paper answers this question by using a Stackelberg differential game between departments and scholars. We show that departments can set tenure rules and standards as incentives for scholars to accumulate academic habits. As a result, academic habits have a lasting positive impact in scholar’s productivity, leading to higher scholar’s productivity rate of growth and higher productivity level.Role of economists; sociology of economics.

Black holes and the double copy

Recently, a perturbative duality between gauge and gravity theories (the double copy) has been discovered, that is believed to hold to all loop orders. In this paper, we examine the relationship between classical solutions of non-Abelian gauge theory and gravity. We propose a general class of gauge theory solutions that double copy to gravity, namely those involving stationary Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their higher-dimensional equivalents) emerge as special cases. We also discuss plane wave solutions. Furthermore, a recently examined double copy between the self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a momentum-space generalisation of the Kerr-Schild framework.Comment: 22 pages; typos corrected and references adde

From Moyal deformations to chiral higher-spin theories and to celestial algebras

We study the connection of Moyal deformations of self-dual gravity and self-dual Yang-Mills theory to chiral higher-spin theories, and also to deformations of operator algebras in celestial holography. The relation to Moyal deformations illuminates various aspects of the structure of chiral higher-spin theories. For instance, the appearance of the self-dual kinematic algebra in all the theories considered here leads via the double copy to vanishing tree-level scattering amplitudes. Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop algebra of $W_{\wedge}$, and we obtain here the analogous deformation of a Kac-Moody algebra corresponding to Moyal-deformed self-dual Yang-Mills theory. We also introduce the celestial algebras for various chiral higher-spin theories.Comment: 30 pages, 3 figures; v2: minor change

Holographic Models for Theories with Hyperscaling Violation

We study in detail a variety of gravitational toy models for hyperscaling-violating Lifshitz (hvLif) space-times. These space-times have been recently explored as holographic dual models for condensed matter systems. We start by considering a model of gravity coupled to a massive vector field and a dilaton with a potential. This model supports the full class of hvLif space-times and special attention is given to the particular values of the scaling exponents appearing in certain non-Fermi liquids. We study linearized perturbations in this model, and consider probe fields whose interactions mimic those of the perturbations. The resulting equations of motion for the probe fields are invariant under the Lifshitz scaling. We derive Breitenlohner-Freedman-type bounds for these new probe fields. For the cases of interest the hvLif space-times have curvature invariants that blow up in the UV. We study the problem of constructing models in which the hvLif space-time can have an AdS or Lifshitz UV completion. We also analyze reductions of Schroedinger space-times and reductions of waves on extremal (intersecting) branes, accompanied by transverse space reductions, that are solutions to supergravity-like theories, exploring the allowed parameter range of the hvLif scaling exponents.Comment: version 3: matches published versio

Colour-Kinematics Duality for One-Loop Rational Amplitudes

Colour-kinematics duality is the conjecture of a group theory-like structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar progress has been lacking at loop level, where the power of the duality would be most significant. Here we explore colour-kinematics duality at one loop using the self-dual sector as a starting point. The duality is shown to exist in pure Yang-Mills theory for two infinite classes of amplitudes: amplitudes with any number of particles either all of the same helicity or with one particle helicity opposite the rest. We provide a simple Lagrangian-based argument in favour of the double copy relation between gauge theory and gravity amplitudes in these classes, and provide some explicit examples. We further discuss aspects of the duality which persist after integration, leading to relations among partial amplitudes. Finally, we describe form factors in the self-dual theory at tree level which also satisfy the duality.Comment: 36 pages, 5 figures; v2: published versio

Disparity compensation using geometric transforms

This dissertation describes the research and development of some techniques to enhance the disparity compensation in 3D video compression algorithms. Disparity compensation is usually performed using a block matching technique between views, disregarding the various levels of disparity present for objects at different depths in the scene. An alternative coding scheme is proposed, taking advantage of the cameras setup information and the object’s depth in the scene, to compensate more complex spatial distortions, being able to improve disparity compensation even with convergent cameras. In order to perform a more accurate disparity compensation, the reference picture list is enriched with additional geometrically transformed images, for the most relevant object’s levels of depth in the scene, resulting from projections of one view to another. This scheme can be implemented in any state-of-the-art video codec, as H.264/AVC or HEVC, in order to improve the disparity matching accuracy between views. Experimental results, using MV-HEVC extension, show the efficiency of the proposed method for coding stereo video, presenting bitrate savings up to 2.87%, for convergent camera sequences, and 1.52% for parallel camera sequences. Also a method to choose the geometrically transformed inter view reference pictures was developed, in order to reduce unnecessary overhead for unused reference pictures. By selecting and adding to the reference picture list, only the most useful pictures, all results improved, presenting bitrate savings up to 3.06% for convergent camera sequences, and 2% for parallel camera sequences

Additive Manufacturing of Resettable-Deformation Bi-Stable Lattices Based on a Compliant Mechanism

Metamaterials allow for the possibility to design and fabricate new materials with enhanced me- chanical properties, through the use of additive manufacturing. There are some certain materials’ struc- tures that exhibit excellent properties to withstand externally applied forces. One example of this type of structure is a bi-stable switching mechanism which can regain its original position, after being sub- mitted to a compressive force. This kind of structure should be flexible and strong since it needs to undergo a certain deflection. Another important aspect that was addressed in this work is the structure’s geometry, because of the effect that it has on flexibility. Therefore, this thesis will focus on the proper study, design, 3D printing, and mechanical characterization of a novel unitary compliant bi-stable struc- ture, and its use to build two larger cellular compliant bi-stable structures, a four-cell and a multicell structure, using the unitary one as a building block. All structures were designed in the CAD software Fusion 360 and fabricated with Polylactic Acid filament using the Fused Filament Fabrication process. The fabricated structures were submitted to compressive tests, from where Force vs. Displacement plots were obtained. These results proved that the multicell structure was the stiffest, since it required higher compressive force to perform its function, when compared to the other two structures. The conducted tests were important to check the behavior of each structure while being compressed, where both struc- tures that had more than one cell showed a layered switching behavior. Also, the tests were important to check if the position recovery of the structures was possible to achieve, which was observed in all of them. After the compressive tests, all structures were also submitted to repetitive solicitation tests, to study their repeatability behavior. These results envisage the successful application of these mechanisms towards their implementation in microelectromechanical systems.Os metamateriais permitem fabricar novos materiais com propriedades mecânicas aprimoradas, através do uso de manufatura aditiva. Existem algumas estruturas de determinados materiais que apresentam excelentes propriedades para resistir às forças externas aplicadas sobre eles. Um exemplo deste tipo de estrutura é um mecanismo complacente biestável que pode recuperar a sua posição original, após ser submetido a uma força de compressão. Este tipo de estrutura precisa de ser flexível e forte, porque é projetado para sofrer uma certa deflexão. Outro aspeto importante que foi abordado neste trabalho é a geometria da estrutura, devido ao efeito que esta tem na flexibilidade. Portanto, esta dissertação concentrar-se-á no estudo adequado, desenho, impressão 3D e caracterização mecânica de uma nova estrutura complacente biestável unitária, e o seu uso para construir duas estruturas celulares complacentes biestáveis, uma de quatro células e outra multicelular, usando a estrutura unitária como bloco de construção. Todas as estruturas foram desenhadas no software de CAD Fusion 360 e fabricadas com filamento de Ácido Poliláctico usando o processo de Fabricação com Filamento Fundido. As estruturas fabricadas foram submetidas a ensaios de compressão, de onde foram obtidos gráficos de Força vs. Deslocamento. Estes resultados comprovaram que a estrutura multicelular era a mais rígida, porque necessitou de uma maior força compressiva para desempenhar a sua função. Os testes realizados foram importantes para analisar o comportamento de cada estrutura durante a compressão, onde ambas as estruturas multicelulares apresentaram um comportamento de transição camada a camada. Além disso, os testes foram também importantes para verificar se a recuperação da posição das estruturas era possível, o que foi observado para todas. Após os ensaios de compressão, todas as estruturas foram submetidas a ensaios de solicitação repetitiva, para estudar o seu comportamento de repetibilidade. Estes resultados vislumbram o sucesso da implementação destes mecanismos em sistemas microelectromecânicos