Dualisation of the Symmetric Space Sigma Model with Couplings

The first-order formulation of the G/K symmetric space sigma model of the scalar cosets of the supergravity theories is discussed when there is coupling of (m-1)-form matter fields. The Lie superalgebra which enables the dualized coset formulation is constructed for a general scalar coset G/K with matter coupling where G is a non-compact real form of a semi-simple Lie group and K is its maximal compact subgroup.Comment: 17 page

Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes

We explicitly confirm the expectation that generic Lovelock gravity in D dimensions has a unitary massless spin-2 excitation around any one of its constant curvature vacua just like the cosmological Einstein gravity. The propagator of the theory reduces to that of Einstein's gravity, but scattering amplitudes must be computed with an effective Newton's constant which we provide. Tree-level unitarity imposes a single constraint on the parameters of the theory yielding a wide range of unitary region. As an example, we explicitly work out the details of the cubic Lovelock theory.Comment: 9 pages, 2 references adde

Regret Bounds for Reinforcement Learning with Policy Advice

In some reinforcement learning problems an agent may be provided with a set of input policies, perhaps learned from prior experience or provided by advisors. We present a reinforcement learning with policy advice (RLPA) algorithm which leverages this input set and learns to use the best policy in the set for the reinforcement learning task at hand. We prove that RLPA has a sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and that both this regret and its computational complexity are independent of the size of the state and action space. Our empirical simulations support our theoretical analysis. This suggests RLPA may offer significant advantages in large domains where some prior good policies are provided

Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator

A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.Comment: 19 page

Dualisation of the Salam-Sezgin D=8 Supergravity

The first-order formulation of the Salam-Sezgin D=8 supergravity coupled to N vector multiplets is discussed. The non-linear realization of the bosonic sector of the D=8 matter coupled Salam-Sezgin supergravity is introduced by the dualisation of the fields and by constructing the Lie superalgebra of the symmetry group of the doubled field strength.Comment: 15 page

Canonical transformations in three-dimensional phase space

Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J. Mod. Phys.

Does It Matter How and How Much Politicians are Paid?

An important question in representative democracies is how to ensure that politicians behave in the best interest of citizens rather than their own private interests. Aside from elections, one of the few institutional devices available to regulate the actions of politicians is their pay structure. In this paper, we provide fresh insights into the impact of politician salaries on their performance using a unique law change implemented in 2012 in Turkey. Specifically, the members of the parliament (MPs) in Turkey who are retired from their pre-political career jobs earn a pension bonus on top of their MP salaries. The law change in 2012 significantly increased the pension bonus by pegging it to 18 percent of the salary of the President of Turkey, while keeping the salaries of non-retired MPs unchanged. By exploiting the variation in total salaries caused by the new law in a difference-in-differences framework, we find that the salary increase had a negative impact on the performance of the retired MPs. In particular, the overall performance of these MPs was lowered by 12.3 percent of a standard deviation as a result of the increase in salary caused by the new law. This finding is robust to numerous specification tests. Furthermore, the results obtained from an auxiliary analysis suggest that one of the mechanisms through which MPs reduce their performance is absenteeism

All unitary cubic curvature gravities in D dimensions

We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.Comment: 24 pages, 1 figure, v2: A subsection on cubic curvature extensions of critical gravity is added, v3: The part regarding critical gravity is revised. Version to appear in Class. Quant. Gra

Gravitating Instantons In 3 Dimensions

We study the Einstein-Chern-Simons gravity coupled to Yang-Mills-Higgs theory in three dimensional Euclidean space with cosmological constant. The classical equations reduce to Bogomol'nyi type first order equations in curved space. There are BPS type gauge theory instanton (monopole) solutions of finite action in a gravitational instanton which itself has a finite action. We also discuss gauge theory instantons in the vacuum (zero action) AdS space. In addition we point out to some exact solutions which are singular.Comment: 17 pages, 4 figures, title has changed, gravitational instanton actions are adde

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include