Learning to Race through Coordinate Descent Bayesian Optimisation

In the automation of many kinds of processes, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise control policies for individual stages of the process might not be applicable, and instead the whole policy might have to be optimised at once. On the other hand, the cost to evaluate the policy's performance might also be high, being desirable that a solution can be found with as few interactions as possible with the real system. We consider the problem of optimising control policies to allow a robot to complete a given race track within a minimum amount of time. We assume that the robot has no prior information about the track or its own dynamical model, just an initial valid driving example. Localisation is only applied to monitor the robot and to provide an indication of its position along the track's centre axis. We propose a method for finding a policy that minimises the time per lap while keeping the vehicle on the track using a Bayesian optimisation (BO) approach over a reproducing kernel Hilbert space. We apply an algorithm to search more efficiently over high-dimensional policy-parameter spaces with BO, by iterating over each dimension individually, in a sequential coordinate descent-like scheme. Experiments demonstrate the performance of the algorithm against other methods in a simulated car racing environment.Comment: Accepted as conference paper for the 2018 IEEE International Conference on Robotics and Automation (ICRA

Vertex Operators for Closed Superstrings

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any generic background in presence of Ramond-Ramond (RR) fields. We extend the procedure to all massive states of open and closed superstrings and we identify two new nilpotent charges which are used to impose the gauge fixing on the physical states. We solve iteratively the equations of the vertex for linear x-dependent RR field strengths. This vertex plays a role in studying non-constant C-deformations of superspace. Finally, we construct an action for the free massless sector of closed strings, and we propose a form for the kinetic term for closed string field theory in the pure spinor formalism.Comment: TeX, harvmac, amssym.tex, 41 pp; references adde

Knots, Braids and BPS States in M-Theory

In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N=2 supersymmetry.Comment: 38 page

Equilibrium molecular energies used to obtain molecular dissociation energies and heats of formation within the bond-order correlation approach

Ab initio calculations including electron correlation are still extremely costly except for the smallest atoms and molecules. Therefore, our purpose in the present study is to employ a bond-order correlation approach to obtain, via equilibrium molecular energies, molecular dissociation energies and heats of formation for some 20 molecules containing C, H, and O atoms, with a maximum number of electrons around 40. Finally, basis set choice is shown to be important in the proposed procedure to include electron correlation effects in determining thermodynamic properties. With the optimum choice of basis set, the average percentage error for some 20 molecules is approximately 20% for heats of formation. For molecular dissociation energies the average error is much smaller: ~0.4.Comment: Mol. Phys., to be publishe

Non-Critical Pure Spinor Superstrings

We construct non-critical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the non-critical pure spinor space, which is different from the ten-dimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the non-critical pure spinor type IIA superstring on AdS_4 with RR 4-form flux.Comment: LaTeX2e, 76 pages, no figures, JHEP style; v2: references and acknowledgments added, typos corrected; v3: typos corrected and minor changes to match published versio

Continuous approximation of binomial lattices

A systematic analysis of a continuous version of a binomial lattice, containing a real parameter $\gamma$ and covering the Toda field equation as $\gamma\to\infty$, is carried out in the framework of group theory. The symmetry algebra of the equation is derived. Reductions by one-dimensional and two-dimensional subalgebras of the symmetry algebra and their corresponding subgroups, yield notable field equations in lower dimensions whose solutions allow to find exact solutions to the original equation. Some reduced equations turn out to be related to potentials of physical interest, such as the Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like approximate solution is also obtained which reproduces the Eguchi-Hanson instanton configuration for $\gamma\to\infty$. Furthermore, the equation under consideration is extended to $(n+1)$--dimensions. A spherically symmetric form of this equation, studied by means of the symmetry approach, provides conformally invariant classes of field equations comprising remarkable special cases. One of these $(n=4)$ enables us to establish a connection with the Euclidean Yang-Mills equations, another appears in the context of Differential Geometry in relation to the socalled Yamabe problem. All the properties of the reduced equations are shared by the spherically symmetric generalized field equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic

Comments on BRST quantization of strings

The BRST quantization of strings is revisited and the derivation of the path integral measure for scattering amplitudes is streamlined. Gauge invariances due to zero modes in the ghost sector are taken into account by using the Batalin-Vilkovisky formalism. This involves promoting the moduli of Riemann surfaces to quantum mechanical variables on which BRST transformations act. The familiar ghost and antighost zero mode insertions are recovered upon integrating out auxiliary fields. In contrast to the usual treatment, the gauge-fixed action including all zero mode insertions is BRST invariant. Possible anomalous contributions to BRST Ward identities due to boundaries of moduli space are reproduced in a novel way. Two models are discussed explicitly: bosonic string theory and topological gravity coupled to the topological A-model.Comment: 23 pages, latex; v2: typos fixed, footnote and reference adde