Recursos de colección
Caltech Authors (147.369 recursos)
Repository of works by Caltech published authors.
Type = Report or Paper
Repository of works by Caltech published authors.
Type = Report or Paper
Meier, Kevin; Chung, Soon-Jo; Hutchinson, Seth
We present a simultaneous localization and mapping (SLAM) algorithm that uses Bézier curves as static landmark primitives rather than feature points. Our approach allows us to estimate the full 6-DOF pose of a robot while providing a structured map which can be used to assist a robot in motion planning and control. We demonstrate how to reconstruct the 3-D location of curve landmarks from a stereo pair and how to compare the 3-D shape of curve landmarks between chronologically sequential stereo frames to solve the data association problem. We also present a method to combine curve landmarks for mapping purposes,...
Ngo, Henry; Knutson, Heather A.; Bryan, Marta L.; Blunt, Sarah; Nielsen, Eric L.; Batygin, Konstantin; Bowler, Brendan P.; Crepp, Justin R.; Hinkley, Sasha; Howard, Andrew W.; Mawet, Dimitri
Our Keck/NIRC2 imaging survey searches for stellar companions around 144 systems with radial velocity (RV) detected giant planets to determine whether stellar binaries influence the planets' orbital parameters. This survey, the largest of its kind to date, finds eight confirmed binary systems and three confirmed triple systems. These include three new multi-stellar systems (HD 30856, HD 86081, and HD 207832) and three multi-stellar systems with newly confirmed common proper motion (HD 43691, HD 116029, and HD 164509). We combine these systems with seven RV planet-hosting multi-stellar systems from the literature in order to test for differences in the properties of planets with semimajor axes ranging between 0.1-5 au in...
Sanghavi, Suniti; Millar-Blanchaer, Maxwell A.; Shporer, Avi; Riedel, Adric; Tinyatont, Samaporn; Nilsson, Ricky; Kataria, Tiffany; Mawet, Dimitri
It has long been known that an envelope of scattering particles like free electrons, atoms and molecules, or particulate aggregates like haze or cloud grains affect the intensity and polarization of radiation emitted by a rotating body (Chandrasekhar 1946; Harrington and Collins 1968, Sengupta and Marley 2010, Marley and Sengupta 2011, de Kok et al. 2011). Due to their high rotation rates, brown dwarfs (BDs) are expected to be considerably oblate. We present a conics-based radiative transfer scheme for computing the disc-resolved and disc-integrated polarized emission of an oblate body. Using this capability, we examine the photopolarimetric signal of BDs as a function of the scattering properties of its...
Gomez Gonzalez, C. A.; Wertz, O.; Absil, O.; Christiaens, V.; Defrere, D.; Mawet, D.; Milli, J.; Absil, P.-A.; Van Droogenbroeck, M.; Cantalloube, F.; Hinz, P. M.; Skemer, A. J.; Karlsson, M.; Surdej, J.
We present the Vortex Image Processing (VIP) library, a python package dedicated to astronomical high-contrast imaging. Our package relies on the extensive python stack of scientific libraries and aims to provide a flexible framework for high-contrast data and image processing. In this paper, we describe the capabilities of VIP related to processing image sequences acquired using the angular differential imaging (ADI) observing technique. VIP implements functionalities for building high-contrast data processing pipelines, encompass- ing pre- and post-processing algorithms, potential sources position and flux estimation, and sensitivity curves generation. Among the reference point-spread function subtraction techniques for ADI post-processing, VIP includes several flavors of principal component analysis (PCA) based algorithms, such as...
Hellerman, Simeon; Kobayashi, Nozomu; Maeda, Shunsuke; Watanabe, Masataka
In this note we search for the ground state, in infinite volume, of the D = 3 WilsonFisher conformal O(4) model, at nonzero values of the two independent charge densities ρ1,2 . Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios ρ1 /ρ2 . This result confirms, within the context of a well-defined effective theory, a recent no-go result of  . We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of ρ1/ρ2 containing a neighborhood of zero. This suggests that...
Cuomo, Gabriel Francisco; Karateev, Denis; Kravchuk, Petr
We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their main ingredients (tensor structures and differential operators) and establish a precise connection between them. We supplement the discussion by additional details like classification of tensor structures of n-point functions, normalization of 2-point functions and seed conformal blocks, Casimir differential operators and treatment of conserved operators and permutation symmetries. Finally, we implement our framework in a Mathematica package and make it freely available.
Chang, Chi-Ming; Lin, Ying-Hsuan
We bootstrap N = (1, 0) superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming E8 flavor group, we present universal bounds on the central charge CT and the flavor central charge CJ . Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on CJ , and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS7 × S^4/Z_2.
Cheung, Clifford; Shen, Chia-Hsien; Wen, Congkao
We derive new amplitudes relations revealing a hidden unity among wide-ranging theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as...
Dedushenko, Mykola; Gukov, Sergei; Putrov, Pavel
We propose a way of computing 4-manifold invariants, old and new, as chiral correlation functions in half-twisted 2d N = (0, 2) theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of some known statements about Seiberg-Witten invariants, such as the basic class condition, and gives a prediction for structural properties of the multi-monopole invariants and their non-abelian generalizations.
Kahn, Jeremy; Markovic, Vladimir
We survey our recent results including the Surface Subgroup Theorem and the Ehrenpreis Conjecture. Applications and future direction are discussed.
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Siedentop, Heinz
The increasing interest in the Müller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock functional, but with a modified exchange term in which the square of the density matrix (x, x′) is replaced by the square of y^(1/2)(x,x′). After an extensive introductory discussion of densitymatrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing y’s have unique densities p(r), which is a physically desirable property often absent in HF theory. We show that minimizers exist if N ≤...
Frank, Rupert L.; Hansson, Anders
We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generalized diamagnetic inequality which was proposed by Erdos, Loss and Vougalter. Numerical studies complement these results.
Frank, Rupert L.; Loss, Michael; Weidl, Timo
We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Pόlya's conjecture is not true in the presence of a magnetic field.
Markovic, Vladimir; Šarić, Dragomir
Let M be a closed surface. By Homeo(M) we denote the group of orientation preserving homeomorphisms of M and let MC(M) denote the Mapping class group. In this paper we complete the proof of the conjecture of Thurston that says that for any closed surface M of genus g ≥ 2, there is no homomorphic section є : MC(M) → Homeo(M) of the standard projection map P : Homeo(M) → MC(M).
Kahn, Jeremy; Markovic, Vladimir
Let S and R be two hyperbolic finite area surfaces with cusps. We show that for every є > 0 there are finite degree unbranched covers Sє → S and Rє → R, such that the Weil-Petersson distance between Sє and Rє is less than є in the corresponding Moduli space.
Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic; Gomez, John A.; Gull, Emanuel; Guo, Sheng; Jiménez-Hoyos, Carlos; Lan, Tran Nguyen; Li, Jia; Ma, Fengjie; Millis, Andrew J.; Prokof'ev, Nikolay V.; Ray, Ushnish; Scuseria, Gustavo E.; Sorella, Sandro; Stoudenmire, Edwin M.; Sun, Qiming; Tupitsyn, Igor S.; White, Steven R.; Zgid, Dominika; Zhang, Shiwei
We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bondlength, with a confidence bound given on all uncertainties.
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
We consider relativistic many-particle operators which – according to Brown and Ravenhall – describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light. We show that the leading quasi-classical behavior given by the Thomas-Fermi theory is raised by a subleading correction, the Scott correction. Our result is valid for the maximal range of coupling constants, including the critical one. As a technical tool, a Sobolev-Gagliardo-Nirenberg type inequality is established for the critical atomic Brown-Ravenhall operator. Moreover, we prove sharp upper and lower bound on the eigenvalues...
Frank, Rupert L.; Laptev, Ari
We prove sharp Lieb-Thirring inequalities for Schrödinger operators with potentials supported on a hyperplane and we show how these estimates are related to Lieb-Thirring inequalities for relativistic Schrödinger operators.
This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl–Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to the study of ergodic Schr¨odinger operators where one of our new results implies that, in complete generality, the spectral measure is supported on a set of zero Hausdorff dimension (indeed, of capacity zero) in the region of strictly positive Lyapunov exponent. There are many examples and some new conjectures and indications of new research directions. Included are appendices on...
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
We find sharp conditions on the growth of a rooted regular metric tree such that the Neumann Laplacian on the tree satisfies a Hardy inequality. In particular, we consider homogeneous metric trees. Moreover, we show that a non-trivial Aharonov-Bohm magnetic field leads to a Hardy inequality on a loop graph.