Efficient Learning and Inference for High-dimensional Lagrangian Systems

Learning the nature of a physical system is a problem that presents many challenges and opportunities owing to the unique structure associated with such systems. Many physical systems of practical interest in engineering are high-dimensional, which prohibits the application of standard learning methods to such problems. This first part of this work proposes therefore to solve learning problems associated with physical systems by identifying their low-dimensional Lagrangian structure. Algorithms are given to learn this structure in the case that it is obscured by a change of coordinates. The associated inference problem corresponds to solving a high-dimensional minimum-cost path problem, which can be solved by exploiting the symmetry of the problem. These techniques are demonstrated via an application to learning from high-dimensional human motion capture data. The second part of this work is concerned with the application of these methods to high-dimensional motion planning. Algorithms are given to learn and exploit the struc- ture of holonomic motion planning problems effectively via spectral analysis and iterative dynamic programming, admitting solutions to problems of unprecedented dimension com- pared to known methods for optimal motion planning. The quality of solutions found is also demonstrated to be much superior in practice to those obtained via sampling-based planning and smoothing, in both simulated problems and experiments with a robot arm. This work therefore provides strong validation of the idea that learning low-dimensional structure is the key to future advances in this field

Sparse Identification of Lagrangian for Nonlinear Dynamical Systems via Proximal Gradient Method

Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing equations from observation data. However, SINDy faces certain difficulties when the dynamics contain rational functions. The principle of the least action governs many mechanical systems, mathematically expressed in the Lagrangian formula. Compared to the actual equation of motions, the Lagrangian is much more concise, especially for complex systems, and does not usually contain rational functions for mechanical systems. Only a few methods have been proposed to extract the Lagrangian from measurement data so far. One of such methods, Lagrangian-SINDy, can extract the true form of Lagrangian of dynamical systems from data but suffers when noises are present. In this work, we develop an extended version of Lagrangian-SINDy (xL-SINDy) to obtain the Lagrangian of dynamical systems from noisy measurement data. We incorporate the concept of SINDy and utilize the proximal gradient method to obtain sparse expressions of the Lagrangian. We demonstrated the effectiveness of xL-SINDy against different noise levels with four nonlinear dynamics: a single pendulum, a cart-pendulum, a double pendulum, and a spherical pendulum. Furthermore, we also verified the performance of xL-SINDy against SINDy-PI (parallel, implicit), a recent robust variant of SINDy that can handle implicit dynamics and rational nonlinearities. Our experiment results show that xL-SINDy is 8-20 times more robust than SINDy-PI in the presence of noise

Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO

The observation of double and triple scalar boson production at hadron colliders could provide key information on the Higgs self couplings and the potential. As for single Higgs production the largest rates for multiple Higgs production come from gluon-gluon fusion processes mediated by a top-quark loop. However, at variance with single Higgs production, top-quark mass and width effects from the loops cannot be neglected. Computations including the exact top-quark mass dependence are only available at the leading order, and currently predictions at higher orders are obtained by means of approximations based on the Higgs-gluon effective field theory (HEFT). In this work we present a reweighting technique that, starting from events obtained via the MC@NLO method in the HEFT, allows to exactly include the top-quark mass and width effects coming from one- and two-loop amplitudes. We describe our approach and apply it to double Higgs production at NLO in QCD, computing the needed one-loop amplitudes and using approximations for the unknown two-loop ones. The results are compared to other approaches used in the literature, arguing that they provide more accurate predictions for distributions and for total rates as well. As a novel application of our procedure we present predictions at NLO in QCD for triple Higgs production at hadron colliders.Comment: 24 pages, 8 figure

Mapping 6D N = 1 supergravities to F-theory

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the gauge group; each block depends only on the group factor and the matter charged under it. All 6D chiral supergravity models can be constructed by gluing such blocks together in accordance with constraints from anomalies. Associating a geometric structure to each block gives a dictionary for translating a supergravity model into a set of topological data for an F-theory construction. We construct the dictionary of F-theory divisors explicitly for some simple gauge group factors and associated matter representations. Using these building blocks we analyze a variety of models. We identify some 6D supergravity models which do not map to integral F-theory divisors, possibly indicating quantum inconsistency of these 6D theories.Comment: 37 pages, no figures; v2: references added, minor typos corrected; v3: minor corrections to DOF counting in section

Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces

BRST-BFV method for constrained Lagrangian formulations (LFs) for (ir)reducible half-integer HS Poincare group representations in Minkowski space is suggested. The procedure is derived by 2 ways: from the unconstrained BRST-BFV method for mixed-symmetry HS fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in arXiv:1211.1273[hep-th]) by extracting the second-class constraints, $\widehat{O}_\alpha=(\widehat{O}_a, \widehat{O}^+_a)$, from a total superalgebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, $\widehat{O}_a$. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST $Q_C$ and spin operators $\sigma^i_C$. The closedness of the superalgebra $Q_C, \widehat{O}_a, \sigma^i_C$ guarantees that the final gauge-invariant LF is compatible with off-shell constraints $\widehat{O}_a$ imposed on field and gauge parameter vectors of Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to $\widehat{O}_a$, in comparison with vectors for unconstrained BRST-BFV LF. The suggested constrained BRST-BFV approach is valid for both massive HS fields and integer HS fields in the second-order formulation. It is shown that the respective constrained and unconstrained LFs for (half)-integer HS fields with a given spin are equivalent. The constrained Lagrangians in ghost-independent and component (for initial spin-tensor field) are obtained and shown to coincide with Fang-Fronsdal formulation for constrained totally-symmetric HS field. The triplet and unconstrained quartet LFs for the latter field and gauge-invariant constrained Lagrangians for a massive field of spin n+1/2 are derived. A concept of BRST-invariant second-class constraints for a general dynamical system with mixed-class constraints is suggested.Comment: 55 pages, typos corrected, published version; footnote 1 added, typo in (3.15) correcte

Supersymmetry - When Theory Inspires Experimental Searches

We review, in the first part of this work, many pioneering works on supersymmetry and organize these results to show how supersymmetric quantum field theories arise from spin-statistics, N{\oe}ther and a series of no-go theorems. We then introduce the so-called superspace formalism dedicated to the natural construction of supersymmetric Lagrangians and detail the most popular mechanisms leading to soft supersymmetry breaking. As an application, we describe the building of the Minimal Supersymmetric Standard Model and investigate current experimental limits on the parameter space of its most constrained versions. To this aim, we use various flavor, electroweak precision, cosmology and collider data. We then perform several phenomenological excursions beyond this minimal setup and probe effects due to non-minimal flavor violation in the squark sector, revisiting various constraints arising from indirect searches for superpartners. Next, we use several interfaced high-energy physics tools, including the FeynRules package and its UFO interface that we describe in detail, to study the phenomenology of two non- minimal supersymmetric models at the Large Hadron Collider. We estimate the sensitivity of this machine to monotop production in R-parity violating supersymmetry and sgluon-induced multitop production in R-symmetric supersymmetry. We then generalize the results to new physics scenarios designed from a bottom-up strategy and finally depict, from a theorist point of view, a search for monotops at the Tevatron motivated by these findings.Comment: Habilitation thesis; 266 pages; 49 figures; 19 tables; a few references adde