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The nuclear pore complex (NPC) is the sole bidirectional gateway for nucleocytoplasmic transport. Despite recent progress in elucidating the NPC symmetric core architecture, the asymmetrically decorated cytoplasmic face, essential for mRNA export and a hotspot for nucleoporin-associated diseases, has remained elusive. Here, we report a composite structure of the entire human cytoplasmic face obtained by combining biochemical reconstitution, crystal structure determination, docking into cryo-electron tomographic reconstructions, and physiological validation, accounting for a third of the NPC’s mass. Whereas an evolutionarily conserved ∼540 kDa hetero-hexameric cytoplasmic filament nucleoporin complex is anchored by species-specific motifs above the central transport channel, attachment of the pentameric NUP358 bundles depends on the double-ring arrangement of the coat nucleoporin complex. Our results and the predictive power of our composite structure provide a rich foundation for elucidating the molecular basis of mRNA export and nucleoporin diseases.

The study of collision events with missing energy as searches for the dark matter (DM) component of the Universe are an essential part of the extensive program looking for new physics at the LHC. Given the unknown nature of DM, the interpretation of such searches should be made broad and inclusive. This report reviews the usage of simplified models in the interpretation of missing energy searches. We begin with a brief discussion of the utility and limitation of the effective field theory approach to this problem. The bulk of the report is then devoted to several different simplified models and their signatures, including s-channel and t-channel processes. A common feature of simplified models for DM is the presence of additional particles that mediate the interactions between the Standard Model and the particle that makes up DM. We consider these in detail and emphasize the importance of their inclusion as final states in any coherent interpretation. We also review some of the experimental progress in the field, new signatures, and other aspects of the searches themselves. We conclude with comments and recommendations regarding the use of simplified models in Run-II of the LHC.

In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also presented from an experiment for a model system: a ball rolling without sliding on a rotating table. Both sets of equations of motion for the model system are compared with the experimental results. The effects of various forms of friction are considered in the nonholonomic equations. With appropriate friction terms, the nonholonomic equations of motion for the model system give reasonable agreement with the experimental observations.

The recent proposal of Almheiri et al.[http://arxiv.org/abs/1411.7041], together with the Ryu-Takayanagi formula, implies the entanglement wedge hypothesis for certain choices of boundary subregions. This fact is derived in the pure AdS space. A similar conclusion holds in the presence of quantum corrections, but in a more restricted domain of applicability. We also comment on this [http://arxiv.org/abs/1601.05416] and some similarities and differences with this work.

In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is also derived. This condition involves a new object which we call the {\em symmetric product}. Of particular interest is a definition of "equilibrium controllability" for which we are able to derive computable sufficient conditions. Examples illustrate the theory.

These twenty-two lectures, with exercises, comprise the extent of what was meant to be a full-year graduate-level course on the strong interactions and QCD, given at Caltech in 1987-88. The course was cut short by the illness that led to Feynman's death. Several of the lectures were finalized in collaboration with Feynman for an anticipated monograph based on the course. The others, while retaining Feynman's idiosyncrasies, are revised similarly to those he was able to check. His distinctive approach and manner of presentation are manifest throughout. Near the end he suggests a novel, nonperturbative formulation of quantum field theory in D dimensions. Supplementary material is provided in appendices and ancillary files, including verbatim transcriptions of three lectures and the corresponding audiotaped recordings.

Many interesting control systems are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical systems to obtain analysis tools which are suitable for these systems. In this dissertation we take the first steps towards a methodical treatment of mechanical control systems. First we develop a framework for analysis of certain classes of mechanical control systems. In the Lagrangian formulation we study "simple mechanical control systems" whose Lagrangian is "kinetic energy minus potential energy." We propose a new and useful definition of controllability for these systems and obtain a computable set of conditions for this new version of controllability. We also obtain decompositions of simple mechanical systems in the case when they are not controllable. In the Hamiltonian formulation we study systems whose control vector fields are Hamiltonian. We obtain decompositions which describe the controllable and uncontrollable dynamics. In each case, the dynamics are shown to be Hamiltonian in a suitably general sense. Next we develop intrinsic descriptions of Lagrangian and Hamiltonian mechanics in the presence of external inputs. This development is a first step towards a control theory for general Lagrangian and Hamiltonian control systems. Systems with constraints are also studied. We first give a thorough overview of variational methods including a comparison of the "nonholonomic" and "vakonomic" methods. We also give a generalised definition for a constraint and, with this more general definition, we are able to give some preliminary controllability results for constrained systems.