Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment

This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path integral control framework, which forms the backbone of the proposed method, re-writes the Hamilton-Jacobi-Bellman equation as a statistical inference problem; the resulting inference problem is solved by a sampling procedure that computes the distribution of controlled trajectories around the trajectory by the passive dynamics. For motion control of robots in a highly cluttered environment, however, this sampling can easily be trapped in a local minimum unless the sample size is very large, since the global optimality of local minima depends on the degree of uncertainty. Thus, a homology-embedded sampling-based planner that identifies many (potentially) local-minimum trajectories in different homology classes is developed to aid the sampling process. In combination with a receding-horizon fashion of the optimal control the proposed method produces a dynamically feasible and collision-free motion plans without being trapped in a local minimum. Numerical examples on a synthetic toy problem and on quadrotor control in a complex obstacle field demonstrate the validity of the proposed method.Comment: arXiv admin note: text overlap with arXiv:1510.0534

Lattice-coupled Antiferromagnet on Frustrated Lattices

Lattice-coupled antiferromagnetic spin model is analyzed for a number of frustrated lattices: triangular, Kagome, and pyrochlore. In triangular and Kagome lattices where ground state spins are locally ordered, the spin-lattice interaction does not lead to a static deformation of the lattice. In the pyrochlore structure, spin-lattice coupling supports a picture of the hexagon spin cluster proposed in the recent experiment[S. H. Lee et al. Nature, 418, 856 (2002)]. Through spin-lattice interaction a uniform contraction of the individual hexagons in the pyrochlore lattice can take place and reduce the exchange energy. Residual hexagon-hexagon interaction takes the form of a 3-states Potts model where the preferred directions of the spin-loop directors for nearby hexagons are mutually orthogonal

A mild and efficient approach to enantioenriched α-hydroxyethyl α,β-unsaturated δ-lactams

A straightforward approach toward enantioenriched α-substituted α,β-unsaturated δ-lactams is described. Although a considerable number of approaches toward α,β-unsaturated δ-lactams have been reported, there are relatively few examples of enantioenriched α,δ-disubstituted α,β-unsaturated δ-lactams formation. The δ-stereocenter was formed by addition of allylmagnesium bromide to an N-tert-butylsulfinyl imine. The α,β-unsaturated δ-lactam was furnished by ring-closing metathesis. Although Baylis–Hillman chemistry failed on this cyclic compound, introduction of the hydroxyethyl group prior to ring-closing metathesis was successful. A Baylis–Hillman reaction was used to introduce the substituent at the α-position of the α,β-unsaturated lactam

Atroposelective Synthesis of PINAP via Dynamic Kinetic Asymmetric Transformation

The atroposelective synthesis of PINAP ligands has been accomplished via a palladium‐catalyzed C−P coupling process through dynamic kinetic asymmetric transformation. These catalytic conditions allow access to a wide variety of alkoxy‐ and benzyloxy‐substituted PINAP ligands in high enantiomeric excess. The methods described in this communication afford valuable P,N ligands in good yields and high enantioselectivity using low catalyst loading

Catalytic Enantioselective Construction of Quaternary Stereocenters: Assembly of Key Building Blocks for the Synthesis of Biologically Active Molecules

The ever-present demand for drugs with better efficacy and fewer side effects continually motivates scientists to explore the vast chemical space. Traditionally, medicinal chemists have focused much attention on achiral or so-called “flat” molecules. More recently, attention has shifted toward molecules with stereogenic centers since their three-dimensional structures represent a much larger fraction of the chemical space and have a number of superior properties compared with flat aromatic compounds. Quaternary stereocenters, in particular, add greatly to the three-dimensionality and novelty of the molecule. Nevertheless, synthetic challenges in building quaternary stereocenters have largely prevented their implementation in drug discovery. The lack of effective and broadly general methods for enantioselective formation of quaternary stereocenters in simple molecular scaffolds has prompted us to investigate new chemistry and develop innovative tools and solutions. In this Account, we describe three approaches to constructing quaternary stereocenters: nucleophilic substitution of 3-halooxindoles, conjugate addition of boronic acids to cyclic enones, and allylic alkylation of enolates. In the first approach, malonic ester nucleophiles attack electrophilic 3-halooxindoles, mediated by a copper(II)-bisoxazoline catalyst. A variety of oxindoles containing a benzylic quaternary stereocenter can be accessed through this method. However, it is only applicable to the specialized 3,3-disubstituted oxindole system. To access benzylic quaternary stereocenters in a more general context, we turned our attention to the enantioselective conjugate addition of carbon nucleophiles to α,β-unsaturated carbonyl acceptors. We discovered that in the presence of catalytic palladium-pyridinooxazoline complex, arylboronic acids add smoothly to β-substituted cyclic enones to furnish ketones with a β-benzylic quaternary stereocenter in high yields and enantioselectivities. The reaction is compatible with a wide range of arylboronic acids, β-substituents, and ring sizes. Aside from benzylic quaternary stereocenters, a more challenging motif is a quaternary stereocenter not adjacent to an aromatic group. Such centers represent more general structures in chemical space but are more difficult to form by asymmetric catalysis. To address this greater challenge, and motivated by the greater reward, we entered the field of palladium-catalyzed asymmetric allylic alkylation of prochiral enolate nucleophiles about a decade ago. On the basis of Tsuji’s work, which solved the issue of positional selectivity for unsymmetrical ketones, we discovered that the phosphinooxazoline ligand effectively rendered this reaction enantioselective. Extensive investigations since then have revealed that the reaction exhibits broad scope and accepts a range of substrate classes, each with its unique advantage in synthetic applications. A diverse array of carbonyl compounds bearing α-quaternary stereocenters are obtained in excellent yields and enantioselectivities, and more possibilities have yet to be explored. As an alternative to palladium catalysis, we also studied iridium-catalyzed asymmetric allylic alkylations that generate vicinal quaternary and tertiary stereocenters in a single transformation. Overall, these methods provide access to small molecule building blocks with a single quaternary stereocenter, can be applied to various molecular scaffolds, and tolerate a wide range of functional groups. We envision that the chemistry reported in this Account will be increasingly useful in drug discovery and design

Effective Vortex Mass from Microscopic Theory

We calculate the effective mass of a single quantized vortex in the BCS superconductor at finite temperature. Based on effective action approach, we arrive at the effective mass of a vortex as integral of the spectral function $J(\omega)$ divided by $\omega^3$ over frequency. The spectral function is given in terms of the quantum-mechanical transition elements of the gradient of the Hamiltonian between two Bogoliubov-deGennes (BdG) eigenstates. Based on self-consistent numerical diagonalization of the BdG equation we find that the effective mass per unit length of vortex at zero temperature is of order $m (k_f \xi_0)^2$ ($k_f$=Fermi momentum, $\xi_0$=coherence length), essentially equaling the electron mass displaced within the coherence length from the vortex core. Transitions between the core states are responsible for most of the mass. The mass reaches a maximum value at $T\approx 0.5 T_c$ and decreases continuously to zero at $T_c$.Comment: Supercedes prior version, cond-mat/990312

Experimental observation of hidden Berry curvature in inversion-symmetric bulk 2H-WSe2

We investigate the hidden Berry curvature in bulk 2H-WSe2 by utilizing the surface sensitivity of angle resolved photoemission (ARPES). The symmetry in the electronic structure of transition metal dichalcogenides is used to uniquely determine the local orbital angular momentum (OAM) contribution to the circular dichroism (CD) in ARPES. The extracted CD signals for the K and K' valleys are almost identical but their signs, which should be determined by the valley index, are opposite. In addition, the sign is found to be the same for the two spin-split bands, indicating that it is independent of spin state. These observed CD behaviors are what are expected from Berry curvature of a monolayer of WSe2. In order to see if CD-ARPES is indeed representative of hidden Berry curvature within a layer, we use tight binding analysis as well as density functional calculation to calculate the Berry curvature and local OAM of a monolayer WSe2. We find that measured CD-ARPES is approximately proportional to the calculated Berry curvature as well as local OAM, further supporting our interpretation.Comment: 6 pages, 3 figure

A Diastereodivergent Synthetic Strategy for the Syntheses of Communesin F and Perophoramidine

An efficient, unified, and stereodivergent approach toward communesin F and perophoramidine was examined. The C(3) all-carbon quaternary center of an oxindole was smoothly constructed by base-promoted indolone-malonate alkylation chemistry. The complementary relative stereochemistry of the crucial vicinal quaternary centers found in communesin F and perophoramidine was selectively installed by substrate-controlled decarboxylative allylic alkylations