Agents use object-oriented reasoning to solve problems more quickly.
problem Finding solutions to problems more efficiently.
method Hierarchical controller directs low-level agent to simulate alternate states of the world.
result Achieves similar reward levels as non-hierarchical agents but with better data efficiency.
Study helical motions of lines in 3D spaces, solving control problems.
problem Controlling helical motions of lines in 3D spaces.
method Analyzing control systems on manifolds of oriented geodesics in 3D spaces of different curvatures.
result The system is controllable if and only if alpha^2 ≠ kappa.
New method uses patchworking to represent oriented matroids.
problem Representing oriented matroids from polyhedral structures.
method Variant of Viro's patchworking, controlled cell merging process.
result Achieved a combinatorial manifestation of patchworking.
We describe how the dynamical system of rolling two n-dimensional connected, oriented Riemannian manifolds M and M^ without twisting or slipping, can be lifted to a nonholonomic system of elements in the product of the oriented orthonormal frame bundles belonging to the manifolds. By considering the lifted pr…
The study analyzes how wartime controls influenced zaibatsu stock prices in Japan.
problem How wartime economic controls affected zaibatsu stock prices in Japan.
method Developed a four-portfolio asset-pricing model and used a CAPM-AR(p)-SV event-study framework.
result Wartime economic controls influenced stock prices through financing wedges and zaibatsu affiliation.
Paper proposes a method to generate task-oriented dialogue queries.
problem Scarcity of training data for task-oriented dialogue systems.
method Conditional variational autoencoder for intent-specific sentence generation and query transfer protocol.
result Our method improves the diversity of generated queries without compromising quality.
Hypernom uses VR headset orientation to navigate a 4D polytope in 3D space.
problem Navigating a 4D polytope in a 3D VR environment.
method Radial projection to S^3, stereographic projection to 3D, quaternion-based orientation control.
result Players can explore all orientations of a 4D polytope in a 3D VR game.
An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature k-symplectic formalism is used to provide the optimal control problems associated to some families of partial dif…
Paper proposes a new method for quantizing channel state information to optimize resource allocation.
problem Optimizing resource allocation for a receiver sending quantized channel state information to a transmitter.
method Introducing a task-oriented approach where the receiver sends the right amount of information to the transmitter.
result Analytical solution for optimal task-oriented CSI quantizer found for a specific energy-efficient power control problem.
New conditions for stabilizing systems are shown to be independent but stronger under certain conditions.
problem Necessary conditions for stabilizing feedback control systems.
method Extensions of Brockett's and Coron's conditions in fiber and vector bundle pictures.
result The conditions are independent in the fiber bundle picture but stronger in the vector bundle picture under specific conditions.
Study helps start-ups choose best activities to succeed through milestones.
problem Navigating multiple milestones in multi-activity start-ups.
method Stochastic control model with multiple controls, optimal policy analysis.
result Optimal strategies depend on riskiness and cost-effectiveness.
This paper presents a study in task-oriented approach to stroke rehabilitation by controlling a haptic device via near-infrared spectroscopy-based brain-computer interface (BCI). The task is to command the haptic device to move in opposing directions of leftward and rightward movement. Our study consists of data acquis…
The paper studies the geometry of flat manifolds with controlled holonomy.
problem Investigating the geometry of asymptotically flat manifolds with specific properties.
method Analyzes torus fibrations and Hitchin-Thorpe inequalities for Ricci-flat 4-manifolds.
result Proves that certain flat metrics on 4-manifolds are isometric to Euclidean or Taub-NUT.
CitySim dataset captures vehicle trajectories for safety research.
problem Lack of fine-grain vehicle trajectories for safety-oriented research.
method Five-step procedure: video stabilization, object filtering, stitching, detection, and error filtering.
result CitySim dataset improves safety evaluations and facilitates digital-twin research.
This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show for example that the configuration space of two points on the complete graph of fi…
Proposes a new reinforcement learning method to improve agent performance in control tasks.
problem Shortcomings of maximum likelihood estimation in model-based reinforcement learning.
method Directly optimizes expected returns using implicit differentiation of a Bellman optimality function.
result Empirical evidence shows improved performance in model misspecification regime.
Unified method for managing dynamic power flows using convex optimization.
problem Optimizing power flows in networks over time.
method Unified method based on convex optimization, including model predictive control and handling uncertainty.
result Developed a real-time control strategy for dynamic power flows.
New constructions show manifold volumes are dense in non-negative reals.
problem Understanding the spectrum of simplicial volumes in manifolds.
method Group homology constructions and manifold constructions using cross-products and Thom realisation.
result The set of simplicial volumes of orientable closed connected manifolds is dense in R≥0 for dimensions > 3, and every non-negative rational number is a simplicial volume for dimension 4. FPL allows users to control their data in federated top-N recommendation.
problem Data privacy in recommendation services.
method Federated Learning with learning to rank optimization.
result Users can control the amount of sensitive data shared with a central server.
Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose sectional curvature is locally controlled and whose thick part becomes asymptotically hyperbolic and has a sufficiently small volume, then M is Seifert fibred or contains an inco…
Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a decomposition as required for (i) for all closed, oriented 4-manifolds. As a corollary, w…
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with …
Study dynamics and topology of flows near non-saddle sets or W-sets.
problem Understanding the dynamics and topology of flows near specific invariant sets.
method Cohomological relations and global properties analysis.
result Dynamical classification of surfaces and robustness of non-saddle-sets.
Study optimizes portfolio to minimize relative drawdown duration, penalizing unfavorable performance states.
problem Minimizing relative drawdown duration in portfolio optimization relative to a benchmark.
method Introduces a benchmark-relative drawdown-duration criterion penalizing unfavorable performance states. Uses a one-dimensional Markovian representation and Hamilton-Jacobi-Bellman equation.
result Derives explicit projection-based characterization of the optimal feedback control and identifies geometric settings for unique strong solutions.
In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? We do so by constructing compact Riemann surfaces from oriented 3-regular graphs. The set for such Riemann surfaces is dense in the space of all compact Riemann surfaces, namely Belyi su…
Novel BCI algorithm combines imitation learning with optimal control.
problem Training brain-computer interfaces for naturalistic movements.
method Adapting imitation learning (DAgger) to brain-computer interfaces.
result Characterized algorithmic variants and bounds on regret rates.
Proves path-connectedness of metrics on 3-manifolds with positive scalar curvature.
problem Proving path-connectedness of metrics on 3-manifolds with positive scalar curvature.
method Uses Ricci flow with surgery and infinite connected sums with geometry control.
result Proves the moduli space of metrics is path-connected.
The paper finds a special hypersurface in a manifold with positive Ricci curvature.
problem Finding a special hypersurface in a manifold with positive Ricci curvature.
method Equivariant min-max method applied to G-manifolds. result The hypersurface is a multiplicity one minimal G-hypersurface. Study develops a data-based model for in-cylinder pressure and cyclic variations in RCCI engines.
problem Lack of models capturing cyclic variations in combustion concepts like RCCI.
method Combines Principle Component Decomposition and Gaussian Process Regression.
result Model predicts combustion measures with high accuracy, especially peak-pressure rise-rate.
Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We define folded holomorphic maps, i.e. pseudo-holomorphic maps that are discontinuou…
The paper defines criteria for when graph manifold groups have isomorphic profinite completions.
problem Determining properties of 3-manifolds from their profinite completions.
method Criteria for isomorphic profinite completions of graph manifold groups.
result Criteria for isomorphic profinite completions of graph manifold groups.
Estimates hypersurface closeness to geodesic spheres using second fundamental form norms.
problem Understanding the closeness of hypersurfaces to geodesic spheres.
method Explicit estimates and inverse mean curvature flow.
result Best possible order of decay in C∞-bounded hypersurfaces. A new algorithm tracks aircraft rotations using multiple sensors.
problem Tracking aircraft rotations with multiple sensors in a robust and unique solution.
method Developed a distributed quaternion Kalman filter for three-dimensional space.
result The algorithm is robust to sensor and link failure and avoids gimbal lock.
We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly positive isotropic curvature. We also generalize the same nonexistence result to higher dimensions provided that the ambient …
Proves contractibility of a curve traced multiple times under certain length constraints.
problem Contractibility of a curve traced multiple times under length constraints.
method Analyzes simple closed curves on Riemannian manifolds and their homotopies.
result If a multiple-traced curve is contractible, the original curve is contractible under similar length constraints.
Unified framework for optimizing treatment quantiles considering risk and efficacy.
problem Maximizing treatment outcomes while controlling risk in sequential clinical decisions.
method Risk-Aware Quantile Dynamic Treatment Regimes (RQDTR) framework that optimizes a prespecified quantile of the cumulative potential outcome while incorporating treatment-related risk.
result Improves tail-oriented efficacy and achieves more favorable benefit-risk trade-offs compared to existing methods.
The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description …
New instability criterion for semi-Riemannian geodesics.
problem Stability of closed geodesics in semi-Riemannian geometry.
method Spectral flow and Morse indices.
result General instability criterion for timelike and spacelike geodesics.
The paper proves the existence of CMC surfaces with controlled topology in 3-manifolds.
problem Proving the existence of constant mean curvature surfaces with specific topological constraints.
method Min-max construction and convergence to a CMC-parametrized varifold.
result Existence of a non-trivial, branched immersion of a closed Riemann surface with constant mean curvature in a 3-manifold.
CoDA augments data with counterfactuals from local causal structures.
problem Improving sample efficiency in RL with complex dynamic processes.
method Local causal models (LCMs) and Counterfactual Data Augmentation (CoDA).
result CoDA significantly improves RL agent performance in locally factored tasks.
Study on oriented disingquandles for distinguishing singular links.
problem Distinguishing singular links of different colors.
method Introduced oriented dichromatic singular links and oriented disingquandles to define invariants.
result Found invariants that can distinguish some singular links.
The paper explores when ML estimator outperforms MMSE in finite-length experiments.
problem When does maximum likelihood estimator outperform minimum mean square error estimator?
method Application-oriented optimal experiment design with end-performance metrics.
result ML estimator can outperform MMSE in certain finite-length experiments.
The paper defines H-orientability for surfaces in the Heisenberg group and finds non-H-orientable surfaces.
problem Defining orientability in the Heisenberg group for surfaces.
method Defined H-orientability for H-regular 1-codimensional surfaces in Hn. result Existence of non-H-orientable H-regular surfaces in H1. Paper extends group actions on Seifert manifolds with non-orientable base space.
problem Finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds with non-orientable base space.
method Constructing a double cover and isomorphism between fiber-preserving diffeomorphisms and actions on the cover.
result Construction of all actions satisfying a condition on the obstruction term and structure of finite groups.
Analog of Kauffman bracket for non-orientable knots in thickened surface.
problem Defining an invariant for non-orientable knots in a non-orientable surface.
method Proposes an analog of the Kauffman bracket polynomial with modified sign rules.
result Polynomial is an isotopy invariant and independent of classical Kauffman for orientable covers.
Paper proves achiral Lefschetz fibrations from non-orientable Lefschetz fibrations.
problem Understanding achiral Lefschetz fibrations from non-orientable ones.
method Composition of standard orientation double covering map and non-orientable Lefschetz fibration.
result Specification of a monodromy factorization for the composition.
Study trisections of non-orientable 4-manifolds with boundary.
problem Understanding trisections in non-orientable 4-manifolds.
method Introduced trisections of non-orientable 4-manifolds with boundary, proved a non-orientable analogue of a theorem, and discussed adaptation of trisection theory.
result Existence of trisection diagrams and Kirby diagrams for closed non-orientable 4-manifolds.
Non-orientable Lagrangian cobordisms exist for Legendrian knots, differing from orientable ones.
problem Understanding non-orientable Lagrangian cobordisms for Legendrian knots.
method Analyzing symplectization of standard contact 3-space and using exact, non-orientable Lagrangian cobordisms.
result Existence of non-orientable Lagrangian endocobordisms with crosscap genus being a positive multiple of 4.