A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Geodesics on Kähler manifold potentials are paths of least action.
The paper introduces metrics to rank potential outcomes for better decision-making.
hyperSBINN improves drug cardiosafety assessment by efficiently modeling cardiac action potentials.
As Computer Vision moves from a passive analysis of pixels to active analysis of semantics, the breadth of information algorithms need to reason over has expanded significantly. One of the key challenges in this vein is the ability to identify the information required to make a decision, and select an action that will …
The Ma-Trudinger-Wang curvature --- or cross-curvature --- is an object arising in the regularity theory of optimal transportation. If the transportation cost is derived from a Hamiltonian action, we show its cross-curvature can be expressed in terms of the associated Jacobi fields. Using this expression, we show the l…
Three types of Einstein metrics are disqualified as potential local maxima.
Kähler soliton surfaces are typically toric under generic conditions.
New method minimizes decision errors in large treatment spaces.
We identify action representations from video data, proving their statistical benefits.
Explores new perspectives in transverse index theory for Lie group actions.
Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on the Kaehler reduction of M. As a consequence we can derive improvements of several classical results known for more general Hamiltonian red…
Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the cost is given by minimizing a Lagrangian action.
We utilize the Ozsvath-Szabo contact invariant to detect the action of involutions on certain homology spheres that are surgeries on symmetric links, generalizing a previous result of Akbulut and Durusoy. Potentially this may be useful to detect different smooth structures on 4-manifolds by cork twisting operation.
Improved Bayesian regret bound for linear Thompson sampling with general distributions.
Study on spectral sequence for abelian Lie group actions, with bounds and applications.
We study the action of conformal transformations of the ambient space on the Dirac operator coming into the Weierstrass (or spinor) representation of a torus in the Euclidean four-space. It is showed that such an action generates a flow acting on the potential of the operator, that this flow is described by a nonlinear…
We consider a natural mechanical system on a Finsler manifold and study its \emph{curvature} using the intrinsic Jacobi equations (called \emph{Jacobi curves}) along the extremals of the least action of the system. The curvature for such a system is expressed in terms of the Riemann curvature and the Chern curvature (i…
We describe the action of the (Mobius) inversion on the data of the Weierstrass representation of surfaces in the three-space and show that the Moutard transformation of two-dimensional Dirac operators has a geometrical meaning: it maps the potential of a surface into the potential of its inversion.
A second order self-adjoint operator is uniquely defined by its principal symbol and potential if it acts on half-densities. We analyse the potential as a compensating field (gauge field) in the sense that it compensates the action of coordinate transformations on the second derivatives in…
UTE improves reinforcement learning by measuring action uncertainty, enhancing policy learning efficiency.
In this technical note we give a purely geometric understanding of discrete torsion, as an analogue of orbifold Wilson lines for two-form tensor field potentials. In order to introduce discrete torsion in this context, we describe gerbes and the description of certain type II supergravity tensor field potentials as con…
We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the Bloch-Wigner functions. We prove the first and second variation formulas for the cla…
For a compact Riemannian manifold with boundary, endowed with a magnetic potential , we consider the problem of restoring the metric and the magnetic potential from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this…
Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.
The universal Liouville action equals the renormalized volume of a hyperbolic 3-manifold.
New algorithm reduces regret in private online learning with optimal gap-dependent rate.
Paper tackles optimal policy learning with observational data in multi-action scenarios.
MaxMax Q-Learning improves coordination in multi-agent reinforcement learning by refining action selection.
Probabilistic model for exhaustion in infinite-genus curve complexes.
The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not efficiently capture the setting where the set of available decisions (actions) at each time step is stochastic. Recently, the stochastic action set Markov decision process (SAS-MDP) formulation has b…
A method to generate long-range human actions by leveraging graph convolutional networks and self-attention.
We study relations between quaternionic Riemannian manifolds admitting different types of symmetries. We show that any hyperKahler manifold admitting hyperKahler potential and triholomorphic action of S^1 can be constructed from another hyperKahler manifold (of lower dimention) with an action of S^1 which fixes one com…
Intelligent agents can learn to represent the action spaces of other agents simply by observing them act. Such representations help agents quickly learn to predict the effects of their own actions on the environment and to plan complex action sequences. In this work, we address the problem of learning an agent's action…
Let O be a nilpotent orbit in g^C where G is a compact, simple group and g=Lie(G). It is known that O carries a unique G-invariant hyperKähler metric admitting a hyperKähler potential compatible with the Kirillov-Kostant-Souriau symplectic form. In this work, the hyperKähler potential is explicitly calculated when O is…
Advanced driver assistance systems (ADAS) can be significantly improved with effective driver action prediction (DAP). Predicting driver actions early and accurately can help mitigate the effects of potentially unsafe driving behaviors and avoid possible accidents. In this paper, we formulate driver action prediction a…
We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a funct…
Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the can…
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how to obtain the invariantized Euler-Lagrange equations and the space of conservati…
New algorithm allows IGL to work with action-inclusive feedback.
New algorithm optimizes online decision-making with dynamically generated actions.
We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish …
Math verifies Aganagic's proposal for Khovanov homology.
Adaptive discretization improves model-based RL in large spaces.
Training deep reinforcement learning agents complex behaviors in 3D virtual environments requires significant computational resources. This is especially true in environments with high degrees of aliasing, where many states share nearly identical visual features. Minecraft is an exemplar of such an environment. We hypo…
Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the prepotential of the special Kahler geometry.
Mathematical models of a cellular action potential in cardiac modelling have become increasingly complex, particularly in gating kinetics which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalised medicine to inform clinical decision-making, it is cri…
New method for natural policy gradients converges linearly.
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we propose an actor-critic reinforcement learning algorithm that provably converges t…