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.
Efficient RL in large POMDPs with latent determinism and embeddings.
Divides state space into regions with identical term structure shapes.
In this paper, we calculate the values of the state sum invariants for the lens spaces . In particular, we show that the values of the invariants are determined by and . As a corollary, we show that the state sum is a homotopy invariant for the oriented lens spaces.
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space…
Proves Seidel's conjectures about ideal tetrahedra in hyperbolic 3-space.
Develops a learning model predictive controller for competitive racing.
Active learning selects inputs for GPSSM to learn latent states.
The volume of the quantum mechanical state space over -dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of the determinant in the general setting too. The case when the state space is endo…
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the derivative formulas for this frame field we obtain seven invariant functions. Our…
A new RL paradigm reduces state-action-value function approximation inefficiency.
We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions w…
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…
On certain manifolds, the phase which appears in the scalar product of two coherent state vectors is twice the symplectic area of the geodesic triangle determined by the corresponding points on the manifold and the origin of the system of coordinates. This result is proved for compact Hermitian symmetric spaces using t…
The known manifolds of positive sectional curvature are either homogeneous spaces or biquotients, i.e. quotients of a compact Lie group by a group acting on the left and right simultaneously. The full isometry group of the homogeneous metrics of positive curvature were determined by K.Shankar. Here we determine the iso…
New method uses Indexed Markov Chains for financial data analysis.
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map of Weingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundament…
A financial contract's value is determined by a quantum measurement outcome, and a pricing state exists to value it.
Reduces policy space complexity for reinforcement learning.
The paper proves fundamental theorems for timelike surfaces in Minkowski 4-space.
We propose the application of a high-speed maximum likelihood clustering algorithm to detect temporal financial market states, using correlation matrices estimated from intraday market microstructure features. We first determine the ex-ante intraday temporal cluster configurations to identify market states, and then st…
Study timelike surfaces with parallel mean curvature in Minkowski 4-space.
Adler had shown in 1979 that the Toda system can be given a coad- joint orbit description. We quantize the Toda system by viewing it as a single orbit of a multiplicative group of lower triangular matrices of determinant one with pos- itive diagonal entries. We get a unitary representation of the group with square inte…
The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.
Hill-ADAM optimizes loss landscapes by exploring state space deterministically.
We give a Weierstrass type representation for semi-discrete minimal surfaces in Euclidean 3-space. We then give explicit parametrizations of various smooth, semi-discrete and fully-discrete catenoids, determined from either variational or integrable systems principles. Finally, we state the shared properties that those…
We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential eq…
New proof for symmetric spaces with rectangular lattices.
The paper proves a rigidity theorem for non-compact convex sets in hyperbolic 3-space.
Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equati…
The paper defines and studies canonical parameters on surfaces in 4D space.
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This allows us to introduce principal lines and an invariant moving frame field. Writing derivative formulas…
We give an integral representaion of the zeta-reguralized determinant of Laplacians on three dimensional Heisenberg manifolds, and study a behaivior of the values when we deform the uniform discrete subgroups. Heiseberg manifolds are the total space of a fiber bundle with a torus as the base space and a circle as a typ…
The paper proves a generalized Kauffman-Harary conjecture for prime determinant links.
Feature selection predicts immune state changes in RA mouse model.
A new method for state space partitioning in block particle filtering reduces bias and variance.
Method explains MDP optimal policies and reward collection.
Improved RL in BMDPs reduces regret to O(sqrt(T)+n).
Cohort effects are important factors in determining the evolution of human mortality for certain countries. Extensions of dynamic mortality models with cohort features have been proposed in the literature to account for these factors under the generalised linear modelling framework. In this paper we approach the proble…
This paper is devoted to the problem of choosing the most suitable model of a geometrical system for describing the real crystallographic space. It has been shown that all 230 crystallographic groups used to describe the crystalline structures in a Euclidean space can be presented by elliptic motions in the closed spac…
Study TMF-valued TQFT for closed 3-manifolds using torsion linking pairings.
Natural gradient descent is a robust optimization method for machine learning.
Deep state space model forecasts time series with uncertainty.
A new algorithm for deep Q-learning with robustness to state transition uncertainty.
SPECTRA improves probabilistic energy forecasting by separating trends and uncertainties.
New conditions for GRW space-times to be perfect-fluid space-times.
This work learns a distance function for goal-conditioned RL without prior knowledge.
This paper continues our study, initiated in [arXiv:1108.3370], of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolic links, we show that the geometric type of these surfaces in the Thurston trichotomy is completely determined by a simple gr…