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.
Framework for transforming manifold constraints into unconstrained problems.
Taking configuration space as a Lie group, the trivialized Euler-Lagrange and Hamilton's equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyjew's symplectic space. Euler-Poincaré and Lie-Poisson equations are presented as Lagrangian submanifolds of the reduced Tulczyjew's symplecti…
Paper defines dynamical coherence for flows and proves it under specific conditions.
We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both Hamiltonian and Lagrangian dynamics on Tulczyjew's symplectic space which is tangent o…
Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality in terms of dynamical properties of generators of the holonomy groups are found. The non-triviality for…
This paper is devoted to rigidity of smooth bundles which are equipped with fiberwise geometric or dynamical structure. We show that the fiberwise associated sphere bundle to a bundle whose leaves are equipped with (continuously varying) metrics of negative curvature is a topologically trivial bundle when either the ba…
In this communication, complex systems with a near trivial dynamics are addressed. First, under the hypothesis of equiprobability in the asymptotic equilibrium, it is shown that the (hyper) planar geometry of an -dimensional multi-agent economic system implies the exponential (Boltzmann-Gibss) wealth distribution an…
Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler-Poincaré equations on the matched pair of Lie algebra…
A (smooth) dynamical system with transformation group is a triple , consisting of a unital locally convex algebra , the -torus and a group homomorphism $α:\mathbb{T}^n\rightarrow\Aut(A)$, which induces a (smooth) continuous action of on . In this…
We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of the classical dynamical Yang-Baxter equation on simple Lie algebras as classified by the same authors. O…
In this paper we investigate some connections between Topological Dynamics, the theory of G-Principal Bundles, and the theory of Locally Trivial Groupoids.
New sampling method on Lie groups converges quickly.
It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic two-form and canonical Poisson bracket are explicitly written. Various symplectic…
We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to choose sub-sets of a problem which are most amenable to its abilities to focus on s…
Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic s…
Study ping-pong dynamics in hyperbolic-like groups with non-simple points.
New kernels from ELU and GELU networks reveal non-trivial fixed points.
We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affe…
Study of volume dynamics at market spread in Bitcoin/USD.
Neuromorphic Computing is a nascent research field in which models and devices are designed to process information by emulating biological neural systems. Thanks to their superior energy efficiency, analog neuromorphic systems are highly promising for embedded, wearable, and implantable systems. However, optimizing neu…
We study the dynamical behavior of high-frequency data from the Korean Stock Price Index (KOSPI) using the movement of returns in Korean financial markets. The dynamical behavior for a binarized series of our models is not completely random. The conditional probability is numerically estimated from a return series of K…
Chronological Causal Bandits (CCB) tackles dynamic causal decision-making.
A fast spectral algorithm detects community structure in evolving graphs.
In this work we analyse quantitatively the interplay between the loss landscape and performance of descent algorithms in a prototypical inference problem, the spiked matrix-tensor model. We study a loss function that is the negative log-likelihood of the model. We analyse the number of local minima at a fixed distance …
Let F be a codimension-one, C^2-foliation on a manifold M without boundary. In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is non-zero, then F has a hyperbolic resilient leaf. Our approach is based on methods of C^1-dynamical systems, and does not use the classification theory of C^2-foliations.…
Explains planetary motion in a sub-Riemannian setting.
We give a lower bound for the length of a non-trivial geodesic loop on a simply-connected and compact manifold of even dimension with a non-reversible Finsler metric of positive flag curvature. Harris and Paternain use this estimate in their recent paper [HP] to give a geometric characterization of dynamically convex F…
Derives effective continuous dynamics for adaptive SGD methods.
New obstruction found for embedding Riemannian manifolds into Euclidean spaces.
PenduMAV is a 6-input omnidirectional MAV without internal forces.
The possibility that the collective dynamics of a set of stocks could lead to a specific basket violating the efficient market hypothesis is investigated. Precisely, we show that it is systematically possible to form a basket with a non-trivial autocorrelation structure when the examined time scales are at the order of…
New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear state space models provide an interpretable signal processing framework by combinin…
New method detects long-term structures with internal dynamics in time series data.
Study of adjoint orbits in simplest non-trivial Lie algebra case.
Neural networks improve predictions of complex network dynamics.
New algorithms minimize dynamic regret in non-stationary online learning.
A framework for stable dynamic network embeddings using static methods.
Study of flows on circle bundles over translation surfaces, showing decay of correlations.
Study on dynamics of non-linear autoencoders learning principal components.
Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average <f(i)>: sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The non-trivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provid…
New surfaces with special geodesic and horocycle behaviors discovered.
Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this work, we uncover a phenomenon in which the behavior of these complex networks -- …
We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence…
We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is equal to 1/3. We found a formula connecting characteristic exponents with explicit …
Doubly fair dynamic pricing ensures equal prices for different groups over time.
Study of spacetime dynamics in 2+1 gravity leads to Thurston boundary.
In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, which require the prior choice of a connection. Bearing these facts in mind, we analyze the situation in the jet-bundle description of time-depe…
We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the -action associated to this vector field is not necessarily trivial. We generalize the averaging procedure \cite{A…