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.
Study on elastic curves with variable stiffness, derived from bending energy.
Paper solves pendulum swing-up problem using RL.
In this paper we show that there are applications that transform the movement of a pendulum into movements in . This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to the equation of a pendulum. Those properties are also considered in…
This paper studies the topology of the constant energy surfaces of the double spherical pendulum.
Generative ODE model learns unknown variables in medical systems.
Discover conservation laws from trajectories using a neural network.
Study of sub-Riemannian problem on specific Lie groups, revealing symmetries and bounds.
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 …
This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised fea…
An energy based approach for stabilizing a mechanical system has offered a simple yet powerful control scheme. However, since it does not impose such strong constraints on parameter space of the controller, finding appropriate parameter values for an optimal controller is known to be hard. This paper intends to generat…
This paper classifies Legendre singularities of sub-Riemannian geodesics on surfaces.
This note complements the inspiring work on dimensional analysis and market microstructure by Kyle and Obizhaeva [18]. Following closely these authors, our main result shows by a similar argument as usually applied in physics the following remarkable fact. If the market impact of a meta-order only depends on four well-…
Method learns low-dim. state vars from noisy high-dim. data.
This paper detects Markov violations in RL with noise, improving policy development.
Reinforcement Learning methods are capable of solving complex problems, but resulting policies might perform poorly in environments that are even slightly different. In robotics especially, training and deployment conditions often vary and data collection is expensive, making retraining undesirable. Simulation training…
Formula for integrating random variables on hyperbolic surfaces.
Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn universal embeddings of time series. Unlike previous works, it is scalable with respe…
Based on empirical financial time-series, we show that the "silence-breaking" probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going low-variability period. Such a scaling law has been previously predicted theoretically [R. …
A new kernel Stein test assesses fit for variable-length sequential data.
Recurrent neural networks and sequence to sequence models require a predetermined length for prediction output length. Our model addresses this by allowing the network to predict a variable length output in inference. A new loss function with a tailored gradient computation is developed that trades off prediction accur…
Estimates system parameters from a single observation using kernel-based score.
SentenceMIM is a probabilistic auto-encoder for language data, trained with Mutual Information Machine (MIM) learning to provide a fixed length representation of variable length language observations (i.e., similar to VAE). Previous attempts to learn VAEs for language data faced challenges due to posterior collapse. MI…
\textit{SummerTime} seeks to summarize globally time series signals and provides a fixed-length, robust summarization of the variable-length time series. Many classical machine learning methods for classification and regression depend on data instances with a fixed number of features. As a result, those methods cannot …
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
The task of clustering unlabeled time series and sequences entails a particular set of challenges, namely to adequately model temporal relations and variable sequence lengths. If these challenges are not properly handled, the resulting clusters might be of suboptimal quality. As a key solution, we present a joint clust…
We show that the span of the variable in the Lawrence-Krammer-Bigelow representation matrix of a braid is equal to the twice of the dual Garside length of the braid, as was conjectured by Krammer. Our proof is close in spirit to Bigelow's geometric approach. The key observation is that the dual Garside length of a …
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As a consequence, learning algorithms are rarely applied on safety-crit…
Paper constructs new minimal submanifolds in spheres by spinning given ones.
The prevalence of wearable sensors (e.g., smart wristband) is creating unprecedented opportunities to not only inform health and wellness states of individuals, but also assess and infer personal attributes, including demographic and personality attributes. However, the data captured from wearables, such as heart rate …
New method improves bivariate causal discovery by accurately estimating cause variable complexity.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
Current end-to-end deep Reinforcement Learning (RL) approaches require jointly learning perception, decision-making and low-level control from very sparse reward signals and high-dimensional inputs, with little capability of incorporating prior knowledge. This results in prohibitively long training times for use on rea…
Paper detects hierarchical changes in latent variable models from data streams.
Paper proposes adaptive control for unknown systems using reinforcement learning.
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Cor…
Study finds saddle connections on random surfaces follow Poisson distribution.
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk…
We present a self-contained proof of the Gauss-Bonnet theorem for two-dimensional surfaces embedded in using just classical vector calculus. The exposition should be accessible to advanced undergraduate and non-expert graduate students. It may be viewed as an illustration and exercise in multivariate calculus and…
Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a c…
New coding theorem shows achievable rate matches theoretical limit.
The paper solves pentagon equations using triangulations and edge transformations.
The study constructs a Lorentzian length space and explores its properties and relationships with metric and causal geometry.
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical optimization. Through a computational study involving a stochastic version of a well …
Time Series Motif Discovery (TSMD) is defined as searching for patterns that are previously unknown and appear with a given frequency in time series. Another problem strongly related with TSMD is Word Segmentation. This problem has received much attention from the community that studies early language acquisition in ba…
We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute growth rate of these cluster algebras, p…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined relevance has several drawbacks that prevent the selection of optimal input variables i…
Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the length of each white matter fascicle, termed the local connectome. If communicat…
Inverse reinforcement learning (IRL) is used to infer the reward function from the actions of an expert running a Markov Decision Process (MDP). A novel approach using variational inference for learning the reward function is proposed in this research. Using this technique, the intractable posterior distribution of the…