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.
A new method learns noise characteristics for better state estimation in real-time systems.
Foams have Lie algebra symmetries that simplify web state spaces.
In this work, we give a survey on non characteristic domains of Heisenberg groups. We prove that bounded domains which are diffeomorphic to the solid torus having the center of the group as rotation axis, are non characteristic. Then, we state the following conjecture : The bounded non characteristic domains of the Hei…
Study L^2-Betti numbers in prime characteristic for a conjecture about 2-complex towers.
A ML model accurately replicates chaotic dynamics across various parameters.
The paper generalizes current constructions to cohesive modules and characteristic forms.
The study proposes using TD error for selecting σ in Q(σ, λ).
It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi's diastasis and its domain of definition, the Euler-Poincaré characteristic, the number of Borel-Morse cells, the Kodaira embedding theorem.
We extend knot Floer homology to string links in D^{2} \times I and to d-based links in arbitrary three manifolds, without any hypothesis on the null-homology of the components. As for knot Floer homology we obtain a description of the Euler characteristic of the resulting homology groups (in D^{2} \times I) in terms o…
We present a compared analysis of some properties of indefinite almost -manifolds and indefinite -manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and -sectional curvature of indefinite almost $\…
Survey on ML advances for personalized prediction considering entity characteristics.
We prove Chern conjecture, which states that the Euler characteristic vanishes for closed flat affine manifolds. Our key innovation is a deformation argument for the Euler form.
These are lecture notes prepared for the summer school "Geometric, algebraic and topological methods in quantum field theory", held in Villa de Leyva in July 2017. Our goal is to provide an introduction to a conjecture of Chern that states that the Euler characteristic of a closed affine manifold vanishes. We present p…
We prove a discrete Gauss-Bonnet-Chern theorem which states where summing the curvature over all vertices of a finite graph G=(V,E) gives the Euler characteristic of G.
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus a…
Efficient method classifies locally stationary time series based on second-order characteristics.
New bounds on HOMFLY polynomial for homogeneous links.
We find that factors explaining bank loan recovery rates vary depending on the state of the economic cycle. Our modeling approach incorporates a two-state Markov switching mechanism as a proxy for the latent credit cycle, helping to explain differences in observed recovery rates over time. We are able to demonstrate ho…
The theorems we proved describe the structure of economic equilibrium in the exchange economy model. We have studied the structure of property vectors under given structure of demand vectors at which given price vector is equilibrium one. On this ground, we describe the general structure of the equilibrium state and gi…
We determine several necessary and sufficient conditions for a closed almost-complex orbifold with cyclic local groups to admit a nonvanishing vector field. These conditions are stated separately in terms of the orbifold Euler-Satake characteristics of and its sectors, the Euler characteristics of the underlyin…
State representation learning aims at learning compact representations from raw observations in robotics and control applications. Approaches used for this objective are auto-encoders, learning forward models, inverse dynamics or learning using generic priors on the state characteristics. However, the diversity in appl…
Clusters cryptocurrency market states via cross correlation analysis.
A topological version of a longstanding conjecture of H. Hopf, originally proposed by W. Thurston, states that the sign of the Euler characteristic of a closed aspherical manifold of dimension depends only on the parity of . Gromov defined several hyperbolization functors which produce an aspherical manifold …
Proposes interpretable time series classification through extracted features.
The paper reveals a property of chromatic homology for complete graphs.
We characterize the rigidity of Carnot groups in the class of contact maps in terms of complex characteristics. Furthermore, we obtain a Liouville type theorem for Carnot groups which states that 1-quasiconformal maps form finite dimensional Lie groups.
The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and …
CCs learn high-dimensional distributions from heterogeneous data.
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology by using the "Kauffman states" on a graph diagram.
The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep ne…
Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model. One popular approach is to learn data driven models in order to compensate for i…
Generates synthetic data for benchmarking unsupervised outlier detection.
We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the kernel space. The kernel space contains a set of meta states which are desired …
Enhances investment performance by leveraging cross-market information.
In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generali…
The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded from below by a logarithmic function of the manifold dimension. The main new to…
The recent advent of automated neural network architecture search led to several methods that outperform state-of-the-art human-designed architectures. However, these approaches are computationally expensive, in extreme cases consuming GPU years. We propose two novel methods which aim to expedite this optimization prob…
We define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a chain complex whose generators correspond to Kauffman states for a knot diagram. The definition uses decompositions of knot diagrams: to a co…
Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket. This includes a categorification of brackets skein relation. Then we incorporat…
A Theorem of Kirichenko states that the torsion 3-form of the characteristic connection of a nearly Kähler manifold is parallel. On the other side, any almost hermitian manifold of type admits a unique connection with totally skew symmetric torsion. In dimension six, we generalize Kirichenko's Theorem an…
Spatio-temporal (ST) data, which represent multiple time series data corresponding to different spatial locations, are ubiquitous in real-world dynamic systems, such as air quality readings. Forecasting over ST data is of great importance but challenging as it is affected by many complex factors, including spatial char…
Research in deep reinforcement learning (RL) has coalesced around improving performance on benchmarks like the Arcade Learning Environment. However, these benchmarks conspicuously miss important characteristics like abrupt context-dependent shifts in strategy and temporal sensitivity that are often present in real-worl…
In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defi…
We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be represented as a Markov process with substantially reduced number of states with explicitl…
Algebraic treatment of connection reduction over a special disc.
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also holds for connections with metric torsion in the case of non-positive Euler characte…
The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations h…
The paper explores existence of specific almost complex manifolds with unique Betti numbers.