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.
Rotation systems can't always be drawn in surfaces.
Discrete-time systems can be characterized by simple flat coordinates and their shifts.
Researchers solve boundary and scattering rigidity problems for magnetic systems.
In this paper, we consider a compact Riemannian manifold with boundary, endowed with a magnetic potential and a potential . For brevity, this type of systems are called $\MP$-systems. On simple $\MP$-systems, we consider both the boundary rigidity problem and scattering rigidity problem, see the introduction for…
Paper proves trajectories of Chaplygin systems are reparametrized geodesics.
Geometric models for Lie algebras from simple singularities.
New superintegrable systems derived from Frobenius structures.
Cross-validation methods help learn dynamical systems from data.
A simple guide to understanding hierarchical causality in complex systems.
We classify the simple sheaves microsupported along the conormal bundle of a knot. We also establish a correspondence between simple sheaves up to local systems and augmentations, explaining the underlying reason why knot contact homology representations detect augmentations.
We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved measure and when internal symmetries are present these are factored out via a process…
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
We present a new proof of the classification of complex simple Lie algebras via the projective geometry of homogeneous varieties. Our proof proceeds by constructing homogeneous varieties using the ideals of the secant and tangential varieties of homogeneous varieties already constructed. Our algorithms make no referenc…
In the past, Acoustic Scene Classification systems have been based on hand crafting audio features that are input to a classifier. Nowadays, the common trend is to adopt data driven techniques, e.g., deep learning, where audio representations are learned from data. In this paper, we propose a system that consists of a …
Study Toda systems blowup masses linked to Weyl groups.
Study on magnetic field and potential systems to prove rigidity results.
Improved forecasting for irregularly-sampled time series using kernel flows.
This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the corresponding complete flag variety. The motivation comes from the viewpoint on the Toda field theories as Darboux integrable differential systems as…
In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmuller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmuller geodesics and lines of minima. We also sho…
Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.
We consider collections of disjoint simple closed curves in a compact orientable surface which decompose the surface into pairs of pants. The isotopy classes of such curve systems form the vertices of a 2-complex, whose edges correspond to certain simple moves in which only one curve changes, and whose 2-cells correspo…
We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple…
We classify the systems of -roots of the flag manifolds of the exceptional compact simple Lie groups with the second Betti number .
As energy markets begin clearing at sub-hourly rates, their interaction with load control systems becomes a potentially important consideration. A simple model for the control of thermal systems using market-based power distribution strategies is proposed, with particular attention to the behavior and dynamics of elect…
Automated trading systems on developed and emerging capital markets are studied in this paper. The standard for developed market is automated trading system with 40-days simple moving average. We tested it for the index SIX Industrial for 1000 and 730 trading days of the slovak emerging capital market. The Buy and Hold…
We study velocity correlations induced by diffusion and dissipation in a simple dissipative dynamical system. We observe that diffusion, as a result of time reversible microscopic processes, leads to correlations with different spatial parity from those caused by dissipation, consisting of time irreversible microscopic…
Sharkovskii proved that the existence of a periodic orbit in a one-dimensional dynamical system implies existence of infinitely many periodic orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of shear homeomorphisms of the torus. This is done by obtaining a dynamical order relation on the set of …
Constructs a 4-invariant for graphs at c = 3/8.
We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy-momentum-Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.
Deep neural nets approximate random dynamical system trajectories uniformly in time.
Graphs and local systems count multiwebs.
In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the relationship between the output and input variables. In this paper we present FRU…
Many real-world complex systems across natural, social, and economical domains consist of manifold layers to form multiplex networks. The multiple network layers give rise to nonlinear effect for the emergent dynamics of systems. Especially, weak layers that can potentially play significant role in amplifying the vulne…
Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for s…
Classifies almost-toric systems in four dimensions.
Study focuses on classifying special geometric structures.
Banks in the interbank network can not assess the true risks associated with lending to other banks in the network, unless they have full information on the riskiness of all the other banks. These risks can be estimated by using network metrics (for example DebtRank) of the interbank liability network which is availabl…
A simple spin system is constructed to simulate dynamics of asset prices and studied numerically. The outcome for the distribution of prices is shown to depend both on the dimension of the system and the introduction of price into the link measure. For dimensions below 2, the associated risk is high and the price distr…
Rapid improvements in machine learning over the past decade are beginning to have far-reaching effects. For communications, engineers with limited domain expertise can now use off-the-shelf learning packages to design high-performance systems based on simulations. Prior to the current revolution in machine learning, th…
33 curves on a 3-genus surface, all intersecting at most once.
We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggregate" and "first aggregate, then allocate" type. In both cases, we provide a detailed analysis of the corresponding systemic acceptance sets …
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of linearizability of characteristic webs on all solutions imposes simple second-order con…
The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.
Two geometric realizations of Lie superalgebra found.
We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems with constraints and nonconservative forces, allowing a quite simple and transpar…
A fast method estimates correlations in hybrid systems using observable market data.
Sparse Kernel Flows learns dynamical systems from data.
For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved that this is an Einstein manifold.