arXiv research

Guaranteed reachable set for unknown nonlinear systems on manifolds.

Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional'' fluctuation theorems, gover…

The paper sets sample complexity bounds for identifying LTI systems from a finite set.

New PDE systems generalize Hawking mass monotonicity.

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 …

New decision support systems use prediction sets to help experts update their predictions, improving performance.

Simplified proof for approximations of set systems.

System uses conformal prediction to help experts make accurate decisions without understanding when to trust it.

New method improves predictive systems with better theoretical guarantees.

Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.

This paper focuses on using the first curvature $κ(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al., arXiv:1808.00290] to $n$-dimensional systems. We prove that for a system $\dot{r}(t)=Ar(t)$, (i) i…

This paper uses multivariate probability models to assess financial system risks.

The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.

We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting fr…

We investigated the impact of noisy linguistic features on the performance of a Japanese speech synthesis system based on neural network that uses WaveNet vocoder. We compared an ideal system that uses manually corrected linguistic features including phoneme and prosodic information in training and test sets against a …

Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid contr…

The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-si…

Study connects bank default models using dynamic contagion.

New risk measures for financial networks avoid external capital, reducing systemic risk.

The paper extends static Systemic Risk Measures to a conditional setting.

We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space o…

Improves data-driven reachability estimation for complex systems.

Study dual representations for quasiconvex systemic risk measures.

Framework for managing cyber risks in networks.

Optimizes long-term social welfare in recommender systems by matching users to providers.

In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze her…

Is it possible to generally construct a dynamical system to simulate a black system without recovering the equations of motion of the latter? Here we show that this goal can be approached by a learning machine. Trained by a set of input-output responses or a segment of time series of a black system, a learning machine …

Automated trading system with preprocessing and reinforcement learning.

As machine learning systems move from computer-science laboratories into the open world, their accountability becomes a high priority problem. Accountability requires deep understanding of system behavior and its failures. Current evaluation methods such as single-score error metrics and confusion matrices provide aggr…

The policy objective of safeguarding financial stability has stimulated a wave of research on systemic risk analytics, yet it still faces challenges in measurability. This paper models systemic risk by tapping into expert knowledge of financial supervisors. We decompose systemic risk into a number of interconnected seg…

Recommender system research suffers from a disconnect between the size of academic data sets and the scale of industrial production systems. In order to bridge that gap, we propose to generate large-scale user/item interaction data sets by expanding pre-existing public data sets. Our key contribution is a technique tha…

The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities. In this paper, we resolve two longstanding open problems on bounding the VC-dimension of two fundamental set systems: $k$-fold unions/intersections of half-s…

Study on learning to predict dynamical systems without assuming their structure.

In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.

Paper defines invariants for elliptic Weyl groups and connects them to Frobenius structures.

The study describes metrics geodesically compatible with Nijenhuis operators and their applications to integrable systems.

Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…

The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the interconnectedness of the system entities and the corresponding contagion effects. This has…

Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks (ANNs) can compete with the optimal bounds for linear systems, where convex optim…

Study systemic risk measures adjusted to financial markets.

RoyalFlush system improves multi-speaker ASR in M2MeT challenge.

Finite-gap solutions approximate jets of initial data for certain BKM systems.

Paper reduces sample complexity for bilinear systems identification to nearly constant.

We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…

The paper characterizes potential functions whose level sets are orbits in mechanical systems.

Category theory generalizes finite type invariants using diagrams systems.

In this article, we define an independence system for a classical knot diagram and prove that the independence system is a knot invariant for alternating knots. We also discuss the exchange property for minimal unknotting sets. Finally, we show that there are knot diagrams where the independence system is a matroid and…

Decision-calibrated prediction sets improve power system operations by reducing unnecessary costs.