arXiv research

Survey of weak form's role in equation learning, parameter estimation, and coarse graining.

This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.

Study confirms Indian stock market is weak form inefficient.

Self-test loss functions improve data-driven modeling of weak-form operators and gradient flows.

Online algorithm identifies PDEs from noisy data snapshots.

The Efficient Market Hypothesis has been a staple of economics research for decades. In particular, weak-form market efficiency -- the notion that past prices cannot predict future performance -- is strongly supported by econometric evidence. In contrast, machine learning algorithms implemented to predict stock price h…

WENDy now estimates nonlinear ODEs with noisy data.

Study on Nijenhuis tensor forms and vanishing properties.

We perform detrending moving average analysis (DMA) and detrended fluctuation analysis (DFA) of the WTI crude oil futures prices (1983-2012) to investigate its efficiency. We further put forward a strict statistical test in the spirit of bootstrapping to verify the weak-form market efficiency hypothesis by employing th…

WSINDy algorithm proves robust to noise in identifying differential equations.

We develop a general framework on Dirichlet spaces to prove a weak form of the Bakry-Émery estimate and study its consequences. This estimate may be satisfied in situations, like metric graphs, where generalized notions of Ricci curvature lower bounds are not available.

Paper proposes an EKF for estimating time-varying market efficiency.

In this paper we show that a substantial Riemannian submersion of S(15) with 7- dimensional fibres is congruent to the standard Hopf fibration. As a consequence we prove a slightly weak form of of the Diameter Rigidity theorem for the Cayley plane which is considerably stronger than the very recent Radius Rigidity Theo…

We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary is contained in a line. In both cases we derive weak forms of the resulting fre…

We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the estimation of such processes using constrained and penalized estimators. As an applica…

We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for o…

Algorithm learns stochastic system dynamics from data.

Method identifies IPS governing equations from particle data efficiently.

Constructs infinite families of hyperbolic knots satisfying a volume conjecture.

The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.

For the first time in mathematical finance field, we propose the local weak form meshless methods for option pricing; especially in this paper we select and analysis two schemes of them named local boundary integral equation method (LBIE) based on moving least squares approximation (MLS) and local radial point interpol…

We prove the existence and uniqueness of continuous solutions to the complex Monge-Ampère type equation with the right hand side in $L^p$, $p>1$, on compact Hermitian manifolds. Next, we generalise results of Eyssidieux, Guedj and Zeriahi \cite{EGZ09, EGZ11} to compact Hermitian manifolds which {\em a priori} are not i…

Study shows how information loss and operation loss are related in feature representations.

We prove the following: 1. Let epsilon>0 and let S_1,S_2 be two closed hyperbolic surfaces. Then there exists locally-isometric covers S'_i of S_i (for i=1,2) such that there is a (1+ε) bi-Lipschitz homeomorphism between S'_1 and S'_2 and both covers S'_i have bounded injectivity radius. 2. Let M be a closed hyperbolic…

Weak form of the Efficiency Market Hypothesis (EMH) excludes predictions of future market movements from historical data and makes the technical analysis (TA) out of law. However the technical analysis is widely used by traders and speculators who steadely refuse to consider the market as a "fair game" and survive with…

I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "progr…

$Γ$-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting $Γ$-structures are free over odd degree generators. We prove that this condition is also sufficient for the existence of $Γ$-structures on manifolds which are nilpotent…

Let $Ω\subset \mathbb R^d\,, d\geq 2$, be a bounded open set, and denote by $λ\_j(Ω), j\geq 1$, the eigenvalues of the Dirichlet Laplacian arranged in nondecreasing order, with multiplicities. The weak form of Pleijel's theorem states that the number of eigenvalues $λ\_j(Ω)$, for which there exists an associated eigenf…

Generalized Calabi-Yau structures, a notion recently introduced by Hitchin, are studied in the case of K3 surfaces. We show how they are related to the classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied by Aspinwall and Morrison. It turns out that K3 surfaces and symplectic structures are b…

Authors compute stable homology of torus knots using a new deformation technique.

Study topological hyperbolicity of moduli spaces of elliptic surfaces.

WSINDy for PDEs robustly identifies models from noisy data.

Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.

Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz-Killing valuations. They date back to the remarkable discovery of H. Weyl that the coefficients of the tube volume polynomial are intrinsic invariants of the metric. …

Examines WENDy-IRLS algorithm's noise robustness and efficiency in various differential equations.

Let $Σ$ be a hypersurface in an $n$-dimensional Riemannian manifold $M$, $n\geqslant 2$. We study the isometric extension problem for isometric immersions $f:Σ\to\mathbb R^n$, where $\mathbb R^n$ is equipped with the Euclidean standard metric. We prove a general curvature obstruction to the existence of merely differen…

Let $G$ be a usc decomposition of $S^n$, $H_G$ denote the set of nondegenerate elements and $π$ be the natural projection of $S^n$ onto $S^n/G$. Suppose that each point in the decomposition space has arbitrarily small neighborhoods with ($n-1$)-sphere frontiers or boundaries which miss $π(H_G)$. If all the arcs are tam…

We use geometric methods to show that given any $3$-manifold $M$, and $g$ a sufficiently large integer, the mapping class group $\mathrm{Mod}(Σ_{g,1})$ contains a coset of an abelian subgroup of rank $\lfloor \frac{g}{2}\rfloor,$ consisting of pseudo-Anosov monodromies of open-book decompositions in $M.$ We prove a sim…

In finance, the weak form of the Efficient Market Hypothesis asserts that historic stock price and volume data cannot inform predictions of future prices. In this paper we show that, to the contrary, future intra-day stock prices could be predicted effectively until 2009. We demonstrate this using two different profita…

Omega ratio, defined as the probability-weighted ratio of gains over losses at a given level of expected return, has been advocated as a better performance indicator compared to Sharpe and Sortino ratio as it depends on the full return distribution and hence encapsulates all information about risk and return. We comput…

Study canonical deformations of complex forms and their cohomology properties.

Extends Hess-Schrader-Uhlenbrock inequality for 1-forms in tamed Dirichlet spaces.

New calculus on spacetimes for nonlinear differential equations.

We present and study a family of metrics on the space of compact subsets of $R^N$ (that we call ``shapes''). These metrics are ``geometric'', that is, they are independent of rotation and translation; and these metrics enjoy many interesting properties, as, for example, the existence of minimal geodesics. We view our s…

Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics w…

We empirically investigated the relationships between the degree of efficiency and the predictability in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the dire…

The report explores conditions for positive or non-negative scalar curvature in 3-manifolds and weak Ricci curvature bounds.

New method learns soliton dynamics from scattering data without assuming known equations.