arXiv research

Analyzes intrinsic time in financial markets, linking it to physical time.

Market activity scales near a constant of 0.632 in intrinsic time.

Proves compactness for timed-metric spaces using new distance and maps.

This paper introduces intrinsic time, a new measure of time for complex systems.

Study shows intrinsic timed Hausdorff convergence leads to Gromov-Hausdorff and big bang convergence.

Generally accepted depreciation methods do not compute the intrinsic value of an asset, as they do not factor for the Time Value of Money, a key principle within financial theory. This is disadvantageous, as knowing the intrinsic value of an asset can assist with making effective purchase and sale decisions. By applyin…

New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.

Inference-Time Scaling can be extended to domains prone to systematic failure using intrinsic statistics.

In this article, we study constant mean curvature isometric immersions into $\mathbb{S}^2 \times \mathbb{R}$ and $\mathbb{H}^2 \times \mathbb{R}$ and we classify these isometric immersions when the surface has constant intrinsic curvature. As applications, we use the sister surface correspondence to classify the consta…

In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invari…

In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space E$^3_1$ satisfies a vector differential equation of fourth order. The general so…

New method for long-term sampling of complex dynamics on curved spaces.

Cylinders in warped product spaces have zero curvature.

The intrinsic entropy model accurately estimates stock market volatility.

New method detects anomalies in systems influenced by their environment.

Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) offers a promising way of circumventing the curse and successfully reduces the dep…

We provide the proof that the space of time series data is a Kolmogorov space with $T_{0}$-separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…

Paper introduces CSIE for estimating stock market volatility.

In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$ are given by means of their extrinsic geometry. Under suitable conditions on the shape operator, we classify conformally flat hypersurfaces in terms of …

We compute persistent homology using an intrinsic metric derived from density.

New RL approach uses future state and action visitation measures for better exploration.

Compactness theorem for timed-metric spaces established.

We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent claim as a basis for understanding these phenomena. In a continuous time framewo…

A method uses ITD and XGBoost for precise power transformer fault diagnosis.

The article presents a new entropy model for assessing stock market interest.

Every harmonic map is an intrinsic bi-harmonic map as an absolute minimizer of the intrinsic bi-energy functional, therefore intrinsic bi-harmonic map and its heat flow are more geometrically natural to study, but they are also considerably more difficult analytically than the extrinsic counterparts due to the lack of …

Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.

The paper introduces a new intrinsic reward method for exploration in reinforcement learning.

We introduce an event based framework of directional changes and overshoots to map continuous financial data into the so-called Intrinsic Network - a state based discretisation of intrinsically dissected time series. Defining a method for state contraction of Intrinsic Network, we show that it has a consistent hierarch…

A new reward learning module improves imitation learning in high-dimensional environments.

Survey of intrinsically linked or knotted graphs.

Study on rolling Stiefel manifolds with specific metrics.

The paper studies properties of intrinsically Lipschitz constants in metric spaces.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer th…

Study of potential Carroll structures and special Carrollian manifolds for null hypersurfaces.

We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respe…

This study examines how ChiNext IPOs' initial returns are influenced by regulation regime changes.

New graph shows edge deletion/contraction doesn't always result in intrinsically linked graphs.

Reinforcement learning for embodied agents is a challenging problem. The accumulated reward to be optimized is often a very rugged function, and gradient methods are impaired by many local optimizers. We demonstrate, in an experimental setting, that incorporating an intrinsic reward can smoothen the optimization landsc…

New method estimates intrinsic dimensionality using angles, not distances.

A directed graph $G$ is $\textit{intrinsically linked}$ if every embedding of that graph contains a non-split link $L$, where each component of $L$ is a consistently oriented cycle in $G$. A $\textit{tournament}$ is a directed graph where each pair of vertices is connected by exactly one directed edge. We consider intr…

We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices. For graphs in these families, we verify a conjecture presented in Adams' "The Knot Book": If a vertex is remo…

Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by unveiling the intrinsic mathematical structure of time in Lagrangian mechanics. Moreover…

Sharp estimates for mean curvature flow confirm bounded diameter conjecture.

We show that deleting an edge of a 3-cycle in an intrinsically knotted graph gives an intrinsically linked graph.

Investigates intrinsic Lipschitz sections in nonlinear quotient maps.

We prove that a graph is intrinsically linked in an arbitrary 3-manifold M if and only if it is intrinsically linked in S^3. Also, assuming the Poincare Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S^3.

Recalls intrinsically harmonic forms and open problems.