Depreciation methods ignore the Time Value of Money, leading to suboptimal asset valuation.
problem Depreciation methods do not account for the Time Value of Money, leading to suboptimal asset valuation.
method Formulate a depreciation method that incorporates the Time Value of Money to approximate intrinsic asset value.
result A new depreciation method improves asset valuation, aiding better purchase and sale decisions.
Develops intrinsic Gaussian process regression for manifold-valued data.
problem Lack of intrinsic Gaussian process methods for manifold-valued response variables.
method Proposes an intrinsic covariance structure and a novel intrinsic Gaussian process regression model.
result Establishes asymptotic properties and shows posterior consistency.
h-DQN integrates hierarchical value functions with intrinsic motivation for efficient exploration.
problem Sparse feedback and insufficient exploration in reinforcement learning.
method Hierarchical-DQN framework combining temporal abstraction and intrinsic motivation.
result Demonstrated efficiency in exploration and task-solving on sparse feedback problems.
Study uniformly differentiable graphs in Carnot groups, proving area formulas.
problem Characterize uniformly differentiable intrinsic graphs in Carnot groups.
method Characterize uniform intrinsic differentiability via Hölder properties of projections of vector fields.
result Explicit area formula for uniformly intrinsically differentiable maps in Carnot groups.
This paper explores intrinsic rewards to improve learning from multiple value functions.
problem How to adapt reinforcement learning systems to optimize learning from multiple value functions.
method Investigated and compared 14 different intrinsic reward mechanisms in a new bandit-like parallel-learning testbed.
result Intrinsic rewards based on the amount of learning can generate useful behavior, if each individual learner is introspective.
AutoDIME automates design of multi-agent environments for RL.
problem Designing multi-agent environments for reinforcement learning is challenging.
method Developed intrinsic teacher rewards for multi-agent settings and evaluated them in various tasks.
result Value disagreement was found to be most consistent and effective across tasks.
Geometrically reformulates elasticity theory using exterior calculus.
problem Formulating nonlinear elasticity theory geometrically.
method Using exterior calculus and bundle-valued differential forms.
result Equivalence to standard tensor calculus formulations.
eDCF estimates intrinsic dimension using local connectivity.
problem Challenges in estimating intrinsic dimension due to scale dependence.
method eDCF: a novel, scalable, and parallelizable method based on Connectivity Factor (CF).
result eDCF consistently matches leading estimators with comparable MAE and higher exact intrinsic dimension match rates.
New risk measures for financial networks avoid external capital, reducing systemic risk.
problem Systemic risk in financial networks is underestimated by traditional methods.
method Developed set-valued, intrinsic risk measures for financial networks.
result Systemic intrinsic risk measures are more stable and avoid reliance on external capital.
A new method calculates intrinsic effective sample size for manifold-valued data.
problem Challenges in choosing effective sample size for manifold-valued data.
method Proposes an intrinsic effective sample size based on kernel discrepancy.
result Establishes an exact finite-sample risk interpretation and consistency of the estimator.
The article presents a new entropy model for assessing stock market interest.
problem Assessing investor interest and market sentiment in exchange-traded securities.
method Intrinsic entropy model using actual trading data, without exogenous factors.
result Empirical evidence supports the model's ability to predict trading activity.
We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integration of the square of the norm of the tangential derivative, or equivalently of the approximate local dilatation, of the Lipschitz functions. …
Characterizes density-valued symplectic forms on multisymplectic manifolds.
problem Understanding density-valued symplectic forms on multisymplectic manifolds.
method Intrinsic characterization and Darboux-type theorems.
result Proves Darboux-type theorems for density-valued symplectic forms.
Proves compactness for timed-metric spaces using new distance and maps.
problem Weak convergence of space-times using timed-Hausdorff distance.
method Uses Gromov's original compactness theorem and introduces addresses.
result Establishes compactness theorem for intrinsic timed-Hausdorff convergence.
This study examines how ChiNext IPOs' initial returns are influenced by regulation regime changes.
problem Investors' behavior and pricing of ChiNext IPOs under different regulation regimes.
method Analysis of three time periods with two different regulation regimes and three sets of listing day trading restrictions.
result Regulation regime changes significantly impact ChiNext IPO pricing and overreaction.
The paper conjectures bounds on intrinsic volumes for Riemannian manifolds and Alexandrov spaces.
problem Bounding intrinsic volumes for Riemannian manifolds and Alexandrov spaces.
method Conjectures and suggests extensions of intrinsic volumes to Alexandrov spaces.
result Conjectures on bounds for intrinsic volumes and their behavior under Gromov-Hausdorff limits.
New method for predicting portfolio dynamics using non-Euclidean geometry.
problem Predicting efficient portfolios with geometric structure.
method Non-Euclidean conditional expectation and filtering equations.
result Accurate numerical forecasts of portfolio dynamics.
Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic vol…
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
problem Covariance estimation for random objects on Riemannian manifolds.
method Defines covariance and correlation via parallel transport.
result Proposed covariance is independent of coordinate choices.
New risk measures use internal resources to make positions acceptable.
problem Monetary risk measures can lead to infinite values and lack flexibility.
method Intrinsic risk measures use internal resources and a free choice of eligible assets.
result Intrinsic risk measures avoid infinite values and preserve key properties.
Two new exploration methods for multi-agent systems improve team performance.
problem Exploration in transition-dependent multi-agent settings.
method EITI and EDTI, using mutual information and VoI to encourage coordinated exploration.
result Significant improvement in multi-agent performance through coordinated exploration.
New RL approach uses future state and action visitation measures for better exploration.
problem Improving exploration in reinforcement learning.
method Intrinsic reward based on future state and action visitation measures, using contraction operators.
result Policies achieve good state-action space coverage and high performance.
Minimal surfaces' area bounds proven equivalent, extending known results.
problem Equivalence of area bounds for minimal surfaces.
method Combining recent breakthroughs, extending known results.
result Equivalence of intrinsic and extrinsic area density bounds for minimal immersions.
A new measure of causal influence quantifies intrinsic contributions in DAGs.
problem Quantifying intrinsic causal contributions in Directed Acyclic Graphs (DAGs).
method Recursive decomposition of node contributions, structure-preserving interventions, Shapley symmetrization.
result A measure of intrinsic causal contribution that is invariant to node relabeling.
Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.
problem Investigating curvature in location-scale-shape models under Wasserstein metric.
method Introduced location-scale-shape model and investigated its geometry.
result Location-scale-shape model is intrinsically flat but extrinsically curved in Wasserstein geometry.
Researchers classify and decompose valuations on convex functions.
problem Classifying valuations on convex functions.
method Geometric decomposition of valuations, using properties of special subspaces and Monge-Ampère-type operators.
result Valuations decompose into subspaces defined by vanishing properties.
The intrinsic entropy model accurately estimates stock market volatility.
problem Accurately estimating historical volatility of stock market indices.
method Incorporates traded volumes alongside OHLC prices in daily data.
result Intrinsic entropy model delivers reliable estimates with lower coefficient of variation.
A new multi-objective RL framework improves intrinsic exploration performance.
problem Sub-optimal exploration performance due to ad-hoc handling of intrinsic exploration.
method A multi-objective RL framework where both exploration and exploitation are optimized as separate objectives.
result EMU-Q method outperforms classic and other intrinsic RL methods on benchmarks.
QPass evaluates soccer players' passes based on intrinsic value.
problem Lack of quantitative evaluation of players' contributions to team strategy.
method Developed QPass methodology to quantify player pass value.
result Players losing ball possession can lead to better chances of winning.
Cryptocurrencies' value tied to liquidity, not intrinsic, making stability uncertain.
problem Cryptocurrencies lack tangible value, leading to price instability.
method Examined using asset flow equations and experimental markets.
result Cryptocurrency prices are influenced by liquidity, not intrinsic value.
This paper constructs a function on Gromov-Hausdorff limits of 2-surfaces with curvature constraints.
problem Understanding geometric properties of limits of surfaces with curvature constraints.
method Construction of an integer-valued function on the limit space.
result Existence and classification of functions on Gromov-Hausdorff limits of 2-surfaces.
Active subspaces on Riemannian manifolds generalize Euclidean principles.
problem Understanding how scalar-valued quantities change over Riemannian manifolds.
method Generalization of active subspaces from Euclidean to Riemannian spaces using parallel transport.
result The method provides a new way to study scalar-valued quantities on manifolds, differing from extrinsic approaches.
This paper introduces a new method to compare collections of distributions on manifolds and graphs.
problem Comparing collections of probability distributions over diverse domains.
method Intrinsic slicing construction for Wasserstein distances, Hilbert embedding, resampling, p-value combination.
result Powerful and well-calibrated p-values for comparing distributions on manifolds and graphs.
The paper introduces novel Gaussian process models for vector-valued signals on manifolds.
problem Modeling vector-valued signals on non-Euclidean domains, especially for applications like wind speeds.
method Intrinsically defined Gaussian vector fields on manifolds, accounting for manifold geometry.
result Gaussian vector fields provide more refined inductive biases than extrinsic fields.
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measu…
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
problem Defines tensor eigenvalues and singular values without basis.
method Intrinsic definition of tensor eigenvalues and singular values using concepts from pure mathematics.
result Shows the relationship between tensor analysis and pure mathematics.
In this paper we establish the basic tools to develop the "Calculus" associated with group-valued continuously Pansu differentiable mappings. We develop the technical machinery on which all of our results rely. In particular, the linearization of addends appearing in the Baker-Campbell-Hausdorff formula is one of the m…
HHVG algorithm reconciles boredom and curiosity for better exploration and learning.
problem Effective exploration and superior forward model learning.
method Homeo-Heterostatic Value Gradients (HHVG) algorithm.
result Boredom-enabled agents consistently outperform curious or explorative agents in model building benchmarks.
We define the notion of characteristic classes for supermanifolds endowed with a homological vector field Q. These take values in the cohomology of the Lie derivative operator LQ acting on arbitrary tensor fields. We formulate a classification theorem for intrinsic characteristic classes and give their explicit de…
Study on predicting sequences with Gaussian constraints, linking to intrinsic volumes and metric complexity.
problem Predicting sequences almost as well as the best Gaussian distribution with mean in a given subset.
method Expressed minimax regret in terms of intrinsic volumes, established comparison inequality for Wills functional, characterized global covering numbers and local Gaussian widths.
result Sharp estimates on the log-Laplace transform of intrinsic volume sequence for a general nonconvex set.
Formulas for curvature measures of sublevel sets on manifolds derived from function and derivatives.
problem Calculating intrinsic volumes of sublevel sets on Riemannian manifolds.
method Established formulas involving integrals of functionals of function and its derivatives.
result Formulas for intrinsic volumes of sublevel sets on Riemannian manifolds.
The paper analyzes profitable bidding strategies for BESS in day-ahead and intraday markets.
problem Optimizing profitability of Battery Energy Storage Systems (BESS) in day-ahead and intraday markets.
method Employing the rolling intrinsic approach to model continuous intraday markets, accounting for bid-ask spreads and liquidity constraints.
result Multi-market bidding strategies outperform single-market participation, and relaxing daily cycling constraints can unlock additional value.
Novel equations for nonsmooth level sets on Heisenberg group.
problem Parametrizing level sets of irregular maps on the Heisenberg group.
method Rough path theory equations for sub-Riemannian geometry.
result Well-posedness and calculus on nonsmooth level sets.
The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show how the solution depends on different constraint types including carr…
Three training regimes found for scale-invariant neural networks on the sphere.
problem Training scale-invariant neural networks on the sphere with varying effective learning rate.
method Investigated three regimes of training: convergence, chaotic equilibrium, and divergence.
result Discovered three distinct training regimes with unique characteristics.
Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.
problem Understanding intrinsic Hopf-Lax semigroup and its relation to intrinsic slope.
method Introduces and proves the link between intrinsic Hopf-Lax semigroup and intrinsic slope.
result Intrinsic Hopf-Lax semigroup is a subsolution of Hamilton-Jacobi type equality.
Paper proposes KIIM to infer causal relationships from data.
problem Inferring causal relationships from data is challenging.
method KIIM captures higher order statistics of conditional distributions.
result KIIM outperforms existing methods in causal inference.
We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.
problem Analyzing and comparing trajectories on Riemannian manifolds.
method Riemannian hierarchical model, Bézier splines, Sasaki metric.
result Spline-based approaches outperform state-of-the-art methods in intensity classification of trajectories.