This note proves equivalence between Dorfman brackets and lifts, showing universality of the Courant-Dorfman bracket.
problem Characterizing twistings and symmetries of transitive Dorfman brackets.
method Proving equivalence between Dorfman brackets and lifts, intertwining with Courant-Dorfman bracket.
result Universality of the Courant-Dorfman bracket and characterization of Dorfman brackets via lifts.
Study proposes a more accurate method for classifying transposable elements.
problem Classifying transposable elements for understanding their genetic and evolutionary effects.
method Utilized Support Vector Machines (SVM) for hierarchical classification of transposable elements.
result Proposed a robust approach for hierarchical classification of transposable elements with higher accuracy.
Let X be a simply connected 4-manifold containing a (−1)-sphere e. Fintushel and Stern prove that Dc(exp(te))=Dc(B(t))one⊥ifc⋅eiseven, Dc(exp(te))=Dc−e(S(t))one⊥ifc⋅eisodd, for some universal series $B(t),S(t) \in \Q[x][[t]]$ with x the class of a point. …
Classifies (T)-structures over 2D F-manifolds under formal isomorphisms.
problem Classifying (T)-structures over 2D F-manifolds. method Review of (T) and (TE)-structures, determination of normal forms. result Normal forms for (T)-structures induced by irreducible 2D F-manifolds. We consider the problem of accurately estimating the reliability of workers based on noisy labels they provide, which is a fundamental question in crowdsourcing. We propose a novel lower bound on the minimax estimation error which applies to any estimation procedure. We further propose Triangular Estimation (TE), an al…
Normal forms found for meromorphic connections over a specific F-manifold.
problem Characterizing meromorphic connections over a specific F-manifold.
method Finding normal forms for Euler fields and meromorphic connections.
result Characterized Euler fields induced by (TE)-structures. Investor flows in Korean equity market transmit shared information, not private signals.
problem Whether investor flows transmit private information or only public signals.
method Transfer Entropy networks constructed from investor-type flows over
umNDates{} trading days.
result Investor flows transmit shared information, not private signals.
Proposes a new VAE model to estimate treatment effects from confounded data.
problem Estimating treatment effects in the presence of confounding variables.
method Intact-VAE, a variant of variational autoencoder (VAE), using a latent variable for confounders.
result Proves identification of treatment effects under unconfoundedness and shows state-of-the-art performance.
Unified framework maps financial market dynamics using TE and KM, revealing directional information flow.
problem Challenges in traditional correlation analysis of financial markets, especially during crises.
method Combines Transfer Entropy (TE) and Kramers-Moyal (KM) expansion to analyze dynamic interactions among major indices.
result Increased directional information flow during crises, highlighting gold-dollar and oil-equity linkages.
Paper proposes a method to estimate Transfer Entropy using Copula Entropy.
problem Estimating Transfer Entropy for causal discovery.
method Non-parametric method based on Copula Entropy.
result The proposed method effectively infers causality relationships from data.
New method tackles OOD robustness with a single additional variable.
problem Out-of-distribution generalization with unobserved confounders.
method Identifiability assumptions using a single additional variable.
result Superior empirical performance on benchmark tasks.
TES optimizes black-box functions efficiently with minimal approximations.
problem Efficient Bayesian optimization with minimal approximations and generalization to batch BO.
method TES acquisition function measures information gain on trusted maximizers.
result TES achieves state-of-the-art performance with minimal approximations.
A new VAE model identifies and estimates treatment effects with limited overlap.
problem Identifying and estimating treatment effects when subjects with certain features belong to a single treatment group.
method Developed a latent variable model to estimate a prognostic score, which is sufficient for treatment effects. The model is a new type of VAE called β-Intact-VAE.
result The model identifies individualized treatment effects and provides TE error bounds.
We define Dorfman connections, which are to Courant algebroids what connections are to Lie algebroids. Several examples illustrate this analogy. A linear connection ∇:X(M)×Γ(E)→Γ(E) on a vector bundle E over a smooth manifold M is tantamount to a linear splitting $TE\simeq T^{q_E}E\op…
EPSTE: A geometric token and deep learning approach to estimating transfer entropy in neuroimaging time series
problem Inferring directed interactions between neural systems from EEG and MEG
method Reframing TE estimation as a learnable problem operating on structured symbolic representations
result EPSTE achieves near-perfect recovery of ground-truth directed structure and significantly lower absolute error than the baseline
Proposes a new method to adapt to covariate shifts in supervised learning.
problem Covariate shift in training and testing samples with different marginal distributions.
method Minimax risk classification (MRC) approach that weights both training and testing samples.
result Significantly enhanced classification performance in synthetic and empirical experiments.
New γ-capsule networks improve adversarial robustness and explainability of capsule networks.
problem Improving the robustness and explainability of capsule networks.
method Introducing γ-capsule networks with a new routing algorithm and training method. result Experimental results show γ-capsule networks are more robust and transparent. The aim of these notes is to relate covariant stochastic integration in a vector bundle E (as in Norris \cite{Norris}) with the usual Stratonovich calculus via the connector $\K:TE \rightarrow E$ (cf. e.g. Paterson \cite{Paterson} or Poor \cite{Poor}) which carries the connection dependence.
New insights into overfitting peaks in generalization error for l2 and l1 penalized interpolation.
problem Understanding the phenomenon of overfitting peaks in generalization error for modern machine learning models.
method Introducing a generative and fitting model pair (MiSpaR) and deriving analytical risk curves for l2 and l1 penalties. result The overfitting peak can be dissociated from the point of model flexibility, complicating the interpretation of overfitting as a boundary between classical and modern regimes.
Quantum computing improves fault diagnosis in industrial processes.
problem Fault detection and diagnosis in industrial process systems.
method Integrates quantum computing and deep learning to extract features and diagnose faults.
result Quantum-assisted deep learning achieves high fault detection rates (79.2% and 99.39%).
The paper linearizes higher Courant algebroids using jet and differential operators.
problem Understanding the structure of higher Courant algebroids.
method Isomorphic spaces of sections and linearization of jet and differential operator bundles.
result Higher Courant algebroids can be linearized as pseudo-linearization and Weinstein-linearization.
TES-AE uses tree grammars to speed up autoencoding for tree data.
problem Challenges in autoencoding tree data due to its non-vectorial and discrete nature.
method TES-AE combines reservoir computing with tree grammars for faster training.
result TES-AE outperforms D-VAE in speed and accuracy for tree data.
An optimal algorithm for multi-armed bandits with constraints.
problem Optimizing decisions in constrained multi-armed bandit problems.
method An index-based deterministic algorithm using Locatelli's anytime thresholding under known optimal value assumption.
result The algorithm achieves asymptotic optimality with probability approaching 1.
A new method models continuous-time counterfactual outcomes using neural controlled differential equations.
problem Estimating personalized healthcare outcomes over irregularly sampled data.
method Interpreting data as samples from a continuous-time process, modeling latent trajectory using controlled differential equations, and using adversarial training for time-dependent confounding.
result TE-CDE consistently outperforms existing approaches in irregularly sampled scenarios.
We consider a simple investment project with the following parameters: I>0: Initial investment which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0:…
Sharp inequalities for submanifolds in space forms derived from elliptic operators.
problem Optimal upper bound for eigenvalues of elliptic operators on submanifolds.
method Using a general symmetric, positive definite tensor T, derived an upper bound for the second eigenvalue of elliptic operators.
result Optimal upper bound for eigenvalues given in terms of integration involving tensor properties and normal vector field.
The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.
problem Forming optimal portfolios with constraints in high-dimensional asset spaces.
method CROWN method integrating factor models with nodewise regression for estimation in large dimensions.
result Demonstrates estimation consistency and convergence rates for constrained portfolio weights, risk, and Sharpe Ratio.
New method estimates traffic congestion delays using statistical causality.
problem Accurate estimation of traffic congestion delays during accidents.
method Proposes a novel time delay estimation method using lag-specific transfer entropy (TE) and Markov bootstrap techniques.
result Validated the method's efficacy using simulated and real data.
Lie algebras of quotient groups defined under specific conditions.
problem Conditions for Lie differentiation of quotient groups.
method Diffeological group theory, tangent structure, Lie functor instantiation.
result Lie algebra structure on quotient groups derived from Lie algebras of parent groups.
Establishes equivalent formulations of connections in tangent categories.
problem Generalizing connections in tangent categories.
method Defined and generalized the notion of connection on differential bundles in tangent categories, provided equivalent formulations, and showed equivalences with specific morphisms and diagrams.
result Equivalent formulations of connections in tangent categories reduce the amount of specified structure and axioms required.
New translation equivariant neural processes improve spatio-temporal data modeling.
problem Improving posterior prediction maps for spatio-temporal data.
method Introduced translation equivariant transformers within neural processes.
result TE-TNPs outperform non-equivariant TNPs and other baselines.
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…
Grothendieck's Esquisse d'un programme is often referred to for the ideas it contains on dessins d'enfants, the Teichm{ü}ller tower, and the actions of the absolute Galois group on these objects or their etale fundamental groups. But this program contains several other important ideas. In particular, motivated by surfa…
In this paper we prove certain Hurwitz equivalence properties in Bn. Our main result is that every two Artin's factorizations of Δn2 of the form Hi1...Hin(n−1),Fj1...Fjn(n−1) (with ik,jk∈{1,...,n−1}), where {H1,...,Hn−1},{F1,...,Fn−1} are frames, are…
Study finds significant BTC co-movements with equity markets, highlighting dynamic risk management needs.
problem Understanding the impact of corporate Bitcoin holdings on equity markets.
method Dataset of 39 firms, daily returns analysis, Pearson correlations, single factor model regressions, transfer entropy.
result BTC has a significant positive beta with equity markets, with BTC as the dominant information driver.
Paper proposes a novel method to assess treatment effect estimators using cross-validation.
problem Lack of ground truth to objectively assess treatment effect estimators in RCTs.
method Cross-validation-like methodology combining noisy difference-of-means estimate and aggregation across RCTs.
result Aggressive downweighting or truncation of large values reduces variance and improves treatment effect estimation.
Commentary on Teichmüller's 1938 paper on conformal and quasiconformal mappings.
problem Investigations into conformal and quasiconformal mappings and their applications.
method Detailed development of conformal invariants and applications in value distribution theory.
result Insures the almost circularity of certain loci and the circularity near infinity of quasiconformal maps.
Study examines entropy and transfer entropy in DJIA before 1997 Asian crisis.
problem Analyzing entropy and transfer entropy in financial markets.
method Measures entropy, Pearson correlation, and modified transfer entropy in DJIA.
result Different relationships emerge from conventional Pearson correlations.
A new model for defective media using two scales.
problem Modeling defects in media with two scales.
method Generalization of Riemann-Cartan manifolds and fibre bundle theory, constructing a first-order placement map.
result Emergent behaviors like dislocations and disclinations arise from the interaction of macroscopic and microscopic scales.
ENTED efficiently decomposes binary and count tensors using nonparametric Gaussian processes.
problem Handling high-dimensional and sparse binary and count data with traditional tensor decompositions.
method ENTED uses nonparametric Gaussian processes and sparse orthogonal variational inference to handle binary and count tensors.
result ENTED outperforms traditional methods in binary and count tensor completion tasks.
CNMs detect tipping points in complex systems using causal network markers.
problem Identifying tipping points ahead of critical transitions in complex systems.
method Introducing CNMs that incorporate causality indicators to detect tipping points.
result CNMs show higher predictive power and accuracy than traditional DNB indicators.
NCA improves fault detection in nonlinear processes.
problem Fault detection in nonlinear chemical processes.
method Neural Component Analysis (NCA) using feedforward neural networks with orthogonal constraints.
result NCA outperforms traditional PCA and autoencoder methods in fault detection.
The paper classifies hyperbolic and satellite T-links formed by twisting.
problem Classifying hyperbolic and satellite T-links formed by twisting.
method Classification through Dehn filling and analysis of parent links.
result Classification of hyperbolic and satellite T-links formed by twisting.
Paper constructs Chern character for higher twists and shows isomorphism between K-theory and cohomology.
problem Mapping higher twisted K-theory to higher twisted cohomology.
method Constructing Chern character for higher twists and showing isomorphism.
result Chern character gives isomorphism between higher twisted K-theory and higher twisted cohomology.
We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted K-theory and Courant algebroids. A novel feature is that we must consider two kinds of twists in de Rham coho…
Equivariant T-duality connects bundles with twists.
problem Establishing a relationship between bundles with twists.
method Formulating T-duality in equivariant K-theory for compact Lie group actions.
result T-duality is an isomorphism in equivariant K-theory for compact Lie group actions.
Introduces new K-theory for loop spaces with specific holonomy bundles.
problem Developing a new K-theory framework for loop spaces with exotic twists.
method Defines exotic twisted equivariant K-theory and Chern character.
result Establishes a mapping between new K-theory and cohomology.
New method calculates number of components in twisted torus links.
problem Determining the number of components of twisted torus links.
method Euclidean algorithm-like procedure based on parameters.
result Number of components is a multiple of gcd(p, q, r, s).