Paper explores deformations of Courant algebroids and Dirac structures with a flexible metric.
problem Deformations of Courant algebroids and Dirac structures under a flexible metric.
method Unified concepts of blended Q-manifolds, DGLA, and L-infinity-algebra to control deformations.
result Deformations controlled by blended DGLA and L-infinity-algebra.
Characterizes Q-manifold bundles over C-spaces.
problem Homological characterization of Q-manifolds bundles. method Homological proof of Q-manifolds bundles over C-spaces. result Provides a partial answer to Question QM22.
Study Riemannian Q-manifolds with Killing vector fields, finding them unimodular.
problem Defining and studying Riemannian structures on Q-manifolds.
method Define Riemannian Q-manifolds and show their unimodularity.
result Riemannian Q-manifolds are unimodular.
Reviewing Q-manifolds, modular classes, and applications.
problem Obtaining invariant volumes on Q-manifolds.
method Exploring Q-manifolds, modular classes, and applying to specific examples.
result Applications to L∞-algebroids and higher Poisson manifolds. The study provides homological characterizations for Q-manifolds and l2-manifolds.
problem Density of maps in characterizing Q-manifolds and l2-manifolds. method Investigates weakening the density of Zn-maps and Z-maps to homological maps. result Obtains homological characterizations for Q-manifolds and l2-manifolds. New Q-manifolds theory integrates Lie algebroids.
problem Integrating Lie algebroids over smooth manifolds.
method Introducing Q-groupoids and Q-bundles, proving Lie algebroids arise from Q-manifolds.
result Transitive Lie algebroids over second countable, smooth manifolds are integrated to locally trivial Q-groupoids.
We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd vector field is deformed in a very specific way. This leads to the notion of a quasi…
We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.
Exposes graded and microformal geometry, focusing on Q-manifolds.
problem Describes new geometric structures and their applications.
method Introduces Q-manifolds and microformal geometry. result Establishes connections between Q-manifolds and Lie algebras. Study examines Lie algebroids with homological sections, generalizing Q-manifolds and Lie superalgebras.
problem Exploring Lie algebroids with homological sections.
method Derived bracket formalism to define an odd Loday-Leibniz bracket on sections.
result Sections of inner Q-algebroids come equipped with an odd Loday-Leibniz bracket.
Study modular class of Lie ∞-algebroids and their adjoint actions.
problem Understanding the modular class and adjoint actions of Lie ∞-algebroids.
method Equivalence of descriptions, homotopy invariance, explicit actions and dualities.
result Homotopy invariance of modular classes and explicit adjoint actions.
We show how the relation between Q-manifolds and Lie algebroids extends to ``higher'' or ``non-linear'' analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that arises as a replacement of operations on sections of a Lie algebroid. When the base is a point, we obtain a generalizat…
A Q-manifold M is a supermanifold endowed with an odd vector field Q squaring to zero. The Lie derivative LQ along Q makes the algebra of smooth tensor fields on M into a differential algebra. In this paper, we define and study the invariants of Q-manifolds called characteristic classes. These take value…
This text is meant to be a brief overview of the topics announced in the title and is based on my talk in Vienna (August/September 2007). It does not contain new results (except probably for a remark concerning Q-manifold homology, which I wish to elaborate elsewhere). "Mackenzie theory" stands for the rich circle of n…
In this paper we define a Grassmann odd analogue of Jacobi structure on a supermanifold. The basic properties are explored. The construction of odd Jacobi manifolds is then used to reexamine the notion of a Jacobi algebroid. It is shown that Jacobi algebroids can be understood in terms of a kind of curved Q-manifold, w…
Geometric structures on NQ-manifolds, i.e.~non-negatively graded manifolds with an homological vector field, encode non-graded geometric data on Lie algebroids and their higher analogues. A particularly relevant class of structures consists of vector bundle valued differential forms. Symplectic forms, contac…
Study finds modular classes help in proving Berezin volumes for supersymmetric theories.
problem Existence of Berezin volumes in supergeometric representation theory.
method Cohomological coherence criterion for modular classes of Q-manifolds.
result Established a method to prove the existence of invariant Berezin volumes.
This thesis generalizes structures on Q-manifolds and Lie n-algebroids.
problem Representation theory and linear structures of Q-manifolds and Lie n-algebroids. method Introduces differential graded modules and representations up to homotopy, defines Weil algebra, and studies VB-Lie n-algebroids. result Establishes an equivalence between VB-Lie n-algebroids and (n+1)-term representations up to homotopy of Lie n-algebroids. Normal forms for Q-structures on graded manifolds explained.
problem Understanding structures of Q-manifolds on graded manifolds.
method Local and global normal forms results for Q-structures.
result Structures are concentrated along the zero-locus of curvatures.
Study curvature and torsion in Courant algebroids using graded geometry.
problem Defining curvature and torsion in Courant algebroids.
method Graded geometric approach, introducing K-curvature and K-torsion.
result Natural graded geometric definition of Courant algebroid curvature and torsion.
New algebraic structures on manifolds generalize supergeometry concepts.
problem Developing algebraic structures for non-commutative manifolds.
method Introducing ρ-commutative manifolds, Q-manifolds, and modular classes. result Generalized modular classes for non-commutative spaces.
New model improves volatility forecasting by reducing overestimation and underestimation.
problem SVR-GARCH model overestimates or underestimates volatility, hindering peak or trough behaviors.
method Proposes blending ARCH and augmented blending-ARCH models to improve volatility forecasting.
result Empirical results show improved volatility forecasting ability.
We give a simple characterization of Mackenzie's double Lie algebroids in terms of homological vector fields. Application to the `Drinfeld double' of Lie bialgebroids is given and an extension to the multiple case is suggested.
Study shows ethanol blends and incentives can significantly reduce transportation carbon emissions.
problem Rapid growth in electric vehicles requires complementary strategies to decarbonize transportation.
method Analysis of ethanol blending, regulatory incentives, and economic assessments.
result Ethanol blending, especially E15 and E85, can substantially reduce carbon emissions and provide economic benefits.
A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections in the category of graded manifolds) and each cohomology class of a certain sub…
We show that L∞-algebroids, understood in terms of Q-manifolds can be described in terms of certain higher Schouten and Poisson structures on graded (super)manifolds. This generalises known constructions for Lie (super)algebras and Lie algebroids.
BayesBlend blends multiple models' predictions for better insurance loss predictions.
problem Improving insurance loss predictions by combining multiple models.
method Pseudo-Bayesian model averaging, stacking, and hierarchical stacking.
result BayesBlend provides a user-friendly way to blend model predictions and estimate weights.
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…
Formalizes explanations as blending input and model output.
problem Creating clear and consistent explanations for model predictions.
method Defines properties of explanation functions and links them to model layers.
result Consistency of activations across layers implies consistency of explanations.
Quantum walks blend patterns into splines when averaged.
problem Understanding the asymptotic patterns of quantum random walks.
method Averaging over quantum coins using the Haar measure.
result Patterns blend into splines, showing a unified behavior.
This paper improves level generation using VAEs for coherent, logically following segments.
problem Generating coherent levels of non-fixed length and blending levels from different games.
method Sequential segment-based level generation using VAEs with a classifier for logical placement.
result Generated levels are more coherent and capable of blending levels from different games.
Study evaluates predictive models for blended courses, analyzing performance across different offerings.
problem Limited success in predicting student performance in blended courses.
method Used data from two offerings of two different undergraduate courses to train and evaluate models.
result Models perform better on the same offering and less well on different offerings of the same course.
The paper proposes blending gradient boosted trees and neural networks for hierarchical time series forecasting.
problem Point and probabilistic forecasting of hierarchical time series.
method A blending methodology of gradient boosted trees and neural networks, with feature engineering and diverse model selection.
result Ranked within the gold medal range in both Accuracy and Uncertainty tracks of the M5 Competition.
Combines generalized and graded geometry to explore new structures.
problem Exploring new structures on generalized tangent bundles of graded manifolds.
method Introduces canonical brackets, Dirac structures, and generalized complex structures.
result Canonical bracket on a generalized tangent bundle of a graded manifold.
New PCGML approach generates novel game content across multiple platformer domains.
problem Generating novel game content in new domains.
method Using a new affordance and path vocabulary, variational autoencoders trained on data from six platformer games produce new content with varying proportions of different domains.
result Captures latent level space spanning multiple domains and generates new content with varying proportions of different domains.
The paper presents a framework for optimizing crypto-currency portfolios using generative models.
problem Optimizing crypto-currency portfolios using generative models.
method The approach involves evaluating diverse pairings of generative model forecasts and objective functions, using simulations and blending strategies.
result Eclectic blended portfolios outperform individual generative model-based portfolios.
Generative model blends query input with latent states for structured improvisation.
problem Generating structured music from latent states of a neural network.
method Used a Variational Autoencoder (VAE) trained on a specific style corpus, and controlled blending with a noisy channel.
result Generated music with longer-term structure that blends query input with network style.
A novel approach for augmenting histopathological images by blending Gaussian-Laplacian pyramids.
problem Data imbalance and inter-patient variability in histopathological images.
method Image blending using Gaussian-Laplacian pyramids to distribute inter-patient variability.
result Promising gains in performance compared to existing data augmentation techniques.
BCGD algorithm improves training of quantized neural networks.
problem Training quantized deep neural networks at low bit-widths.
method Introduces coarse gradient descent and blended correction for training.
result BCGD achieves high accuracy in quantized neural networks.
Study examines Indian equity mutual funds' investment style and risk-shifting.
problem Understanding how Indian equity mutual funds' investment styles affect their returns.
method Estimating size and style beta coefficients, identifying breakpoints, analyzing investment styles, and assessing risk-shifting intensity.
result Funds can enhance returns by shifting to high-return styles like Small Value and Small Blend.
It is well-known that a Lie algebroid A is equivalently described by a degree 1 Q-manifold M. We study distributions on M, giving a characterization in terms of A. We show that involutive Q-invariant distributions on M correspond bijectively to IM-foliations on A (the infinitesimal version of Mackenzie's ideal systems)…
OPERA blends multiple OPE estimators to evaluate new policies offline.
problem Lack of reliable offline policy evaluation methods for new policies.
method Adaptive blending of multiple OPE estimators without explicit selection.
result Consistent and reliable policy evaluation framework for offline RL.
This work explores symplectic structures on graded manifolds and higher Lie groupoids.
problem Understanding symplectic structures on graded manifolds and their global counterparts.
method Introduction and study of graded manifolds, symplectic Q-manifolds, higher Lie groupoids, and their symplectic structures.
result Developed a graded analogue of Weinstein's tubular neighborhood theorem and explored its applications.
AMEAN tackles BTDA by learning meta-sub-targets to bridge domain gaps and misalignments.
problem Blending-target Domain Adaptation (BTDA) with multiple sub-targets that are hard to distinguish.
method AMEAN uses two adversarial processes: first to align source and mixed target domains, second to learn meta-sub-targets.
result AMEAN significantly outperforms existing DA algorithms in BTDA scenarios.
A new method quantizes neural networks to low-precision without STE, improving accuracy.
problem Quantization of neural networks to low-precision without a complete theoretical understanding.
method Alpha-blending (AB) using stochastic gradient descent (SGD) to quantize weights and gradually increase the coefficient α. result Improves top-1 accuracy by 0.9% on 1-bit BinaryNet, 0.82% on 8-bit MobileNet v1, and 2.93% on 4-bit ResNet_50 v1/2 compared to STE.
This study introduces a new GAS blending ensemble model for Bitcoin price prediction.
problem Predicting Bitcoin price fluctuations in the cryptocurrency market.
method Integrates advanced ensemble learning methods, feature selection algorithms, and sentiment analysis.
result The GAS model demonstrates excellent performance in daily Bitcoin trend prediction.
Breiman's two cultures reconciled through blending statistical thinking.
problem Tension between parametric statistical and machine learning approaches.
method Establishing a link between parametric statistical and machine learning frameworks.
result Integrated statistical thinking can bridge the gap between two cultures.
Improved prediction of polymer morphology through machine learning and simulations.
problem Understanding and predicting the morphology of multi-component polymer blends.
method Modified Cahn-Hilliard model for simulations, machine learning for clustering and prediction.
result Machine learning achieved ≥ 90% accuracy in predicting polymer morphology.