arXiv research

Reconstructs fundamental groups from liquid local systems.

The classical Brody's theorem asserts the equivalence between two notions of hyperbolicity for compact complex spaces, one named after Kobayashi and one expressed in terms of lack of non constant holomorphic entire functions (compactness is only used to prove the harder implication). We extend this theorem to Deligne-M…

MetaStackVis aids in choosing better metamodels for stacking ensembles.

This paper is a comprehensive introduction to the results of [7]. It grew as an expanded version of a talk given at INdAM Meeting Complex and Symplectic Geometry, held at Cortona in June 12-18, 2016. It deals with the construction of the Teichmüller space of a smooth compact manifold M (that is the space of isomorphism…

The paper establishes a Lagrangian correspondence linking different geometric structures on complex varieties.

StackGenVis simplifies ensemble learning by visualizing model selection and performance.

A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a compl…

The paper explores de Rham theory for singular spaces and stacks.

Constructs the moduli stack of elliptic curves as an orbifold.

Increasing urban concentration raises operational challenges that can benefit from integrated monitoring and decision support. Such complex systems need to leverage the full stack of analytical methods, from state estimation using multi-sensor fusion for situational awareness, to prediction and computation of optimal r…

New theory proves representability of PDE solutions without complex machinery.

A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest thr…

Most real-world networks are incompletely observed. Algorithms that can accurately predict which links are missing can dramatically speedup the collection of network data and improve the validity of network models. Many algorithms now exist for predicting missing links, given a partially observed network, but it has re…

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge fields and $\mathcal{N} = (0, 1)$ supersymmetry. We also consider a theory of free fe…

Stacking is a general approach for combining multiple models toward greater predictive accuracy. It has found various application across different domains, ensuing from its meta-learning nature. Our understanding, nevertheless, on how and why stacking works remains intuitive and lacking in theoretical insight. In this …

We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which are algebraic objects) and large stacks (which are generalized spaces).

In this article, we derive many properties of étale stacks in various contexts, and prove that étale stacks may be characterized categorically as those stacks that arise as prolongations of stacks on a site of spaces and local homeomorphisms. Moreover, we show that the bicategory of étale differentiable stacks and loca…

Constructs cohomology decompositions for symmetric stacks.

New neural stack and Turing Machine architectures prove stability and computational power.

Geometric invariant theory introduces stability conditions mirroring abelian category theory.

Bayesian stacking improves model performance with varying model weights.

Develops relative harmonic metrics and deformation theory for Higgs and flat bundles on compact Kähler manifolds.

Paper combines machine learning and model averaging for robust parameter estimation.

We generalize the notion of a small sheaf of sets over a topological space or manifold to define the notion of a small stack of groupoids over an étale topological or differentiable stack. We then provide a construction analogous to the étalé space construction in this context, establishing an equivalence of 2-categori…

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$. The characterization is described in terms of the action of the connected componen…

The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.

Stacked conformal prediction simplifies model validation.

Constructs moduli stacks for quiver connections and extends non-Abelian Hodge theory.

Study connections on Lie groupoids and stacks using Atiyah sequences.

In this paper, we consider diffeological spaces as stacks over the site of smooth manifolds, as well as the "underlying" diffeological space of any stack. More precisely, we consider diffeological spaces as so-called concrete sheaves and show that the Grothendieck construction sending these sheaves to stacks has a left…

Constructs moduli stacks of quiver bundles and applies to Higgs bundles.

New potentials found for sheaves on Calabi-Yau 4-folds.

We study compositional generalization, viz., the problem of zero-shot generalization to novel compositions of concepts in a domain. Standard neural networks fail to a large extent on compositional learning. We propose Tree Stack Memory Units (Tree-SMU) to enable strong compositional generalization. Tree-SMU is a recurs…

Machine Learning (ML) algorithms have been used for assessing soil quality parameters along with non-destructive methodologies. Among spectroscopic analytical methodologies, energy dispersive X-ray fluorescence (EDXRF) is one of the more quick, environmentally friendly and less expensive when compared to conventional m…

This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The s…

Stacked LSTM networks improve traffic volume forecasting.

Studies geometric structures on Lie groupoids and differentiable stacks.

Stacking improves deep neural network training efficiency.

A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by Toen and Vezzosi, on the site of dg algebras whose cohomologies have finitely many generators in each degree. Stacks represented b…

Study moduli spaces of elliptic PDEs using derived $C^{\infty}$-geometry.

Stacking methods improve the prediction performance of regression models. A simple way to stack base regressions estimators is by combining them linearly, as done by \citet{breiman1996stacked}. Even though this approach is useful from an interpretative perspective, it often does not lead to high predictive power. We pr…

We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choo…

For a compact manifold M and a differentiable stack \cX presented by a Lie groupoid X, we show the Hom-stack Hom(M,\cX) is presented by a Fréchet-Lie groupoid Map(M,X) and so is an infinite-dimensional differentiable stack. We further show that if \cX is an orbifold, presented by a proper étale Lie groupoid, then Map(M…

We propose a novel stacked generalization (stacking) method as a dynamic ensemble technique using a pool of heterogeneous classifiers for node label classification on networks. The proposed method assigns component models a set of functional coefficients, which can vary smoothly with certain topological features of a n…

Paper proves stacking ensembling is effective and proposes a new family of stacked generalizations.

Introduces a new method for symplectic reduction along submanifolds.

The paper studies higher geometric structures and connections on manifolds, constructing moduli stacks and proving equivalence criteria.

Researchers compute differential K-theory for moduli stacks.