Paper develops data-driven compact models for diodes.
problem Manual and time-consuming compact model development.
method Machine Learning techniques for automation.
result Data-driven models accurately predict diode behavior.
Compact models for NOX formation during methane combustion are created using a new algorithm.
problem Creating accurate models for NOX formation during complex combustion processes.
method Adapted Machine Learning Optimization of Chemical Kinetics (MLOCK) algorithm with Latin Square method for virtual reaction network generation.
result Compact models with high fidelity (>75%) in reproducing industry-defined performance targets are generated.
Generative model learns compact codes for video recovery.
problem Efficiently represent and reconstruct videos from missing data.
method Generative network trained to map compact latent codes to images, with low-rank and similarity constraints.
result Can recover true video sequences even if not in pretrained network's range.
We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and nonreductive cases. For example, we prove that there does not exist a compact ma…
We prove a smooth compactness theorem for the space of embedded self-shrinkers in $\RR^3$. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.
This work extends PAC-Bayesian learning guarantees to non-compact symmetries and non-invariant data.
problem Lack of theoretical guarantees explaining the benefits of symmetries in machine learning models.
method Adapting and tightening PAC-Bayes bounds for non-compact symmetries and non-invariant data distributions.
result Theoretical evidence that symmetric models are preferable for symmetric data, beyond compact groups and invariant distributions.
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr…
The paper establishes a duality between non-compact and compact symmetric pairs.
problem Understanding the relationship between non-compact and compact symmetric pairs.
method Developed a duality theorem between non-compact pseudo-Riemannian semisimple symmetric pairs and commutative compact semisimple symmetric triads.
result Explicit description of a one-to-one correspondence between non-compact and compact symmetric pairs.
Compact learning results across various loss functions.
problem Understanding sample complexity in transductive learning.
method Analyzing finite projections and sample complexities for different loss functions.
result Exact compactness of sample complexity holds broadly across realizable and agnostic learning.
Thirty years after the birth of foliations in the 1950's, André Haefliger has introduced a special property satisfied by holonomy pseudogroups of foliations on compact manifolds, called compact generation. Up to now, this is the only general property known about holonomy on compact manifolds. In this article, we give a…
Abstract: Proves compactness theorem for generalized Seiberg-Witten equations in 3D.
problem Compactness of solutions to generalized Seiberg-Witten equations in 3D.
method Abstract compactness theorem for a family of generalized Seiberg-Witten equations in dimension three.
result Recovers and extends known compactness theorems for stable flat connections and Seiberg-Witten equations.
New infinite families of flat spaces found from symmetric spaces.
problem Finding new flat homogeneous spaces.
method Starting from compact symmetric spaces, constructing infinite families of compact homogeneous spaces with invariant Bismut connections.
result Infinite families of compact homogeneous spaces with vanishing Ricci tensor.
3D Adversarial Autoencoder learns compact binary descriptors from 3D point clouds.
problem Learning meaningful representations of 3D shapes for various tasks.
method End-to-end Adversarial Autoencoder model trained on 3D input and output.
result 3D Adversarial Autoencoder (3dAAE) generates state-of-the-art results for 3D points clustering and retrieval.
Localized Multidirectional Correction improves non-refusal target-response behavior in foundation models.
problem Controlled post-training refusal suppression in routed MoE and hybrid-MoE foundation models.
method Introduce Localized Multidirectional Correction (LoMC), a support-gated intervention framework.
result Substantially improves non-refusal target-response behavior while maintaining general capability under a compact intervention footprint.
We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection ∇ on a compact complex surface is locally modelled on a translations-invariant affine connection on $\C^2$, except if ∇ is a generic connection on a princ…
Bayesian neural network predicts planetary instability.
problem Predicting planetary instability in compact systems.
method Novel Bayesian neural network trained on raw orbital elements.
result Model predicts planetary instability times with high accuracy and robust generalization.
We address the problem of finding conditions under which a compact Lorentzian manifold is geodesically complete, a property, which always holds for compact Riemannian manifolds. It is known that a compact Lorentzian manifold is geodesically complete if it is homogeneous, or has constant curvature, or admits a time-like…
Study generalizations of chainability and compactness in metric spaces.
problem Understanding new properties of subsets in metric spaces.
method Exploring and relating new properties of chainability and compactness to existing hypertopologies.
result Relations among Hausdorff, Vietoris, and locally finite hypertopologies established.
Extends optimal regularity and Uhlenbeck compactness to non-Riemannian manifolds.
problem Establishing optimal regularity and compactness for connections on vector bundles over non-Riemannian manifolds.
method Proofs based on RT-equations for connections with Lp curvature, extending to non-compact gauge groups. result Removes singularities at GR shock waves, ensuring existence of geodesics and coordinates.
We consider a generalized Ricci flow with a given (not necessarily closed) three-form and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow. The similar results still hold for a more generalized Ricci flow.
DCAE learns compact latent representations for one-class novelty detection.
problem Learning compact latent representations for one-class novelty detection.
method DCAE learns compact and collapse-free latent representations through internal discriminative layers of GANs, reconstructing in-class data finely and exclusively.
result DCAE achieves state-of-the-art performance on novelty and adversarial example detection.
We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with rather unusual targets, such as compact and non-compact Gepner models…
ConfHit provides valid guarantees for generative models without oracle access.
problem Reliable guarantees for novel candidate generation in generative models.
method Formalizes certification and refinement of generated sets, leveraging weighted exchangeability and density-ratio weighted conformal p-values.
result Consistently delivers valid coverage guarantees and compact certified sets across various generative tasks.
Paper proves non-compact inaudibility of symmetry and commutativity.
problem Proving inaudibility of symmetry and commutativity in non-compact settings.
method Using isospectral pairs of generalized Heisenberg groups.
result Proved inaudibility of weak symmetry and commutativity.
In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones SG in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence…
In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we generalize the results in math.SG/0303255 in two directions: we consider general compact…
Generalizes Dolbeault cohomology computation to Levi-flat CR structures on compact Lie groups.
problem Computing Dolbeault cohomology for Levi-flat CR structures on compact Lie groups.
method Algebraic classification of left-invariant CR structures combined with Pittie's result on compact Lie groups.
result Generalization of Dolbeault cohomology computation to Levi-flat CR structures.
We construct compactifications of Riemannian locally symmetric spaces arising as quotients by Anosov representations. These compactifications are modeled on generalized Satake compactifications and, in certain cases, on maximal Satake compactifications. We deduce that these Riemannian locally symmetric spaces are topol…
Non-compact flow lines for scalar curvature prescription on manifolds.
problem Non-compactness in scalar curvature prescription on manifolds.
method Gradient flow analysis of scalar curvature on Riemannian manifolds.
result A modification of the gradient flow leads to compact flow lines.
Proves compactness of geometric models for certain homogeneous spaces.
problem Existence and uniqueness of geometric models for locally homogeneous spaces.
method Proves existence and uniqueness of geometric models in the pointed C1,α-topology. result Compact set of geometric models for sectional curvature ≤ 1.
Generalized stability theorem for compact manifolds with boundary.
problem Stability of manifolds with boundary.
method Equivariant μ-bubbles technique.
result Yamabe invariant of compact manifolds with boundary is positive if and only if the invariant of the manifold times S^1 is positive.
Study classifies symmetric spaces without compact models.
problem Determining which symmetric spaces can't model compact manifolds.
method Cohomological obstruction and classification of semisimple symmetric spaces.
result Classification of semisimple symmetric spaces not modeling compact manifolds.
Compact groups with polynomial growth have specific embeddings.
problem Understanding groups with polynomial growth.
method Embedding into semidirect products of Lie and compact groups.
result Groups can be embedded as co-compact subgroups.
New method for invariant neural networks using probabilistic symmetries.
problem Improving neural network performance in data-scarce, non-i.i.d., or unsupervised settings.
method Characterizing neural network structures invariant under compact group actions using probabilistic symmetry.
result Established a link between functional and probabilistic symmetry, yielding generative representations of invariant distributions.
We discuss our recent results on the existence and classification problem of complex and Kaehler structures on compact solvmanifolds. In particular, we determine in this paper all the complex surfaces which are diffeomorphic to compact solvmanifolds (and compact homogeneous manifolds in general).
New local method solves Yamabe problems on compact and non-compact manifolds.
problem Yamabe problems on compact and non-compact manifolds.
method Local method for compact and non-compact manifolds.
result Generalizes Brezis and Nirenberg's nonlinear eigenvalue problem to subsets of manifolds.
Develops scalar curvature in generalized Kahler geometry and shows constant scalar curvature on compact Lie groups.
problem Defines scalar curvature in generalized Kahler geometry.
method Introduces scalar curvature in terms of pure spinors formalism and develops a moment map framework.
result Scalar curvature is given by the moment map, generalizing results from ordinary Kahler geometry.
For a compact surface S, let I(S) denote the Torelli group of S. For a compact orientable surface Σ, I(Σ) is generated by BSCC maps and BP maps. For a non-orientable closed surface N, I(N) is generated by BSCC maps and BP maps. In this paper, we give an explicit normal genera…
The paper proves a compactness theorem for Yang-Mills flow in higher dimensions.
problem Proving compactness for Yang-Mills flow solutions.
method General Uhlenbeck compactness theorem for Riemannian manifolds of dimension n≥4. result Rectifiability of the singular set at finite or infinite time.
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous negatively curved manifolds. A main conjecture provides a general description; an extend…
Study compares and unifies finiteness properties of locally compact groups.
problem Understanding finiteness properties of locally compact groups.
method Comparing and unifying three families of finiteness properties: type Cn, coarse (n−1)-connectedness, and type Fn. result All three families lead to the same notion for locally compact groups.
We prove that a compact nilmanifold admits a Sasakian structure if and only if it is a compact quotient of the generalized Heisenberg group of odd dimension by a co-compact discrete subgroup.
Projective geometry aids in analyzing fields near compact manifolds.
problem Analyzing fields near compact manifolds.
method Developed a projective exterior differential tractor calculus.
result Analogous calculus for projectively compact manifolds.
Generalized Gauss-Bonnet formula for conical metrics on compact Riemann surfaces.
problem Proving a generalized Gauss-Bonnet formula for conical metrics.
method Analyzing Gaussian curvature and Lebesgue integrability.
result Proved a generalized Gauss-Bonnet formula for conical metrics.
Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such foliations by studying the infinitesimal model associated to the canonical connection. …
Minimal surfaces exist for most metrics on compact manifolds with boundary.
problem Existence of minimal surfaces in specific geometric settings.
method Proving existence for almost all Riemannian metrics on compact manifolds with boundary.
result Existence of compact, properly embedded free boundary minimal hypersurfaces for generic metrics.
We study a class of compact surfaces in R3 introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced metrics and Gauss curvatures.
Extends weak continuity of Yang-Mills connections to a broader class.
problem Weak compactness of Ω-Yang-Mills connections. method Compensation compactness argument applied to Yang-Mills fields.
result Weak continuity result extended to Ω-Yang-Mills connections.