arXiv research

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …

Deep models generate geometric objects with global properties.

Introduces bounded scale measure and generalizes property A.

We present examples of metric spaces that are not Riemannian manifolds nor dimensionally homogeneous that satisfy the Tetrahedral Property. In spite of that, Euclidean cones over metric spaces with small diameter do not satisfy this property. We extend Sormani's Tetrahedral Property to a less restrictive property and p…

Paper proves naturally reductive property is inaudible for certain manifolds.

The study examines groups with a specific automorphism property using BNS-invariant.

Bi-orderable groups from left-orderable ones, showing non-profinite properties.

Although machine learning has been successfully used to propose novel molecules that satisfy desired properties, it is still challenging to explore a large chemical space efficiently. In this paper, we present a conditional molecular design method that facilitates generating new molecules with desired properties. The p…

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group $G$ with a …

Paper proposes a method to design molecules with specific properties.

Study compares and unifies finiteness properties of locally compact groups.

Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalized distance-squared mapping of equidimensional case is not injective. Nevertheless, in this paper, it is shown that the non-singular property…

Generative neural network designs novel 3D molecules with specified properties.

This paper generalizes property (QT) to a broader class of groups.

Study generalizes property elicitation to imprecise probabilities.

There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove the genus 3 case, even in the absence of new progress on the generalized Propert…

We say that a group has property $R_{\infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\infty}$. We define a solvable generalization $Γ(S)$ of these groups which we show to have proper…

Extends p-harmonic map theory for new properties.

IH-GAN models cellular structures accurately and improves structural performance.

The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.

This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property…

We prove recognition theorems for codimension one manifold factors of dimension $n \geq 4$. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that $X \times \mathbb{R}$ i…

Drug discovery aims to find novel compounds with specified chemical property profiles. In terms of generative modeling, the goal is to learn to sample molecules in the intersection of multiple property constraints. This task becomes increasingly challenging when there are many property constraints. We propose to offset…

Study builds ML models to predict fuel properties accurately.

The paper studies groups with specific actions on hyperbolic spaces and finds that subgroups are either amenable or contain a free group.

Designing a molecule with desired properties is one of the biggest challenges in drug development, as it requires optimization of chemical compound structures with respect to many complex properties. To augment the compound design process we introduce Mol-CycleGAN - a CycleGAN-based model that generates optimized compo…

Study generalizations of chainability and compactness in metric spaces.

This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal, almost) contact and generalized Sasakian structures. A few of these properties are n…

In this paper we provide a general framework for estimating symmetric properties of distributions from i.i.d. samples. For a broad class of symmetric properties we identify the easy region where empirical estimation works and the difficult region where more complex estimators are required. We show that by approximately…

We assume that a high-dimensional datum, like an image, is a compositional expression of a set of properties, with a complicated non-linear relationship between the datum and its properties. This paper proposes a factorial mixture prior for capturing latent properties, thereby adding structured compositionality to deep…

We study generalized moment maps for a Hamiltonian action on a connected compact $H$-twisted generalized complex manifold introduced by Lin and Tolman and prove the convexity and connectedness properties of the generalized moment maps for a Hamiltonian torus action.

In this paper, we propose a property which is a natural generalization of Kazhdan's property $(T)$ and prove that many, but not all, groups with property $(T)$ also have this property. Let $\G$ be a finitely generated group. One definition of $\G$ having property $(T)$ is that $H^1(\G,π,\fh)=0$ where the coefficient mo…

The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.

We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre's Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including $SL(n,\Z)$ for $n\geq 3$. We also give a way of thinking about Property (QFA) by breaking it down …

Proves a vanishing property for symplectic manifold cohomology.

It is shown that if the exterior of a link L in the three sphere admits a genus 2 Heegaard splitting, then L has Generalized Property R.

We propose a novel computational strategy for de novo design of molecules with desired properties termed ReLeaSE (Reinforcement Learning for Structural Evolution). Based on deep and reinforcement learning approaches, ReLeaSE integrates two deep neural networks - generative and predictive - that are trained separately b…

Study shows infoGAN's generalization error bound for two-layer networks.

We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…

Establishes geometric properties of elements in the positive semigroup of a general real semisimple Lie group.

If there are any 2-component counterexamples to the Generalized Property R Conjecture, a least genus component of all such counterexamples cannot be a fibered knot. Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions. The simplest plausible counterexample to the Gene…

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.

Graph products inherit Morse local-to-global property from their components.

Study geometric properties of generalized vacuum static spaces.

Study on descent properties of complex affine surfaces under proper morphisms.

We present a deep learning framework for wide-field, content-aware estimation of absorption and scattering coefficients of tissues, called Generative Adversarial Network Prediction of Optical Properties (GANPOP). Spatial frequency domain imaging is used to obtain ground-truth optical properties from in vivo human hands…

Projectors defined in virtual Temperley-Lieb algebra with properties similar to Jones-Wenzl projectors.

Groups of importance in group theory have flexible stability properties.