arXiv research

We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of real points is equipped with a pair of opposite orientations and a Spin structure…

Study rationality of meromorphic functions between real algebraic sets in the plane.

Study real line subbundles on curves, extending classical work.

Study of real polytopes with group and symplectic involutions.

We construct a compact convex generating set $\mathcal{C}_n$ of the moduli set of closed connected projective special real manifolds of fixed dimension $n$. We show that a closed connected projective special real manifold corresponds to an inner point of $\mathcal{C}_n$ if and only if it has regular boundary behaviour.…

New real algebraic maps with prescribed images and compositions are constructed locally like moment maps.

Study complex slices on real algebraic varieties and their properties.

The paper classifies orbits of semisimple elements in real semisimple Lie algebras.

Study real logarithms of semi-simple matrices, focusing on differential structure.

Operators on the ring of algebraically constructible functions are used to compute local obstructions for a four-dimensional semialgebraic set to be homeomorphic to a real algebraic set. The link operator and arithmetic operators yield $2^{43}-43$ independent characteristic numbers mod 2, which generalize the Akbulut-K…

Real bordered Floer homology computes 3-manifolds with involution.

A new method learns from synthetic data without needing real-world examples.

New model detects crying in real-world settings with improved accuracy.

Whitney type examples of maps $f\in C^k(\real^m,\real^n)$ for a maximal possible real $k$, and multidimensional space-filling curves with special properties are constructed.

Ever growing volume and velocity of data coupled with decreasing attention span of end users underscore the critical need for real-time analytics. In this regard, anomaly detection plays a key role as an application as well as a means to verify data fidelity. Although the subject of anomaly detection has been researche…

Moduli spaces of semi-stable real and quaternionic vector bundles of a fixed topological type admit a presentation as Lagrangian quotients, and can be embedded into the symplectic quotient corresponding to the moduli variety of semi-stable holomorphic vector bundles of fixed rank and degree on a smooth complex projecti…

We explicitly compute the intrinsic volume of the set of real (and real symmetric) matrices of Frobenius norm one and given corank (the case of matrices with zero determinant as a special case). We give asymptotic formulas for our computations and we discuss several examples and applications.

This paper provides a stratification of semi-algebraic sets in the plane with finitely many geodesic segments.

We determine the expected curvature polynomial of random real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group. In particular, the expected Euler characteristic of such random real projective…

We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological spaces that admit functions similar to the Kempf-Ness function. The point of this…

In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real projective manifold. When the target manifold is strictly convex, our results imply t…

For generic torus-invariant metrics, eigenspaces are 2D and nodal sets are connected hypersurfaces.

Dividing local Gaussian processes improve real-time prediction efficiency.

The paper analyzes heat trace asymptotics for de Rham and Dolbeault complexes in both real and complex settings.

We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozek…

This work shows how to use simulators to learn efficient exploration in real-world RL.

This paper speeds up SVC clustering by compressing data while preserving key properties.

Two groups with specific limit sets in hyperbolic spaces are identified.

We prove that the set of non-properness of a polynomial mapping of the three dimensional space which is a local homeomorphism cannot be homeomorphic to the real line $\R.$

Study evaluates scalability and real-world impact of disentangled representations.

Study derives error decay rates for kernel classification under source and capacity conditions.

Study robust regression learning under adversarial attacks.

Transforms uniquely determine Higgs fields on real-analytic manifolds.

Extends Tanimoto kernel to real-valued functions.

In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactification. We also count the number of singular phenomena at infinity, called "cleaving" and "vanishing" in the same setting. Finally, we give an…

We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally homogeneous on all of the surface. In particular, we prove that such connections exist. This classification relies in a local result that cla…

MPS selects models for nonstationary time series in real-time.

This work studies reinforcement learning in the Sim-to-Real setting, in which an agent is first trained on a number of simulators before being deployed in the real world, with the aim of decreasing the real-world sample complexity requirement. Using a dynamic model known as a rich observation Markov decision process (R…

We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…

Defines real link Floer homology for specific types of links.

Real vector bundles are determined by their Dirac indices on specific spin manifolds.

Constructs real algebraic maps with specific geometric constraints.

In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also closed under the bool…

Supposing that X is a Riemannian manifold, a Z/2 spinor on X is defined by a data set consisting of a closed set in X to be denoted by Z, a real line bundle over X-Z, and a nowhere zero section on X-Z of the tensor product of the real line bundle and a spinor bundle. The set Z and the spinor are jointly constrained by …

Real Heegaard Floer homology gets a new grading for certain 3-manifolds.

Research on deep learning generalization in real-world applications.

The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not efficiently capture the setting where the set of available decisions (actions) at each time step is stochastic. Recently, the stochastic action set Markov decision process (SAS-MDP) formulation has b…

A new method for real-time CCA on streaming data.