A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New framework formalizes estimating valid transport maps, revealing their statistical limits.
DMPS uses diffusion maps and LAWGD for efficient generative modeling.
The study reveals simplicity bias in neural networks leading to better compositional mappings.
New bounds on mapping degrees for geometric 3-manifolds.
For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the surface of the environment using a continuous mesh of triangular surface element…
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from a -dimensional space form into a -dimensional model space. We also give a…
Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.
Space mapping speeds up shape optimization for PDEs.
sFML learns stochastic dynamical systems from data.
A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network variationally via loss functions from the underlying physical models. Solve-trai…
Quantum machine learning models can approximate any continuous function.
Discrete Flow Maps bypass sequential prediction limits for parallel text generation.
Graph neural network predicts optimal coarse-grained mapping operators.
Paper introduces a novel map learning algorithm for domain translation and adaptation.
Develops TCD maps to relate discrete differential geometry and cluster algebras.
In image-based camera localization systems, information about the environment is usually stored in some representation, which can be referred to as a map. Conventionally, most maps are built upon hand-crafted features. Recently, neural networks have attracted attention as a data-driven map representation, and have show…
A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a me…
Saliency maps are often used in computer vision to provide intuitive interpretations of what input regions a model has used to produce a specific prediction. A number of approaches to saliency map generation are available, but most require access to model parameters. This work proposes an approach for saliency map gene…
Study of Gauss maps for minimal surfaces in a specific 3D model.
Develops a unified framework for computing n-dimensional quasi-conformal mappings.
In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth -valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of -valued m…
Evaluating, explaining, and visualizing high-level concepts in generative models, such as variational autoencoders (VAEs), is challenging in part due to a lack of known prediction classes that are required to generate saliency maps in supervised learning. While saliency maps may help identify relevant features (e.g., p…
The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …
We construct a model of differential K-theory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circle-integration maps for these models using classical homotopy-theoretic constructions, by incorp…
New method improves interpretability of fMRI decoding models.
Study Gauss maps of surfaces in Heisenberg group using hyperbolic geometry.
Space mapping calibrates financial models, shown feasible for Heston model.
We study a new set of coupled field equations motivated by the non-linear supersymmetric sigma model of quantum field theory. These equations couple a map into a Riemannian manifold controlled by a harmonic map like action with a spinor field along that map. We study the solutions which we call Dirac-harmonic maps from…
The theory of principal -bundles over a Lie groupoid is an important one, unifying the various types of principal -bundles, including those over manifolds, those over orbifolds, as well as equivariant principal -bundles. In this paper, we study the differential geometry of these objects, including connections …
Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.
Geometric models help classify infinite-type surface mapping class groups.
Several methods were recently proposed for the task of translating images between domains without prior knowledge in the form of correspondences. The existing methods apply adversarial learning to ensure that the distribution of the mapped source domain is indistinguishable from the target domain, which suffers from kn…
An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential gro…
In this paper, we study biharmonic maps into Sol and Nil spaces, two model spaces of Thurston's 3-dimensional geometries. We characterize non-geodesic biharmonic curves in Sol space and prove that there exists no non-geodesic biharmonic helix in Sol space. We also show that a linear map from a Euclidean space into Sol …
Study develops a new method for creating fair models.
We propose analogues of horizontal and vertical projections for model filiform jet space Carnot groups. Every pair consisting of the jet of a smooth function on and a vertical hyperplane with first coordinate fixed provides a splitting of a model filiform group, which induces mappings of the group. We prov…
New framework for learning KR maps from data, ensuring stable generalization.
The paper generalizes Thurston's earthquake map to cluster algebras of finite type.
We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries that have an associated momentum map. In these papers the momentum map played a cru…
A fundamental problem in geophysical modeling is related to the identification and approximation of causal structures among physical processes. However, resolving the bidirectional mappings between physical parameters and model state variables (i.e., solving the forward and inverse problems) is challenging, especially …
New LP method recovers MAP solution from noisy stable instances.
We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class of factorizations by unitons. We show how these specialize to give explicit formu…
Efficiently maps indoor magnetic fields with SKI and D-SKI.
Pseudo horizontally weakly conformal maps extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find in this larger class critical points for the (generalized) Faddeev-Hopf energy. Their stability is also discussed in some cases.
New framework models high-Hopf-index hopfions using generalized fold maps.
In this paper we make a detailed and self-contained study of the conformalGauss map. Then, starting from the seminal work of R. Bryant and the notion of conformal Gauss map, we recover many fundamental properties of Willmore surfaces. We also get new results like some characterizations of minimal and constant meancurva…
Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.