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.
The study characterizes round spheres in Euclidean space based on r-mean curvature conditions.
A new Euclidean approach reveals the pentagram map's beauty.
Study on hypersurfaces in pseudo-Euclidean space with constant curvature or rotational properties.
Study expanding gradient Ricci solitons with Euclidean base.
In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on particular kind of these surfaces.
These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.
Paper uses non-Euclidean analysis to classify brain structure variations.
Extends illumination bodies to non-Euclidean spaces and proves their volume derivative defines surface area.
Piecewise flat approximations for curvature in Euclidean and non-Euclidean spaces.
Paper defines a new functional for spinors on Euclidean manifolds.
The study compares Euclidean and cosine distances in medical drug prescription prediction.
New method for learning with non-Euclidean data using decomposable kernels.
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distanc…
We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.
Paper proposes a matrix optimization model for reliable Euclidean embedding from noisy data.
Study of filtering and smoothing in submanifolds of Euclidean space.
Develops weak formulation for spacelike flows in pseudo-Euclidean space.
Non-Euclidean BPM extends optimization theory to non-Euclidean norms.
Unified framework for Riemannian deep learning across manifold-valued representations.
We propose a modification of the three-manifold invariant based on the use of Euclidean metric values ascribed to the elements of manifold triangulation. We thus obtain a nontrivial invariant that can, in particular, distinguish non-homeomorphic lens spaces.
Unified framework for non-Euclidean CPD under scalable stochastic mirror descent.
Improves hierarchical clustering in Euclidean space using autoencoders.
We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein condition, we construct a Lyapunov function based on curvature estimates which come f…
We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special result. The existence of such maps on a differentiable manifold is discussed. S…
The paper studies momentum-based minimization for Ginzburg-Landau on Euclidean spaces and graphs.
Revisits Isomap, showing it constructs Euclidean representations of geodesic structure.
We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermion…
We study surfaces with decorations and prove uniformization in non-Euclidean geometries.
The paper extends manifold learning to arbitrary norms, improving molecular motion mapping.
We construct invariants of four-dimensional piecewise-linear manifolds, represented as simplicial complexes, with respect to rebuildings that transform a cluster of three 4-simplices having a common two-dimensional face in a different cluster of the same type and having the same boundary. Our construction is based on t…
We consider timelike and spacelike reductions of 4D, N = 2 Minkowskian and Euclidean vector multiplets coupled to supergravity and the maps induced on the scalar geometry. In particular, we investigate (i) the (standard) spatial c-map, (ii) the temporal c-map, which corresponds to the reduction of the Minkowskian theor…
New graph convolution captures local features on non-Euclidean grids.
Kernel-Gradient Drifting improves generative modeling for non-Euclidean data.
This paper tightens the generalization error bound for graph embedding in non-Euclidean spaces.
Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen…
A new method compares unaligned datasets using log-Euclidean signatures of SPD matrices.
New method for nonlinear SDR of complex non-Euclidean data.
The Piola identity is a central result in the mathematical theory of elasticity. We prove a generalized version of the Piola identity for mappings between Riemannian manifolds, using two approaches, based on different interpretations of the cofactor of a linear map: on…
For collapsing sequences of Riemannian manifolds which satisfy a uniform lower Ricci curvature bound it is shown that there is a sequence of scales such that for a set of good base points of large measure the pointed rescaled manifolds subconverge to a product of a Euclidean and a compact space. All Euclidean factors h…
We study warped products semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n-dimensional pseudo Euclidean space and invariant under the action of an translation group. We provide all such solutions in the case Ricci flat when the base is conformal to an n-dimensional pseudo-Eu…
Extends diffusion models to non-Euclidean spaces with geometric priors.
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is ma…
Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them quickly infeasible for moderate to large scale datasets. A significant effort t…
New optimization method combines gradient clipping and non-Euclidean smoothness.
EF21-Muon optimizes deep learning with error feedback, improving efficiency and accuracy.
In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. The latter result can be viewed as an analog of the well-known theorem of Bi…
Imaging-based early diagnosis of Alzheimer Disease (AD) has become an effective approach, especially by using nuclear medicine imaging techniques such as Positron Emission Topography (PET). In various literature it has been found that PET images can be better modeled as signals (e.g. uptake of florbetapir) defined on a…