arXiv research

The paper uses polyhedral expansions to capture the shape of compact metric spaces.

Computational method approximates homology groups of compact metric spaces.

In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inve…

We construct sequences of pseudo-Anosov mapping classes whose dilatations behave asymptotically like the inverse of the Euler characteristic of the surface they are defined on. These sequences are used to show that if the genus, g, and punctures, n, of a surface are related by a rational ray g=rn then the minimal dilat…

Deep learning models have shown state-of-the-art performance in many inverse reconstruction problems. However, it is not well understood what properties of the latent representation may improve the generalization ability of the network. Furthermore, limited models have been presented for inverse reconstructions over ti…

The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define inverse persistence as a new kind of persistence process.

In extension theory, in particular in dimension theory, it is frequently useful to represent a given compact metrizable space X as the limit of an inverse sequence of compact polyhedra. We are going to show that, for the purposes of extension theory, it is possible to replace such an X by a better metrizable compactum …

MCGDiff uses SGM to guide SMC for solving ill-posed linear inverse problems.

We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of $n$-dimensional Riemannian manifolds with bounded diameter and sectional curvature. It is w…

Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints - the lack of which might lead to undesirable results. To overcome this issue, we have deve…

Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carl…

We show that any nontrivial reduced knot projection can be obtained from a trefoil projection by a finite sequence of half-twisted splice operations and their inverses such that the result of each step in the sequence is reduced.

Geometric framework for inverse problems using foliations and dual connections.

Finite approximations help reconstruct countable metric and ultrametric spaces.

The paper characterizes $G$-ANR spaces and their properties.

Deep learning networks have shown state-of-the-art performance in many image reconstruction problems. However, it is not well understood what properties of representation and learning may improve the generalization ability of the network. In this paper, we propose that the generalization ability of an encoder-decoder n…

We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is independent of the sequence index. The problem is hard because it involves possibly m…

Hierarchical clustering uses OWA operators to generalize linkage methods and avoid dendrogram inversions.

An inverse limit of a sequence of covering spaces over a given space $X$ is not, in general, a covering space over $X$ but is still a lifting space, i.e. a Hurewicz fibration with unique path lifting property. Of particular interest are inverse limits of finite coverings (resp. finite regular coverings), which yield fi…

In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomorphic curve into complex projective space or the inversion of a minimal…

We state the problem of inverse reinforcement learning in terms of preference elicitation, resulting in a principled (Bayesian) statistical formulation. This generalises previous work on Bayesian inverse reinforcement learning and allows us to obtain a posterior distribution on the agent's preferences, policy and optio…

The paper shows how to use fine shape to understand infinite-dimensional spaces.

We construct an inverse system of unstable Vassiliev spectral sequences on the spaces of plumbers' knots, which model the homotopy type of the space of long knots, and show that the limit of these sequences contains the finite type invariants in their usual complexity. Utilizing the cell structure on the discriminant o…

We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite-order (short exact) variational sequence which i…

A new method uses mixture approximations to improve diffusion models for Bayesian inverse problems.

Solving the RNA inverse folding problem is a critical prerequisite to RNA design, an emerging field in bioengineering with a broad range of applications from reaction catalysis to cancer therapy. Although significant progress has been made in developing machine-based inverse RNA folding algorithms, current approaches s…

Study inverse problems with measure samples, improving estimator calibration and recovery.

Deep learning model improves seismic rock property estimation.

Inversion-free natural gradient method for Riemannian manifolds.

We study the stability of the Positive Mass Theorem (PMT) in the case where a sequence of regions of manifolds with positive scalar curvature $U_T^i\subset M_i^3$ are foliated by a smooth solution to Inverse Mean Curvature Flow (IMCF) which may not be uniformly controlled near the boundary. Then if $\partial U_T^i = Σ_…

Microfluidic devices are utilized to control and direct flow behavior in a wide variety of applications, particularly in medical diagnostics. A particularly popular form of microfluidics -- called inertial microfluidic flow sculpting -- involves placing a sequence of pillars to controllably deform an initial flow field…

A classical result by Pachner states that two $d$-dimensional combinatorial manifolds with boundary are PL homeomorphic if and only they can be connected by a sequence of shellings and inverse shellings. We prove that for balanced, i.e., properly $(d + 1)$-colored, manifolds such a sequence can be chosen such that bala…

Temporal point process is an expressive tool for modeling event sequences over time. In this paper, we take a reinforcement learning view whereby the observed sequences are assumed to be generated from a mixture of latent policies. The purpose is to cluster the sequences with different temporal patterns into the underl…

A new algorithm speeds up EEG source localization using $\ell_1$ regularization.

Several new properties of weighted Hilbert transform are obtained. If mu is zero, two Plancherel-like equations and the isotropic properties are derived. For mu is real number, a coerciveness is derived and two iterative sequences are constructed to find the inversion. The proposed iterative sequences are applicable to…

This is part 2 of a 3-part article where we provide an $O(n^2)$-algorithm to produce a surgery presentation of a 3-manifold induced by a gem with a resolution. In this part we produce a sequence of colored simplicial 2-complexes which are inverses and dual to the sequence of gems produced in the first part. The refinem…

Researchers extend topological classification to knotted semimetals in 3D.

New spatiotemporal Besov process improves CT image reconstruction and other inverse problems.

Robo-advisor uses ML to optimize investment performance.

In this work, we aim to solve data-driven optimization problems, where the goal is to find an input that maximizes an unknown score function given access to a dataset of inputs with corresponding scores. When the inputs are high-dimensional and valid inputs constitute a small subset of this space (e.g., valid protein s…

New approach uses inverse reinforcement learning to improve language model training.

A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. However, non-tri…

Paper presents a unique method to recover signals from their bispectrum.

This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz bound on the mean curvature of the boundary. The second is to establish geometric c…

A new method for sampling complex posterior distributions in DDMs.

Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This paper is primarily concerned with the case of compacta, in which Steenrod homot…

New algorithm infers reward function from agent's learning trajectories.

Efficient inference method for adaptive experiments with tighter confidence sequences.