arXiv research

In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each other and well-posed for the odd signature operator $\mathcal{B}$ in the sense of Se…

SOLVAR efficiently analyzes cryo-EM data's structural variability.

This work generates synthetic 3D thermal facial data using 2D facial data and deep learning.

The refined analytic torsion on compact Riemannian manifolds with boundary has been discussed by B. Vertman and the authors, but these two constructions are completely different. Vertman used a double of de Rham complex consisting of the minimal and maximal closed extensions of a flat connection and the authors used we…

Study on smoothness of solutions to nonlinear equations on Riemannian manifolds.

In the previous work ([14]) we introduced the well-posed boundary conditions ${\mathcal P}_{-, {\mathcal L}_{0}}$ and ${\mathcal P}_{+, {\mathcal L}_{1}}$ for the odd signature operator to define the refined analytic torsion on a compact manifold with boundary. In this paper we discuss the gluing formula of the refined…

Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based representation of the volumetric data and then, posing the tree extraction as a graph …

A key step to driver safety is to observe the driver's activities with the face being a key step in this process to extracting information such as head pose, blink rate, yawns, talking to passenger which can then help derive higher level information such as distraction, drowsiness, intent, and where they are looking. I…

Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in partic…

We introduce a scalable approach for object pose estimation trained on simulated RGB views of multiple 3D models together. We learn an encoding of object views that does not only describe an implicit orientation of all objects seen during training, but can also relate views of untrained objects. Our single-encoder-mult…

Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require. We formulate and develop the Structured Prediction Cascade architecture: a seque…

Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In this work, we propose Graphite, an algorithmic framework for unsupervised learn…

Quantitative susceptibility mapping (QSM) is a powerful MRI technique that has shown great potential in quantifying tissue susceptibility in numerous neurological disorders. However, the intrinsic ill-posed dipole inversion problem greatly affects the accuracy of the susceptibility map. We propose QSMGAN: a 3D deep con…

We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a $d_1$ by $d_2$ matrix $\mathbfΘ^*$ that defines the reward…

New inequality for refined knot invariants in a specific space.

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…

Refines neural network predictions using background knowledge for improved accuracy.

New research shows label refinement and weak training have limitations for aligning LLMs.

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.

In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …

Docking is an important tool in computational drug discovery that aims to predict the binding pose of a ligand to a target protein through a combination of pose scoring and optimization. A scoring function that is differentiable with respect to atom positions can be used for both scoring and gradient-based optimization…

Refined 3D index uses surgery and gradings to distinguish 3-manifolds.

Counterexamples show Salter's question on Burau image is negative for n=4.

We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general unidentifiable, so recent and classical results on parameter recovery do not apply. Secondl…

We propose a method to generate multiple diverse and valid human pose hypotheses in 3D all consistent with the 2D detection of joints in a monocular RGB image. We use a novel generative model uniform (unbiased) in the space of anatomically plausible 3D poses. Our model is compositional (produces a pose by combining par…

Cryptocurrency forecasting model considers macro, sentiment, and technical indicators.

Refines deep generative models to improve data density precision.

The paper learns pose variations within shape populations using constrained mixtures of factor analyzers.

Established a stable cohomotopy refinement for Pin(2) monopole invariants.

Active localization is the problem of generating robot actions that allow it to maximally disambiguate its pose within a reference map. Traditional approaches to this use an information-theoretic criterion for action selection and hand-crafted perceptual models. In this work we propose an end-to-end differentiable meth…

Refined 1-cocycle for knots helps quantify isotopies.

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy …

Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …

We note that our stable homotopy refinements of Khovanov's arc algebras and tangle invariants induce refinements of Chen-Khovanov and Stroppel's platform algebras and tangle invariants, and discuss the topological Hochschild homology of these refinements.

The paper analyzes the observability of relative pose estimation using dual quaternions.

EGR refines and assesses protein complex structures.

Recent advances in deep pose estimation models have proven to be effective in a wide range of applications such as health monitoring, sports, animations, and robotics. However, pose estimation models fail to generalize when facing images acquired from in-bed pressure sensing systems. In this paper, we address this chal…

A novel framework refines diffusion models iteratively for better downstream reward optimization.

We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the $Ω$-background. This form enables us to relate refined C…

Study uses AI to refine loan assessments, improving credit default predictions.

Let $E$ be a flat complex vector bundle over a closed oriented odd dimensional manifold $M$ endowed with a flat connection $\nabla$. The refined analytic torsion for $(M,E)$ was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…

The refined analytic torsion, defined by M. Braverman and T. Kappeler on closed manifolds, can be viewed as a refinement of the Ray-Singer torsion, since it is a canonical choice of an element with Ray-Singer norm one, in case of unitary representations. The complex phase of the refinement is given by the rho-invariant…

Refined BN-S model improves crude oil hedging with machine learning.

We review the construction and context of a stable homotopy refinement of Khovanov homology.

The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the underlying data distribution setting where connections to maximal marginal diver…

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Herm…

Refined invariants for 4D 2-handlebodies, linking quantum groups and cohomology.

Paper introduces EnDKF for more accurate pose tracking.