Study uses CNNs to estimate BMI from photos.
problem Estimating BMI from photos with limited data.
method Used deep learning (CNNs) to process silhouette images.
result High correlation between estimated and actual BMI.
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48 results for “body mass index”
Neural networks can predict BMI from faces, and can be fooled into wrong predictions.
problem Vulnerability of BMI prediction models to adversarial attacks.
method Test-time adversarial attacks on neural networks trained to infer BMI from facial images.
result Neural networks can be tricked into predicting incorrect BMI values, posing a risk of insurance fraud.
Alternative approach to model selection using transformation analysis.
problem Over-simplistic models lead to erroneous interpretations.
method Step-wise complexity reduction to identify simpler, better-interpretable models.
result Transformation models improve model fit and interpretability.
Bifurcation of periodic orbits for the -body problem, from a non geometrical family of solutionsmath.DS
New periodic solution found in 4-body problem, not part of expected geometrical family.
problem Finding new periodic solutions in the 4-body problem not fitting the expected geometrical family.
method Analytic continuation of a numerical solution to discover a new family of solutions.
result Existence of a non-planar periodic solution for any pair of masses and integer n.
Formula calculates equilibria of convex bodies based on evolute winding number.
problem Determining equilibria of convex bodies in terms of their geometric properties.
method Formula derived from winding number of evolute of convex body boundary.
result Formula extends to cases where center of mass lies on evolute.
New index characterizes non-smooth Zoll convex bodies.
problem Characterizing non-smooth Zoll convex bodies.
method Defining systolic -index and using it to introduce generalized Zoll convex bodies.
result Generalized Zoll convex bodies coincide with classical ones under certain conditions.
Examining orbits ending in binary collisions for three equal masses under an inverse cube force.
problem Analyzing orbits ending in binary collisions for three equal masses under an inverse cube force.
method Reparametrizing orbits as geodesics on a negatively curved metric on a pair of pants.
result Visibility properties of negatively curved surfaces describe orbits beginning or ending in binary collisions.
We consider the two body problem with central interaction on two point homogeneous spaces from point of view of the invariant differential operators theory. The representation of the two particle Hamiltonian in terms of the radial differential operator and invariant operators on the symmetry group is found. The connect…
The paper proves a theorem linking convex body centroids and category theory.
problem Understanding centroids of sections of convex bodies.
method Lusternik-Schnirelmann category theory.
result At least n hyperplanes exist such that the center of mass of their intersection with a convex body lies on the boundary of the convex body.
We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the assumption of the maximal condition, and use a notion of size which is easily computab…
This monograph describes a Riemannian geometric reduction approach to the three-body problem. The fundamental theorems are presented in the introductory part, whereas their proofs are provided in later chapters where specific topics are analyzed in more detail. The basic idea is to reduce the kinematic and dynamics of …
Study finds periodic orbits in a complex gravitational system.
problem Existence of periodic solutions in a gravitational system with multiple primaries.
method Proves existence of periodic solutions when primaries move on a Hip-Hop solution.
result Proves the existence of periodic solutions in the restricted -body problem.
In this paper, we propose a new deep feature selection method based on deep architecture. Our method uses stacked auto-encoders for feature representation in higher-level abstraction. We developed and applied a novel feature learning approach to a specific precision medicine problem, which focuses on assessing and prio…
Bayesian method infers contextual bandit policies robustly.
problem Inference of contextual bandit policies in small sample sizes.
method Empirical likelihood for Bayesian inference.
result Accurate uncertainty measurements and policy comparison.
The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The appro…
The paper studies symmetrization effects on Lelong numbers and Monge-Ampère masses of plurisubharmonic functions.
problem Analyzing symmetrization effects on Lelong numbers and Monge-Ampère masses of plurisubharmonic functions.
method Schwarz symmetrization of -invariant plurisubharmonic functions on balanced domains in .
result The Monge-Ampère mass decreases under Schwarz symmetrization for toric functions with a single pole at the origin.
The -body problem with a potential has, in addition to translation and rotational symmetry, an effective scale symmetry which allows its zero energy flow to be reduced to a geodesic flow on complex projective -space, minus a hyperplane arrangement. When we get a geodesic flow on the two-sphere min…
Consider the equal mass planar -body problem with a potential corresponding to an inverse \textit{cube} force. The Jacobi-Maupertuis principle reparametrizes the dynamics as geodesics of a certain metric. We examine the curvature of this geodesic flow in the reduced space on the collinear and parallelogram invariant…
The paper establishes geometric inequalities for quasi-local masses.
problem Lower bounds for quasi-local masses in terms of charge, angular momentum, and horizon area.
method Hamiltonian approach to three quasi-local masses: Brown-York, Liu-Yau, and Wang-Yau.
result Geometric inequalities motivated by ADM mass, interpreted as localized versions.
The study examines the index of MOTS in Kerr-Newman-de Sitter spacetime and its relation to mass and charge.
problem Investigating the index of MOTS in Kerr-Newman-de Sitter spacetime.
method Analyzing the spatial cross section of the cosmological horizon in the Kerr-Newman-de Sitter spacetime, proving index bounds and establishing area-charge estimates.
result Established bounds on the index of MOTS and a connection between MOTS with index one and General Relativity.
The simplest non-collision solutions of the N-body problem are the "relative equilibria", in which each body follows a circular orbit around the centre of mass and the shape formed by the N bodies is constant. It is easy to see that the moment of inertia of such a solution is constant. In 1970, D. Saari conjectured tha…
Given a Riemannian 3-ball of non-negative scalar curvature, Bartnik conjectured that admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined b…
In this paper, we give a relationship between the eigenvalues of the Hodge Laplacian and the eigenvalues of the Jacobi operator for a free boundary minimal hypersurface of a Euclidean convex body. We then use this relationship to obtain new index bounds for such minimal hypersurfaces in terms of their topology. In part…
Study periodic solutions in N-body problem, revealing braids with complex dynamics.
problem Periodic solutions of the planar Newtonian N-body problem with equal masses.
method Analyze braid structures derived from periodic solutions, proving pseudo-Anosov types.
result Braids from Yu's periodic solutions are pseudo-Anosov, with stretch factors reflecting complexity.
Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The formula is based on the fact that the space of similarity classes of triangles …
We generalize the Riesz potential of a compact domain in by introducing a renormalization of the -potential for . This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renorm…
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of -body solutions for the Einstein equation, which patently…
A n n-body system is a labelled collection of n point masses in Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are n-configuration, configuration space, internal s…
Reduces 3-body problem to shape and spherical geometry.
problem Investigates the motion of three bodies in a plane.
method Geometric reduction using equivariant Riemannian geometry.
result Time parametrization of moduli curve determined by shape curve and potential function.
Compact proof for Brown-York mass positivity and rigidity in flat and spherical spaces.
problem Positivity of Brown-York mass and rigidity of manifolds with mean-convex boundaries.
method Spinorial proof and optimal lower bound for eigenvalues.
result Optimal lower bound for first non-null eigenvalue of Dirac operator.
Paper bounds index of free boundary surfaces.
problem Estimating the index of free boundary surfaces.
method Proved Morse index lower bound as linear function of genus and boundary components.
result Morse index lower bound by linear function of genus and boundary components.
New black hole solutions with positive and negative masses in 4 and 5 dimensions.
problem Constructing static vacuum black hole solutions with signed masses.
method Axisymmetric and bi-axisymmetric solutions in 4 and 5 dimensions, using Weyl-Papapetrou coordinates.
result Signed mass black holes can be superposed, with specific topologies in 5 dimensions.
Paper proposes a method to model health outcomes using varying-coefficients and KNN-based LASSO.
problem Modeling health outcomes like BMI and cholesterol levels with varying age effects.
method Varying-coefficients regional quantile regression via KNN fused LASSO, with ADMM algorithm.
result Efficacy in capturing complex age-dependent associations between health outcomes and risk factors.
Sharp bounds for charged Hawking mass in electrostatic space-times.
problem Bounding charged Hawking mass in electrostatic space-times.
method Proving sharp lower bounds and upper bounds for the charged Hawking mass.
result Sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times.
Modeling individual cardiovascular responses from wearable sensor data.
problem Capturing and understanding cardiovascular responses to physical activity and sleep changes.
method Attentional convolutional neural network to learn signatures from minute-level sensor data.
result Generated signatures generalize and outperform baseline models in predicting cardiovascular variables.
Fixed points of mean section operators found in convex bodies.
problem Characterizing fixed points of mean section operators in convex bodies.
method Characterization of rotation equivariant operators using spherical Laplacian mass distribution, and application of Minkowski valuations.
result Euclidean balls are the only fixed points of mean section operators in a neighborhood of the unit ball.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
problem Stochastic guidance of spin states of rigid bodies over a hard deadline.
method Structural analysis of Kantorovich optimal coupling formulation for nonlinear dynamics.
result Derives the ground cost for optimal transport of angular velocity.
In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the -body problem with general masses and any potential with . We also observe dynamical consequences of these curvature values for relati…
A new distance measure for circular Heegaard splittings helps understand knot exteriors.
problem Understanding the structure of knot exteriors using circular Heegaard splittings.
method Defining and analyzing circular distance for circular Heegaard splittings.
result Circular distance bounds properties of knot exteriors, like the uniqueness of minimal-genus Seifert surfaces.
Background: Many authors have described MELD as a predictor of short-term mortality in the liver transplantation waiting list. However MELD score accuracy to predict long term mortality has not been statistically evaluated. Objective: The aim of this study is to analyze the MELD score as well as other variables as a pr…
We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the mass center of the generalized body enclosed by the immersed capillary hypersurface and the wetted part of the sphere is located at the origin, then the hypersurface is unstable. An immediate result is that all known ex…
Local mass perspective on Bayesian inference
problem Measuring distributional discrepancy in Bayesian inference
method Introducing Mass Index and Regularised Extended KL
result Proving inequalities for comparing local small-ball masses
The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale f…
Mathematical proof of index equality for lattice Dirac operators and continuum operators.
problem Equality of indices for lattice and continuum Dirac operators.
method Using K-theory, we prove equivalence of one-parameter families of continuum and lattice Dirac operators.
result Indices of continuum and lattice Dirac operators are equal.
We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which …
We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifo…
Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes (instead of the returns) possess multifractality. We find that the mass exponent is l…
Paper uses RL to optimize daily step distribution for better health biomarkers.
problem Lack of personalized PA distribution recommendations for health biomarkers.
method Developed an offline reinforcement learning algorithm to learn optimal PA distributions.
result Learned optimal policy suggests more consistent daily steps and tailored recommendations.