The paper studies third-order PDEs invariant under affine transformations and connects them to the Fubini-Pick invariant.
problem Investigating third-order PDEs invariant under affine transformations.
method Using a general method introduced in [D.V. Alekseevsky, J. Gutt, G. Manno, and G. Moreno: A general method to construct invariant PDEs on homogeneous manifolds].
result Derives third-order PDEs from the Fubini-Pick invariant.
This paper classifies hypersurfaces in n+1 with parallel Fubini-Pick form.
problem Classifying hypersurfaces with parallel Fubini-Pick form in \(\mathbb{R}^{n+1}\).
method Defining a generalized Calabi product and proving decomposition theorems.
result Complete classification of Calabi hypersurfaces in \(\mathbb{R}^{n+1}\) with parallel Fubini-Pick form.
Classifies Calabi hypersurfaces with parallel Fubini-Pick form.
problem Classifying Calabi hypersurfaces with specific geometric properties.
method Classification based on parallel Fubini-Pick form and Levi-Civita connection.
result Classification of 2 and 3-dimensional Calabi hypersurfaces.
Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.
problem Comparing geometric quantities of circle packings with different boundary values.
method Combinatorial Calabi flows and maximum principle.
result Discrete Schwarz-Pick lemma proven for generalized circle packings.
The paper studies special normalizations of ruled surfaces in 3D Euclidean space.
problem Investigating relative normalizations of skew ruled surfaces.
method Investigates new formulae for Pick invariant, relative curvature, mean curvature, and relative metric.
result Determines ruled surfaces that make the surface an improper or proper relative sphere.
Transformed geometry into algebra to prove Pick's theorem efficiently.
problem Translating geometric Pick's theorem into formal algebraic proof.
method Formalized geometric Pick's theorem into algebraic proof using Lean.
result Efficient formal proof of Pick's theorem.
KLT picker automates particle picking for cryo-EM, especially for low SNR images.
problem Challenges in particle picking, especially for low SNR micrographs.
method Data-driven optimal templates learned via Karhunen Loeve Transform.
result High-quality results with minimal manual effort on publicly available data sets.
We study fibrations $\cV$ of toric varieties over the flag variety G/T, where G is a compact semisimple Lie group and T is a maximal torus. From symplectic data, we construct test configurations of $\cV$ and compute their Futaki invariants by employing a generalization of Pick's Theorem. We also give a simple for…
Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.
problem Understanding geometric relationships between complex hyperbolic spaces and Hilbert spaces.
method Use a complex analog of the cosine of a vertex angle as a novel technical tool.
result Describe possible triangular faces of tetrahedra in hyperbolic space and three-dimensional subspaces in Hilbert spaces with Pick kernels.
Minimal maps on curved surfaces decrease area.
problem Understanding area behavior of minimal maps on curved surfaces.
method Proved a Schwarz-Pick lemma for minimal maps between negatively curved Riemannian surfaces.
result Minimal maps between negatively curved Riemannian surfaces are area decreasing.
We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.
The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.
problem Proving the Discrete Schwarz-Pick Lemma for circle packings with various inversive distances.
method Using a variational principle for circle packings with inversive distances, the paper extends the lemma to a broader range of packings.
result The Discrete Schwarz-Pick Lemma holds for circle packings with inversive distances in (−1,1], provided an additional condition on triangle weights. Optimal trend-following strategy uses simple EMA, avoiding complex cherry-picked signals.
problem Cherry-picking signals for trend-following strategies.
method Simple EMA for trend capture, avoiding complex indicators.
result Simple EMA is optimal for capturing trend, complex indicators are risky.
Study finds cherry-picking load shaping strategies outperforms others in reducing grid CO2 emissions.
problem Lack of detailed counterfactual data makes it hard to assess load shaping strategies' effectiveness.
method Calibrated granular ERCOT simulations for counterfactual analysis of load shaping strategies.
result LMP-based load shaping outperforms other strategies in reducing grid CO2 emissions.
We present an intriguing question about lattice points in triangles where Pick's formula is "almost correct". The question has its origin in knot theory, but its statement is purely combinatorial. After more than 30 years the topological question was recently solved, but the lattice point problem is still open.
We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature K in the Euclidean space R3, which are characterized by the support functions (α)q=∣K∣α for α∈R (Manhart's relative normalizations). All ruled surfaces for…
Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction are extensively used to reveal structural information on macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron microscopes automatically acquire thousands of high-quality micrographs. Particles are…
Sharp estimate on harmonic maps at conformal points in balls.
problem Estimating harmonic maps at conformal points in balls.
method Sharp estimate on differential norm using Schwarz-Pick lemma.
result Generalizes classical Schwarz-Pick lemma and gives optimal for n≥3. Topaz uses neural networks to pick particles from cryoEM images efficiently.
problem Manual particle picking is time-consuming and requires post-processing.
method Positive-Unlabeled (PU) learning with minimal labeled data.
result Topaz improves cryoEM reconstruction resolution by up to 0.15 Å.
We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost complex manifold. This relation is analogous to the miraculous cancellation formula…
New rationalization method avoids spurious correlations.
problem Spurious correlations in rationalization criteria.
method Invariant rationalization using game theory constraints.
result Rationales generalize better and align with human judgments.
New method prevents cherry-picking in machine learning reports.
problem Selection bias in reporting machine learning innovations.
method Post-reporting solution to verify bias using another set of results.
result False reports of innovation can be prevented even if no actual improvement exists.
NeuRewriter learns to choose and rewrite heuristics in combinatorial problems.
problem Time-consuming tuning of heuristics in combinatorial optimization.
method NeuRewriter uses reinforcement learning to learn a policy for picking heuristics and rewriting solutions.
result NeuRewriter outperforms existing methods in various combinatorial tasks.
Study limits of convex domains in projective plane, proving specific results.
problem Understanding limits of convex domains in projective plane.
method Analyzing sequences of properly convex domains with bounded multiplicity.
result Determined all Hausdorff limit domains after normalization.
Study analyzes 3,171 stocks to pick efficient portfolios using quantum and classical solvers.
problem Creating efficient stock portfolios from a large dataset.
method Used classical and quantum solvers to optimize portfolios of 3,171 US stocks.
result Demonstrated the effectiveness of quantum and classical solvers in portfolio optimization.
Mass spectrometry (MS) is an important technique for chemical profiling which calculates for a sample a high dimensional histogram-like spectrum. A crucial step of MS data processing is the peak picking which selects peaks containing information about molecules with high concentrations which are of interest in an MS in…
Randomized graph construction ensures giant component with fewer edges.
problem Efficiently constructing sparse graphs with good connectivity.
method Randomly connecting points to a subset of their nearest neighbors.
result A sparser graph with comparable connectivity properties.
Paper improves XMLC by no-regretly generalizing HSM to PLTs.
problem Efficiently tagging instances with a small subset of relevant labels from a large pool.
method Probabilistic label trees (PLTs) as a no-regret multi-label generalization of hierarchical softmax (HSM).
result XT (extremeText) outperforms HSM with pick-one-label heuristic and XML-CNN.
Model predicts startup success based on data-driven analysis.
problem Evaluating the quality of startup companies.
method Developed a model using a dataset of startup companies, their founders, and investors. Used a Bayesian approach to calculate features and exit probabilities.
result Model constructs portfolios with high exit rates, nearly double that of top venture capital firms.
Solves the initial CV problem for molecular simulations using machine learning.
problem Selecting appropriate collective variables for enhancing sampling in molecular simulations.
method Data-driven approach inspired by supervised machine learning (SML).
result Various SML algorithms can be used as initial collective variables (SML_cv) for accelerated sampling.
TossingBot learns to throw objects accurately with residual physics.
problem Learning to throw arbitrary objects accurately and quickly.
method End-to-end formulation that learns control parameters from visual observations.
result TossingBot achieves 600+ grasps per hour with 85% throwing accuracy.
CAP algorithm controls FCR in online selective prediction.
problem Online predictive tasks with temporal multiplicity and FCR control.
method CAP framework with adaptive pick rule and calibration set construction.
result CAP achieves exact selection-conditional coverage guarantee and FCR control.
We derive asset pricing formula for markets with incomplete information and subjective views.
problem Asset pricing in markets with informational imperfections and subjective investor beliefs.
method Closed-form market equilibrium formula based on Merton's model, non-linear system of equations, conditional posterior distribution.
result Derivation of market reference model for excess returns under random shadow-costs.
Automates key steps in NMR protein structure elucidation.
problem Laborious data analysis limits NMR spectroscopy potential.
method Combination of deep learning, non-parametric models, and combinatorial optimization.
result Automated detection and assignment of signals in NMR data.
We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the theorem, due to Benoist and Hulin, that the Hilbert metric and Blaschke metric are comparable.
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p∈M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. $S…
In this article, we advocate the ensemble approach for variable selection. We point out that the stochastic mechanism used to generate the variable-selection ensemble (VSE) must be picked with care. We construct a VSE using a stochastic stepwise algorithm, and compare its performance with numerous state-of-the-art algo…
New method finds significant high-order interactions efficiently.
problem Finding statistically significant high-order interactions in high-dimensional data.
method Extends selective inference to high-order interaction models with pruning strategy.
result Demonstrated efficient and powerful method for high-order interactions.
The paper solves circle packings on surfaces with boundaries.
problem Circle packing on surfaces with boundaries and finite genus.
method Using Thurston's algorithm and discrete Schwarz-Pick lemma.
result A unique solution to the boundary value problem exists.
This paper introduces a novel, well-founded, betweenness measure, called the Bag-of-Paths (BoP) betweenness, as well as its extension, the BoP group betweenness, to tackle semisupervised classification problems on weighted directed graphs. The objective of semi-supervised classification is to assign a label to unlabele…
Let Σ be a closed surface, G a compact Lie group, not necessarily connected, with Lie algebra g, endowed with an adjoint action invariant scalar product, let ξ:P→Σ be a principal G-bundle, and pick a Riemannian metric and orientation on Σ so that the corresponding Yang-Mills equations are defined.…
AI optimizing for risk-adjusted return may choose unethical strategies.
problem AI optimization for risk-adjusted return may lead to unethical outcomes.
method Defined Unethical Odds Ratio (Υ) to calculate probability of unethical strategies, derived formula for limit as strategy space grows, provided algorithm for estimation.
result Probability of picking an unethical strategy can become high even with small proportion of unethical strategies.
Algorithm identifies fractal system's scaling exponents in high dimensions.
problem Statistical identification of Hurst distribution in high-dimensional fractal systems.
method Wavelet random matrices, modified spectral clustering, model selection.
result Algorithm consistently estimates Hurst distribution in moderately high dimensions.
New method interprets neural networks at multiple scales.
problem Interpreting neural networks at various scales and identifying important subsets of inputs.
method Rank Projection Trees framework using any scoring function.
result Successfully identifies biologically important genes and gene sets.
We pick up the regime switching model for asset returns introduced by Rogers and Zhang. The calibration involves various markets including implied volatility in order to gain additional predictive power. We focus on the calculation of risk measures by Fourier methods that have successfully been applied to option pricin…
Almost all local minima in neural networks are strongly convex.
problem The prevalence of strongly convex neighborhoods around local minima in neural network optimization landscapes.
method Rigorous analysis of shallow neural networks with analytic activation functions, dividing parameter space into efficient and redundant domains.
result For shallow neural networks on the efficient domain, almost all local minima are strongly convex.
Study combines chit-chat and goal-oriented dialogue in fantasy games.
problem Combining naturalistic chit-chat with goal-oriented tasks in fantasy games.
method Trained a goal-oriented model with reinforcement learning against an imitation-learned chit-chat model using two approaches.
result Both models outperform a baseline and can converse naturally to achieve goals.
Players choose rebalancing rules to maximize their wealth relative to others in a continuous-time trading game.
problem Optimizing wealth in a continuous-time trading game between two players.
method Players choose rebalancing rules to maximize their expected wealth ratio, using the Kelly rule in equilibrium.
result The Kelly rule emerges as the optimal strategy in both short and long time intervals.