Develops an algorithm to find the best subset of points for maximizing the coefficient of determination.
problem Finding the optimal subset of points for maximizing the coefficient of determination in robust correlation analysis.
method The extit{quadratic sweep} method, which involves projecting points into \(\mathbb{R}^5\) and iterating over linearly separable \(k\)-subsets.
result The method optimally finds the best subset of points for maximizing the coefficient of determination without error over several million trials up to \(n=30\).
Continuous Sweep improves binary quantifier performance.
problem Estimating class prevalence in datasets.
method Parametric binary quantifier inspired by Median Sweep, using parametric class distributions and mean of Adjusted Count estimates.
result Continuous Sweep outperforms other quantifiers in simulations and empirical data analysis.
Two sweeps of the Brennan-Schwartz algorithm solve American options under negative rates.
problem Inability of the Brennan-Schwartz algorithm to solve American options under negative interest rates.
method Two sweeps of the Brennan-Schwartz algorithm in two directions.
result Recovery of the exact solution for American options under negative rates.
We prove the absence of a universal diameter bound on lengths of curves in a sweep-out of a Riemannian 2-sphere. If such bound existed it would yield a simple proof of existence of short geodesic segments and closed geodesics on a sphere of small diameter.
Informed traders need to trade fast in order to profit from their private information before it becomes public. Fast electronic markets provide such liquidity. Slow markets provide execution in an auction based trading floor. Hybrid markets combine both execution venues. In its main result, the paper shows that to comp…
Paper estimates area covered by a line-sweep sensor in robotics.
problem Accurately estimating the area covered by a line-sweep sensor.
method Relies on coverage measure and topological degree in the plane.
result Guaranteed characterization of the explored area using interval analysis.
It is known that the almost-Kaehler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show here by example that this subset is not generally closed, and so need not sweep out entire connected components in the moduli space. Our construction …
The paper proves the existence of CMC surfaces with controlled topology in 3-manifolds.
problem Proving the existence of constant mean curvature surfaces with specific topological constraints.
method Min-max construction and convergence to a CMC-parametrized varifold.
result Existence of a non-trivial, branched immersion of a closed Riemann surface with constant mean curvature in a 3-manifold.
Paper tackles non-uniform coverage planning for robots.
problem Non-uniform coverage planning for robots that need to visit some points more frequently.
method Proposes a novel reinforcement learning approach in a Semi-Markov Decision Process.
result Significant improvement over existing greedy approach in simulations.
Study efficient power iteration for tensor models, proving convergence under specific conditions.
problem Simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models.
method Finite-iteration local theory, geometrically decaying transient, fixed-order multilinear noise event, warm-start mechanism.
result Convergence to the unique informative local fixed point under specific conditions.
Our goal is to generalize the Choe-Hoppe helicoid and Clifford cones in Euclidean space. By sweeping out L indpendent Clifford cones in R2N+2 via the multi-screw motion, we construct minimal submanifolds in RL(2N+2)+1. Also, we sweep out the L-rays Clifford cone (introduced in Sectio…
We present a new model-based reinforcement learning algorithm, Cooperative Prioritized Sweeping, for efficient learning in multi-agent Markov decision processes. The algorithm allows for sample-efficient learning on large problems by exploiting a factorization to approximate the value function. Our approach only requir…
SMC analysis reveals key transient effects in macroeconomic ABM.
problem Analysis of complex ABMs is challenging and often relies on ad hoc methods.
method Statistical model checking (SMC) implemented through MultiVeStA.
result Clear contrast across parameter families in macro-financial and structural sweeps.
Study on 3D surfaces and tangles formed by Poncelet triangles.
problem Geometric and topological properties of 3D surfaces and tangles.
method Exploration of Poncelet triangles and associated points.
result Properties of 3D surfaces and tangles formed by Poncelet triangles.
We give a stereological version of the Gauss-Bonnet formula in order to compute the Euler characteristic of a domain with boundary in a smooth orientable surface in R^3, by looking at contacts with a "sweeping" plane.
Tool manipulation is vital for facilitating robots to complete challenging task goals. It requires reasoning about the desired effect of the task and thus properly grasping and manipulating the tool to achieve the task. Task-agnostic grasping optimizes for grasp robustness while ignoring crucial task-specific constrain…
We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.
We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward a…
We improve MoE models for classification with rigorous guarantees and practical methods.
problem Limited guarantees for stable maximum-likelihood training and model selection in softmax-gated MoE models.
method Derived a batch MM algorithm with closed-form updates, proved finite-sample rates, and developed a dendrogram selector.
result Achieved near-parametric optimal rates for parameter recovery and improved accuracy over baselines.
Proves local noncollapsing estimate for mean curvature flow.
problem Ensuring noncollapsing in mean curvature flow.
method Combining local estimate with earlier work on ancient solutions.
result Ancient convex solutions that sweep out entire space are noncollapsed.
We use Khovanov-Rozansky gl(N) link homology to define invariants of oriented smooth 4-manifolds, as skein modules constructed from certain 4-categories with well-behaved duals. The technical heart of this construction is a proof of the sweep-around property, which makes these link homologies well defined in the 3-sphe…
3D spheres can't be swept by short curves, complicating geodesic length estimates.
problem Obstructing geodesic length estimates in 3D spheres.
method Constructing specific 3D spheres with controlled diameter and volume.
result Min-max methods for geodesic lengths fail for certain 3D spheres.
Paper uses SciPhyRL for optimizing large institutional portfolios.
problem Optimizing large institutional portfolios with cumulative costs and practical short horizons.
method Formulates a continuous-time optimization problem, reduces it to solving an HJB equation, and uses PINN for direct solution.
result Learned Gibbs policy yields substantial out-of-sample Sharpe ratio improvements.
This paper improves bond market making by adjusting hit-ratios for client flow quality.
problem Economic misleading of raw hit-ratios in corporate bond market making.
method Stochastic-control framework with residual-quality-adjusted hit-ratio.
result Optimal quotes decompose into various components, improving service/economics frontier.
Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides t…
We show that the sum of the Morse indices of the Willmore spheres realising the width of Willmore type sweep-outs is bounded by the number of the parameters of the min-max. As an application, we deduce that among the true Willmore spheres realising the min-max sphere eversion, at most one of them one has index 1, while…
15 Einstein 4-manifolds with positive conformal curvature are classified.
problem Classifying compact Einstein 4-manifolds with positive conformal curvature.
method Classification based on previous results and new insights into Einstein moduli spaces.
result Exactly 15 manifolds carry such metrics, each with one connected component in the moduli space.
A new principle for optimizer selection improves training speed and performance.
problem Finding the best optimizer hyperparameters for faster training.
method Formulate optimizer selection as maximizing the expected drop rate in loss, treating gradients and updates as signals and an optimizer as a causal filter.
result Greedy optimizer selection yields stable and effective momentum rules.
Comparing two probability measures supported on heterogeneous spaces is an increasingly important problem in machine learning. Such problems arise when comparing for instance two populations of biological cells, each described with its own set of features, or when looking at families of word embeddings trained across d…
In this paper, we use several techniques with conventional vocal feature extraction (MFCC, STFT), along with deep-learning approaches such as CNN, and also context-level analysis, by providing the textual data, and combining different approaches for improved emotion-level classification. We explore models that have not…
We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed, symmetry-invariant representations of cluster arrangements into conditional probabilities. Th…
We establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse function whose level set volume is bounded in terms of the volume of the manifold. As a c…
We analyse all Mini Flash Crashes (or Flash Equity Failures) in the US equity markets in the four most volatile months during 2006-2011. In contrast to previous studies, we find that Mini Flash Crashes are the result of regulation framework and market fragmentation, in particular due to the aggressive use of Intermarke…
Ancient pancake solutions found for curvature flows.
problem Finding unique ancient solutions to curvature flows.
method Constructing and analyzing O(1)imesO(n)-invariant ancient solutions. result Unique O(n)-invariant ancient solutions found. Page's Einstein metric on CP_2 # (-CP_2) is conformally related to an extremal Kaehler metric. Here we construct a family of conformally Kähler solutions of the Einstein-Maxwell equations that deforms the Page metric, while sweeping out the entire Kaehler cone of CP_2 # (-CP_2).The same method also yields analogous sol…
A general theory of partial balayage on Riemannian manifolds is developed, with emphasis on compact manifolds. Partial balayage is an operation of sweeping measures, or charge distributions, to a prescribed density, and it is closely related to (construction of) quadrature domains for subharmonic functions, growth proc…
When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided …
Flip symmetry on knot diagrams affects Khovanov homology.
problem Understanding the flip map on Khovanov homology.
method Analyzing the behavior of the flip map on unlinks and using it to determine the involution.
result The flip map is the identity map over \(\mathbb{F}_2\), confirming a conjecture.
A Monge surface is a surface obtained by sweeping a generating plane curve along a trajectory that is orthogonal to the moving plane containing the curve. Locally, they are characterized as being foliated by a family of planar geodesic lines of curvature. We call surfaces with the latter property PGF surfaces, and inve…
We prove that given a three manifold with an arbitrary metric (M3,g) of positive Ricci curvature, there exists a sweepout of M by surfaces of genus ≤3 and areas bounded by Cvol(M3,g)2/3. We use this result to construct a sweepout of M by 1-cycles of length at most Cvol(M3,g)1/3. The sweepo…
Unified framework for SGMoE resolves estimation and selection issues.
problem Non-identifiability, coupled differential relations, and tight coupling in softmax-Gated models.
method Unified statistical framework with Voronoi-type loss functions and dendrograms of mixing measures.
result Consistent selection of the number of experts without model sweeps, optimal parameter rates under overfitting.
We provide a comprehensive overview and tooling for GP modeling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensional GP models in O(n) time and memory complexity. While existing literature has focused on the connection between GP regression …
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of rational helices to obtain a simpler construction of these curves and apply this t…
We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length…
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a finite dimensional case (which actually belongs more to multivariable calculus than …
Develops a method to construct entire minimal graphs of odd dimensions.
problem Constructing entire minimal graphs of odd dimensions and arbitrary codimensions.
method Evolving-plane ansatz reducing minimal surface system to geodesic equation on Grassmannian.
result Yields a rich family of explicit entire minimal graphs of odd dimension and arbitrary codimension.
We construct a finitely presented group G with non-quadratic Dehn function f majorizable by a quadratic function on arbitrary long intervals.
Modern reinforcement learning algorithms reach super-human performance on many board and video games, but they are sample inefficient, i.e. they typically require significantly more playing experience than humans to reach an equal performance level. To improve sample efficiency, an agent may build a model of the enviro…