Minimal dilatations found on nonorientable surfaces with two accumulation points.
problem Determining minimal dilatations for nonorientable surfaces.
method Representing dilatations as roots of Alexander polynomials and comparing using skein relation.
result Sequence of minimal Penner dilatations has two accumulation points on nonorientable surfaces.
In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of C2, it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisel…
New method analyzes accumulation precision in deep learning networks.
problem Lack of precision analysis for accumulation in deep learning training.
method Statistical approach to analyze partial sum accumulations and derive equations for minimum required bits.
result Reduced accumulation precision can lead to loss of information and degraded network quality.
Infinite rank surface cluster algebras extend traditional concepts to surfaces with accumulation points.
problem Extending surface cluster algebras to infinite surfaces with accumulation points.
method Consider infinite mutation sequences and hyperbolic structures to define cluster variables as lambda lengths of arcs.
result Established transitivity of infinite mutation sequences on triangulations of infinite surfaces and provided expansion formulas for cluster variables.
In this paper we consider sparse approximation problems, that is, general l0 minimization problems with the l0-"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) me…
Paper excludes the lowest energy level as an accumulation point for harmonic maps into analytic manifolds.
problem Analytic manifolds and their harmonic maps energy spectrum.
method Exclusion of the lowest energy level as an accumulation point using obstructions to the gluing of harmonic spheres and Lojasiewicz-estimates.
result Proves that the lowest energy level is not an accumulation point for generic 3-manifolds.
The aim of the present article is to offer a strictly mathematical, statistical treatment of the current account balances in EU and in the Eurozone. Based on Eurostat data, an overview of the total and annual balances is first made for different collections among the EU countries. Then, using the Mathematica technical …
Optimal control trajectories have limited irregularities.
problem Regularity of time-optimal control trajectories in control-affine systems.
method Generic conditions on drift and controlled vector field are used to prove smoothness out of a countable set of times, up to K-th order iterated singularities.
result Control trajectories are smooth out of a countable set of times, with singularities limited to K-th order iterated.
The study improves bounds on pseudo-Anosov maps and certifies minimum and accumulation points of normalized dilatations.
problem Understanding the set of normalized dilatations of fully-punctured pseudo-Anosov maps.
method Improving bounds on the number of tetrahedra in veering triangulations and using computational means.
result Certified that the minimum element of the set of normalized dilatations is μ2 and the minimum accumulation point is μ4. We show that for a C1 residual subset of diffeomorphisms far away from tangency, every non-trivial chain recurrent class that is accumulated by sources ia a homoclinic class contains periodic points with index 1 and it's the Hausdorff limit of a family of sources.
We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric series of local minima.
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
EKSS uses ensembles of KSS for subspace clustering with theoretical guarantees.
problem Subspace clustering with poor empirical performance and lack of theoretical guarantees.
method EKSS leverages ensembles of KSS via evidence accumulation clustering framework.
result EKSS achieves theoretical recovery guarantees and excellent empirical performance.
Training deep neural networks with 8-bit floating point numbers is now possible and more efficient.
problem Challenges in training DNNs with reduced precision, especially for gradient computations.
method Introduction of chunk-based accumulation and floating point stochastic rounding to reduce arithmetic precision to 16 bits.
result Successful training of DNNs using 8-bit floating point numbers, maintaining accuracy on various models and datasets.
Bias correction needed after deep learning regression training.
problem Systematic error accumulation in deep learning regression models.
method Adjust bias of the machine learning model post-training.
result Bias correction efficiently solves error accumulation.
We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize 1/L satisfies the $L…
The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.
problem Determining inextendibility of spacetimes near singularities.
method Asymptotic analysis of volume-distance-ratio (VDR) to prove inextendibility criteria.
result Failure of VDR convergence to the Minkowski value implies inextendibility of spacetime.
The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\in \C\{z,w\}$, using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac ph…
Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
Model predicts cash accumulation for assets with unknown prices.
problem Cash accumulation for assets with unpredictable future prices.
method Discretized Wiener Process matched using ordinary integrals.
result Model efficiently predicts cash accumulation for various asset scenarios.
Study pseudo-Anosov monodromies' lengths in 3-manifolds' arc complex.
problem Investigate pseudo-Anosov monodromies' asymptotic translation lengths in 3-manifolds' arc complex.
method Define normalized asymptotic translation length functions μ_d and analyze their accumulation points.
result Sets of accumulation points of μ_d graphs are nice and depend only on the slice's shape.
Study finds bifurcation and local rigidity points for solutions to the Yamabe problem on Aloff-Wallach Spaces.
problem Yamabe problem on Aloff-Wallach Spaces
method Constructing 1-parameter families of solutions and examining changes in the Morse index as the parameter varies.
result Identifies bifurcation and local rigidity points for homogeneous solutions to the Yamabe problem.
The condensed nearest neighbor (CNN) algorithm is a heuristic for reducing the number of prototypical points stored by a nearest neighbor classifier, while keeping the classification rule given by the reduced prototypical set consistent with the full set. I present an upper bound on the number of prototypical points ac…
Study of geodesic branching in 2D sub-Riemannian manifolds.
problem Branching of geodesics in sub-Riemannian manifolds of rank two.
method Analysis of geodesic behavior in sub-Riemannian geometry.
result Continuous families of strictly abnormal branching geodesics and accumulation of branching points.
Financial investment returns lead to growing wealth inequality.
problem Recent rise in wealth inequality in active financial markets.
method Minimalist modelling strategy combining financial markets, wealth accumulation, and compound interest.
result Accumulated financial investment returns cause ever-increasing wealth concentration and inequality.
Unfolding paths in Outer space accumulate on a simplex, not converge.
problem Understanding accumulation points in Outer space.
method Constructing an unfolding path in Outer space.
result Unfolding paths accumulate on a 1-simplex, not converge.
New data accumulation prevents model collapse in generative models.
problem Model collapse in generative models trained on their own outputs.
method Empirical study of language models, diffusion models, and variational autoencoders; analytically tractable framework for linear models.
result Accumulating synthetic data alongside real data avoids model collapse, preventing performance degradation.
Latent Block-Diffusion Temporal Point Processes (LBDTPP) is a semi-autoregressive framework for generating asynchronous event sequences.
problem Generating asynchronous event sequences
method Latent Block-Diffusion Temporal Point Processes
result Outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks
Study of historic stock returns distributions, highlighting asymmetry and outliers.
problem Understanding the asymmetry in accumulated gains and losses in stock returns over time.
method Analyzing decades-long historic distributions of S&P500 returns, comparing gains and losses, using statistical U-tests and fitting log-log scale linearly.
result The mean of de-trended distributions increases linearly with the number of days of accumulation, and the overall skew is negative, indicating heavier tails of losses.
We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigi…
The notion of limit roots of a Coxeter group W was recently introduced (see arXiv:1112.5415 and arXiv:1303.6710): they are the accumulation points of directions of roots of a root system for W. In the case where the root system lives in a Lorentzian space W admits a faithful representation as a discrete reflection grou…
Income redistribution boosts cooperation in spatial public goods games, but the effect depends on the model of redistribution.
problem The impact of income redistribution on cooperation in spatial public goods games.
method Two models of income redistribution were used: local and global. Spatial public goods games were employed to study the evolution of cooperation.
result The cooperation level is significantly higher with local redistribution of income, but lower with global redistribution.
Model of capital accumulation in a complex exchange space.
problem Capital accumulation dynamics in heterogeneous producer-consumer systems.
method Statistical field theory approach to analyze interactions and dynamics.
result Capital accumulation and agent position in the exchange space are correlated.
Accumulator module improves reinforcement learning by delaying decisions based on evidence.
problem Incomplete information, limited sensing, and stochastic environments lead to risky decisions.
method Integrates evidence for each action, delays action until confident, using dynamic competition.
result Accumulator module outperforms traditional reinforcement learning methods in a guessing game.
Proves boundedness of log Fano cone singularities with bounded local volumes.
problem Understanding the boundedness of log Fano cone singularities.
method Analyzes K-semistable log Fano cone singularities with bounded volumes.
result The set of local volumes of klt singularities has zero as the only accumulation point.
We define a generalization of Coxeter graphs and an associated Coxeter system and Coxeter mapping class. These can be used to construct periodic Coxeter mapping classes on surfaces with arbitrarily large genus, preserving lots of symmetries. The periodic mapping classes can in turn be used to construct sequences of pse…
A new method for MARL with partial observations reduces communication overhead.
problem Inefficient MARL algorithms in large-scale problems due to state and action information sharing.
method Distributed zeroth-order policy optimization with local policy gradient estimation using consensus.
result The method converges to a policy that is a stationary point of the global objective function.
The paper studies umbilics on surfaces in Lorentz-Minkowski space.
problem Properties of umbilics on space-like or time-like surfaces in L3. method Analyzes curvature line flows and proves properties of umbilics.
result Existence of germs with isolated umbilics of various indices.
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming pro…
Maps minimize periodic points for high periods, but not for low periods.
problem Understanding periodic points of maps on infinite type surfaces.
method Analysis of isotopic maps, spun pseudo-Anosov maps, and Handel-Miller maps.
result Spun pseudo-Anosov maps minimize periodic points for sufficiently high periods.
A new theory quantifies how societies accumulate and diversify their knowledge.
problem Lack of a unified quantitative formalism for understanding societal knowledge accumulation.
method Combines analytical, numerical, and empirical approaches to quantify and predict societal diversification.
result Measurable quantities to predict future societal developments.
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
Improved statistical computation through efficient matrix sampling.
problem Reducing computational cost in large-scale statistical methods.
method Accumulative sub-sampling method to improve statistical efficiency.
result Effective matrix size control improves computational efficiency.
Our study shows that many firms would accumulate at zero output level (namely, Bankruptcy status) if a perfectly competitive market reaches full employment (namely, those people who should obtain employment have obtained employment). As a result, appearance of economic crisis is determined by two points; that is, (a). …
Methods estimate physical load and fatigue from wearable data.
problem Estimating physical load and fatigue from wearable data.
method Statistical and machine learning methods based on kurtosis-skewness diagram.
result Different levels of physical activities and fitness can be distinguished from the kurtosis-skewness diagram.
DANCE method improves large-scale learning efficiency via accumulating sample strategy.
problem Efficiently solving large-scale empirical risk minimization problems.
method Distributed Accumulated Newton Conjugate gradient (DANCE) method with multistage approach.
result The method achieves satisfactory statistical accuracy with fewer passes over data.
Study shows limits of volume-constrained sets are finite unions of Wulff shapes.
problem Analyzing the behavior of sets with degenerating ellipticity.
method Proving rigidity of L1-accumulation points of volume-constrained almost-critical sets. result Limits of volume-constrained sets are finite unions of φ-Wulff shapes. ADD-THIN improves TPP forecasting by handling long-term data sequences.
problem Sequential limitations in autoregressive models for TPPs.
method Diffusion model for TPPs that operates on entire sequences.
result ADD-THIN outperforms state-of-the-art models in forecasting.