Talked about the Veech group of a specific surface.
problem Identifying the Veech group of a translation surface of infinite type.
method Analyzing the golden ladder surface.
result Answered a question posed by Hooper and Treviño.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “infinite ladder surface”
The paper finds pseudo-Anosov-like maps on an infinite ladder surface.
problem Exploring dynamics on infinite surfaces.
method Lifts Penner-type pseudo-Anosov maps from a closed surface to an infinite ladder surface.
result Existence and properties of pseudo-Anosov-like maps on the infinite ladder surface.
This paper finds minimal sets of generators for mapping class groups of specific surfaces.
problem Finding minimal sets of generators for mapping class groups of infinite-type surfaces.
method Analyzing specific surfaces to determine minimal sets of generators.
result Minimal sets of generators for are identified for (3 elements), (4 elements), and (2 elements).
Characterizes quasiconformally homogeneous ladder surfaces.
problem Characterize quasiconformally homogeneous Riemann surfaces.
method Breaks the problem into four cases and proves one case.
result Every quasiconformally homogeneous ladder surface is quasiconformally equivalent to a regular cover of a closed surface.
The paper studies mapping class groups of cyclic covers and their liftable counterparts.
problem Understanding the structure of liftable mapping class groups for cyclic covers.
method Analyzes the liftable mapping class groups of regular cyclic covers and derives explicit generating sets.
result The family of self-normalizing subgroups forms an infinite family in .
Study on minimal torsion topological generators for mapping class groups of infinite-type surfaces.
problem Minimal topological generating sets of mapping class groups consisting of torsion elements.
method Investigation of minimal topological generating sets for consisting entirely of torsion elements, with special attention to involutions.
result Minimal topological generating sets for consisting of torsion elements are found for various .
This work defines a new function space for multi-layer neural networks.
problem Characterizing the function space of multi-layer neural networks.
method Defining a neural Hilbert ladder (NHL) as an infinite union of reproducing kernel Hilbert spaces (RKHSs).
result Established theoretical properties of the new function space, including generalization guarantees and dynamics of random fields.
Mack's estimator improves chain ladder prediction for large exposure insurance models.
problem Uncertainty quantification in compound Poisson loss models.
method Large exposure asymptotics applied to Mack's estimator.
result Chain ladder prediction uncertainty can be quantified without model assumptions.
A method for analysing the risk of taking a too low reserve level by use of Chain Ladder method is developed. We give an answer to the question of how much safety loading in terms of the Chain Ladder standard error has to be added to the Chain Ladder reserve in order to reach a specified security level in loss reservin…
We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the number of rungs: there are similar relations for ladders of even and odd lengths, re…
Study gluing of Lorentzian length spaces and their causal ladder properties.
problem Compatibility of Lorentzian amalgamation with length space properties.
method Conditions for gluing Lorentzian length spaces and criteria for causal ladder preservation.
result Gluing of Lorentzian length spaces yields again a Lorentzian length space under certain conditions.
Study parabolicity of Riemann surfaces via Fenchel-Nielsen parameters.
problem Determine conditions for a Riemann surface to be of parabolic type.
method Use Fenchel-Nielsen parameters and non-standard half-collars to study parabolicity.
result Obtain sufficient conditions for parabolicity in terms of Fenchel-Nielsen parameters.
The paper introduces a test to distinguish spatial graphs based on their knot diagrams.
problem Distinguishing isotopic spatial graphs from diagrams.
method Using the writhe of knot diagrams from cycles in the graph.
result A necessary condition for distinguishing isotopic spatial graphs.
We used the Ladder Network [Rasmus et al. (2015)] to perform Hyperspectral Image Classification in a semi-supervised setting. The Ladder Network distinguishes itself from other semi-supervised methods by jointly optimizing a supervised and unsupervised cost. In many settings this has proven to be more successful than o…
We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in .
Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last class, pole ladder is a simplification of Schild's ladder for the parallel transp…
Semi-supervised learning (SSL) partially circumvents the high cost of labeling data by augmenting a small labeled dataset with a large and relatively cheap unlabeled dataset drawn from the same distribution. This paper offers a novel interpretation of two deep learning-based SSL approaches, ladder networks and virtual …
New ladder methods improve numerical accuracy in parallel transport on manifolds.
problem Lack of convergence analysis for ladder schemes on manifolds.
method Taylor approximations and iterative constructions of geodesic parallelograms.
result Ladder methods converge quadratically with quadratic speed.
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative prop…
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex learning tasks that benefit from iterative inference and temporal modeling. The arch…
This paper introduces a new market making approach using scaled beta distributions.
problem Inventory management challenges faced by market makers.
method Scaled beta distribution policies for flexible market making actions.
result Flexibility in volume distribution across price intervals improves market making performance.
New causal distances improve evaluation of causal discovery algorithms.
problem Evaluating causal discovery algorithms using graphical distances is limited.
method Defined causal distances based on causal distributions rather than graphical structure.
result Improved evaluation of causal discovery algorithms on synthetic and real-world datasets.
Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that…
Chain-ladder reserving is sensitive to outliers, leading to unreliable estimates.
problem Sensitivity of loss reserving techniques to outliers.
method Derivation of impact functions for reserves and mean squared errors of prediction under Mack's Model.
result Impact of outliers varies widely in a loss triangle and depends on other cells.
We combine supervised learning with unsupervised learning in deep neural networks. The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training. Our work builds on the Ladder network proposed by Valpola (…
We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a -holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an super-polynomial of knots in 3-space, as was conjectured by string theorists. …
Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted Standard and Poor's (S\&P 500) portfolio (see \cite{Bloom}, \cite{Uppal}, \cite{Jacobs…
The leaderboard in machine learning competitions is a tool to show the performance of various participants and to compare them. However, the leaderboard quickly becomes no longer accurate, due to hack or overfitting. This article gives two pieces of advice to prevent easy hack or overfitting. By following these advice,…
The use of unsupervised data in addition to supervised data in training discriminative neural networks has improved the performance of this clas- sification scheme. However, the best results were achieved with a training process that is divided in two parts: first an unsupervised pre-training step is done for initializ…
New method simplifies individual claims reserving.
problem Insufficient flexibility and robustness in existing methods.
method Building on classical chain-ladder method, introduces new perspective.
result Advances toward a new standard for micro-level reserving.
Paper proposes robust methods to detect and treat outliers in multivariate loss reserving.
problem Distortion of traditional reserving techniques by outliers in past claims data.
method Two robust bivariate chain-ladder techniques: Adjusted Outlyingness and Bagdistance.
result Improved accuracy in estimating outstanding claim liabilities through robust methods.
We describe the geometrical ladder of equations for Abelian bundles and gerbes, as well as higher generalisations, in terms of the cohomology of an operator that combines de Rham and Cech cohomology.
New method for individual claims reserving using machine learning.
problem Traditional claims reserving methods are limited in individual claim prediction.
method Restructured data utilization for CL prediction, using multi-period factors.
result Neural networks applied for individual claims reserving.
We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite mutation sequences. We show transitivity of infinite mutation sequences on tria…
Book explores infinite translation surfaces, challenging traditional geometry.
problem Understanding infinite-type translation surfaces.
method Detailed classification, construction, and analysis of symmetries.
result Complex dynamics in infinite-type translation flows.
We present the Video Ladder Network (VLN) for efficiently generating future video frames. VLN is a neural encoder-decoder model augmented at all layers by both recurrent and feedforward lateral connections. At each layer, these connections form a lateral recurrent residual block, where the feedforward connection repres…
Countable modular groups found on surfaces with infinite type.
problem Finding modular groups of infinite type surfaces.
method Proving countable modular groups for orientable infinite type surfaces.
result Every orientable infinite type surface has a countable modular group.
The paper explores Finsler-type objects and their variational problems on spacetimes.
problem Generalizing Einstein equations to the Finsler setting.
method Study of the ladder of Finsler-type objects and their variational problems.
result Application of the ladder structure to variational proposals for Finsler spacetimes.
Infinite-genus surfaces have many isospectral hyperbolic structures.
problem Finding many isospectral hyperbolic structures on infinite-genus surfaces.
method Constructing families of isospectral hyperbolic structures on infinite-type surfaces without planar ends.
result Uncountable families of isospectral and quasiconformally distinct hyperbolic structures on infinite-genus surfaces with self-similar end spaces.
Study Euler class of surface bundles with nontrivial results.
problem Euler class of infinite-type surface bundles with a section.
method Analyzing smooth orientable infinite-type surface bundles with a section.
result Nontrivial Euler class and dependence on genus and end types.
In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by their colour, or by their type. Different attributes form a hierarchy, and we could …
Study flip graphs for surfaces of infinite type, finding uncountably many connected components.
problem Understanding relationships between triangulations of infinite type surfaces via flips.
method Associate triangulations to flip graphs and study sequences of simultaneous flips.
result Flip graphs for infinite type surfaces have uncountably many connected components.
Study infinite genus surfaces and Schottky groups for uniformization.
problem Investigate infinite genus surfaces and Schottky groups for uniformization.
method Definitions and proofs for infinite genus surfaces and Schottky groups, showing uniformization by Schottky groups.
result Infinite genus surfaces and handlebodies can be topologically and quasiconformally uniformized by Schottky groups.
Overview of infinite surface mapping class groups.
problem Understanding mapping class groups of infinite surfaces.
method Survey of recent research findings.
result Recent developments in mapping class groups of infinite surfaces.
The paper solves curvature problems on infinite hyperbolic surfaces.
problem Prescribed curvature flow on hyperbolic surfaces with infinite topological type.
method Introduced a prescribed curvature flow adapted to infinite cellular decompositions.
result Established well-posedness of the flow and proved convergence under certain conditions.
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter a…
Simple infinite presentations for the mapping class group of a compact non-orientable surfacemath.GT
Simplified presentations for non-orientable surface mapping class groups.
problem Presenting the mapping class group of non-orientable surfaces.
method Provided simpler infinite presentations.
result Simplified presentations for the group.