New concept of strongly keen Heegaard splittings found.
problem Finding Heegaard splittings with specific properties.
method Introducing and proving existence of strongly keen Heegaard splittings.
result Existence of Heegaard splittings with specified genus and Hempel distance.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
problem Extending keenness concept to bridge splittings and finding conditions for existence.
method Extending the concept of keenness to bridge splittings and proving existence conditions.
result Existence of strongly keen (g,b)-splitting of a link with distance n for certain integers g, b, and n. This paper constructs keen weakly reducible Heegaard splittings of arbitrary genus.
problem Creating Heegaard splittings with specific properties.
method Construction of keen weakly reducible splittings.
result Arbitrary genus Heegaard splittings can be constructed.
The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.
problem Characterizing and finding examples of keen weakly reducible bridge spheres.
method Analyzing bridge spheres and their properties in terms of compressing disks and width complex.
result Infinitely many examples of keen weakly reducible bridge spheres for links in b-bridge position.
KEEN Universe provides reproducible and transferable knowledge graph embeddings.
problem Lack of reproducibility and transferability in KGE experiments.
method Developed an ecosystem with Python packages for reproducible and transferable KGEs.
result KEEN Universe facilitates sharing of trained KGE models across different fields.
This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Mo…
Model analyzes inventory growth cycles with debt-financed investment.
problem Understanding inventory growth cycles in economies with debt financing.
method Continuous-time stock-flow consistent model for inventory dynamics.
result Model reveals Kitchin cycles in short-run dynamics.
We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely…
Study of complex moduli spaces for Kleinian groups.
problem Understanding moduli spaces of Kleinian groups.
method Review and extension of existing work on the Riley slice.
result Extension of Riley slice results to new Kleinian groups.
We study a monetary version of the Keen model by merging two alternative extensions, namely the addition of a dynamic price level and the introduction of speculation. We recall and study old and new equilibria, together with their local stability analysis. This includes a state of recession associated with a deflationa…
There are certain families of words and word sequences (words in the generators of a two-generator group) that arise frequently in the Teichm{ü}ller theory of hyperbolic three-manifolds and Kleinian and Fuchsian groups and in the discreteness problem for two generator matrix groups. We survey some of the families of su…
An irreducible representation of the free group on two generators X,Y into SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study the diagonal slice of representations for which X,Y and XY have equal trace. Using the three-fold symmetry and Keen-Series pleating rays we locate those groups which a…
Identifies half-space neighborhoods of pleating rays in the Riley slice of Schottky groups.
problem Determining points in the Riley slice of Schottky groups.
method Adapting ideas from L. Keen and C. Series, identifying half-space neighborhoods of pleating rays.
result Provides a provable method to determine if a point is in the Riley slice.
We consider the following question: Which parameters in the extension of a rational pleating ray across the boundary of $\Cal M$, the Maskit embedding of the Teichmüller space of once punctured tori correspond to a Kleinian group? Using methods of Keen and Series and Wright we prove a local result, stating that on each…
Baccalaureate institutions seek to integrate statistics into data science.
problem Graduate statisticians losing ground in data science.
method Reviewing historical contributions of statisticians and calling for integration.
result Baccalaureate institutions need to integrate statistics into data science education.
Investigates the impact of narrow banking on macroeconomics.
problem The risks and benefits of a full reserve requirement on demand deposits.
method Extended Goodwin-Keen model with time deposits and central bank reserves; numerical examples.
result Narrow banking does not reduce economic growth but improves financial stability.
A new neural network improves the accuracy of predicting constants of motion.
problem Discovering constants of motion in dynamical systems.
method A novel neural network architecture using SVD and a two-phase training algorithm.
result The new approach retains advantages of COMET and improves performance.
Exact learning of tree-structured models with side info and noise.
problem Learning tree-structured graphical models with side information and noise.
method Probabilistic tools from strong large deviations theory.
result Exact asymptotics of structure learning from samples.
In [4]: `The Riley slice of Schottky space', (Proc. London Math. Soc. 69 (1994), 72-90), Keen and Series analysed the theory of pleating coordinates in the context of the Riley slice of Schottky space R, the deformation space of a genus two handlebody generated by two parabolics. This theory aims to give a complete des…
Measuring systemic risk or fragility of financial systems is a ubiquitous task of fundamental importance in analyzing market efficiency, portfolio allocation, and containment of financial contagions. Recent attempts have shown that representing such systems as a weighted graph characterizing the complex web of interact…
BERT improves Chinese word segmentation performance.
problem Chinese word segmentation task.
method Applying BERT to CWS task using benchmark datasets.
result BERT can improve performance even with inconsistent labels.
Novel methods combining autoregressive models and variable transformations improve density estimation.
problem Improving density estimation methods for complex data.
method Combining autoregressive models and variable transformations.
result Jointly leveraging transformations and autoregressive models improves performance.
Defines strongly Gauduchon spaces and their properties.
problem Generalization of strongly Gauduchon manifolds in complex spaces.
method Definition and properties of strongly Gauduchon spaces and class SG.
result Similarities and properties of strongly Gauduchon spaces to Kahlerian spaces.
Brief introduction to deep learning for math students.
problem Understanding deep neural networks and training methods.
method Explains deep neural networks, training methods, and uses MATLAB and software.
result Illustrates the application of deep learning in image classification.
Links can be transformed into many others using a specific operation.
problem Understanding the relationship between strongly quasipositive links and their concordance.
method Used a satellite operation with a slice knot to transform links.
result Strongly quasipositive links can be transformed into infinitely many other links.
Links can be transformed into strongly quasipositive links.
problem Understanding the relationship between different types of links.
method Generalized Rudolph's algorithm to show topological concordance.
result Every link is topologically concordant to a strongly quasipositive link.
Study of strongly invertible Legendrian links in contact 3-space.
problem Characterizing and understanding strongly invertible Legendrian links.
method Equivariant analogs of basic results for strongly invertible and Legendrian links.
result Existence of maximal equivariant Thurston-Bennequin number for strongly invertible links.
New spacetimes found that are refocusing but not strongly refocusing.
problem Characterizing spacetimes that are refocusing but not strongly refocusing.
method Analyzing globally hyperbolic spacetimes and introducing new refocusing concepts.
result Existence of spacetimes that are refocusing but not strongly refocusing.
Paper introduces new method for statistical inference with stochastic gradients.
problem Uncertainty quantification for solutions from iterative optimization methods.
method Moment-adjusted stochastic gradient descent.
result Established non-asymptotic theory for statistical inference.
In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones SG in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence…
We investigate refocusing and strong refocusing of light rays in a space-time. A strongly refocusing space-time is refocusing. The converse is unknown. We construct examples of space-times which are refocusing, but not strongly so, at a particular point. These space-times are strongly refocusing at other points. The ge…
Characterizes strongly quasipositive quasi-alternating and Montesinos links.
problem Characterizing strongly quasipositive links and detecting new classes of Montesinos links.
method Analyzing quasi-alternating links and their crossings, and using properties of Seifert surfaces.
result Strongly quasipositive links have specific properties related to their crossings and Seifert surfaces.
Model explains stock price bubbles through debt crises and financial crashes.
problem Analyzing financial fragility and stock price bubbles.
method Stock-flow consistent model integrating macroeconomic and financial market dynamics.
result Model demonstrates how credit expansion and crash risk lead to recurrent boom-bust cycles.
Strongly convex bodies can be approximated by smooth ones.
problem Approximating strongly convex bodies with smooth ones.
method Using C2 locally strongly convex bodies. result Smooth approximations of strongly convex bodies exist and can be controlled in terms of Hausdorff distance.
Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.
problem Understanding gaps in genus between strongly invertible knots and their invariant Seifert surfaces.
method Analysis of invariant Seifert surfaces and proof of genus gaps, with variants of Edmonds' theorem.
result Gap between equivariant genus and usual genus can be arbitrarily large for strongly invertible knots.
Table of symmetric diagrams for knots up to 10 crossings.
problem Finding symmetric diagrams for strongly invertible knots.
method Compilation of symmetric diagrams for knots up to 10 crossings.
result Similarity of transversal diagrams to symmetric union diagrams for strongly invertible knots.
New algorithm proves most inflexible manifolds are not strongly inflexible.
problem Existence of simply-connected strongly inflexible manifolds.
method Algorithm based on Sullivan models.
result One example of simply-connected inflexible manifold is not strongly inflexible.
New examples of Howson groups that are not strongly Howson found.
problem Understanding the difference between Howson and strongly Howson groups.
method Constructing specific examples of groups to demonstrate the distinction.
result First examples of Howson groups that are not strongly Howson.
The paper simplifies strongly convex problems to simplicial structures.
problem Strongly convex problems with Cr smoothness. method Generic linear perturbations and singularity theory.
result Strongly convex C1 problems are C0 simplicial. Develops equivariant grid homology for strongly invertible knots.
problem Invariants of strongly invertible knots.
method Equivariant grid diagrams and mapping cones.
result Equivariant unknotting numbers and genus bounds.
New findings on knot genera using advanced techniques.
problem Understanding the 4-genus of knots, especially strongly invertible and periodic ones.
method Innovative concordance group invariants, Donaldson's theorem, and g-signature.
result Many new examples showing the equivariant 4-genus is larger than the 4-genus.
The paper characterizes complex Finsler metrics that are projectively flat or dually flat.
problem Characterizing complex Finsler metrics with specific geometric properties.
method Proving conditions for projective flatness and dually flatness in terms of Minkowski metrics.
result Strongly convex complex Finsler metrics are projectively flat or dually flat if and only if they come from Minkowski metrics.
The paper proves a Schwarz lemma for weakly Kähler-Finsler manifolds.
problem Estimating distance functions and proving Schwarz lemma for weakly Kähler-Finsler manifolds.
method Establishing theorems about distance functions and applying them to prove the Schwarz lemma.
result Holomorphic mappings from weakly Kähler-Finsler manifolds to pseudoconvex Finsler manifolds are constant under certain conditions.
Specialized knot theory theorems for strongly involutive links.
problem Classical Alexander and Markov theorems for links.
method Equivariant closure map for strongly involutive links.
result Surjective equivariant closure map up to equivalence of strongly involutive links.
A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle structures with strongly irreducible monodromy.
Study proves obstructions to equivariantly slice strongly negative amphichiral knots.
problem Proving obstructions for equivariantly slice strongly negative amphichiral knots.
method Using determinant, Spinc-structures, Donaldson's theorem, and Heegaard Floer correction terms.
result 8 out of 16 strongly negative amphichiral knots with 12 or fewer crossings are not equivariantly slice.
New method solves non-strongly convex optimization problems without quadratic regularization.
problem Minimizing the sum of an average of smooth convex components and a non-differentiable convex function.
method Accelerated randomized mirror descent algorithm without strongly convex assumption.
result Performance of algorithms improved without quadratic regularization.
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.