Paper shows how online betting algorithms' regret can be used to create tight confidence sequences.
problem Estimating the expectation of random variables from samples and creating time-uniform confidence sequences.
method Converts the regret guarantee of universal portfolio algorithms into time-uniform concentration inequalities and confidence sequences.
result Numerically obtained confidence sequences are never vacuous and satisfy the law of iterated logarithm.
New optimal trading strategies found for risk-averse and cumulative prospect theory traders in illiquid markets.
problem Optimal trading strategies for risk-averse and cumulative prospect theory traders in illiquid markets.
method An extension of Skorohod's representation theorem for tight sequences of probability measures.
result Existence of optimal strategies for agents with cumulative prospect theory preferences in continuous-time illiquid markets.
New proof of Giroux Correspondence for tight contact 3-manifolds.
problem Proving the Giroux Correspondence for tight contact 3-manifolds.
method Introducing tight Heegaard splittings, using refinement process, and translating moves between splittings to moves between open books.
result Proves the tight Giroux Correspondence for contact 3-manifolds.
Extends model geometries for surface bundles over graphs using tight trees.
problem Constructing model geometries for surface bundles over graphs.
method Generalizing tight geodesics to tight trees and using them to construct model geometries.
result Uniformly Gromov-hyperbolic geometric model spaces equipped with geometric G−actions. New method for learning evolving tasks with performance guarantees.
problem Learning tasks in a sequence with evolving similarity.
method Adaptable learning methodology with performance guarantees.
result Improved performance in multiple scenarios with reliable guarantees.
Develops confidence bounds for off-policy evaluation in contextual bandits.
problem Evaluating policies that were not used to collect data.
method Martingale analysis for non-asymptotic, non-parametric, and valid confidence sequences.
result Empirically tight bounds on failure probability and width.
The paper extends confidence sequences for infinite variance data.
problem Addressing confidence sequences for distributions with infinite variance.
method Establishing lower bounds and deriving tight confidence sequences for relaxed bounded pth-moment distributions. result Derived confidence sequences are tighter than those using Dubins-Savage inequality.
This research extends topological recursion to hyperbolic surfaces with tight boundaries and conical defects.
problem Calculating volumes of hyperbolic surfaces with special boundaries.
method Generalized topological recursion to handle tight boundaries and conical defects.
result Weil-Petersson volumes are polynomial in boundary lengths for hyperbolic surfaces with tight boundaries and conical defects.
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probabil…
Paper debunks value aggregation's convergence and provides stability conditions.
problem Value aggregation's convergence in imitation learning problems.
method Iterative policy optimization and evaluation in an online learning setting.
result Identified a critical stability condition for convergence and provided a performance bound.
Ozsvath and Szabo show that there is a spectral sequence whose E^2 term is the reduced Khovanov homology of L, and which converges to the Heegaard Floer homology of the (orientation reversed) branched double cover of S^3 along L. We prove that the E^k term of this spectral sequence is an invariant of the link L for all…
Single-timescale analysis improves convergence in multi-sequence stochastic approximation.
problem Finite-time convergence of nonlinear stochastic approximation with multiple coupled sequences.
method Smoothness property of fixed points and analysis of fine-grained single-timescale SA.
result Improved iteration complexity for achieving ε-accuracy in multi-sequence single-timescale SA.
AbDiffuser generates full-atom antibodies with sequence and structure fidelity.
problem Generating high-fidelity antibodies with both structure and sequence information.
method Equivariant and physics-informed diffusion model with novel protein structure representation.
result AbDiffuser generates antibodies with sequence and structural properties matching a reference set.
The paper provides bounds for LSA with fixed stepsizes under random estimates.
problem Analyzing the performance of LSA algorithms with fixed stepsize.
method Non-asymptotic analysis based on new results about matrix moments and high probability bounds.
result Derives high probability bounds on LSA performance under weaker conditions than previous works.
Study flute surfaces and Loch Ness monster, proving their parabolicity and uniformization.
problem Characterizing parabolicity and uniformization of flute surfaces and the Loch Ness monster.
method Associate sequences to Fuchsian groups and analyze their properties.
result Zero-twist flute surfaces are parabolic if and only if the series diverges.
Transformers tend to learn more symmetric functions in sequence data.
problem Understanding inductive bias in Transformers with infinitely over-parameterized models.
method Analyzing Transformers in the Gaussian process limit, using representation theory of the symmetric group.
result Transformers are biased towards more permutation symmetric functions, and this can be quantitatively predicted.
Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known tight triangulated manifolds are stacked. It is known that locally stacked tight t…
New geodesics found that are not tight but still have useful properties.
problem Understanding geodesics in curve complexes and Teichmüller spaces.
method Introducing and studying weak tight geodesics with canonical constructions.
result Found examples of weak tight geodesics with gaps between them.
We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups of Hermitian type give rise to tight totally geodesic maps of Hermitian symmetr…
Study tight contact structures on figure-eight knot surgeries.
problem Classify tight contact structures on surgeries of figure-eight knot.
method Analyzes surgeries on figure-eight knot, determining tightness, symplectic fillability, and universality.
result First classification of tight contact structures on surgeries of figure-eight knot.
The study identifies conditions for algorithms to have tight generalization bounds.
problem Understanding which algorithms have tight generalization bounds.
method Analyzing conditions that preclude tight generalization bounds and identifying stable algorithms.
result Stable algorithms have tight generalization bounds, while unstable ones do not.
Surgery on knots always admits a tight contact structure.
problem Understanding tight contact structures on knots after surgery.
method Smooth (-r)-surgery on knots, using Heegaard Floer contact invariant.
result Tight contact structures detected for all knots after surgery.
Tight maps was introduced along tight homomorphisms by Burger, Iozzi and Wienhard with aims towards maximal representations. In this paper we classify tight maps into classical Hermitian symmetric spaces and give a partial result for the exceptional spaces.
Paper analyzes convergence of OMD algorithms with geometric conditions.
problem Analyzing convergence of online mirror descent algorithms.
method Presented necessary and sufficient conditions for convergence of OMD with step size sequences.
result Established conditions for convergence and linear convergence under specific variances.
3-manifold triangulations are Golod and tight, proven through a topological characterization.
problem Understanding Golodness and tightness in 3-manifold triangulations.
method Topological characterization of a polyhedral product for a tight-neighborly manifold triangulation.
result Golodness and tightness are equivalent for 3-manifold triangulations.
Simply connected spaces of tight frames identified.
problem Understanding the connectivity of spaces of tight frames.
method Viewing tight frames as elements of Stiefel manifolds and identifying simply connected spaces.
result Spaces of tight frames, including finite unit-norm tight frames, are simply connected.
The study finds many tight contact structures on hyperbolic 3-spheres.
problem Finding tight contact structures on hyperbolic 3-spheres.
method Constructing hyperbolic homology 3-spheres and analyzing their tight contact structures.
result Produces hyperbolic homology 3-spheres with multiple distinct tight contact structures.
Study tight contact structures on specific 3-manifolds.
problem Counting and constructing tight contact structures on plumbed 3-manifolds.
method Algorithm to construct stein diagrams for tight structures without Giroux torsion.
result Explicit algorithm to construct tight contact structures.
Classifies tight contact structures on surgeries of the Whitehead link.
problem Classifying tight contact structures on surgeries of the Whitehead link.
method Analyzes various surgeries on the Whitehead link to classify tight contact structures.
result Determines tight contact structures, Stein fillability, and virtually overtwisted properties.
5D contact structures are universally tight via Bourgeois construction.
problem Understanding tightness of 5D contact structures.
method Explicit construction of contact structures on VimesT2. result All constructed contact structures are universally tight.
Study non-stationary distributions, proving risk bounds for density estimation.
problem Estimating current distribution under gradual changes.
method Proves tight minimax risk bounds for nonparametric density estimation under drift.
result Generalizes previous results on agnostic learning under drift.
Study finds tight contact structures on many hyperbolic 3-manifolds.
problem Existence of tight contact structures on hyperbolic 3-manifolds.
method Dehn surgeries on hyperbolic surface bundles.
result Existence of infinitely many hyperbolic 3-manifolds with tight contact structures.
In \cite{confol} Y. Eliashberg and W. Thurston gave a definition of tight confoliations. We give an example of a tight confoliation ξ on T3 violating the Thurston-Bennequin inequalities. This answers a question from \cite{confol} negatively. Although the tightness of a confoliation does not imply the Thurston-Benn…
In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. We also prove that any lens space admits only finitely many tight contact structures.
Classifies real tight contact structures on lens spaces and solid tori.
problem Classifying real tight contact structures on specific 3-manifolds.
method Equivariant contact isotopy, real open book decompositions, and isolated real algebraic surface singularities.
result Unique real tight structures on S3 and RP3, at most one on L(p,±1), and bounds on the count. The study finds algebraically overtwisted tight 3-manifolds via contact surgeries.
problem Finding algebraically overtwisted tight 3-manifolds.
method Executing Avdek's algorithm to perform contact surgeries.
result Contact surgeries on standard contact 3-sphere yield algebraically overtwisted and tight 3-manifolds.
Tight contact foliations can be made less restrictive.
problem Homotopy invariance of tightness in contact foliations.
method Turbulisation procedure to make tight foliations less restrictive.
result Tightness is not a homotopy invariant property.
Study shows optimal online learning with almost perfect expert advice.
problem Multiclass online learning with advice from up to b experts, focusing on the case where b is small.
method Analyzed the regime where the best expert makes at most b mistakes, showing the optimal forecaster's mistake bound.
result The optimal forecaster's expected number of mistakes is at most log_4(n) + o(log_4(n)) when b = o(log_4(n)).
We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group G acting on a G--space X, we prove that if G contains a strongly contracting eleme…
We determine all tight Lagrangian surfaces in S2×S2. In particular, globally tight Lagrangian surfaces in S2×S2 are nothing but real forms.
Study non-fibered links' relation to tight contact structures.
problem Understanding non-fibered links and their tight contact structures.
method Analyze non-fibered links with induced partial open books and contact structures.
result Strongly quasipositive non-fibered links induce tight contact structures, but the converse is not always true.
New 3D shapes found without certain special flows.
problem Finding 3D shapes without specific special flows.
method Rational surgeries on the figure eight knot.
result First infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows.
The paper proves that the support norm of tight contact structures adds up.
problem Understanding the support norm of contact structures.
method Analyzing open books supporting contact structures.
result Additivity of the support norm for tight contact structures.
We prove gluing theorems for tight contact structures. In particular, we rederive (as special cases) gluing theorems due to Colin and Makar-Limanov, and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a genus 4 h…
We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.
Classifies tight contact structures on specific Seifert fibered manifolds.
problem Classifying tight contact structures on Seifert fibered manifolds.
method Constructed contact structures using Legendrian surgery and used convex surface theory for the upper bound.
result Found the lower and upper bounds for tight contact structures.