The Ham Sandwich Theorem helps find bounds on Laplacian eigenvalues.
problem Finding bounds on Laplacian eigenvalues for convex domains.
method Applied Gromov's ham sandwich method to get monotonicity and inequalities.
result Universal inequalities for Neumann eigenvalues of Laplacian on convex domains.
A theorem divides hyperplanes evenly with a line through the origin.
problem Dividing hyperplanes evenly with a line.
method Direct proof using measures on hyperplanes.
result A line through the origin divides hyperplanes evenly.
The paper proves a geodesic sandwich theorem and applies it to manifold inequalities.
problem Proving inequalities in Riemannian manifolds with bounded curvature.
method Geodesic convex functions and sectional curvature bounds.
result Gradient of convex functions is orthogonal to geodesics.
The study connects projective codes to the distribution of zeros of odd maps.
problem Understanding the distribution of zeros of odd maps from spheres to Euclidean space.
method Using the topology of the space of probability measures on the sphere.
result Generalization of the Borsuk-Ulam theorem and its four consequences.
Polyak-Ruppert CLT for SA-Adam with momentum and non-convergent adaptive preconditioning
problem Adaptive optimizers combining momentum and non-convergent preconditioning
method Proving positive drift stability and a non-autonomous Polyak-Ruppert CLT for SA-Adam
result The iterate-marginal covariance is exactly the plain stochastic gradient descent (SGD) sandwich
Note proves bi-Lipschitz embeddings for Ham(S^2) metrics.
problem Entropy norms on Ham(S^2) bi-Lipschitz embeddings.
method Proves bi-Lipschitz embeddings for Ham(S^2) with entropy metrics.
result Existence of bi-Lipschitz embeddings for Ham(S^2) metrics.
New financial model with sandwiched volatility for option pricing.
problem Developing a new financial model for option pricing.
method Introducing a new model with stochastic volatility driven by a Gaussian Volterra process, ensuring the solution is sandwiched between two arbitrary Hölder continuous functions.
result Developed an algorithm for pricing options with discontinuous payoffs using Malliavin calculus.
Study symplectic fillings of sandwiched singularities.
problem Contrast deformation theory and symplectic topology of Milnor fibers.
method Develop an analog of de Jong--van Straten's theory in the symplectic setting using spinal open books and nearly Lefschetz fibrations.
result Minimal symplectic fillings of links are generated by certain immersed disk arrangements.
Researchers develop a method to infer reference measures from observed functionals.
problem Tackles the challenge of identifying or recovering a reference measure from observed functionals.
method Uses the property of law-invariant functionals defining lower or upper supporting sets in dual spaces of signed measures.
result Illustrates the methodology with examples and develops a modification for Value-at-Risk.
The paper proves a gravity conjecture in higher dimensions.
problem The validity of Wheeler's thin sandwich conjecture in arbitrary dimensions.
method Extending results from 3D to nD, the paper shows geometric conditions for the conjecture's validity.
result The thin sandwich problem is well-posed on any compact n-dimensional manifold, n ≥ 3.
Revisits fuzzy neural networks with generalized Hamming distance, simplifying BN and ReLU.
problem Improving neural network techniques using fuzzy logic and generalized Hamming distance.
method Introducing generalized Hamming distance to reinterpret BN and ReLU, proposing GHN.
result Batch normalization and ReLU can be simplified or removed without loss of performance.
Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.
problem Finding invariant measures for contact Hamiltonian systems.
method Splitting the system into Reeb and Liouville dynamics; using invariant measures and symplectic sandwiches.
result Invariant measure found for Reeb dynamics; characterization of Liouville dynamics invariant measure.
We prove that π1(Ham(M)) contains an infinite cyclic subgroup, where Ham(M) is the Hamiltonian group of the one point blow up of CP3. We give a sufficient condition for the group π1(Ham(M)) to contain an infinite cyclic subgroup, when M is a general toric manifold.
We verify here some variants of topological and dynamical flavor of the injectivity radius conjecture in Hofer geometry, Lalonde-Savelyev \cite{citeLalondeSavelyevOntheinjectivityradiusinHofergeometry} in the case of Ham(S2) and Ham(Σ,ω), for Σ a closed positive genus surface. In particular we show that any lo…
This paper compares FAISS and FENSHSES for nearest neighbor search in Hamming space.
problem Comparing nearest neighbor search systems in Hamming space.
method Comprehensive evaluations of indexing speed, search latency, and RAM consumption.
result Better understanding of trade-offs between main memory and secondary memory systems.
This paper develops a method to estimate the rate-distortion function for general data sources.
problem Estimating the rate-distortion function for general data sources.
method Develops an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source using i.i.d. data samples.
result Estimates R-D sandwich bounds for various data sources, including natural images, indicating potential for improving compression methods.
A new model optimizes Bloom filters using machine learning.
problem Improving the efficiency of Bloom filters for data sets.
method Modeling learned Bloom filters with machine learning, optimizing with sandwiching method.
result Optimized learned Bloom filters provide improved performance.
Develops homotopies for Lagrangian field theory using advanced algebraic structures.
problem Formulating a consistent framework for Lagrangian field theory.
method Introduces L∞ algebras and homotopies to enrich the Batalin-Vilkovisky framework. result Provides an explicit lift of the Batalin-Vilkovisky framework to local forms.
The paper constructs quasimorphisms on surface diffeomorphism groups with entropy bounds.
problem Entropy bounds on surface diffeomorphism groups.
method Constructing homogeneous quasimorphisms and defining entropy metrics.
result There are infinitely many linearly independent quasimorphisms with entropy bounds.
In an L∞-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures…
Lower bound found for fragmentation norm, embedding provided.
problem Fragmentation norms on Hamiltonian diffeomorphisms of surfaces.
method Lower bound calculation and bi-Lipschitz embedding construction.
result Lower bound for fragmentation norm and embedding provided.
NESTA accelerates neural networks by compressing Hamming weights.
problem Efficiently computing convolution layers in deep neural networks.
method NESTA reformats convolutions into 3imes3 batches and uses Hamming Weight Compressors to process each batch, approximating partial sums and adding residuals. result Significantly speeds up convolution computations with reduced energy consumption.
Paper analyzes RTSE on AE manifolds and closed manifolds, showing well-posedness and parametrization of solutions.
problem Analyzing well-posedness of RTSE on AE manifolds and closed manifolds.
method Analyzes RTSE on AE manifolds and closed manifolds, considering specific conditions for well-posedness.
result On AE manifolds, RTSE solutions parametrize an open subset in the space of ECE solutions.
New STH distance finds patterns in event timeseries without resampling.
problem Lack of efficient analysis methods for event and state timeseries.
method Define STE-ts, propose STH, leveraging both time and state duration.
result Improved precision and computation time compared to resampled metrics.
Maximal extractable value in CFMMs can degrade or improve routing quality, with reordering MEV showing logarithmic impact.
problem Maximal extractable value in constant function market makers (CFMMs) and its impact on routing quality.
method Game theoretic analysis of MEV in CFMMs, constructing price of anarchy and analyzing reordering MEV.
result Conditions under which reordering MEV shows logarithmic impact, and implications for MEV searchers and CFMM designers.
Classifies homeomorphism groups of countable Stone spaces up to coarse equivalence.
problem Classifying non-locally compact topological groups using geometric group theory.
method Classification based on coarsely bounded sets and quasi-isometry.
result Groups in the second class are quasi-isometric to the Hamming cube.
Paper proves SVV model reproduces power-law skew in implied volatilities.
problem Reproducing power-law behavior in implied volatility skew.
method Analytical proof using Malliavin calculus and Volterra kernel selection.
result SVV model reproduces power-law skew under correct kernel choice.
We relate previously defined quantum characteristic classes to Morse theoretic aspects of the Hofer length functional on $\ls$. As an application we prove a theorem which can be interpreted as stating that this functional behaves "virtually" as a perfect Morse-Bott functional with a flow. This can be applied to study t…
Let Σ_g be a closed orientable surface let Diff_0(Σ_g; area) be the identity component of the group of area-preserving diffeomorphisms of Σ_g. In this work we present an extension of Gambaudo-Ghys construction to the case of a closed hyperbolic surface Σ_g, i.e. we show that every non-trivial homogeneous quasi-morphism…
In this work we construct Calabi quasi-morphisms on the universal cover of the group Ham(M) of Hamiltonian diffeomorphisms for some non-monotone symplectic manifolds. This complements a result by Entov and Polterovich which applies in the monotone case. Moreover, in contrast to their work, we show that these quasi-morp…
Simple framework explains adversarial examples with small changes.
problem Understanding the ease of switching between decisions in targeted attacks.
method Developed a mathematical framework based on the geometry of L0 (Hamming) metric. result Quantitatively analyzed the number of input coordinates to change for misdirection.
In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an (n−m)×n (m>0) CS matrix A and a positive k, we are interested in computing αk={z:Az=0,z=0}max{K:∣K∣≤k}max ∥zK∥1∥z∥1, where …
The paper develops methods to optimize ranking metrics for hashing.
problem Improving hashing for better retrieval performance.
method Developed tie-aware learning to rank formulations for hashing.
result Established new state-of-the-art for image retrieval by Hamming ranking.
HOMER improves robustness and efficiency in estimating means of heavy-tailed data.
problem Lack of robustness and efficiency in estimating means of heavy-tailed data.
method HOMER aggregates block means through a radial Huber center, interpolating between robustness and mean efficiency.
result HOMER maintains robustness while approaching mean efficiency, especially under finite third moments.
Let Σg be a closed hyperbolic surface of genus g and let Ham(Σg) be the group of Hamiltonian diffeomorphisms of Σg. The most natural word metric on this group is the autonomous metric. It has many interesting properties, most important of which is the bi-invariance of this metric. In this work we show that $…
Study reveals risks of investing in new crypto-tokens in decentralized exchanges.
problem Risks associated with investing in newly created tokens in decentralized exchanges.
method Analysis of financial impact, market dynamics, profitability, and liquidity manipulations.
result Significant market liquidity trapped in honeypots, reducing market efficiency and misleading investors.
ExDAG solves DAG learning problems with low structural Hamming distance.
problem Learning DAGs with low structural Hamming distance under identifiability assumptions.
method Mixed-integer quadratic programming (MIQP) with branch-and-bound-and-cut algorithm and lazy constraints.
result ExDAG guarantees global convergence and provides a real-time quality assessment.
Nontrivial bundles over S2 from coadjoint orbits.
problem Understanding the fundamental groups of coadjoint orbits.
method Associated bundles to nontrivial elements of fundamental groups, analyzed using cohomology.
result Induced map π1(ρ) is injective, strengthening previous results. Study robust mean estimation under coordinate-level corruptions using Hamming distance.
problem Robust mean estimation under realistic coordinate-level corruptions.
method Introduce a novel Hamming distance-based measure and present information-theoretic analysis.
result Data cleaning-inspired approaches can match information theoretic bounds for robust mean estimation.
New loss function and training scheme improve binary hash codes for better similarity search.
problem Improving binary hash codes for better similarity search tasks.
method Log likelihood loss on Hamming distance target, novel training scheme, multi-indexing.
result Significant improvements in MAP (84%) and query cost reduction for ImageNet and SIFT 1M.
Paper develops malware detection methods using Hamming distance.
problem Detecting and preventing spread of Android malware.
method Four detection methods using Hamming distance for similarity.
result Accuracy rates of proposed algorithms are more than 90%.
We introduce here a natural functional associated to any b∈QH∗(M,ω): \emph{spectral length functional}, on the space of "generalized paths" in Ham(M,ω), closely related to both the Hofer length functional and spectral invariants and establish some of its properties. This functional is smooth on its…
New findings on QHD smoothing for graphs with 3 or 4 large nodes.
problem Identifying graphs with QHD smoothing and constraints on large nodes.
method Reduction algorithm and enumeration for graphs with QHD smoothings, using the picture deformation technique.
result No singularity with 3 or 4 large nodes has a QHD smoothing.
Asynchronous Gibbs sampling can accurately estimate expectations of functions of all variables under certain conditions.
problem Estimating expectations of functions of all variables in graphical models.
method Coupling synchronous and asynchronous Gibbs samplers to control expected Hamming distance, using concentration of measure results.
result The bias in estimating expectations of polynomial functions is smaller than the standard deviation of the function value in the true model.
We prove that every RAAG (a Right-Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of the 2-sphere.
Ethereum block builders can earn up to $14M/month by reordering transactions, harming users.
problem Block builders can exploit transaction reordering to earn significant profits, harming users.
method Estimation of MEV payments and analysis of reordering effects.
result Block builders can earn up to $14M/month by reordering transactions, skewing the distribution.
Study on deformations of symmetric spaces using Jordan algebras.
problem Deformability of symmetric Einstein metrics on compact Lie algebras.
method Developed sandwich operators and quadratic Casimir operators for compact Lie algebras; calculated obstruction integrals from invariant polynomials; explored relation to simple Jordan algebras.
result Proved the nonlinear instability of most infinitesimally deformable irreducible compact symmetric spaces.
A novel hash learning approach using codewords in Hamming space.
problem Hash learning for supervised, unsupervised, and semi-supervised scenarios.
method Uses codewords inferred from data to capture grouping aspects of hash codes, with regularization for automatic codeword selection. Solves via Block Coordinate Descent and SVM.
result Demonstrates superior performance in content-based image retrieval.