Conditions for forming nontrivial knots from vector collections.
problem Conditions for forming nontrivial knots from vector collections.
method Analyzing vector collections and their reordering to form knots.
result For n≥7, it's always possible to reorder vectors to form a nontrivial knot. Study collective pricing and hedging with admissible risk exchanges forming a finitely generated convex cone.
problem Collective pricing and hedging with exchanges forming a finitely generated convex cone.
method Extend collective First Fundamental Theorem of Asset Pricing and pricing-hedging duality.
result No collective arbitrage implies the closedness of the aggregate feasibility cone.
Abstract not provided enough details, focusing on vector bundles and orbits.
problem Understanding continuous representations of semisimple Lie groups.
method Not specified in the abstract.
result Not specified in the abstract.
Indices of vector fields and 1-forms studied for singular varieties and actions.
problem Understanding indices of vector fields and 1-forms in various contexts.
method Generalization to singular varieties and actions of finite groups.
result New insights into indices of vector fields and 1-forms.
New algorithms reduce costly feature collection in bandits.
problem Costly feature collection in contextual bandits.
method Proposes algorithms avoiding unnecessary feature collection.
result Strong regret guarantees maintained with reduced feature collection.
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the collection. Recently, "self expression", the idea of using a small subset of data vect…
Analyzes when vector fields can be real analytic in coordinates.
problem When can vector fields be represented by real analytic functions in coordinates?
method Provides necessary and sufficient conditions for real analytic coordinates.
result Necessary and sufficient conditions for real analytic coordinates exist.
Methodology monitors processes using system call count vectors.
problem Detecting anomalies in process behavior.
method Collects system call streams, sends to server, uses ML for analysis.
result Effective in identifying process anomalies in corporate networks.
A canonically defined mod 2 linear dependency current is associated to each collection of m sections of a real rank n vector bundle. This current is supported on the linear dependency set of the collection of sections. It is defined whenever the collection satisfies a weak measure theoretic condition called "atomicity"…
This paper explores coordinates adapted to vector fields on smooth manifolds.
problem Finding coordinates where vector fields are smoother.
method Quantitative techniques from ODEs and PDEs.
result Results on smoothness and regularity of coordinates.
Torch-Struct simplifies structured prediction for deep learning.
problem Difficulty in integrating structured prediction algorithms with deep learning frameworks.
method Develops a library (Torch-Struct) that integrates structured prediction with vectorized, auto-differentiation-based frameworks.
result Significant performance gains over fast baselines and cross-algorithm efficiency.
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measure…
We address challenges in estimating parameters from adaptively collected data.
problem Estimating parameters from data collected adaptively leads to non-normal asymptotic distributions.
method We develop semi-parametric estimators that account for adaptivity in data collection.
result Our estimators are asymptotically normal under certain conditions.
The study detects and classifies touch gestures with high accuracy.
problem Detecting and classifying touch gestures from touch screens.
method Supervised learning techniques using a capacitive sensor array to record touch and swipe gestures.
result Logistic Regression models achieved over 95% accuracy for all gesture types.
Solves the initial CV problem for molecular simulations using machine learning.
problem Selecting appropriate collective variables for enhancing sampling in molecular simulations.
method Data-driven approach inspired by supervised machine learning (SML).
result Various SML algorithms can be used as initial collective variables (SML_cv) for accelerated sampling.
Study on recovering sparse linear classifiers from mixed binary responses.
problem Learning a mixture of sparse linear classifiers from binary responses.
method Query-based approach to identify all sparse vectors from a set.
result Upper bounds on the number of queries required for recovery.
Geometrically interprets cup products and defines combinatorial Pin structures.
problem Understanding Steenrod's cup products and their geometric interpretation.
method Constructs vector fields and combinatorial frames to interpret cochain-level formulas.
result Geometrically interprets cup products and defines Pin structures combinatorially.
Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., ℓ0-optimal representations. Here we consider the problem of finding optimal dictionaries …
Paper improves learning mixtures of sparse signals from noisy measurements.
problem Learning mixtures of sparse linear regressions from noisy measurements.
method Improves upon state-of-the-art results using sparse polynomials and error-correcting codes.
result First robust reconstruction algorithm for mixtures of more than two sparse signals.
We compute the cohomology with group ring coefficients of the complement of a finite collection of affine hyperplanes in a finite dimensional complex vector space. It is nonzero in exactly one degree, namely the degree equal to the rank of the hyperplane arrangement.
New methods reveal compatible liquid crystal phases in 3D.
problem Understanding compatible director fields in 3D liquid crystals.
method Re-derived compatibility conditions using vector calculus.
result Characterized a wide range of compatible liquid crystal phases.
CDM improves fingerprinting-based positioning accuracy.
problem Quantifying similarity of collections with missing attributes.
method Combining vector-based distance metrics and set operations.
result Improves positioning accuracy by 5% on average.
We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra of evolutionary vector fields of the jet space are subject to collective commutation closure. The linear space of such operators becomes an a…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors. In its simplest instances, this algorithm works by finding the minimal position …
The paper explores grids and warps in triple vector bundles, proving a zero-sum property and applying it to manifold and vector bundle contexts.
problem Understanding the structure and commutativity of triple vector bundles.
method Intrinsic proof of the sum of warps being zero, applied to specific cases like tangent bundles and vector bundles.
result The sum of warps in a triple vector bundle is zero, with applications to manifold and vector bundle structures.
In non-compact manifolds, geodesic flowers exist.
problem Existence of geodesic flowers in non-compact manifolds.
method Proving the existence of non-trivial geodesic flowers in complete non-compact manifolds with locally convex ends.
result Non-trivial geodesic flowers exist in every complete non-compact manifold with locally convex ends.
Exact universal interpolation property for landmark configurations in Euclidean space.
problem Representing and deforming landmark configurations through flows of vector fields.
method Explicitly describe vector fields for exact universal interpolation property in all dimensions.
result Achieve controllability by combining constant and polynomial vector fields.
Three definitions of a differential form on a tangent structure are considere. It is proved that the (covariant) definition given by Souriau (as a collection of forms indexed by the plaques) is equivalent to a smooth section of the corresponding vector bundle if the space does not have transverse points.
Model infers utility from lion GPS data using Gaussian processes.
problem Understanding lion decision-making based on GPS data.
method Gaussian processes, vector calculus, Kullback-Leibler divergence.
result Identifies significant landmarks influencing lion trajectories.
A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show …
Geometric vector perceptrons improve protein structure learning.
problem Learning from protein structure with efficient and natural representations.
method Introducing geometric vector perceptrons to extend dense layers for Euclidean vectors, integrating geometric and relational reasoning.
result Improves model quality assessment and computational protein design over existing methods.
New method recovers sparse vectors from random sinusoidal features.
problem Recovering sparse vectors from random sinusoidal features.
method Proposes a numerically stable algorithm for sparse vector reconstruction.
result Sparse vectors can be reliably recovered from random sinusoidal features.
Efficient methods for linear/logistic regression with network-dependent responses.
problem Regression with dependent responses in networked data.
method Projected gradient descent on negative log-likelihood, proving strong convexity and consistency.
result Strong consistency results for vector of coefficients and dependency strength.
Researchers find optimal dictionaries for minimizing average squared coefficients in random vector representations.
problem Finding optimal dictionaries for minimizing the average squared coefficients in random vector representations.
method Using rank-1 decompositions and majorization theory, the study provides a complete characterization of optimal dictionaries.
result Complete characterization of ℓ2-optimal dictionaries with polynomial time algorithms. Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), K-means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. W…
SecVM preserves user privacy in training SVMs for classification tasks.
problem Training supervised classifiers on sensitive user data while maintaining privacy.
method A novel secret vector machine (SecVM) framework for training linear SVMs in a distributed, privacy-preserving manner.
result SecVM outperforms baselines in a large-scale online evaluation, preserving user privacy and classification accuracy.
The paper provides concentration bounds for embeddings of generative models.
problem Establishing accurate statistical analysis of generative models.
method Data Kernel Perspective Space embedding method.
result Required number of sample responses for accurate approximation.
A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is used in showing that double (or higher) vector bundles present in the literatur…
The abstract generalizes a construction for splitting supermanifolds and studies Lie supergroup cases.
problem Splitting supermanifolds and understanding their structure.
method Using n-fold vector bundles and graded manifolds, the abstract generalizes a construction for splitting supermanifolds. result The images of these embeddings into the category of graded manifolds satisfy universal properties of graded coverings or semicoverings for Lie supergroups and Lie superalgebras.
Study robust covariance estimation in large data with concentrated vectors.
problem Estimating robust covariance in large data with concentrated vectors.
method Fixed point of a contracting function using stable semi-metric and concentration of measure.
result Existence and uniqueness of robust estimator with evaluated limiting spectral distribution.
The paper establishes concentration bounds for embeddings of generative models.
problem Analyzing statistical properties of generative models.
method High probability concentration bounds on sample vector embeddings using Data Kernel Perspective Space.
result Determines the number of samples needed for accurate approximation of generative model embeddings.
Top2Vec finds topic vectors from documents and words without needing stop words or custom settings.
problem Topic modeling weaknesses, including needing known topics, stop words, and custom settings.
method Joint document and word semantic embedding to find topic vectors automatically.
result Top2Vec finds more informative and representative topics than probabilistic models.
Deep learning model improves Vietnamese NER accuracy.
problem Vietnamese named entity recognition (NER) accuracy.
method Combining Bi-LSTM and CRF with word embeddings and semantic features.
result Achieved state-of-the-art NER results on VLSP2016 dataset.
Transformers approximate mean-field dynamics of indistinguishable particles.
problem Approximating the dynamics of indistinguishable particles in complex systems.
method Using transformers to model the mean-field dynamics of interacting particle systems.
result Theoretical bounds on the distance between true and transformer-obtained mean-field dynamics.
The paper establishes conditions for complex structures on manifolds with given vector fields.
problem Conditions for complex structures on manifolds with given vector fields.
method Intrinsic, diffeomorphic invariant conditions for vector fields to have desired regularity.
result Quantitative results for sub-Hermitian geometry and formally integrable elliptic structures.
The paper uses MDM theory to analyze multifiltering functions on simplicial complexes.
problem Understanding multifiltering functions through discrete Morse theory.
method Applying multiparameter discrete Morse theory to vector-valued multifiltering functions.
result Any multifiltering function can be approximated by a compatible MDM function.
Optimal algorithms identify non-dominated arms in multi-output linear bandit models.
problem Identifying the Pareto Set in multi-output linear bandit models.
method Design-based algorithms for Pareto Set Identification (PSI) in a structured multi-output linear bandit model.
result Nearly optimal guarantees in both fixed-budget and fixed-confidence settings.
ATOL vectorizes measures for topological learning, separating clusters of persistence diagrams.
problem Challenges in applying topological information to machine learning frameworks.
method A fast, unsupervised vectorization method for measures in Euclidean spaces.
result Successfully discriminates important space regions in persistence diagrams.