Paper explores conditions for constructing new quasi-alternating links.
problem Applying construction method to non-alternating and opposite type tangles.
method Substituting quasi-alternating crossings with rational tangles of same type.
result Identifies conditions and specific tangles for construction validity.
Paper proposes an alternative method to price American options using HJM approach.
problem Price American options efficiently and accurately.
method Utilizes HJM technique to model term structure of volatility for equity markets.
result Proposes a new value function, stopping criteria, and stopping time for American options.
An alternative method is described for determining the hyperbolic structure on a link complement, and some of its elementary consequences are examined. The method is particularly suited to alternating links.
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to be one of the most accurate and efficient, and formed a major component of the wi…
New theory connects geometry without relying on connections.
problem Developing geometric structures without connections.
method Proposed alternative approach to Lie groups and geometric structures.
result Geometric structures can be developed independently of connections.
Improved clustering algorithm for large datasets.
problem Finding alternative partitions in large datasets.
method Iterative Spectral Method (ISM) for alternative clustering.
result Significantly improved scalability and computation time.
Proposes an alternative method for HJM models' existence.
problem Existence of affine realizations for HJM term structure models.
method Alternative approach applicable to various models, conceptually clear.
result Provides insights into term structure model geometry.
New invariant for prime alternating knots from error-correcting codes
problem Distinguishing prime alternating knots
method Alexander-Briggs code
result New invariant succeeds in separating knots that other invariants fail
Alternative approach to curve shortening flow solutions.
problem Understanding singularity formation in mean curvature flow.
method Simple ODE description and alternative proof of self-similar solutions.
result Self-similar solutions lie in planes.
Machine learning monitors fueling infrastructure reliability.
problem Ensuring reliability of alternative fueling infrastructure for ZEV adoption.
method Unsupervised temporal clustering algorithm and survey analysis.
result Infrastructure performance and reliability determined for hydrogen stations in California.
Alternative metric defined on vector bundles, proving vanishing theorem.
problem Defining singular Hermitian metrics on vector bundles.
method Alternative definition of singular Hermitian metric, discussing Griffiths and Nakano positivities.
result Generalised Griffiths' vanishing theorem proved.
Investigates optimal consumption and investment using alternative data sources.
problem Optimal consumption and investment decisions under hidden economic regimes.
method Develops a novel duality theory for a jump-diffusion process with alternative data.
result Provides conditions for using control approach based on dynamic programming.
We show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of L-space knots, every sufficiently large surgery may be realized as the two-fold branch…
Efficiently completes low-rank matrices with nearly linear time complexity.
problem Completing low-rank matrices from a few observed entries.
method Robust alternating minimization framework with approximate updates.
result Achieves nearly linear time complexity in matrix completion.
Alternative construction of Rumin complex on Lie groups.
problem Constructing Rumin complex on homogeneous nilpotent Lie groups.
method Using ideas from parabolic geometry, an alternative construction to the classical one on Carnot groups.
result Explicit computations for the Engel group using the new approach.
The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.
problem Understanding alternating links in thickened surfaces and their invariants.
method Using integer flows on Tait graphs and disc mutations, the paper proves invariants and compares link properties.
result Found alternating knots with isometric flow lattices but different linking forms.
PCMC-Net uses neural networks to estimate transition rates in choice models, improving accuracy over traditional methods.
problem Inference limitations of traditional PCMC models when examples are scarce or new alternatives are observed.
method Amortized inference approach embedding PCMC definition into a neural network.
result Neural network outperforms feature engineered and machine learning models in airline booking prediction.
Characterizes a specific type of neural network for alternating group equivariance.
problem Understanding and characterizing neural networks with alternating group equivariance.
method Characterization of all possible An-equivariant neural networks using tensor powers of Rn. result Found a basis of matrices for learnable, linear An-equivariant layer functions. Curious Meta-Controller alternates between model-based and model-free control to improve sample efficiency.
problem Combining the benefits of model-based and model-free control to enhance sample efficiency.
method Adaptive alternation between model-based and model-free control using curiosity feedback.
result Significantly improved sample efficiency and near-optimal performance on robotic tasks.
DANTE trains neural networks using an alternating minimization approach.
problem Training neural networks with mixed activation functions efficiently.
method DANTE uses alternating minimization and quasi-convexity to handle neural networks with both differentiable and non-differentiable activation functions.
result DANTE-trained neural networks are promising and competitive in terms of quality and training speed.
The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
Study optimizes sampling to avoid extreme tail risks in unknown heavy-tailed distributions.
problem Identify optimal alternative with minimal extreme tail risk from unknown heavy-tailed distributions.
method Data-driven sequential sampling policies to maximize likelihood of selecting the optimal alternative.
result Proposed methods outperform existing approaches in identifying the optimal alternative.
The paper derives formulas for braid index of alternating links.
problem Determining the braid index of alternating links.
method Diagrammatic approach based on minimum projections.
result Explicit formulas for braid index of many alternating links.
Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface in…
Unified approach to estimating class-prior and classifier from PU data.
problem Learning binary classifier from positive and unlabeled data with class-prior estimation.
method Alternately estimating class-prior and training classifier.
result Unified approach improves classifier performance by accounting for class-prior estimation error.
Develops an alternative approach to Tanaka's prolongation of geometric structures.
problem Generalizing Tanaka's prolongation of G-structures to a broader class of geometric structures.
method Alternative constructive approach based on quasi-gradations and filtered vector spaces.
result Constructs an alternative method for describing local invariants and automorphism groups of Tanaka structures.
Model optimizes mediation for insolvent suppliers by finding an optimal contract solution.
problem Optimizing contract outcomes for insolvent suppliers in disputes.
method Linear optimization model with complex number phasor approach and Gompertz function for supplier offers.
result Optimal solution adherence to initial contract terms.
Proposes methods to find alternative blockmodels in networks.
problem Discover secondary blockmodel representations of networks that are dissimilar to a given blockmodel.
method Incorporates non-negative matrix factorisation (NMF) with inclusion of cannot-link constraints and dissimilarity between image matrices.
result Validated the effectiveness of the proposed methods in discovering alternative blockmodels.
Paper accelerates NMF algorithms using extrapolation.
problem Efficiently solving nonnegative matrix factorization problems.
method Inspired by convex optimization, uses extrapolation for two-block exact coordinate descent algorithms.
result Significantly accelerates NMF algorithms on various data sets.
Link invariants fail to detect most links with high probability.
problem Detecting specific link types using invariants.
method Mathematical proof and big-data analysis.
result Link invariants have a zero probability of detecting alternating links.
Model analyzes cooccurrence data for recommender systems and item relevance.
problem High-dimensional cooccurrence data from online platforms.
method Shared parameter Alternating Tweedie (SA-Tweedie) model with Fisher scoring and learning rate adjustment.
result SA-Tweedie model outperforms other methods in optimizing parameters.
A meta-learning approach improves the performance of alternating minimization for non-convex optimization problems.
problem Optimizing non-convex problems with multiple variables using alternating minimization.
method Meta-learning based alternating minimization (MLAM) to replace handcrafted updating rules.
result The proposed MLAM method outperforms traditional AM-based methods in various non-convex optimization problems.
Alternative neural network training using monotone variational inequality.
problem Training neural networks efficiently and with guarantees.
method Using monotone variational inequality to solve non-convex problems efficiently.
result Our approach leads to fast convergence and competitive performance compared to traditional methods.
A new method constrains PARAFAC2 for better pattern recovery.
problem Challenges in analyzing multi-way measurements with variations across one mode.
method AO-ADMM approach to fit PARAFAC2 model with flexible constraints.
result The proposed method allows for flexible constraints, recovers patterns accurately, and is computationally efficient.
The thesis examines when double branched covers of alternating knots arise via Dehn surgery.
problem When the double branched cover of an alternating knot can arise by Dehn surgery on a knot in S3. method Surgery obstruction combining Donaldson's Diagonalization Theorem and Heegaard Floer homology.
result Alternating knots with an unknotting crossing have unknotting number one.
Introduces a new geometric method for optimal experimental design.
problem Restrictive invariance properties of traditional OED approaches based on probability densities.
method Mutual transport dependence (MTD) using optimal transport theory.
result Demonstrates high-quality designs and flexibility compared to standard methods.
New method improves predictive systems with better theoretical guarantees.
problem Constructing predictive systems with out-of-sample calibration guarantees.
method Residual Distribution Predictive Systems (RDPs) that nest conformal predictive systems and offer flexibility.
result Empirically, RDPs perform competitively with conformal predictive systems and can be implemented with various regression methods.
Two new methods for option pricing without or with a riskless asset.
problem Traditional option pricing methods require a riskless asset and may not be market-complete.
method Develops two approaches: one without a riskless asset and one with.
result Both methods produce the same option prices as classical approaches.
New method for probabilistic clustering using matrix norm couplings.
problem Probabilistic clustering of discrete random variables.
method Local information theoretic approach with convex maximization problem solved via gradient ascent and alternating maximization.
result Our approach is competitive with existing techniques and worthy of further investigation.
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
Alternative proof of weak solutions to mean curvature flow using minimizing movements.
problem Existence of weak solutions to mean curvature flow and volume preserving mean curvature flow.
method Proposes a new existence proof using a minimizing movements scheme and a novel proxy for distance.
result Unconditional convergence towards a De Giorgi solution for the minimizing movements scheme.
Alternative approach to rigidity of high-dimensional isometric immersions.
problem Rigidity of high-dimensional isometric immersions between compact manifolds.
method Quantitative rigidity estimates, reducing to Euclidean setting and applying Friesecke-James-Müller rigidity estimate.
result Quantitative results showing close proximity to isometric immersions for small stretching and bending energy.
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, fo…
In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In order to reduce the number of computer experiments, many other approaches known as …
Solves a mix of many random linear equations using tensor decomposition and alternating minimization.
problem Estimating multiple linear models from mixed samples with unknown labels.
method Combination of tensor decomposition and alternating minimization.
result Guaranteed exact solution with linear sample complexity in dimension and polynomial in k. Study improves efficiency of MIMO systems' sum rate estimation.
problem Maximizing sum rate in MIMO systems with PAPC constraints.
method Proposes two new low-complexity approaches: alternating optimization and machine learning.
result Demonstrates superior performance compared to existing methods.
New method improves matrix factorization speed and accuracy.
problem Matrix factorization optimization problems suffer from biased solutions and lack of convergence guarantees.
method Proposes a novel Bregman distance for matrix factorization, enabling non-alternating schemes with convergence proof.
result Convergence to a stationary point proved for matrix factorization problems.
Derives FACT, an alternative to NFA for neural networks, explaining feature learning.
problem Understanding how neural networks learn representations.
method First-principles approach using first-order optimality conditions.
result FACT explains why NFA holds and provides a principled alternative.