Improved chromosome for genetic algorithms handles large n and interaction terms.
problem Chromosome formulation struggles with large n and interaction terms.
method Introduced a modified chromosome formulation for better scalability and sparsity.
result Indexed chromosome formulation shows improved efficiency and sparsity on high-dimensional datasets.
Automated image segmentation distinguishes overlapping human chromosomes.
problem Distinguishing overlapping human chromosomes for medical diagnostics.
method Customized convolutional neural network for image segmentation.
result IOU scores of 94.7% for overlapping regions, 88-94% for non-overlapping regions.
Paper solves NP-hard haplotyping problem using matrix completion.
problem Reconstructing inherited genetic variations from DNA sequencing data.
method Binary matrix factorization and alternating minimization.
result The proposed technique achieves lower haplotype reconstruction error.
New method infers centromere locations in yeast using Hi-C data.
problem Difficulty in inferring centromere locations in yeast.
method Simulation-based inference using Hi-C data and simulated contact maps.
result Infers stochastic locations of all centromeres in budding yeast.
A Bayesian Boolean Matrix Factorization for cancer genomics
problem Identifying coordinated feature changes in cancer
method Bayesian Boolean Matrix Factorization
result Captures widespread, near-simultaneous chromosome-number changes
Optimization approach for efficient sampling in optical mapping for structural variant detection.
problem Efficient sampling strategy for structural variant detection using optical mapping.
method Developed an optimization approach using a hyper-geometric distribution and probabilistic concentration inequalities.
result Optimal sampling strategy requires sampling most chromosomal fragments to detect variants at high confidence with little biological material.
New nonparametric HMM improves genetic sequence analysis.
problem Improving genetic sequence data analysis for hidden states and transitions.
method Developed a nonparametric hierarchical Dirichlet process HMM for genetic sequence data.
result Our model provides more parsimonious parameterization of genetic processes.
New models analyze stability of gene regulation networks with coregulation.
problem Stability and structure of gene regulation networks with shared regulatory motifs.
method Developed formalism for modeling coregulation rules in RBN, analyzed stability through mean-field approach.
result Coregulation can increase network stability, especially in autoregulated multi-gene modules and hierarchical gene complexes.
A method for estimating the cross-correlation Cxy(τ) of long-range correlated series x(t) and y(t), at varying lags τ and scales n, is proposed. For fractional Brownian motions with Hurst exponents H1 and H2, the asymptotic expression of Cxy(τ) depends only on the lag τ (wide-sense stationarit…
New topological surgery concepts for natural phenomena.
problem Understanding topological changes in natural processes.
method Extending topological surgery to natural phenomena, introducing new concepts.
result Enhanced understanding of topological changes in natural phenomena.
G2Ns combine genetic genes with neural networks for reinforcement learning.
problem Improving sample efficiency and performance in reinforcement learning.
method Genetic-Gated Networks (G2Ns) that integrate binary genetic genes with neural network hidden layers.
result G2Ns achieve significant improvements in sample efficiency and performance in reinforcement learning.
Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the correlations between the projections are maximized. The solution is invariant to any lin…
A genetic algorithm improves multivariate kernel density estimation.
problem Efficiently estimating multivariate kernel density functions.
method Genetic algorithm applied to subsamples of the original data.
result The genetic algorithm-based estimator performs better than traditional methods.
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more dependent on a first target variable or a second. Dependence is measured via the Hilbe…
Graphs represent gene segment organization, revealing complex interrelationships in a scrambled genome.
problem Understanding gene segment organization and interrelationships in a scrambled genome.
method Directed graphs representing gene segments and their relationships, with graph properties mapped to higher-dimensional space for analysis.
result Emerging star-like structures indicate complex interrelationships, including segments from multiple genes interleaving or overlapping.
Generates new human genomic sequences for LAI training.
problem Lack of accessible reference data sets for LAI.
method Class-conditional VAE-GAN to generate realistic sequences.
result Generated sequences improve LAI method performance.
Novel method REACH-3D reconstructs 3D chromatin structure from HiC data.
problem Understanding the 3D structure of the genome and its temporal behavior.
method Autoencoders with recurrent neural units for manifold learning.
result REACH-3D outperforms existing methods in reconstructing chromatin structure and dynamics.
CN-SBM clusters cancer samples and regions based on copy number variants.
problem Clonal evolution in cancer monitored by noisy copy number variants.
method Probabilistic framework using bipartite categorical block model.
result Improved model fit and clinically relevant subtypes identified.
Bayesian framework for model uncertainty identifies complex heterogeneity without strong assumptions.
problem Identifying complex heterogeneity in factorial data with varying covariates.
method Rashomon Partition Sets (RPS) using l0 prior for robust model uncertainty.
result RPS provides a robust set of models capturing complex heterogeneity without strong assumptions.
Optimal data-driven formulations are found for learning and decision-making with historical data.
problem Designing optimal learning and decision-making formulations from historical data.
method Define a yardstick for measuring formulation quality, then construct an optimal formulation that is uniformly closer to the true cost.
result Existence of three distinct out-of-sample performance regimes with corresponding optimal formulations.
A new DR formulation improves metric learning for faster and more stable performance.
problem Learning embeddings for class separation in metric learning.
method Distance-ratio (DR) formulation for metric learning.
result DR formulation achieves improved or comparable generalization performances.
New formulations for Ricci flows without smoothness.
problem Characterize Ricci flows without smooth solutions.
method Weak formulations of super Ricci flows with saturation condition.
result Generalized formulations for singular settings.
Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.
problem Reducing the number of binary variables in QUBO formulations for Bayesian network learning.
method Proposes a new QUBO formulation that minimizes binary variables.
result Significantly reduces the number of binary variables required for Bayesian network structure learning.
Defines a metric and form for a bundle moduli space, leading to a zero-curvature formulation.
problem Formulating a metric and form for a bundle moduli space.
method Defines an algebraic metric and closed 3-form on a subspace of the moduli of G-bundles. result Shows a zero-curvature formulation for a σ-model with target the moduli space. We study ranking quantilized mean-field games to select top-performing agents.
problem Selecting top-performing agents in competitive scenarios.
method Developed two formulations: target-based and threshold-based, and provided analytic and semi-explicit solutions.
result Analytic and semi-explicit solutions for quantilized mean-field consistency conditions.
Deep learning predicts pharmaceutical formulations with high accuracy.
problem Laborious, time-consuming and costly traditional trial-and-error approach in pharmaceutical formulation development.
method Used deep learning for automatic feature extraction, developed automatic dataset selection algorithm, compared with six machine learning methods.
result Deep neural networks achieved accuracies above 80% in predicting pharmaceutical formulations.
New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
Geometric structures help in understanding nonequilibrium thermodynamics.
problem Formulating nonequilibrium thermodynamics using geometric objects.
method Using Dirac structures to formulate nonequilibrium thermodynamics.
result Dirac structures provide a consistent extension of mechanics to nonequilibrium thermodynamics.
Equivalent formulations for low-rank matrix optimization are proven.
problem Low-rank matrix optimization with rank constraints.
method Established geometric landscape connections between manifold and factorization formulations.
result Equivalence between manifold and factorization formulations at FOSPs, SOSPs, and strict saddles.
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the ℓ1- and ℓ2-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.
problem Formulating the Raychaudhuri equation in non-Riemannian geometries.
method Established a formal connection between the expansion scalar and the cross-sectional volume of the congruence. Derived a Lagrangian and Hamiltonian formulation.
result The expansion scalar equals the fractional rate of change of volume, weighted by a scalar factor.
Paper offers a dual formulation for consumption problem with multiplicative habit.
problem Optimal consumption with multiplicative habit formation.
method Dual formulation using Fenchel's Duality Theorem.
result Strong duality result linking primal and dual controls.
The paper tackles robust statistical methods using Wasserstein DRO formulations.
problem Distributional uncertainty in learning from limited samples.
method Min-max distributionally robust optimization with Wasserstein DRO formulations.
result Error bounds free from the curse of dimensionality.
Continuous formulation of machine learning models and algorithms.
problem Generalization error and implicit regularization in machine learning.
method Continuous formulation in calculus of variations and differential-integral equations, with new models and algorithms.
result Conventional models and algorithms can be recovered as particular discretizations.
Bayesian optimization identifies optimal alloy formulations.
problem Accelerated discovery in materials science with autonomous systems.
method Bayesian optimization over problem formulation space.
result Framework converges on optimal alloy formulations.
Neural networks predict ODT formulations, reducing development time.
problem Efficiently predicting ODT formulations for quality control.
method Artificial Neural Network (ANN) and Deep Neural Network (DNN) techniques.
result DNN model outperformed ANN in predicting ODT disintegrating time.
New formulations capture aversion to ambiguity about volatility.
problem Capturing aversion to ambiguity about unknown and time-varying volatility.
method Introduces novel preference formulations and compares them with existing models.
result Illustrates the impact of ambiguity aversion in static and dynamic models.
The paper develops a mathematical model for strategic shifts.
problem Finding optimal moments for strategy changes in market dynamics.
method Explicit strategy formulation using fluctuation theory.
result Analytical results predict optimal strategy shifts.
SpInGP speeds up Gaussian process computations with sparse matrices.
problem Efficiently computing Gaussian processes for large datasets.
method Sparse precision Gaussian process formulation and parallelizable matrix routines.
result The parallelized SpInGP reduces time complexity to sublinear.
ROCK method generalizes MOCK for learning dynamical systems efficiently.
problem Learning dynamical systems from data efficiently.
method Variational formulation in Reproducing Kernel Hilbert Spaces.
result ROCK method is more computationally efficient and performs better on benchmarks.
In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed module cocycle and cocycle 1- and 2-gauge transformation with a non standard do…
We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthet…
The paper proves an index theorem for loop spaces of compact manifolds.
problem Defining an index theorem for loop spaces of compact manifolds.
method Formulated and proved an equivariant index theorem for non-compact manifolds with S1-actions, using a ring of formal power series. result Found an appropriate form of the index theorem for loop spaces.
Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation…
Designs a robust data-driven decision-making model to handle multiple overfitting sources.
problem Overfitting in data-driven models due to statistical error, data noise, and data misspecification.
method Holistic distributionally robust optimization formulation combining Kullback-Leibler and Lévy-Prokhorov approaches.
result Guaranteed holistic protection against statistical error, data noise, and data misspecification.
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic formulation of first-order field theories. The Lagrange-d'Alembert formalism is also d…
Unified formulation bridges adversarial and nonstationary bandits.
problem Handling time-varying reward distributions in multi-armed bandit problems.
method Unified oracle that switches between adversarial and nonstationary bandit oracles based on window size.
result Optimal regret achieved with matching lower bound.