Study finds volume lower bounds for specific 3-orbifolds.
problem Finding volume lower bounds for hyperbolic 3-orbifolds with certain suborbifolds.
method Analyzing the topology of essential 2-suborbifolds and computing their guts.
result Obtained lower bounds on the volume of specific hyperbolic 3-orbifolds.
Invariants for 3-manifolds with toral boundaries, related by sutured decompositions.
problem Invariants for 3-manifolds with toral boundaries and non-degenerate Thurston norm.
method Constructing an invariant called guts and proving its invariance under sutured decompositions.
result The guts of different homology classes are related by sutured decompositions.
New models found for guts of nearly fibered knots.
problem Characterizing nearly fibered knots topologically.
method Provided three models for the guts of nearly fibered knots.
result Nearly fibered condition can be purely topologically characterized.
Guts determine the leading coefficients of L2-Alexander torsions for 3-manifolds.
problem Determining the leading coefficient of L2-Alexander torsions for 3-manifolds. method Using a new criterion for the convergence of Fuglede-Kadison determinants and the work of Agol and Zhang on guts of 3-manifolds.
result The leading coefficient equals the relative L2-torsion of the guts associated to the cohomology class. Efficient algorithm for analyzing compositional data.
problem Compositional data analysis with nonnegative values summing to one.
method Proposes an efficient solution path algorithm for l1 regularized regression with compositional data. result The proposed algorithm is faster than existing methods, especially in high-dimensional cases.
New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Study uses machine learning to identify IBD biomarkers from gut microbiota.
problem Identifying biomarkers for Inflammatory Bowel Disease (IBD) from gut microbiota.
method Ensemble feature selection methods (CMIM, FCBF, mRMR, XGBoost) applied to IBD-associated metagenomics dataset.
result XGBoost minimizes microbiota used for IBD diagnosis, improving classification accuracy.
Let M be a hyperbolic manifold of finite volume which fibers over the circle with fiber a once punctured torus, and let S be an arbitrary incompressible surface in M. We determine the characteristic JSJ-subpair of M-S and show, in particular, that the guts of (M,S) is empty.
Researchers found the minimum volume of a 3-cusped hyperbolic 3-manifold.
problem Finding the minimum volume of a 3-cusped orientable hyperbolic 3-manifold.
method Using guts in sutured and pared manifolds.
result The volume of a 3-cusped orientable hyperbolic 3-manifold is at least 5.49... = 6 × Catalan's constant.
New method improves support estimation for unknown distributions.
problem Estimating the support size of an unknown distribution.
method Regularized Weighted Chebyshev Approximations, joint optimization of bias and variance, linear programming.
result Significant improvements in worst-case risk for synthetic data and accurate bacterial genus estimation for microbiome data.
Modified proof for a broader class of links.
problem Recovering twist number and volume bounds.
method Modified proof for a broader class of links.
result Modified proof works for a broader class of links.
Study handles in sutured manifolds and knots, finding varied handle numbers and unique surfaces.
problem Understanding handle numbers and incompressible Seifert surfaces in sutured manifolds and nearly fibered knots.
method Extending Haken's Theorem, analyzing product annuli and disks, and examining specific knot types.
result Variety of handle numbers and unique incompressible Seifert surfaces in nearly fibered knots.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
Hierarchical CNNs improve diagnosis of GI diseases from histopathological images.
problem Diagnosing GI diseases from histopathological images is challenging due to heterogeneity and shared features.
method Embedded a class hierarchy into a VGGNet to address the hierarchical structure of GI diseases.
result The hierarchical model achieved better results than a flat model for multi-category diagnosis of GI disorders.
We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions. In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the exist…
Paper tackles multi-source domain adaptation for regression.
problem Predicting HDL cholesterol levels using gut microbiome data.
method Two-step procedure: 1) Extend a flexible single-source DA algorithm for classification to regression. 2) Augment with ensemble learning for multi-source DA.
result Consistent improvement in HDL cholesterol level prediction performance over existing methods.
Develops CNNs for omics data, enabling deep learning on metagenomics and transcriptomics.
problem Applying CNNs to omics data due to lack of distance function.
method Proposes a Keras layer (OmicsConv) for metagenomics and transcriptomics, enabling CNNs on these data types.
result Demonstrates OmicsCNN on gut microbiota sequencing data for IBD, showing its effectiveness.
We prove a finiteness result for the ∂-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and ∂-irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a…
Bayesian model for understanding gut bacteria interactions.
problem Understanding complex interactions in gut microbiome dynamics.
method Bayesian nonparametric model with interaction modules, efficient inference algorithm.
result Efficiently learned clusters of latent variables with reduced interaction coefficients.
We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We also show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 4, and if the image of the cup …
We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and …
In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c2(X)=c2(V) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explic…
DPE embeds non-Euclidean objects into Hilbert space for independence testing.
problem Testing independence of non-Euclidean random objects.
method Distance Profile Embedding (DPE) maps objects into Hilbert space.
result Unified framework for marginal and conditional independence testing.
If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that pi_1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In particular, we show this for tight essential laminations with solid torus guts. We also show that pseudo-Anosov fl…
Study links in 3-manifolds, linking volume to polynomial coefficients.
problem Understanding the volume of hyperbolic links in 3-manifolds.
method Using Kauffman bracket functions and polynomial invariants, linking volume to polynomial coefficients.
result Coefficients of polynomial provide 2-sided linear bounds on the volume of hyperbolic links.
This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.
problem Measurement errors in high-dimensional regression models involving compositional covariates.
method Calibration approach for the linear log-contrast model under lenient sparsity conditions.
result Established asymptotic normality of the estimator for inference.
Paper uses time series transformers to predict investment success.
problem Optimizing investment sourcing in VC and GC.
method Transformer-based Multivariate Time Series Classifier (TMTSC).
result TMTSC improves decision making in VC and GC investments.
Proposes a convex method to estimate GGMs with covariates.
problem Improving conditional independence structure estimation with covariates.
method Convex optimization framework for joint estimation of mean and precision matrix.
result Improved theoretical guarantees and practical utility demonstrated.
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
problem Challenges in inferring conditional dependence relationships in high-dimensional compositional data.
method Composition adaptive regularized estimation (CARE) method for sparse basis precision matrix.
result CARE estimator achieves minimax optimality in high dimensions, performing as well as if the basis were observed.
Many complex ecosystems, such as those formed by multiple microbial taxa, involve intricate interactions amongst various sub-communities. The most basic relationships are frequently modeled as co-occurrence networks in which the nodes represent the various players in the community and the weighted edges encode levels o…
Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.
problem Graphical models in high-dimensional data analysis need to handle clustering and sparsity simultaneously.
method MGLasso combines clustering and graph inference through a convex relaxation of k-means and hierarchical clustering. It uses CONESTA for regularization.
result MGLasso improves network interpretability by estimating graphs at multiple scales.
Tree-based variational inference improves PLN model for hierarchical count data.
problem Limited applicability of PLN model in ecosystems due to lack of hierarchical tree structures.
method Introduced PLN-Tree model integrating structured variational inference techniques.
result Enhanced generative improvements and practical interpretability in microbiome modeling.
A new metric evaluates generative models by comparing real and generated samples.
problem Evaluating the quality of generative models.
method Relative Density Ratio (RDR) function, optimization on variational form of φ-divergence.
result The RDR function provides a clear, interpretable, and numerically stable evaluation metric.
This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses that arise naturally in the study of knot polynomial invariants (A- or B-adequacy), we prove that the growth of the…
Quantum computing speeds up multi-period asset allocation.
problem High computational complexity in classic computing for multi-period asset allocation.
method Applied quantum computing to simulate multi-asset portfolio using historic data.
result Quantum computing offers significant advantages over classical computing in finance.
Hybrid approach reduces computation time and decoding complexity.
problem Straggling servers in distributed computing.
method Coded partial gradient computation (CPGC) that balances gradient accuracy and completion time.
result Reduces both computation time and decoding complexity.
The paper analyzes the pricing of a new compute futures asset.
problem Uncertainty in AI adoption and pricing of compute capital.
method An asset-pricing framework for compute futures, including synthetic futures pricing.
result Preliminary evidence suggests a positive compute risk premium.
Quantum computing offers energy savings over classical computing.
problem Energy efficiency in computing services.
method Cournot competition model constrained by energy usage.
result Quantum computing firms can outperform classical counterparts in energy efficiency.
The paper introduces reservoir computing models for complex systems.
problem Modeling complex engineering systems using nonlinear autoregression.
method Introduces reservoir computing with output feedback as stationary and ergodic infinite-order nonlinear autoregressive models.
result Demonstrates versatility of classical and quantum reservoir computers in modeling synthetic and real data.
Knot theory applied to quantum computing models.
problem Using knot theory for quantum computing models.
method Exploring knot theory applications in quantum computing.
result Knot theory introduces topological concepts to quantum computing.
This work makes neural sequence models more efficient by controlling computation.
problem Fixed compute for all examples in neural networks.
method Conditional computation to adapt compute to example complexity.
result Conditional Computation Transformer (CCT) improves efficiency and performance.
Defines computable learning for binary classification over metric spaces.
problem Defines computable PAC learning for binary classification over computable metric spaces.
method Provides sufficient conditions for ERM learners to be computable and bounds the strong Weihrauch degree of an ERM learner.
result Gives a hypothesis class that does not admit any proper computable PAC learner with computable sample function.
Automatic computation speeds up crosscap number calculation for alternating knots.
problem Computing crosscap numbers for alternating knots efficiently.
method Introduced an automatic computation with complexity O(E3). result Crosscap numbers of alternating knots can be computed in O(E3) time. TKFT models computation via smooth vector fields, simulating functions in a single dynamical step.
problem Modeling computation in a single step.
method Established Topological Kleene Field Theory (TKFT) as a new model of computation.
result Any computable function can be simulated in a single go of a dynamical system.
Predicts and classifies computational jobs for efficient resource allocation in cloud centers.
problem Efficiently scheduling and assigning resources to computational jobs in cloud centers.
method Applied LSTM neural network for job arrival prediction and BIRCH clustering for job classification.
result Improved accuracy in predicting and classifying computational jobs compared to existing methods.
Stochastic reservoir computing is shown to be a universal approximator.
problem Theoretical justification for using stochastic reservoirs in machine learning.
method Investigated stochastic reservoir computing using probabilities of reservoir states as readout.
result Stochastic reservoir computers are universal approximating classes.
Machine learning impacts computational math, offering new functions approximations.
problem Machine learning's black box nature hinders further progress in computational math.
method Analyzes machine learning's impact on computational math and vice versa.
result Integrating computational math with machine learning can enhance both fields.
Method for computing Khovanov homology of tangles.
problem Limited explicit computational studies of Khovanov homology for tangles.
method Arc reduction approach to compute Khovanov homology.
result Derived and computed Poincaré polynomials for simple and complex tangles.