Unified Minkowski problem discussed for (p,q)-mixed quermassintegrals.
problem Unified Minkowski problem for (p,q)-mixed quermassintegrals.
method Introducing (p,q)-mixed quermassintegrals and (p,q)-dual mixed curvature measure to study the Minkowski problem.
result Derivation of important properties and geometric inequalities for (p,q)-mixed quermassintegrals.
New method trains Boltzmann machines without supervision.
problem Training unsupervised learning models.
method Mixed binary quadratic feasibility problem formulation.
result Theory validated on XOR patterns.
Research on mixed polynomials, extending non-degeneracy concepts to complex variables.
problem Extending non-degeneracy concepts to mixed polynomials in complex variables.
method Generalization of Mondal's partial non-degeneracy to mixed polynomials, introducing new concepts and proving properties.
result Strong partial non-degeneracy implies isolated singularities, and mixed polynomials that are strongly inner non-degenerate satisfy the strong Milnor condition.
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…
Paper defines new curvature measures for foliated manifolds and proves new theorems.
problem Estimating the diameter and splitting theorems for foliated manifolds.
method Introduced weighted mixed curvatures and new conditions to update estimates.
result Updated estimates of diameter and proved new splitting theorems.
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
Study kernel density estimation for dynamical systems with unique invariant density.
problem Density estimation for dependent observations from dynamical systems.
method Employing C-mixing to measure dependence, universal consistency and convergence rates are established. result Kernel density estimator is universally consistent and achieves convergence rates under L1-norm and L∞-norm. Proposes a new model for context-dependent decision-making.
problem Constant preference parameters in decision models are too rigid.
method Introduces Context-aware Bayesian mixed multinomial logit model using neural networks.
result Models context-dependent intra-respondent heterogeneity effectively.
Improved anomaly detection in time series data using kervolutional neural networks.
problem Anomaly detection in time series data.
method Mixed kervolutional and convolutional layers in a temporal auto-encoder.
result The mixed model detects anomalies more sensitively in time series data.
New weighted surface area measures for convex bodies with applications.
problem Generalizing surface area measures to weighted Borel measures.
method Formulating and analyzing weighted surface area measures, proving integral formula and Bézout-type inequality.
result New integral formula for mixed measure of three bodies, generalizing Bézout-type inequality.
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
problem Solving parametric mixed-integer linear optimization problems with changing data.
method Introducing cutting-plane layers (CPLs) for differentiable cutting-plane generation.
result The algorithm computes solutions with low integrality gaps and generalizes to unseen instances.
A neural network visualizes data structure and concepts.
problem Data visualization and concept understanding.
method Mixing autoencoder and classifier for multi-perspective visualization.
result The network produces different topological maps based on training as autoencoder or classifier.
In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally the almost cosymplectic manifold is modeled on the 'mixed' space RxCn. There is g…
New approach tackles nonidentifiability in nonlinear blind source separation.
problem Nonidentifiability in nonlinear blind source separation.
method Independent mechanism analysis, incorporating causal assumptions.
result Empirical and theoretical evidence shows improved identifiability.
Machine learning monitors detect motor overheating, adapting to concept drift.
problem Early detection of motor overheating in ships' propulsion systems.
method Machine learning and statistical methods using historical data to adapt to concept drift.
result The proposed monitors provide early detection of overheating during and after concept drifts.
The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver has reported to the insurance company during the last years. Classically these p…
ExDBN learns dynamic Bayesian networks using mixed-integer programming.
problem Learning dynamic causal relationships from time series data.
method Score-based learning algorithm using mixed-integer quadratic programming with branch-and-cut method.
result The proposed method produces more accurate results than state-of-the-art approaches.
Fewer data weight updates lead to faster convergence in machine learning models.
problem Improving robustness of machine learning models through data mixing.
method Analyzing convergence behavior of data mixing with a finite number of inner steps.
result The optimal number of inner steps scales with the budget and type of gradients used.
Prob2Vec embeds problems for adaptive tutoring, achieving high similarity accuracy.
problem Retrieve problems with similar mathematical concepts for adaptive tutoring.
method Hierarchical problem embedding algorithm (Prob2Vec) combining abstraction and embedding steps.
result 96.88% accuracy on problem similarity test, significantly outperforming state-of-the-art sentence embedding methods.
New balanced metrics introduced for SPD matrices, improving metric choice.
problem Lack of principles for choosing SPD matrix metrics.
method Introducing balanced metrics that relate existing metrics.
result Two new balanced metric families introduced: mixed-power-Euclidean and mixed-power-affine.
New tool predicts option evolution with mixed price times.
problem Uncertainty in predicting option prices at specific times.
method Financial Hamiltonian for predicting system evolution.
result Prediction of option evolution with mixed price times.
A Ph.D. thesis proposes an efficient approach for optimizing aircraft eco-design with high-dimensional mixed integer variables.
problem Optimizing aircraft eco-design with high-dimensional mixed integer variables.
method EGO optimization approach based on sequential enrichment of adaptive surrogate models, adapted for high-dimensional and mixed variable spaces.
result Effective parameterization tools significantly reduce the number of design variables, enabling optimization of complex aircraft concepts.
Enhances topology optimization with multiclass microstructures using latent variable Gaussian process.
problem Lack of an inherent ordering or distance measure between different classes of microstructures.
method Extended latent-variable Gaussian process (LVGP) models to multi-response LVGP (MR-LVGP) models for metamaterials.
result Improved performance through consistent load-transfer paths for micro- and macro-structures.
The paper extends knotoid theory to annular and toroidal settings.
problem Extending knotoid theory to new geometric settings.
method Introducing new knotoid types, extending bracket polynomials.
result Universal bracket polynomials for annular and toroidal knotoids.
MEBoost improves classification of imbalanced datasets by mixing two weak learners.
problem Class imbalance in real datasets.
method Mixing two weak learners with boosting.
result Significant improvement over existing methods on imbalanced datasets.
Paper develops methods for estimating gradients of Finslerian Schrödinger equations.
problem Estimating gradients of Finslerian Schrödinger equations.
method Develops new Laplacian comparison theorem and applies it to Finslerian Schrödinger equation.
result Global and local Li-Yau type gradient estimates for positive solutions.
In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. The presence of ties in the agents' best-response correspondences yields discontinuous payoff functi…
The Orlicz-Brunn-Minkowski theory receives considerable attention recently, and many results in the Lp-Brunn-Minkowski theory have been extended to their Orlicz counterparts. The aim of this paper is to develop Orlicz Lφ affine and geominimal surface areas for single convex body as well as for multiple convex bod…
The paper explores tail diversification in financial markets using entropy and mutual information.
problem Tail diversification in financial time series.
method Statistical independence through differential entropy and mutual information, using moments as contrast functions.
result Tail covariance matrix is a key driver of tail diversification.
Codebook for Institutional Grammar 2.0 simplifies policy encoding.
problem Facilitating consistent policy encoding for diverse analytical needs.
method Revised Institutional Grammar with multiple levels of expressiveness.
result Enhanced flexibility and specificity in policy encoding.
New algorithm discovers causal relationships in complex data.
problem Discovering causal relationships in data with cycles, latent confounders, and non-linearities.
method Introducing σ-connection graphs and extending σ-separation to handle these complexities.
result First algorithm capable of handling non-linear, cyclic, and latent confounders.
Flow on weighted graphs sharpens Bakry-Émery curvature.
problem Sharp curvature in weighted graphs.
method Bakry-Émery curvature flow on mixed weighted graphs.
result Limits of curvature flow are curvature sharp.
New general volume concept solves Minkowski problem for star bodies.
problem Minkowski problem for star bodies
method General volume concept, new curvature measure, variational formulas, Minkowski-type inequality
result Solution to the Minkowski problem for the new general dual Orlicz curvature measure
HOUDINI learns algorithms across domains using program synthesis.
problem Lifelong learning of algorithmic tasks mixing perception and reasoning.
method Combining gradient descent with combinatorial search over programs.
result HOUDINI transfers high-level concepts more effectively than traditional methods.
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
Introduces GANGs to model GANs as games, solving them with RB-NE.
problem Training difficulties in GANs.
method Explicitly models GANs as a zero-sum game between generator and classifier using mixed strategies, defines resource-bounded best responses and Nash Equilibrium.
result Solves GANGs with RB-NE, demonstrating better performance than standard GANs.
DCMIX learns channel importance for high content imaging.
problem Lack of channel importance information in deep learning-based image analysis.
method Image blending concepts with alpha compositing for arbitrary channels.
result DCMIX learns biologically relevant channel importance without sacrificing prediction performance.
DRNets combine deep learning and reasoning for complex tasks.
problem Solving complex tasks, especially in scientific discovery, with limited supervision.
method DRNets integrate logic and neural network optimization to encode structured latent spaces constrained by prior knowledge.
result DRNets outperform state-of-the-art models in scientific discovery tasks, recovering more precise crystal structures.
Mixed-SCORE+ improves community detection in weak signal networks.
problem Detecting communities in weak signal networks.
method Proposes Mixed-SCORE+ combining properties of Mixed-SCORE and SCORE+.
result Significantly improves detection error rates on Polblogs and weak signal networks.
In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …
Study develops a data-based model for in-cylinder pressure and cyclic variations in RCCI engines.
problem Lack of models capturing cyclic variations in combustion concepts like RCCI.
method Combines Principle Component Decomposition and Gaussian Process Regression.
result Model predicts combustion measures with high accuracy, especially peak-pressure rise-rate.
The paper explores knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
problem The study of knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
method Introducing new knotoid and braidoid concepts, isotopy theorems, state sum formulas, and Alexander and Markov theorems.
result Formulation and proof of Alexander and Markov theorems for mixed knotoids and mixed pseudo knotoids.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
problem Mixed memberships in community detection.
method Spectral clustering on symmetrized Laplacian inverse matrix.
result Mixed-SLIM methods outperform state-of-the-art methods.
Mixing endomorphisms found on toroidal groups and their products.
problem Finding topologically mixing endomorphisms on toroidal groups and their products.
method Analyzing continuous endomorphisms on toroidal groups and their countable products.
result Proves existence of infinitely many topologically mixing endomorphisms on countable infinite toroidal groups.
New mixed-platonic 3-manifolds from different polyhedra types.
problem Finding new hyperbolic knot complements with hidden symmetries.
method Defined mixed-platonic 3-manifolds and studied their properties.
result No mixed-platonic hyperbolic knot complement has hidden symmetries.
The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the β-mixing rate based on a single stationary sample…
Constructs mixed Hodge structures on Kähler manifolds.
problem Real variations of mixed Hodge structures over compact Kähler manifolds.
method Using Sullivan's 1-minimal models of differential graded algebras associated with real variations of Hodge structures.
result Constructs real variations of mixed Hodge structures.
Mix-IRLS solves imbalanced mixed linear regression problems efficiently.
problem Imbalanced mixed linear regression problems.
method Sequential robust regression approach.
result Mix-IRLS outperforms other methods on imbalanced mixtures and real-world datasets.