Deep learning enhances business analytics and operations research performance.
problem Scarcity of deep learning research in business analytics and operations research.
method Review and analysis of existing literature, computational experiments, case studies.
result Deep neural networks improve operational performance in business analytics and operations research.
New framework uses OR to ensure AI systems make safe decisions.
problem Ensuring generative AI systems make safe decisions as they gain autonomy.
method Developed a conceptual framework combining flow-based models and adversarial robustness.
result Increased autonomy requires new OR approaches for feasibility, robustness, and stress testing.
This study explores the index theory of Heisenberg elliptic and transversally Heisenberg elliptic operators using K K KK K K -theory.
problem Analyzing the index theory of Heisenberg elliptic and transversally Heisenberg elliptic operators.
method Applying Kasparov's methodology and examining specific conditions using Fourier transform of the nilpotent group C ∗ C^* C ∗ -algebra. result Demonstrated enhanced methods for analyzing hypoellipticity and defined transversal Heisenberg ellipticity in a K K KK K K -theoretic context. Paper uses replica analysis to optimize net present value in investment portfolios.
problem Maximizing net present value in portfolios of multiple development projects.
method Replica analysis applied to optimization problem with budget and investment constraints.
result Replica analysis yields higher net present value than conventional methods.
Researchers create a family of conformally covariant operators.
problem Developing a comprehensive set of conformally covariant operators.
method Constructing a family of conformally covariant tridifferential operators as tangential operators in the Fefferman--Graham ambient space.
result Symmetrization of ambient operators is formally self-adjoint.
Researchers develop weighted GJMS operators for smooth metric measure spaces.
problem Developing mathematical tools for smooth metric measure spaces.
method Constructing and proving formal self-adjointness of weighted GJMS operators.
result Formal self-adjointness of weighted GJMS operators proved.
The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other…
We enhance autonomous materials research with problem-aware models.
problem Complex decision-making in autonomous materials.
method Bayesian framework, machine learning, physics-based models, operational considerations.
result Improved models reflect problem-specific structure.
Enhances construction input modeling with Bayesian deep neural networks.
problem Deriving reliable simulation input models from construction data.
method Bayesian deep neural networks integrated with multi-source construction data.
result Derives detailed input models for construction operations.
Paper uses LightGBM for mobile user credit assessment.
problem Improving credit evaluation methods for communication operators.
method Data preprocessing, feature engineering, multiple machine learning models integration.
result Established a suitable fusion model for operator user credit evaluation.
Researchers create new operators from Riemannian invariants.
problem Developing new mathematical tools for Riemannian geometry.
method Introducing formally self-adjoint conformally covariant polydifferential operators.
result Found a fourth-order, conformally covariant tridifferential operator.
This research develops approximation theory for OOMs of infinite-dimensional processes.
problem Developing an approximation theory for OOMs of infinite-dimensional processes.
method Establishing an inner product structure and proving continuity of observable operators.
result A fundamental obstacle in making an infinite-dimensional space of future distributions into a Hilbert space is described.
MIOpen optimizes deep learning operators for GPUs, accelerating research.
problem Optimizing deep learning operators for efficient GPU execution.
method Highly optimized implementations, fusion, auto-tuning, bfloat16 support.
result Accelerates time to discovery in deep learning research.
Researchers describe local properties of Haantjes operators.
problem Understanding Haantjes operators with vanishing torsion.
method Complete local description of gl-regular Haantjes operators.
result Complete local description of gl-regular Haantjes operators.
These notes were originally written for the Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, in February of 2011. The seminar was attended and supported by members of the Research Training Group, with the author being partially supported by NSF gran…
In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always resu…
QRAFTI uses multi-agent framework to improve equity factor research.
problem Replicating and developing new equity factors in large financial datasets.
method Integrates a research toolkit with MCP servers for data access and custom coding operations.
result Improves performance and explainability in multi-step empirical tasks.
Researchers find higher symmetries in symplectic Dirac operator.
problem Understanding symmetries in symplectic Dirac operator.
method Constructing higher symmetry algebra of symplectic Dirac operator D a i s e 0.22 e x / s {D}\kern-0.5em
aise0.22ex\hbox{/}_s D ai se 0.22 e x / s . result Higher symmetry algebra structure corresponds to a completely prime primitive ideal.
Researchers use symplectic Dirac operator to study projective structure and its symmetries.
problem Understanding symmetries in projective structure and spinor fields.
method Realized symplectic spinor fields and operator in homogeneous projective structure framework.
result Symplectic Dirac operator's symmetry group is S L ~ ( 3 , R ) \widetilde{\mathrm{SL}}(3,{\mathbb R}) SL ( 3 , R ) . Researchers create a parametrix for resolvents on manifolds with ends.
problem Essential self-adjointness of elliptic symmetric differential operators on manifolds with ends.
method Introduced semiclasical pseudodifferential operators compatible with the end structure.
result Essential self-adjointness of elliptic symmetric differential operators proved.
Researchers solve Yamabe problems for specific operators, finding both uniqueness and nonuniqueness.
problem Prescribing scalar, Q-, or σ₂-curvatures in conformal classes.
method Formally self-adjoint, conformally covariant, polydifferential operators.
result Uniqueness results on the sphere, nonuniqueness in general.
The paper proposes a fast method to predict tactical solutions to operational problems under imperfect information.
problem Predicting tactical solutions to operational planning problems under imperfect information.
method Formulated as a two-stage optimal prediction stochastic program, solved with a supervised machine learning algorithm using training data from deterministic problems.
result Deep learning algorithms produce highly accurate predictions in very short computing time (milliseconds or less).
Paper proposes a method to quantify and explain machine learning uncertainty in predictive process monitoring.
problem Neglect of data-driven estimation, point forecasts without model uncertainty, and lack of explanations.
method Quantile Regression Forests for interval predictions and SHapley Additive Explanations for uncertainty.
result Effective handling of model uncertainty in predictive process monitoring.
Research resolves sign conventions in Floer theory for Morse-Bott case.
problem Sign conventions in filtered A ∞ A_{\infty} A ∞ -operations for Lagrangian Floer theory. method Defined filtered A ∞ A_{\infty} A ∞ -operations and verified formulae using de Rham model. result Resolved sign issues in Bott-Morse setting.
Researchers classify invariant operators on weighted densities.
problem Classifying invariant differential operators on weighted densities.
method Investigated the a f f ( n ∣ 1 ) \mathfrak{aff}(n|1) aff ( n ∣1 ) -module structure and invariant binary differential operators. result Computed the first a f f ( n ∣ 1 ) − \mathfrak{aff}(n|1)- aff ( n ∣1 ) − relative differential cohomology. Neural networks enhance linear programming for complex decision-making problems.
problem High-dimensional and combinatorial operations research problems.
method Hybrid solution method combining linear programming and neural networks.
result Neural network value function approximations outperform polynomial approximations in a transportation problem.
Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.
problem Understanding spectral asymmetry for the massless Dirac operator.
method Constructing a negative order pseudodifferential asymmetry operator from spectral projections.
result Computed the principal symbol of the asymmetry operator, accounting for gauge invariance.
Researchers solve the Calderón problem for fractional Dirac operators.
problem Determining the metric and structure from boundary measurements.
method Analyzing the fractional Dirac operator on vector bundles.
result The Calderón problem is solved uniquely for the fractional Dirac operator.
Researchers found explicit solutions to a complex equation in advanced geometry.
problem Critical Yamabe type equation in sub-Finsler geometry.
method Computed a two-parameter family of explicit positive solutions.
result Explicit solutions to a critical equation in sub-Finsler geometry.
Researchers construct an index map for contact manifolds using K-theory.
problem Constructing an index for maximally hypoelliptic operators on contact manifolds.
method Using Higson's construction for symbol class in K-theory, they derive a series of maps whose induced map in K-theory is the Heisenberg Atiyah-Singer index map.
result Explicit construction of a series of maps leading to the Heisenberg Atiyah-Singer index map.
Koopman operator theory simplifies complex systems analysis.
problem Analyzing nonlinear dynamical systems and complex networks.
method Estimating Koopman operator from data to reveal system properties.
result Koopman operators provide insights into system characteristics.
Researchers factorize Dirac operators on Riemannian submersions.
problem Understanding factorization of Dirac operators on submersions.
method Factorization of Dirac operators using Riemannian submersions and unbounded KK-theory.
result The Dirac operator on the total space is unitarily equivalent to a tensor sum of operators on the base and fibers.
Researchers derive symmetry operators from twistor spinors in curved spacetime.
problem Deriving symmetry operators for gauged twistor spinors in curved backgrounds.
method Using gauged twistor spinors and conformal Killing-Yano forms, symmetry operators are constructed.
result Symmetry operators can be obtained from ordinary twistor spinors in constant curvature backgrounds.
New RL method improves on standard discounted RL for operations research.
problem Applying RL to operations research problems, especially with non-zero rewards.
method Near-Blackwell-optimal RL algorithm that assesses average reward per step.
result Proves viability on challenging queuing system problems.
Researchers add random metrics to data models to enable operations.
problem Lack of meaningful operations in learned low-dimensional representations.
method Endow latent space of generative models with a random Riemannian metric.
result Derived tight error bounds on expected distances in deterministic approximations.
Researchers prove index invariance under cobordism for Callias-type operators.
problem Index calculation for elliptic operators on compact manifolds.
method Introduce cobordism of Callias-type operators and prove index invariance.
result Index is preserved by cobordism of Callias-type operators.
This paper is a mixture of expository material and current research material. Among new results are examples of generalised harmonic spinors and their gauged version, the generalised Seiberg-Witten equations.
The volume of steady-state solutions in economic models is studied.
problem Understanding the fragility of economic circuits.
method Represented as a CSP, volume computed using operations research and metabolic network methods.
result Volume depends on constraints and reveals potential economic fragility.
This paper studies gl-regular Nijenhuis operators and their properties.
problem Characterizing and understanding gl-regular Nijenhuis operators.
method Analyzing the properties of gl-regular Nijenhuis operators and proving their existence in a coordinate system.
result Discoveries of normal forms for singular points and topological restrictions for gl-regular Nijenhuis operators on closed surfaces.
Researchers compute a residue cocycle for Dirac-type operators using modified Getzler calculus.
problem Computing the residue cocycle for Dirac-type operators.
method Modified Getzler calculus for computation.
result Computed residue cocycle for a class of Dirac-type operators.
Data mining methods have been widely applied in financial markets, with the purpose of providing suitable tools for prices forecasting and automatic trading. Particularly, learning methods aim to identify patterns in time series and, based on such patterns, to recommend buy/sell operations. The objective of this work i…
Paper tackles real-world e-commerce search efficiency and user experience.
problem Efficiently rank large-scale e-commerce search results with multiple factors.
method Design and deploy a novel Cascade ranking model in a large-scale operational e-commerce search application.
result Demonstrates the advantage of the proposed model in addressing multiple factors of effectiveness, efficiency, and user experience.
The paper proposes a fast method to predict operational solutions under uncertainty.
problem Predicting tactical descriptions of operational solutions in two-stage stochastic programming.
method Formulated as a stochastic optimal prediction program, solved with supervised machine learning.
result Deep learning models produce accurate predictions in milliseconds, close to lower bounds.
Researchers create compatibility complexes for Einstein metrics.
problem Constructing solutions to the conformal-to-Einstein operator.
method Using a method that leverages symmetries and geometric properties.
result At most one independent solution exists under genericity assumptions.
Researchers transform equations and define integral operators on a ball.
problem Transforming equations from half space to ball.
method Identify Poisson kernel, define extension operator, prove inequalities.
result Uniqueness of extremal functions in limit case.
Researchers develop neural networks for approximating functions in Banach spaces.
problem Approximating Banach space valued continuous functions.
method Quasi-interpolation Banach space valued neural network operators using algebraic sigmoid functions.
result Jackson type inequalities for function approximation.
Researchers classify differential operators between 3-sphere and 2-sphere bundles.
problem Classifying differential symmetry breaking operators between 3-sphere and 2-sphere bundles.
method Constructing and classifying all differential symmetry breaking operators D_{λ,ν}^m.
result Necessary and sufficient conditions for the existence of these operators.
Researchers compute heat kernel coefficients for 2D diffusion operators.
problem Analyzing heat kernel coefficients for 2D hypoelliptic operators.
method Explicit computation of heat kernel coefficients and interpretation in terms of curvature.
result Interpretation of heat kernel asymptotics for non-sub-Riemannian operators.