This article examines five common misunderstandings about case-study research: (1) Theoretical knowledge is more valuable than practical knowledge; (2) One cannot generalize from a single case, therefore the single case study cannot contribute to scientific development; (3) The case study is most useful for generating …
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48 results for “Case Studies”
GenAI improves actuarial practices through case studies.
problem Improving actuarial practices using AI.
method Four case studies using LLMs, Retrieval-Augmented Generation, and vision-enabled LLMs.
result GenAI enhances claim cost prediction, market comparisons, and car damage classification.
Study evaluates and compares numerical differentiation methods on three case studies.
problem Evaluating and comparing numerical differentiation methods for efficiency.
method Forward, Backward, and Centered Finite-Difference methods applied at two levels of precision.
result Different methods perform differently across case studies, with varying levels of computational cost and accuracy.
Statistical inference for case-control logistic regression via integrating external summary datastat.ME
A method for logistic regression inference using both internal and external data.
problem Inability to estimate intercept and marginal case proportion in case-control logistic regression.
method Empirical likelihood approach integrating internal and external data.
result Intercept parameter becomes identifiable with external information, and all parameters are estimable consistently.
Investigation of the Estimation Accuracy of 5 Different Numerical ODE Solvers on 3 Case Studiesmath.NA
Study compares 5 ODE solvers on 3 case studies, finding varying accuracy.
problem Comparing estimation accuracy of 5 ODE solvers on 3 case studies.
method Used 5 different numerical ODE solvers (Euler's, Heun's, Midpoint, Runge-Kutta 4th order, ODE45) on 3 case studies and compared their results.
result Different solvers have varying accuracy depending on the case study.
Study on gradient Ricci solitons with isoparametric potential functions.
problem Characterizing gradient Ricci solitons with isoparametric potential functions.
method Analyzes complete gradient Ricci solitons with isoparametric potential functions, proving theorems for steady and shrinking cases.
result Critical level sets of codimension greater than one for steady case, partial results for shrinking case.
Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.
problem Understanding extreme-case risk measures under distributional ambiguity and increasing failure rate.
method Characterized extreme-case range Value-at-Risk under mean and variance constraints with increasing failure rate.
result Characterized specific characteristics of extreme-case distributions under IFR constraints.
Analysis of different Mathematical Models for Different Case Studies Using Statistical Fittingmath.DG
Study evaluates different mathematical models for three case studies using statistical fitting.
problem Estimating outcomes in population dynamics, temperature variations, and market equilibrium.
method Applied various statistical equations (e.g., fractional exponential, sinusoidal) to three case studies.
result Optimal models differ by case study (fractional exponential for population dynamics, sinusoidal for temperature and market equilibrium).
Study pseudo-holomorphic disks in real analytic hypersurfaces using exterior differential systems.
problem Existence of pseudo-holomorphic disks in non-integrable real analytic hypersurfaces.
method Theory of exterior differential systems.
result Non-existence of certain equivalent structures in the non-integrable case.
The application of equivalence method to classify Monge-Ampère system leads to three orbits, parabolic case, hyperbolic case and elliptic case wich correspond to three types of Monge-Ampère systems. In this paper we will study the elliptic case and give a presentation of the group as a complex group.
Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.
The study assesses external validity by evaluating worst-case treatment effects across subpopulations.
problem Underrepresentation of marginalized groups and limited study populations.
method Develops a semiparametrically efficient estimator for worst-case treatment effects (WTE) and uses cross-fitting to guard against brittle findings.
result The proposed framework guards against invalid findings due to unanticipated population shifts.
Clustering methods based on deep neural networks have proven promising for clustering real-world data because of their high representational power. In this paper, we propose a systematic taxonomy of clustering methods that utilize deep neural networks. We base our taxonomy on a comprehensive review of recent work and v…
We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable fundamental group.
Case study shows impact of co-optimizing energy and reserve for wind energy.
problem Impact of lack of co-optimization of energy and reserve in high wind penetration scenarios.
method Developed two models with and without co-optimization, calibrated with Spanish market parameters.
result Models show significant differences in energy and reserve management.
Study identifies and measures biases in legal case data.
problem Addressing representation biases and sentencing disparities in legal case data.
method Utilizes two regression models: a baseline and a fair judge model.
result Quantifies biases across demographic groups in criminal data from Cook County (Illinois).
Case Law has a significant impact on the proceedings of legal cases. Therefore, the information that can be obtained from previous court cases is valuable to lawyers and other legal officials when performing their duties. This paper describes a methodology of applying discourse relations between sentences when processi…
The paper studies magnetic geodesic flows on 2-surfaces with integrable structures.
problem Analyzing magnetic geodesic flows on 2-surfaces with additional integrals.
method Constructing exact solutions to semi-Hamiltonian systems of PDEs using generalized hodograph method and Legendre transformation.
result Exact solutions constructed for semi-Hamiltonian systems of PDEs.
Corner manifoldsmath.DG
Extends corner structure study to general case, constructs normal Trans-Sasakian structures.
problem Extending corner structure study to general case without conditions.
method Extends corner structure to general case, constructs Trans-Sasakian structures from non-normal corner structures.
result Constructs normal Trans-Sasakian structures from non-normal corner structures.
The topology of Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)math.DG
Study topological properties of integrable case on Lie algebra so(4).
problem Topological analysis of integrable case for Euler's equations on so(4).
method Construction of bifurcation diagrams, determination of critical points, description of Liouville tori bifurcations, computation of loop molecules.
result Some topological properties of Kovalevskaya case can be derived from the case on so(4).
Study of degenerate contrast functions on Lie groupoids and their geometric structures.
problem Understanding geometric structures on Lie groupoids with degenerate metrics.
method Using Lie groupoids and algebroids, analyze contrast functions and degenerate two-forms.
result Reduction of degenerate two-forms to pseudometric structures under regular conditions.
Study spectral properties of sub-Riemannian Laplacians, proving quantum ergodicity and heat kernel asymptotics.
problem Spectral properties of sub-Riemannian Laplacians.
method Quantum ergodicity results, small-time asymptotics of sub-Riemannian heat kernels, Weyl law.
result Weyl law and spectral concentration on Lie brackets of length r-1.
Study examines noncompact cases of Gauss Curvature Flow on revolution surfaces.
problem Noncompact cases of Gauss Curvature Flow on revolution surfaces.
method Examines two noncompact cases of Gauss Curvature Flow on revolution surfaces.
result Examines noncompact cases of Gauss Curvature Flow on revolution surfaces.
We study many properties concerning weak Kählerianity on compact complex manifolds which admits a holomorphic submersion onto a Kähler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the Kähler case), Michelson (the balanced case), Popovici (the sG case) and others.
Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea & Leobacher (2017)]. Supermixed fractals constitute a significant generalisation of mixed l…
The causal assumptions, the study design and the data are the elements required for scientific inference in empirical research. The research is adequately communicated only if all of these elements and their relations are described precisely. Causal models with design describe the study design and the missing data mech…
Complex-valued (p,q)-harmonic morphisms defined and studied.
problem Defining and studying (p,q)-harmonic morphisms between Riemannian manifolds.
method Introducing and characterizing complex-valued (p,q)-harmonic morphisms.
result Characterization and new non-trivial examples of complex-valued (p,q)-harmonic morphisms.
Study probabilistic category and complexity bounds, comparing with classical invariants.
problem Bounding classical category and complexity in probabilistic settings.
method Probabilistic Lusternik-Schnirelmann category and topological complexity computations.
result Established a universal upper bound in finite cases, contrasting with classical invariants.
We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally to the study of the case of foliations with singularities. A first extension theo…
It's easy to fool yourself: Case studies on identifying bias and confounding in bio-medical datasetscs.LG
Confounding variables are a well known source of nuisance in biomedical studies. They present an even greater challenge when we combine them with black-box machine learning techniques that operate on raw data. This work presents two case studies. In one, we discovered biases arising from systematic errors in the data g…
Generalized (κ,μ)-space forms are introduced and studied. We examine in depth the contact metric case and present examples for all possible dimensions. We also analyse the trans-Sasakian case.
Study extends holomorphic forms on noncompact Kahler manifolds.
problem Extension of holomorphic canonical forms on noncompact Kahler manifolds.
method L2 analytic methods and L2 Hodge theory.
result Generalizes classical results to noncompact cases.
This paper provides a study of algebraic Ricci solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous algebraic Ricci solitons are expanding algebraic Ricci solitons. In this paper, we obtain a steady algebraic Ricci soliton and a shrinking algebraic Ricci soliton in the Lorentzian s…
Study null energy condition impacts on special hypersurfaces in static spacetimes.
problem Effects of null energy condition on totally umbilic hypersurfaces.
method Characterization of embedded surfaces and photon surfaces using Alexandrov Theorem and other methods.
result Full characterization of embedded surfaces with constant spacetime mean curvature.
Study phase transitions in shuffled regression problems.
problem Phase transitions in shuffled regression problems.
method Transformed permutation recovery into probabilistic graphical model, used message passing (MP) algorithm and branching random walk process.
result Characterized impact of signal-to-noise-ratio ($\snr$) on permutation recovery, proposed Gaussian approximation method.
We analyze degenerate homogeneous structures of linear type in the pseudo-Kähler and para-Kähler cases. The local form and the holonomy of pseudo-Kähler or para-Kähler manifolds admitting such structure are obtained. In addition the associated homogeneous models are studied exhibiting their relation with the incomplete…
We propose a simple mathematical model for unemployment. Despite its simpleness, we claim that the model is more realistic and useful than recent models available in the literature. A case study with real data from Portugal supports our claim. An optimal control problem is formulated and solved, which provides some non…
Study evaluates how changes in mobility affect COVID-19 case rates.
problem Mixed evidence on mobility-COVID-19 case rate associations.
method Modified treatment policy (MTP) approach with TMLE and Super Learner ensemble.
result Shifts in mobility do not consistently affect subsequent case rates after adjusting for confounders.
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
Paper improves worst-case regret bounds for RLSVI in reinforcement learning.
problem Minimizing regret in reinforcement learning with randomized value functions.
method Introduces a clipping variant of Thompson Sampling for RLSVI.
result Achieves a worst-case regret bound.
The paper offers a checklist for comparing human and machine visual perception.
problem Comparing human and machine visual perception.
method Designing, conducting, and interpreting experiments to investigate mechanisms.
result Feedback mechanisms may not be necessary for visual reasoning tasks.
In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and decomposable cases we provide a classification. In the nilpotent case, we are able to des…
Study on proper learning under relaxed worst-case robust loss for VC classes.
problem Proper adversarially robust PAC learning under relaxed worst-case robust loss.
method Introduced a family of robust loss relaxations and showed their effectiveness for proper learnability.
result VC classes are properly PAC learnable with sample complexity close to standard PAC learning setup.
We study a variant of decision-theoretic online learning in which the set of experts that are available to Learner can shrink over time. This is a restricted version of the well-studied sleeping experts problem, itself a generalization of the fundamental game of prediction with expert advice. Similar to many works in t…
Study on special warped product manifolds with Einstein metrics.
problem Characterizing Einstein metrics in specific warped product manifolds.
method Derive general formulas and prove existence of solutions for invariant families.
result Existence of families of solutions invariant under transformations for positive constant Ricci curvature.
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these algorithms perform in "typical" scenarios, or how far the best known theoretical…
Study negative scalar curvature metrics with positive boundary mean curvature.
problem Bounding conformal metrics with specific curvature properties.
method Analyzing Riemannian manifolds with boundary conditions.
result A priori boundedness of metrics in specific cases.
Study KMS measures in Poisson geometry, focusing on -Poisson manifolds.
problem Characterize KMS measures in Poisson geometry.
method Generalize symplectic results to -Poisson manifolds.
result Complete characterization of KMS measures on -Poisson manifolds.