Young investors, especially students, dominate Indonesian stock exchanges.
problem Investment behavior of young and rookie investors in the stock market.
method Qualitative approach with descriptive analysis and interviews.
result Perception of behavioral control influences investment decisions.
New method detects asset price bubbles in young markets.
problem Detecting asset price bubbles in young, immature markets.
method Proposed a simple but effective statistical method to capture and quantify bubbles.
result New method applicable to immature markets without sufficient data.
Develops strategies to minimize trading costs in volatile markets.
problem Minimizing trading costs in volatile markets with uncertain asset price paths.
method Constructs dynamic, pathwise optimal trade execution strategies using random Young differential equations.
result Good trade execution strategies minimize trading costs in a pathwise sense, not just expected costs.
We determine the optimal strategies for purchasing term life insurance and for investing in a risky financial market in order to maximize the probability of reaching a bequest goal while consuming from an investment account. We extend Bayraktar and Young (2015) by allowing the individual to purchase term life insurance…
Paper studies Fenchel-Young losses for classifier construction.
problem Creating effective loss functions for classifiers.
method Analyzes Fenchel-Young losses from generalized entropies, formulates conditions for separation margins and sparse support.
result Fenchel-Young losses can induce predictive distributions with separation margins and sparse support.
Conjectures closed-form expressions and cyclotomic expansions for knot invariants.
problem Calculating HOMFLY-PT invariants of knots colored by rectangular diagrams.
method Interpolation Macdonald polynomials and cyclotomic expansions.
result Conjectured closed-form expressions and cyclotomic expansions for knot invariants.
Introduces Fitzpatrick losses, tighter than Fenchel-Young losses.
problem Improving loss functions for machine learning.
method Introduces Fitzpatrick losses based on the Fitzpatrick function.
result Fitzpatrick losses are tighter than Fenchel-Young losses.
Paper introduces Fenchel-Young losses for supervised learning tasks.
problem Choosing the right loss function for supervised learning tasks.
method Introduces Fenchel-Young losses as a generic way to construct convex loss functions.
result Fenchel-Young losses unify and create new loss functions.
Study uses NLP to analyze emotions and challenges of young people with IDD.
problem Challenges faced by young people with IDD during transition to adulthood.
method Natural language processing, unsupervised machine learning, topic modeling.
result NLP methods can assist psychologists in analyzing emotions and summarizing key topics.
Study on price fluctuations in NFT market, showing heavy-tailed distributions and long-range memory.
problem Characterizing price fluctuations in NFT market.
method Analysis of capitalization, floor price, transactions, inter-transaction times, and volume value of NFTs.
result NFT market exhibits heavy-tailed probability distribution functions, well described by stretched exponentials, with long-range memory.
We construct complexes P1n of Soergel bimodules which categorify the Young idempotents corresponding to one-column partitions. A beautiful recent conjecture of Gorsky-Rasmussen relates the Hochschild homology of categorified Young idempotents with the flag Hilbert scheme. We prove this conjecture for P1n an…
We present a novel algorithm, Westfall-Young light, for detecting patterns, such as itemsets and subgraphs, which are statistically significantly enriched in one of two classes. Our method corrects rigorously for multiple hypothesis testing and correlations between patterns through the Westfall-Young permutation proced…
Study identifies clusters of EU countries with similar young mortality patterns.
problem Identify clusters of EU countries with similar mortality patterns in young population.
method Symbolic data analysis (SDA) with age, gender, and main causes of death dimensions.
result Identified clusters of EU countries with similar mortality patterns in young population.
Categorifies a skein relation for links colored by one-column Young diagrams.
problem Categorification of a skein relation for links.
method Homotopy equivalence between two complexes of singular Soergel bimodules.
result Categorification of the colored skein relation.
Extends Young integral to Hölder differential forms in arbitrary dimensions.
problem Extending the Young integral to Hölder differential forms in arbitrary dimensions.
method Introducing a complex of cochains, α-fractional charges, and defining the exterior product between them.
result The exterior product between α-fractional and β-fractional charges is defined when α + β > 1.
Counterexample shows state-constrained optimal control problems can have Young measure gaps.
problem Existence of Young measure gaps in state-constrained optimal control problems.
method Provided a counterexample for smooth controllable systems state-constrained to the unit ball.
result Gap occurs in a regular setting with non-convex Lagrangian density.
For a convex curve in an even-dimensional affine space we introduce a series of convex domains (called Young hulls), describe their structure and give a formulas fo the volume of the biggest of these domains. This paper is an attempt to generalize the classical isoperimetric inequality for the volume of the convex hull…
The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and …
De Rham theorem extended to Orlicz cohomology.
problem Extending de Rham's theorem to a broader class of cohomology.
method Proving isomorphism between de Rham Lφ-cohomology and simplicial ℓφ-cohomology. result Isomorphism between de Rham Lφ-cohomology and simplicial ℓφ-cohomology. Authors conjecture categorically diagonalizable complex for full twists.
problem Categorically diagonalizing the complex of Soergel bimodules for full twists.
method Utilizes categorical diagonalization theory.
result Proves conjecture in type A, categorifies Young idempotents.
New method improves curvature estimates for stable surfaces.
problem Curvature estimates for stable surfaces in Rn+1. method Replacing Young's inequality with Hölder's inequality simplifies and improves curvature estimates.
result The new method yields a strictly smaller constant and a natural extension to CMC settings.
Model predicts cannabis use disorder risk for adolescents and young adults.
problem Predicting cannabis use disorder progression in adolescents and young adults.
method Bayesian machine learning model trained on longitudinal data.
result Model provides personalized risk assessment with AUC of 0.68-0.75 and E/O ratio of 0.95-1.
New method uses FY loss for better inverse optimization.
problem Estimating unknown parameters from noisy and suboptimal solutions.
method Fenchel-Young loss approach for efficient gradient-based optimization.
result Significant improvement in parameter estimation accuracy and computational speed.
HZ transform applied to knot polynomials reveals hyperbolic knot structures.
problem Understanding the structure of knot polynomials and their factorisability.
method Applying the Harer-Zagier transform to knot polynomials and character expansions.
result Construction of an infinite family of hyperbolic knots and proof of factorisability in the 3-strand case.
Gradient descent converges with arbitrary stepsize for separable data under Fenchel-Young losses.
problem Understanding the conditions under which gradient descent converges with arbitrary stepsize.
method Using Fenchel-Young losses and leveraging the classical perceptron argument to derive convergence rates.
result GD converges with arbitrary stepsize for a majority of Fenchel-Young losses, with better rates for specific loss functions.
We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations of the set of natural numbers. The Schur functions form a complete system of com…
This paper develops sparse alternatives to continuous distributions, including new types of Gaussians and attention mechanisms.
problem Creating flexible continuous distributions with varying support for machine learning applications.
method Defining Ω-regularized prediction maps and Fenchel-Young losses for arbitrary domains, and deriving new types of Gaussians and attention mechanisms. result Sparse alternatives to continuous distributions, including deformed exponential families and β-Gaussians, are introduced. New conditions prevent gaps in optimal control problems.
problem Preventing gaps in optimal control problems with state constraints.
method Developed new sufficient conditions not relying on convexity.
result Derived bounds for the size of the relaxation gap.
AR app enhances young children's understanding of Wudhu.
problem Teaching Wudhu to young children is challenging.
method Needs analysis, system design, implementation, testing (Black Box Testing).
result AR technology improves children's learning interest and understanding of Wudhu.
Foundation for robust finance using rough path theory.
problem Mathematical models of financial markets under Knightian uncertainty.
method Introducing Property (RIE) for càdlàg paths, proving existence of rough integrals, verifying admissibility of trading strategies.
result Existence and stability of rough path integrals for non-gradient integrands.
We show that the triply graded Khovanov-Rozansky homology of the torus link Tn,k stablizes as k→∞. We explicitly compute the stable homology (as a ring), which proves a conjecture of Gorsky-Oblomkov-Rasmussen-Shende. To accomplish this, we construct complexes Pn of Soergel bimodules which categorify t…
We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.
problem Establishing linear regret bounds for convex smooth losses.
method Constructing a convex smooth surrogate loss using Fenchel-Young losses generated by the convolutional negentropy.
result We derive a smooth loss with a linear surrogate regret bound.
Study geometric properties of symmetric matrices with repeated eigenvalues.
problem Investigate geometric properties of symmetric matrices with repeated eigenvalues.
method Explicitly compute the volume of the intersection with the sphere and prove an Eckart-Young-Mirsky-type theorem.
result Prove connections to Real Algebraic Geometry and Random Matrix Theory.
Paper proposes new loss functions for training energy networks.
problem Challenges in computing gradients for training energy networks.
method Proposes generalized Fenchel-Young losses for efficient gradient computation.
result Demonstrates the calibration of excess risk for linear-concave energies.
Algorithm calculates stable multiplicities in cohomology of configuration spaces.
problem Computing stable multiplicities of irreducible representations in cohomology.
method Developed an algorithm to compute stable multiplicities of families of irreducible representations.
result Computed stable multiplicities for all Young diagrams with 23 boxes up to degree 50.
The paper calculates colored Jones polynomials for specific link configurations.
problem Computing colored Jones polynomials in general is difficult, but the paper provides explicit formulas.
method Uses Kuperberg's A2 skein relation and one-row Young diagrams. result Derives the sl3 tail of (2,2m)-torus links and false theta series. Geometric integrals of Hölder continuous functions are defined over a 2D domain.
problem Defining integrals for Hölder continuous functions over a 2D domain.
method Summing discrete Stratonovich or Itô type terms over refining partitions.
result Two-dimensional extension of Young integral that coincides with recent integral.
Study on droplet flow on uneven surfaces, proving existence and properties.
problem Understanding droplet movement on irregular surfaces.
method Existence of smooth flow and 1/2-Hölder continuous minimizing movement solutions.
result Properties of minimizing movements including comparison principles and uniform boundedness.
Physics-based method approximates mean curvature on surface meshes.
problem Estimating mean curvature on triangulated surfaces.
method Derives approximation from Young-Laplace equation and force balance.
result Approximation equivalent to discrete Laplace-Beltrami operator.
We compute q-holonomic formulas for the HOMFLY polynomials of 2-bridge links colored with one-column (or one-row) Young diagrams.
New categorified homology expressions for torus knots and links.
problem Computing homology for colored torus knots and links.
method Recursive construction of categorified Young symmetrizers and comparison with row-colored homology.
result Verification of mirror symmetry conjectures for positive torus knots.
For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A.…
We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1)…
When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove …
Math model helps bees decide between winter survival and raising young.
problem Deciding between winter survival and raising young bees in honeybee colonies.
method Mathematical model considering resource geometry around the hive.
result Optimal resource allocation strategy for honeybee colonies.
We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature tensors.
Bayesian network used to analyze young drivers' risky behaviors in Tuscany.
problem Analyzing risky driving behaviors among young drivers in Tuscany.
method Bayesian probabilistic network applied to machine learning analysis of data.
result Bayesian network reveals relationships between young drivers' characteristics and risky behaviors.
Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure.…