Develops new classifiers using proximity catch digraphs for better class imbalance handling.
problem Class imbalance in classification problems.
method Constructs semi-parametric classifiers using random geometric digraphs called proximity catch digraphs (PCDs).
result PE-PCDs find exact minimum dominating sets in polynomial time, leading to efficient classifiers.
This paper shows GNNs can learn good approximations for graph problems.
problem Learning good approximations for combinatorial graph problems.
method Developed new GNNs and bridged GNN theory with distributed local algorithms.
result Most powerful GNNs can learn approximations for minimum dominating set and vertex cover problems with specific ratios.
Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.
problem Understanding max- and min-stability in stochastic dominance.
method Representation theorem for functionals satisfying max-stability, combining max- and min-stability to define Lambda-quantiles.
result New characterizations of functionals, including Lambda-quantiles, in finance and political science.
New EI strategies using OWA and SSD for excess return.
problem Selecting EI portfolios that stochastically dominate a benchmark.
method Proposes a new OWA-based EI model and introduces a new SSD criterion.
result OWA-based EI portfolios stochastically dominate a benchmark and generate excess return.
Adding random features to GNNs improves their performance.
problem Limitations of GNNs in distinguishing graphs and learning efficient algorithms.
method Adding random features to each node in GNNs.
result Random features enable GNNs to learn optimal algorithms for graph problems.
In a system containing a large number of interacting stochastic processes, there will typically be many non-zero correlation coefficients. This makes it difficult to either visualize the system's inter-dependencies, or identify its dominant elements. Such a situation arises in Foreign Exchange (FX) which is the world's…
Connected domination numbers found for plane triangulations up to 13 vertices.
problem Finding connected domination numbers for plane triangulations.
method Analyzing triangulations of up to 13 vertices and proving the difference between connected and regular domination numbers can be arbitrarily large.
result Connected domination numbers for triangulations up to 13 vertices and upper bound for larger triangulations.
There is intense interest in understanding the stochastic and dynamical properties of the global Foreign Exchange (FX) market, whose daily transactions exceed one trillion US dollars. This is a formidable task since the FX market is characterized by a web of fluctuating exchange rates, with subtle inter-dependencies wh…
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
Paper improves deep neural networks' generalization by focusing on margin distribution complexity.
problem Improving deep neural networks' generalization performance.
method Proves a generalization upper bound based on margin distribution statistics and optimizes a convex margin distribution loss function.
result Optimizing the ratio of margin standard deviation to expected margin enhances generalization performance.
The paper explores arbitrage opportunities in derivative markets under specific conditions.
problem Arbitrage opportunities in derivative markets under different conditions.
method Analyzes the relationship between pricing kernel monotonicity and stochastic arbitrage opportunities.
result Pricing kernel nonmonotonicity is equivalent to stochastic arbitrage opportunities under adequacy.
We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, t…
This paper proposes a new clustering method based on Stochastic Dominance for asset allocation.
problem Traditional clustering methods fail to capture risk dominance relationships among assets.
method Integrates Stochastic Dominance theory with machine learning algorithms to construct a Stochastic Dominance Coefficient Matrix and modify clustering algorithms.
result The proposed method effectively facilitates customized asset allocation for investors.
Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.
problem Optimizing Dominant Set Clustering with various Frank-Wolfe algorithms.
method Unified framework for pairwise, standard, and away-steps Frank-Wolfe algorithms, with explicit convergence rates.
result Explicit convergence rates for Frank-Wolfe methods in Dominant Set Clustering.
This paper uses PCA and FA for feature selection in credit rating.
problem Selecting important features for credit rating prediction.
method Principal Component Analysis and Factor Analysis.
result Factor Analysis reduces feature set significantly without losing much accuracy.
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.
This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) semi-Lagrangian discretization schemes applied to the HJBQVI proble…
Proves rigidity for specific initial data sets under the dominant energy condition.
problem Rigidity of initial data sets with boundary and convex polytopes.
method Solution of boundary value problems for Dirac operators and approximations by manifolds with smooth boundary.
result Proves rigidity for compact smooth spin manifolds and convex polytopes under the dominant energy condition.
We refine Expected Shortfall by controlling different tail portions, offering tailored risk assessments.
problem Risk assessment in financial positions, especially in tail regions.
method Introducing adjusted Expected Shortfall measures that control different tail portions.
result Adjusted Expected Shortfall measures ensure risk does not exceed specified thresholds for various probability levels.
Modified constraint operator for localized deformation with dominant energy condition.
problem Handling localized deformation with initial data sets under the dominant energy condition.
method Introduced a modified constraint operator to absorb metric changes and established local surjectivity theorem.
result Promoted dominant energy condition to strict inequality through compactly supported variations.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
New homology theory connects graph domination to subtle algebraic structures.
problem Understanding graph domination through algebraic homology.
method Interpreting überhomology as poset homology and showing its functorial properties.
result The Euler characteristic of bold homology equals the evaluation of the connected domination polynomial.
Develops tests for Markowitz stochastic dominance spanning using saddle points.
problem Determining if adding securities or relaxing investment constraints improves investment opportunity sets.
method Derives properties of cdfs, defines Markowitz stochastic dominance spanning, constructs non-parametric tests based on subsampling.
result Rejects market portfolio Markowitz efficiency and finds evidence of outperformance.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
The paper analyzes Nordic stock markets' correlation structures and regime shifts.
problem Understanding and exploiting regime shifts in Nordic stock markets.
method Examined two decades of daily data for OMXS30, OMXC20, and OMXH25 universes; proposed an adaptive portfolio allocation framework.
result Documented pronounced regime dependence in rolling correlation matrices; proposed an adaptive portfolio allocation framework.
New insights into Bartnik mass from improvability of dominant energy scalar.
problem Characterizing Bartnik mass minimizing initial data sets.
method Introducing improvability concept, proving non-improvability consequences, and analyzing pp-wave counterexamples.
result Bartnik mass minimizing initial data sets are characterized, advancing conjectures.
Odd-dimensional manifolds have contact maps of non-zero degree.
problem Contact domination in odd-dimensional manifolds.
method Proving existence of maps from tight contact manifolds.
result Existence of non-zero degree maps from Liouville-fillable but not Weinstein-fillable contact manifolds.
New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
The paper optimizes portfolios by selecting financial ratios via PCA for better value investment.
problem Embedding value investment in portfolio optimization models.
method Principal Component Analysis (PCA) to filter out dominant financial ratios, then applying portfolio optimization model with second-order stochastic dominance criteria.
result PCA-SPO(B) strategy outperforms other models in terms of downside deviation, CVaR, VaR, Sortino, Rachev, and STARR ratios.
Smooth dec initial data sets may not extend to smooth spacetimes.
problem Whether every dec initial data set can be extended to a smooth spacetime.
method Examined the converse of the dominant energy condition for initial data sets and spacelike hypersurfaces.
result Not all dec initial data sets can be extended to smooth spacetimes.
Characterizes causal structure dominance for latent variables.
problem Determining dominance relations between causal structures with latent variables.
method Complete characterization for three visible variables, partial for four; uses nontrivial inequality constraints.
result Equivalence classes with nontrivial inequality constraints become ubiquitous as the number of visible variables increases.
Proves density and mass theorems for specific initial data sets.
problem Initial data sets with boundary in spacetime.
method Harmonic asymptotics and dominant energy condition.
result Spacetime positive mass theorem for initial data sets with apparent horizon boundary.
Paper proposes a new method to compare classifiers across multiple datasets.
problem Comparing classifiers over multiple datasets with multiple criteria.
method Adopting decision theory, the paper introduces generalized stochastic dominance for ranking classifiers.
result Generalized stochastic dominance can be used to rank classifiers and statistically tested.
The paper finds minimum Dehn colors for knots and defines useful graphs for coloring.
problem Finding the minimum number of colors for Dehn colorings of knots.
method Analyzes Dehn colorings for knots and defines R-palette graphs. result For Dehn p-colorable knots, the minimum number of colors is at least ⌊log2pfloor+2. The Bethe free energy approximation is reliable when convex on a submanifold, the 'Bethe box'.
problem Accuracy of the Bethe free energy approximation in probabilistic inference.
method Analysis of convexity and verification conditions based on the Bethe Hessian matrix.
result The Bethe approximation is mostly accurate if it is convex on a submanifold, the 'Bethe box'.
SharedRep-RLHF learns shared traits for diverse groups, improving fairness and performance.
problem Uniform-reward RLHF fails to capture diverse preferences, leading to unfairness.
method SharedRep-RLHF learns shared traits among various groups, improving fairness and performance.
result SharedRep-RLHF outperforms MaxMin-RLHF by up to 20% in win rate.
Efficient adjustment sets found for cost-minimized causal estimations.
problem Estimating interventional means with minimum cost in causal graphical models.
method Defined cost-adjustment sets, constructed flow networks, and used maximum flow algorithms.
result Minimum cost optimal adjustment sets exist and can be found efficiently.
HICODE detects hidden communities in social networks.
problem Weak, natural communities hidden within strong, dominant communities.
method HICODE (HIdden COmmunity DEtection) that identifies both hidden and dominant communities.
result HICODE outperforms state-of-the-art methods in uncovering both hidden and dominant communities.
New proof shows equality in spacetime mass theorem.
problem Proving the equality case of spacetime positive mass theorem.
method Uses a new approach requiring only E≥∣P∣ for near initial data sets. result Initial data sets with null ADM energy-momentum must embed into Minkowski space.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.
Optimizes minimum-volume prediction sets for multivariate regression.
problem Lack of efficient methods for multivariate conformal prediction.
method Optimization-driven framework for minimum-volume covering sets.
result Efficient and informative prediction sets with tight coverage.
This note removes technical assumptions and characterizes relatively dominated representations.
problem Geometrically finiteness and Anosov conditions in higher-rank settings.
method Characterization using eigenvalue gaps and limit maps.
result Relatively dominated representations are characterized using eigenvalue gaps and limit maps.
Efficiently estimate Gaussian copulas' tail expectations using novel estimators.
problem Estimating expectations over constrained sets in Gaussian copulas' tails.
method Proposes three estimators based on identifying dominating points and scaling exponential distributions.
result Developed estimators achieve bounded relative error in Gaussian settings and polynomial efficiency in NORTA settings.
The positive energy theorem is proven for certain spacetimes with irregular curvature.
problem Proving the positive energy theorem for spacetimes with irregular curvature.
method Weak asymptotically anti-de Sitter initial data sets with distributional curvature under weak dominant energy condition.
result Positive energy theorem established for weakly irregular spacetimes.
New methods incorporate alpha signals into portfolio construction, improving performance.
problem Signal-blindness in existing portfolio construction methods.
method Introduces three methods: HRP-μ, HRP-Σμ, and CRISP. result CRISP at intermediate γ consistently outperforms other methods. The paper calculates extreme measures in continuous time conic finance.
problem Determining valuation bounds for financial claims.
method Using dynamic spectral risk measures and estimating extreme measures from market data.
result Explicit formulas for extreme measures' Radon-Nykodim derivatives and estimation methods.
Parameter-free clustering method using cluster catch digraphs (CCDs).
problem Finding the correct number of clusters in data without specifying a parameter.
method Hybrid of density-based and graph-based clustering methods using Ripley's K function.
result Minimum dominating sets of RK-CCDs estimate and distinguish clusters from noise.