arXiv research

Connected domination numbers found for plane triangulations up to 13 vertices.

New homology theory connects graph domination to subtle algebraic structures.

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can als…

The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.

Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.

Odd-dimensional manifolds have contact maps of non-zero degree.

Graphs and their complements are intrinsically knotted.

It is shown in this paper that given any closed oriented hyperbolic 3-manifold, every closed oriented 3-manifold is mapped onto by a finite cover of that manifold via a map of degree 1, or in other words, virtually 1-dominated by that manifold. This improves a known result of virtual 2-domination. The proof invokes a r…

Proves non-existence of certain metrics on specific manifolds.

Study on flat connections with controlled irregularity.

We show that the nonzero roots of the torsion polynomials associated to the infinite cyclic covers of a given compact, connected, orientable 3-manifold M are contained in a compact part of the complex plane a priori determined by M. This result is applied to prove that when M is closed, it dominates at most finitely ma…

New interpretation of Mayer-Vietoris sequence using überhomology.

We prove that every Teichmuller geodesic of a finite type surface contains a string of intersecting long, thick and dominant segments, such that the distance between consecutive segments is bounded. This is key to obtaining some results about Teichmuller geodesics which mimic those for hyperbolic geodesics. These resul…

New concept of relatively dominated representations for higher-rank groups.

Faster WIND accelerates iterative BOND for LLM alignment.

Deep Neural Networks, and specifically fully-connected convolutional neural networks are achieving remarkable results across a wide variety of domains. They have been trained to achieve state-of-the-art performance when applied to problems such as speech recognition, image classification, natural language processing an…

Minimal surfaces connect to horizons and electrostatic systems.

We present the alternative topological twisting of N=4 Yang-Mills, in which the path integral is dominated not by instantons, but by flat connections of the COMPLEXIFIED gauge group. The theory is nontrivial on compact orientable four-manifolds with nonpositive Euler number, which are necessarily not simply connected. …

The paper defines almost strict domination for representations and connects it to anti-de Sitter 3-manifolds.

New method amplifies hidden structure in complex networks.

Finite group actions on surfaces extend to 3-manifolds.

New method accelerates neural network training by focusing on flat directions.

Manifolds can be dominated by hypersurfaces in a sphere.

New graph feedback model for bandits with improved regret bounds.

New method ranks multivariate distributions in SMOOP using q-dominance.

New framework for ranking distributions using variable fractional parameters.

We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.

Research examines when 4-manifolds are dominated by geometric ones.

3-manifolds can virtually dominate others with positive simplicial volume.

Penrose conjecture proven for specific initial data sets.

Let $Γ$ be a nonuniform lattice acting on real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of $Γ$ in SO(n,1). Furthermore, in dimensions 2 and 3, there is a semialgebraic subset of the repr…

Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.

Dominant knots have isomorphic Seifert and Tait graphs.

3-manifolds can be virtually dominated by maps of degree 8.

Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.

New EI strategies using OWA and SSD for excess return.

We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …

The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.

We present a proof of the Riemannian Penrose inequality with charge $r\leq m + \sqrt{m^2-q^2}$, where $A=4πr^2$ is the area of the outermost apparent horizon with possibly multiple connected components, $m$ is the total ADM mass, and $q$ the total charge of a strongly asymptotically flat initial data set for the Einste…

Proposes new rule for ranking investment prospects over long horizons.

Develops a new solver for optimizing with stochastic dominance constraints.

Solves risk minimization problem with SSD constraints.

Paper extends stochastic dominance for compound binomial distributions.

The study shows how energy density of harmonic maps dominates in $n$-Fuchsian fibers, leading to unique minimal surfaces.

We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condit…

Unexpectedly, weighted Pareto variables are stochastically dominant.

New class of heavy-tailed distributions shows weighted averages dominate individual variables.

Proves rigidity for specific initial data sets under the dominant energy condition.