arXiv research

A neural network and evolutionary algorithm framework designs nonlinear optical molecules.

Prior work finds a diversity paradox: diversity breeds innovation, and yet, underrepresented groups that diversify organizations have less successful careers within them. Does the diversity paradox hold for scientists as well? We study this by utilizing a near-population of ~1.2 million US doctoral recipients from 1977…

Federated Machine Learning (FML) creates an ecosystem for multiple parties to collaborate on building models while protecting data privacy for the participants. A measure of the contribution for each party in FML enables fair credits allocation. In this paper we develop simple but powerful techniques to fairly calculat…

Study on random representations of surface groups into SU(n), focusing on asymptotic expansions.

In Random Forests, proximity distances are a metric representation of data into decision space. By observing how changes in input map to the movement of instances in this space we are able to determine the independent contribution of each feature to the decision-making process. For binary feature vectors, this process …

FGSV defends against shell company attacks in group data valuation.

New method finds Lie group representations without explicit groups, enabling new neural network architectures.

Facing a heavy task, any single person can only make a limited contribution and team cooperation is needed. As one enjoys the benefit of the public goods, the potential benefits of the project are not always maximized and may be partly wasted. By incorporating individual ability and project benefit into the original pu…

Paper introduces contribution measures for systemic risk in crypto markets.

We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to $\text{PSL}(2,\mathbb{R})$. Using this result, we describe a framework for the full cl…

Survey of combination theorems in geometry and dynamics.

Paper finds non-positive Weyl connections on Lie groups, confirming a conjecture.

We survey contributions of Robert MacPherson to the theory of arithmetic groups. There are two main areas we discuss: (i) explicit reduction theory for Siegel modular threefolds, and (ii) constructions of compactifications of locally symmetric spaces. The former is joint work with Mark McConnell, the latter with Lizhen…

Conference compiles problems on foliations and diffeomorphisms.

Connected components of Morse boundaries are studied in graph of groups.

Group model selection is the problem of determining a small subset of groups of predictors (e.g., the expression data of genes) that are responsible for majority of the variation in a response variable (e.g., the malignancy of a tumor). This paper focuses on group model selection in high-dimensional linear models, in w…

The paper studies the graph geometry of finite groups, creating a dataset and analyzing its properties.

In this paper, a regional knot invariant is constructed. Like the Wirtinger presentation of a knot group, each planar region contributes a generator, and each crossing contributes a relation. The invariant is call a tridle of the link. As in the quandle theory, one can define Alexander quandle and get Alexander polynom…

Estimates KL divergence with fairness considerations for sub-populations.

The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.

The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies, gauge group extensions, and 3-cocycles. The unifying concept is the classical o…

The paper introduces Absolute Shapley Value to handle negative contributions in machine learning model training.

In many application domains, it is important to characterize how complex learned models make their decisions across the distribution of instances. One way to do this is to identify the features and interactions among them that contribute to a model's predictive accuracy. We present a model-agnostic approach to this tas…

The paper characterizes geometrically finite surfaces via geodesic covers.

The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured cl…

This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor decomposition was considered in application to group data analysis. Suggested approach was…

3-manifold groups' word problem solved in nearly linear time.

The paper shows FtU can reduce discrimination without sacrificing accuracy.

The u-plane integral is the contribution of the Coulomb branch to correlation functions of N=2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group SU(2), for an arbitrary four-manifold with (b1,b2+)…

This article is the author's contribution to the volume "Problems on mapping class groups and related topics" which will be published in December 2006, with Benson Farb as Editor. Various individuals were invited by Farb to submit open problems which seemed interesting to them about surface mapping class groups. We sin…

Study on 4-manifolds restricts negatively curved metrics and fundamental groups.

The paper finds small exotic 4-manifolds with free abelian groups.

For a finite-dimensional (but possibly noncompact) symplectic manifold with a compact group acting with a proper moment map, we show that the square of the moment map is an equivariantly perfect Morse function in the sense of Kirwan, and that the set of critical points of the square of the moment map is a countable dis…

The paper develops a theory explaining how machine learning models can amplify biases.

SHAP clustering explains model predictions by grouping similar feature contributions.

Study finds actuarial unfairness in China's pension system, proposing income-dependent annuitization rules.

We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the Bloch-Wigner functions. We prove the first and second variation formulas for the cla…

Construct geometric interpretation of Heston model using group quantization.

The massless supermultiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). In an earlier paper, a dynamical Kaluza-Klein origin of this observation is proposed with internal space th…

On a capital market the social group is formed from traders. Individual behaviour of agents is influenced by the need to associate with other agents and to obtain the approval of other agents in the group. Making decisions an individual equates own needs with those of the other agents. Any two agents from the group may…

Paper generalizes connections between Lie groups and affine connections.

We prove the existence of a continuous $BV$ minimizer with $C^{0}$ boundary value for the $p$-area (pseudohermitian or horizontal area) in a parabolically convex bounded domain. We extend the domain of the area functional from $BV$ functions to vector-valued measures. Our main purpose is to study the first and second v…

Absolute index theorem for warped product manifolds.

This work is a contribution to the area of Strict Quantization (in the sense of Rieffel) in the presence of curvature and non-Abelian group actions. More precisely, we use geometry to obtain explicit oscillatory integral formulae for strongly invariant strict deformation quantizations of a class of solvable symplectic …

Paper tackles inconsistent CATE estimation across group assignments.

This work is about recognizing human activities occurring in videos at distinct semantic levels, including individual actions, interactions, and group activities. The recognition is realized using a two-level hierarchy of Long Short-Term Memory (LSTM) networks, forming a feed-forward deep architecture, which can be tra…

This paper is a contribution to harmonic analysis of compact solvmanifolds. We consider the four-dimensional oscillator group ${\rm Osc}_1$, which is a semi-direct product of the three-dimensional Heisenberg group and the real line. We classify the lattices of ${\rm Osc}_1$ up to inner automorphisms of ${\rm Osc}_1$. F…

New method reduces privacy impact on model accuracy for underrepresented groups.