arXiv research

Finite presentation for a specific group in 3D handlebody topology.

Finite presentations for mapping class groups of surfaces and surfaces with points/boundaries.

Establishes bounds on Andrews-Curtis moves for trivial group presentations.

Estimates causal effects using neural networks for balancing covariates.

New insights on nilpotent groups with balanced presentations.

We study the intrinsic geometrical structure of hypersurfaces in 6-manifolds carrying a balanced Hermitian SU(3)-structure, which we call {\em balanced} SU(2)-{\em structures}. We provide conditions which imply that such a 5-manifold can be isometrically embedded as a hypersurface in a manifold with a balanced SU(3)-st…

Blowing up flat metrics yields balanced ones with constant curvature.

Motivated by problems in topology, we explore the complexity of balanced group presentations. We obtain large lower bounds on the complexity of Andrews-Curtis trivialisations, beginning in rank 4. Our results are based on a new understanding of how Dehn functions of groups behave under certain kinds of push-outs. We co…

Data balancing reduces variance in machine learning models.

Let $M$ be any compact four-dimensional PL-manifold with or without boundary (e.g. the four-dimensional sphere or ball). Consider the space $T(M)$ of all simplicial isomorphism classes of triangulations of $M$ endowed with the metric defined as the minimal number of bistellar transformations required to transform one o…

Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well as the robustness of attractor states of networks of neurons performing memory ta…

The study identifies assets with local balance deviating from global balance to mitigate financial risk.

Improves causal inference with observational data by balancing features and weights.

SurvCaus improves survival CATE estimation using neural nets.

Let $G$ be a group with a finite balanced presentation $P$. We associate a Heegaard Floer homology group $\widehat{HF}_P(G)$ with the pair $(G,P)$ based on some extra choices and technical assumptions. We show that $\widehat{HF}_P(G)$ is independent from these choices and also is invariant under stable Andrews-Curtis t…

In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constituti…

Paper surveys balanced metrics and proves a geodesic convexity result.

LSB is a new MCMC method for discrete spaces that reduces target evaluations.

ADAPT method controls balance between sparse generator and discriminator in GANs.

In this note we present, for every $n \geq 4$, a non-Kähler compact complex manifold $X$ of complex dimension $n$ admitting a balanced metric and an astheno-Kähler metric which is in addition $k$-th Gauduchon for any $1\leq k\leq n-1$.

Study of transformations in 3-manifolds with boundary and their equivalence classes.

We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide range of applications from biology to economics. We present an efficient balancing a…

Characterizes almost abelian Lie algebras with integrable complex structure

Balance corrects biased survey data for more accurate insights.

This paper shows how we can build a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we are able to redefine concepts like account balance, yield curve and the law of diminishing returns. The model provides us with a …

We present a simple, yet realistic, agent-based model of an electricity market. The proposed model combines the spot and balancing markets with a resolution of one minute, which enables a more accurate depiction of the physical properties of the power grid. As a test, we compare the results obtained from our simulation…

Paper introduces Balanced Meta-Softmax for better long-tailed visual recognition.

New findings on 3-manifolds using Heegaard Floer theory.

We present a model of credit card profitability, assuming that the card-holder always pays the full outstanding balance. The motivation for the model is to calculate an optimal credit limit, which requires an expression for the expected outstanding balance. We derive its Laplace transform, assuming that purchases are m…

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance…

A new method detects and removes false trailing balances in credit data.

The basic financial purpose of corporation is creation of its value. Liquidity management should also contribute to realization of this fundamental aim. Many of the current asset management models that are found in financial management literature assume book profit maximization as the basic financial purpose. These boo…

Paper proposes a new model to prevent tariff wars by balancing trade balances.

Paper generalizes balanced metrics existence to singular cases using Quot-scheme limit.

We show that the Andrews-Curtis conjecture holds for all balanced presentations of the trivial group corresponding to Heegaard diagrams of $S^3$.

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, th…

Thurston introduced shear deformations (cataclysms) on geodesic laminations - deformations including left and right displacements along geodesics. For hyperbolic surfaces with cusps, we consider shear deformations on disjoint unions of ideal geodesics. The length of a balanced weighted sum of ideal geodesics is defined…

Analyzes impermanent loss in decentralized exchanges and provides a replication formula.

BICauseTree improves causal effect estimation by identifying clusters and balancing treatment allocation.

Due to the limited predictability of wind power and other stochastic generation, trading this energy in competitive electricity markets is challenging. This paper derives revenue-maximising and risk-constrained strategies for stochastic generators participating in electricity markets with a single-price balancing mecha…

Improved GSPGS estimators reduce bias in noisy function measurements.

This paper explores how balancing and filtering techniques affect predictive multiplicity in machine learning models.

Examples are given to show that some compact contractible 4-manifolds can be knotted in the 4-sphere. It is then proved that any finitely presented perfect group with a balanced presentation is a knot group for an embedding of some contractible 4-manifold in the 4-sphere.

AlphaZero's reward function is replaced with a total ordering, enabling self-play without balancing.

Proposes a novel neural network method to estimate average treatment effect.

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…

We relate the Andrews-Curtis conjecture to the triviality problem for balanced presentations of groups using algorithms from 3-manifold topology. Implementing this algorithm could lead to counterexamples to the Andrews-Curtis conjecture.

Noise balance theory explains SGD's behavior in neural networks.