Generalizing the theorem of Green--Lazarsfeld and Gromov, we classify Kaehler groups of deficiency at least two. As a consequence we see that there are no Kaehler groups of even and strictly positive deficiency. With the same arguments we prove that Kaehler groups that are non-Abelian and are limit groups in the sense …
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48 results for “deficiency 1 groups”
The study shows subgroup separability conditions for specific groups.
problem Conditions for subgroup separability in free-by-cyclic and deficiency 1 groups.
method Analyzes polynomially growing monodromy and asymptotic probability of random groups.
result Random deficiency 1 groups are not subgroup separable with positive probability.
Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.
One-relator Sasakian groupsmath.AG
Proves one-relator groups are fundamental groups of Sasakian manifolds.
problem Characterizing groups that can be fundamental groups of Sasakian manifolds.
method Analyzes one-relator groups and classifies groups of deficiency at least two.
result Proves sufficient and necessary conditions for one-relator groups to be fundamental groups of Sasakian manifolds.
For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A group is the fundamental group of the complement of a contractible submanifold o…
We study "how far away" a finite index subgroup G of SL(2,Z) is from being a congruence group. For this we define its deficiency of being a congruence group. We show that the index of the image of G in SL(2,Z/nZ) is biggest, if n is the general Wohlfahrt level. We furthermore show that the Veech groups of origamis (or …
We address two fundamental and well-known problems of Gromov and Lyndon: \demo{Problem A} (Gromov, see [5]). Consider a category of closed manifolds of dimension with nonzero-degree ways as morphisms. Study a partial order . For which the degrees of maps $f: M \t…
The performance of standard learning procedures has been observed to differ widely across groups. Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). In this work, we point to a more subtle source of loss discrepancy---feature noise. Our mai…
We prove that every finitely presented group with positive first -Betti number that virtually surjects onto is acylindrically hyperbolic. In particular, this implies acylindrical hyperbolicity of finitely presented residually finite groups with positive first -Betti number as well as groups …
We compute the characteristic varieties and the Alexander polynomial of a finitely generated nilpotent group. We show that the first characteristic variety may be used to detect nilpotence. We use the Alexander polynomial to deduce that the only torsion-free, finitely generated nilpotent groups with positive deficiency…
We show that if is the fundamental group of a 4-dimensional infrasolvmanifold then , and give examples realizing each of these values. We also determine the abstract commensurators of such groups. Finally we show that if is a finitely generated group the kernel of the natural homomorphism f…
We study the interplay among Wall's problem, normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex of cohomological dimension 2 with a finite fundamental group, assuming t…
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include groups of small virtual cohomological dimension and irreducible Zariski dense sub…
The study calculates the Smith-Thom deficiency of Hilbert squares and provides conditions for maximality.
problem Calculating the Smith-Thom deficiency of Hilbert squares and conditions for maximality.
method Using Mayer-Vietoris mapping and rank calculations.
result Established necessary and sufficient conditions for maximality of Hilbert squares in projective complete intersections.
Contextual bandit methods fail with deficient support data.
problem Learning from support-deficient data in contextual bandits.
method Three approaches to IPS-based learning: action space restriction, reward extrapolation, and policy space restriction.
result Systematic analysis and empirical evaluation of approaches to IPS-based learning.
The paper addresses flaws in fixed point assertions for digital images.
problem Deficiencies in previously published works on fixed point assertions for digital images.
method Continues a series of studies to identify and rectify issues in fixed point assertions.
result Identifies and corrects flaws in fixed point assertions for digital images.
We study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups of increasing finite index in a fixed finitely generated group , assuming . We focus in particular on finitely presented residually free groups, calculating thei…
The paper calculates the number of oriented rational links with a given deficiency.
problem Counting oriented rational links with a specific deficiency.
method Derived precise formulas for the number of oriented rational links with crossing number n and deficiency d.
result Precise formulas for the number of oriented rational links with crossing number n and deficiency d.
Study -Betti numbers of Dehn fillings for special groups.
problem Investigate -Betti numbers of Dehn fillings.
method Prove -Betti numbers equality for virtually special groups.
result Verify Singer Conjecture for certain Einstein manifolds.
The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.
problem Understanding the structure of Cartesian subgroups in graph products of groups.
method Theory of polyhedral products, lower and upper bounds, algorithm for small presentations.
result Bounds on the number of relations and deficiency in presentations of Cartesian groups.
Analyzes the structure and rank of neural network Hessians.
problem Understanding redundancy in overparameterized neural networks.
method Theoretical tools to analyze Hessian map range and rank deficiency.
result Exact formulas and tight upper bounds for Hessian rank of deep linear networks.
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…
The paper defines new representations and groups related to virtual links.
problem Defining and studying new representations of virtual braid groups and link groups.
method Introducing virtually symmetric representations, virtual link groups, and marked Gauss diagrams.
result Established equivalence of many known representations to virtually symmetric representations.
The paper defines and explores Coxeter type LOTs for ribbon 2-knots.
problem Validity of Whitehead's asphericity conjecture for Ribbon 2-knots.
method Definition and analysis of Coxeter type LOTs and their groups.
result Existence of prime LOTs of Coxeter type with specified rank.
We examine certain symmetries in the deficiencies of a rational surgery on a knot in by comparing the -structures on the rational surgery with those on a related integral surgery. We then provide an application of these symmetries in the form of a theorem that obstructs Dehn surgeries in . Thi…
Specialists tolerate defects to gain flexibility, which can be removed when needed.
problem The economic benefits and limitations of deliberately tolerating defects in decision-making.
method Analyzes the conditions under which defects can be kept and removed, using economic models and structural analysis.
result A defect is profitably removable if certain conditions are met, and the premium is the support function of the class's ROC set.
Specialists tolerate defects to gain flexibility, which can be removed when needed.
problem The economic benefits and limits of deliberately tolerating defects in decision-making.
method Analyzes the economic position of keeping and removing defects, using a coupling lemma and structural economic models.
result A defect is profitably removable if the detector-relevant distinction survives a restriction and the advantage condition holds.
Study uses DHS to classify anemia types using CBC indices.
problem Anemia classification for medical purposes.
method Dynamic Harmony Search (DHS) applied to CBC indices.
result DHS outperforms other models in anemia classification.
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods where feature selection is effected via mixed-norms. Several mixed-norm based spar…
"Deep Learning" methods attempt to learn generic features in an unsupervised fashion from a large unlabelled data set. These generic features should perform as well as the best hand crafted features for any learning problem that makes use of this data. We provide a definition of generic features, characterize when it i…
A new algorithm solves constrained optimization problems with stochastic gradients.
problem Nonlinear equality constrained optimization with rank-deficient Jacobians.
method Step decomposition strategy combining normal and tangential steps.
result Convergence guarantees in rank-deficient Jacobian cases.
A new method combines online and offline learning to tackle contextual bandits with missing action support.
problem Learning optimal policies with logged data when the logging policy has deficient support.
method Hybrid approach using online exploration to exploit supported actions and offline learning to avoid unnecessary explorations.
result Determines an optimal policy with theoretical guarantees using minimal online explorations.
We introduce a notion of the twist of an isometry of the hyperbolic plane. This twist function is defined on the universal covering group of orientation-preserving isometries of the hyperbolic plane, at each point in the plane. We relate this function to a function defined by Milnor and generalised by Wood. We deduce v…
In this paper we address the question of the existence of a model for the string 2-group as a strict Lie-2-group using the free loop group (or more generally for compact simple simply-connected Lie groups ). Baez-Crans-Stevenson-Schreiber constructed a model for the string 2-group using a based loop gro…
Bayesian model predicts iron deficiency from multi-source multi-way molecular data.
problem Predicting iron deficiency in rhesus monkeys from multi-source multi-way molecular data.
method Developed a Bayesian approach with a linear model incorporating multi-way dependence and varying signal sizes across sources.
result Model accurately classifies iron deficiency in monkeys and outperforms simpler models.
Exponential Bellman Equation and Improved Regret Bounds for Risk-Sensitive Reinforcement Learningcs.LG
Improved risk-sensitive RL with exponential Bellman equation and better regret bounds.
problem Exponential gap between upper and lower bounds in risk-sensitive RL.
method Identified and addressed deficiencies in existing algorithms and analysis; developed novel analysis and exploration mechanism.
result Improved regret upper bounds over existing ones.
Develops methods to find most probable paths on complex manifolds.
problem Identifying optimal paths for manifold-valued processes, especially those with non-trivial structures.
method Constructs a general approach to defining and identifying most probable paths by measuring the Onsager-Machlup function on the anti-development of such processes.
result Derives explicit equations for development most probable paths that encompass various manifold-valued processes.
Pricing complexity optionsq-fin.PR
We consider options that pay the complexity deficiency of a sequence of up and down ticks of a stock upon exercise. We study the price of European and American versions of this option numerically for automatic complexity, and theoretically for Kolmogorov complexity. We also consider run complexity, which is a restricte…
We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can be seen as analogous to the fact that determinants of matrices over commutative …
Paper addresses OPE for dependent bandit samples using MDS and batch updates.
problem Evaluating policies from non-i.i.d. historical data in contextual bandits.
method Constructs an MDS-based estimator for dependent samples, solves batch update and deficient support issues.
result Derives an asymptotically normal estimator for evaluation policy value.
New method identifies causal direction with latent confounders.
problem Identifying causal direction in presence of multiple latent variables.
method Use of joint higher-order cumulant matrix properties.
result Causal asymmetry can be seen from rank deficiency properties of cumulant matrices.
Study finds LLMs hallucinate in finance tasks, needing research.
problem Hallucination in LLMs in finance.
method Empirical investigation of four methods to mitigate hallucination.
result LLMs hallucinate in financial tasks.
The study connects knot crossing numbers to surface properties and tunnel numbers.
problem Understanding the relationship between knot crossing numbers and surface properties.
method Combines surface ascending-number estimates, bridge-number estimates, and amalgamation arguments for Heegaard splittings.
result Establishes a linear relationship between the crossing number and the Heegaard deficiency of the surface.
Gradient descent with preconditioning finds global optima in overparameterized nonconvex factorization.
problem Finding global optima in nonconvex Burer-Monteiro factorization.
method Preconditioned gradient descent for overparameterized nonconvex function minimization.
result Gradient descent with preconditioning achieves linear convergence in the overparameterized case.
We investigate the behavior of the higher-order degrees, db_n, of a finitely presented group G. These db_n are functions from H^1(G;Z) to Z whose values are the degrees certain higher-order Alexander polynomials. We show that if def(G) is at least 1 or G is the fundamental group of a compact, orientable 3-manifold then…
New method differentiates square-root Kalman filters robustly.
problem Gradient calculation issues in square-root Kalman filters.
method Closed-form chain rule derived from Gramian identity, resolves non-orthogonal and rank-deficient issues.
result Robust automatic differentiation for Kalman filters, resolving numerical stability and gradient issues.
The paper discusses fairness in bank stress tests, comparing various methods to address institutional differences.
problem Fair aggregation of bank-specific stress test models into a common model.
method Comparing various notions of regression fairness, including estimating and discarding centered bank fixed effects.
result The method of estimating and discarding centered bank fixed effects is preferable for linear models, improving forecast accuracy and equal treatment.
We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and are anisotropic distributed. The family can be interpreted as mos…