Proves congruence subgroup property for mapping class groups of hyperbolic surfaces.
problem Residual finiteness of hyperbolic groups and congruence subgroup property for mapping class groups.
method Assumption of residual finiteness of hyperbolic groups leads to proof of congruence subgroup property.
result Congruence subgroup property for mapping class groups of hyperbolic surfaces.
We examine residual properties of word-hyperbolic groups, adapting a method introduced by Darren Long to study the residual properties of Kleinian groups.
The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) o…
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…
We count meromorphic differentials with fixed residues and poles of fixed orders.
problem Counting meromorphic differentials with fixed residues and poles of fixed orders.
method Intersection theory on compactified moduli spaces of differentials.
result Complete solution to the problem with interesting combinatorial properties.
Fair market valuations ignore future worker profits in employee-owned firms.
problem Ignoring future worker profits in fair market valuations for employee-owned firms.
method Analyzing property rights and residual claimants in employee-owned firms.
result Fair market valuations are inappropriate for employee-owned firms.
Proves 3D Poincaré duality groups without property (T)
problem Residually finite 3D Poincaré duality groups and property (T)
method Using coboundary expansion and recent results on 3-manifold groups
result 3D Poincaré duality groups without property (T)
Non-isomorphic groups with similar profinite completions found.
problem Finding non-isomorphic groups with similar profinite completions.
method Exhibited infinitely many pairs of non-isomorphic groups with specific properties.
result Groups with Property FA and non-trivial actions on trees have isomorphic profinite completions.
We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…
Every non-trivial knot group is fully residually perfect.
problem Understanding the residual properties of knot groups.
method Analyzing the residual properties of knot groups using group theory.
result Every non-trivial knot group is fully residually perfect.
Let p be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually p. Let M=M3 be a virtually fibered 3-manifold. It is well-known that G=π1(M) is residually solvable and even residually finite solvable. We prove that G is always virtually residually p…
This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a "residual" ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and …
Two groups with same profinite completion have different co-Hopfian properties.
problem Understanding co-Hopfian properties in residually finite groups.
method Using a specific construction involving a finitely presented acyclic group with trivial profinite completion.
result Found two groups with same profinite completion but different co-Hopfian properties.
New method improves matrix completion accuracy, especially in noisy data.
problem Noisy matrix completion in recommendation systems and signal processing.
method Residual Spectral Matching criterion and pseudo-gradient algorithms.
result Improved numerical performance in noisy data environments.
The fundamental n-quandles of links are residually finite for n ≥ 2.
problem Residual finiteness of fundamental n-quandles of oriented links.
method Investigation of residual finiteness and subquandle separability of quandles; use of Winker's work on 3-sphere branched covers.
result Fundamental n-quandles of oriented links are residually finite for each n ≥ 2.
The study examines Hopfian properties of conjugation quandles and their underlying groups.
problem Understanding the relationship between Hopfian properties of conjugation quandles and their underlying groups.
method Examined Hopfian and residual finiteness properties of conjugation quandles of specific groups.
result Conjugation quandles of Baumslag-Solitar groups are infinitely generated and not necessarily Hopfian.
Compact manifolds with specific cover properties are hyperbolic.
problem Understanding Gromov hyperbolicity in compact manifolds.
method Proving Gromov hyperbolicity through coboundary expansion in residual covers.
result Compact manifolds with certain cover properties have hyperbolic fundamental groups.
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
We study conformal Spin-subgeometry of submanifolds in a semi-Riemannian Spin-manifold, focusing on conformal Spin-manifolds (M,[h]) and their Poincaré-Einstein metrics (X,g+). Our approach is based on the spectral theory of Dirac operator in the ambient Spin-manifold, and associated spinor valued meromorp…
This paper studies deep learning methodologies for portfolio optimization in the US equities market. We present a novel residual switching network that can automatically sense changes in market regimes and switch between momentum and reversal predictors accordingly. The residual switching network architecture combines …
Let M(Σ,P) be the mapping class group of a punctured oriented surface (Σ,P) (where P may be empty), and let Tp(Σ,P) be the kernel of the action of M(Σ,P) on H1(Σ∖P,Fp). We prove that $\mathcal T_p(Σ, …
We prove that the n th pure braid group of a nonorientable surface (closed or with boundary, but different from RP2) is residually 2-finite. Consequently, this group is residually nilpotent. The key ingredient in the closed case is the notion of p-almost direct product, which is a generalization of the notion of almost…
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data …
Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This…
This paper generalizes property (QT) to a broader class of groups.
problem Proving property (QT) for a wider range of groups.
method Using projection complex machinery and hierarchical hyperbolic groups.
result Established sufficient conditions for groups to have property (QT).
Improved ResNets and DenseNets models for better feature reuse.
problem Diminishing feature reuse in ResNets and DenseNets.
method ResNEsts and DenseNEsts are block-based DNN models with improved representation guarantees.
result Wide ResNEsts with bottleneck blocks can guarantee desirable training properties.
Residual networks with block width max(d_x, d_y) approximate all functions.
problem Achieving universal approximation with residual networks.
method Established bounds on block width for different activation functions.
result Minimum block width for universal approximation is max(d_x, d_y) with inner width 1.
Study various series of groups and their Lie algebras in split extensions.
problem Understanding different series of groups and their Lie algebras in split extensions.
method General construction of N-series, semi-direct products, and monodromy action.
result Generalize the well-known theorem of Falk-Randell to other versions of the LCS.
New groups with special properties found.
problem Finding new groups with specific geometric properties.
method Proved actions on CAT(0) cubical complexes under certain conditions.
result Many groups admit cocompact actions on CAT(0) cubical complexes.
Deep learning enhances options hedging performance.
problem Improving delta hedging for options using neural networks.
method Learning residuals between hedging function and implied Black-Scholes delta using neural networks.
result Deep learning significantly improves hedging performance, often by more than 100%.
Deviance Voronoi residuals improve earthquake insurance risk assessment.
problem Assessing earthquake insurance risk using spatio-temporal point process models.
method Extended Voronoi residuals and created simulation-based approach.
result Proposed formula for country-wide minimum capital test.
Study of pure mapping class groups on infinite graphs.
problem Classifying graphs with specific mapping class groups.
method Completely classified graphs with pure mapping class groups.
result Established semidirect product decomposition and computed first integral cohomology.
A new model improves CT image quality from low-dose scans.
problem Improving CT image quality from low-dose scans.
method Multi-layer Residual Sparsifying Transform (MRST) learning model for low-dose CT reconstruction.
result The MRST model outperforms conventional methods in maintaining subtle details.
We determine the lower central series and corresponding residual properties for braid groups and pure braid groups of orientable surfaces.
Deep residual networks can approximate any continuous function using control theory.
problem Universal approximation capabilities of deep residual neural networks.
method Relating residual networks to control systems and using Lie algebraic techniques.
result Deep residual networks with adequately deep layers can approximate any continuous function on a compact set.
Two ML frameworks predict antibody properties using structural data.
problem Predicting antibody properties using sequence and structural data.
method ANTIPASTI and INFUSSE models using graph representations and neural networks.
result ANTIPASTI predicts binding affinity; INFUSSE predicts residue flexibility.
Paper introduces a new multilinear functional for spectral triples and computes its properties.
problem Computing properties of spectral triples and their associated Hodge operators.
method Introduces a new multilinear functional for spectral triples and computes its properties using noncommutative residue and perturbed de-Rham Hodge operators.
result Recover two forms, torsion of the linear connection, and four forms by the noncommutative residue and perturbed de-Rham Hodge Dirac triple.
Classifies mapping tori of specific groups, generalizing known results.
problem Classifying mapping tori of specific groups.
method Using Hopf-type properties and Poincaré Duality groups.
result Generalizes and provides new proofs for fibered 3-manifolds.
A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this kind of invariants, which means that the definition is satisfied with the same con…
Groups with specific properties have vanishing ℓ2-Betti numbers.
problem Understanding ℓ2-Betti numbers for certain groups. method Introduced cheap 1-rebuilding property and used structure theorem of Tucker-Drob.
result First ℓ2-Betti numbers vanish for specified groups. Study on knot 74 surgeries reveals infinite residue characteristics and infinite order points.
problem Arithmetic properties of Dehn surgery points on knot 74. method Analyzing the canonical component of the SL2(C)-character variety. result Infinite set of ramified places and infinite order points in the Mordell-Weil group.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
A new method boosts exploration in bandit algorithms, reducing regret.
problem Improving exploration in bandit algorithms with bounded or unbounded rewards.
method Residual Bootstrap Exploration (ReBoot) method that injects data-driven randomness.
result Proves logarithmic regret in Gaussian multi-armed bandits with appropriate variance inflation.
Let f:M→N be a continuous map between closed irreducible graph manifolds with infinite fundamental group. Perron and Shalen showed that if f induces a homology equivalence on all finite covers, then f is in fact homotopic to a homeomorphism. Their proof used the statement that every graph manifold is fin…
Homology growth of specific mapping tori vanishes for certain groups.
problem Homology growth of polynomially growing mapping tori in various groups.
method Proof of the cheap rebuilding property for specific groups.
result Torsion homology growth vanishes for Farber sequences in every degree.
The aim of our work is to propose a natural framework to account for all the empirically known properties of the multivariate distribution of stock returns. We define and study a "nested factor model", where the linear factors part is standard, but where the log-volatility of the linear factors and of the residuals are…
Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for quantifying aleatoric uncertainty for deep residual learning and showcase its significant …
Boosted GFlowNets improve exploration by sequentially training GFlowNets with residual rewards.
problem GFlowNets struggle to evenly explore reward landscapes, leading to poor coverage of high-reward areas.
method Sequential training of an ensemble of GFlowNets, each optimizing a residual reward.
result Boosted GFlowNets achieve better exploration and sample diversity on multimodal benchmarks and peptide design tasks.