Proves divisibility relations for symplectic curve polynomials.
problem Divisibility relations for symplectic curve polynomials.
method New proofs of divisibility relations for Oka and Alexander polynomials of symplectic curves.
result Proves Libgober's divisibility relations for symplectic curves.
Tropical division approximates polynomial division for neural networks.
problem Approximating polynomial division in max-plus semiring.
method Approximating Newton Polytope of dividend by divisor, then applying to neural networks.
result Minimizes a two-layer fully connected network for binary classification.
Jones polynomial differences for Cn-equivalent links are divisible by a specific polynomial.
problem Understanding the Jones polynomial differences for Cn-equivalent links. method Analyzing the divisibility of Jones polynomial differences for Cn-equivalent links. result The difference of Jones polynomials for Cn-equivalent links is divisible by a specific polynomial. The Jones polynomial's divisibility is analyzed via local moves on virtual links.
problem Divisibility of the Jones polynomial under local moves on virtual links.
method Developed a general decomposition for the Jones polynomial of virtual links and analyzed divisibility conditions for various local moves.
result Succinct divisibility conditions on the Jones polynomial of virtual links differing via local moves.
Algorithm calculates polynomial Seiberg-Witten invariant from zeta-function of plumbed 3-manifolds.
problem Computing the Seiberg-Witten invariant for plumbed 3-manifolds.
method Némethi's division algorithm for zeta-functions.
result Explicit calculation of polynomial Seiberg-Witten invariant.
If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain knot groups.
We define twisted Alexander polynomials of a complex hypersurface with arbitrary singularities. These generalize the classical Alexander polynomials of high dimensional hypersurfaces and the twisted Alexander polynomial of plane curves. We recover the classical torsionness and divisibility results, which say that, unde…
We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is given by the determinant of its Blanchfield intersection form. Specializing in the…
Lasso method applied to polynomial models with hierarchy constraints.
problem Estimating parameters in polynomial models with hierarchy constraints.
method Using lasso and standard quadratic programming techniques to estimate parameters.
result The proposed methodology outperforms existing techniques in terms of validation error and model size.
Classifies matrices in the quaternionic hyperbolic unitary group.
problem Understanding the structure of matrices in the quaternionic hyperbolic unitary group.
method Used complex representation and characteristic polynomial to study matrices.
result Computed the characteristic polynomial and studied its sign.
The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl_2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra U_h(sl_2) of the Li…
Study of Alexander modules for hyperplane arrangements, distinguishing complements.
problem Distinguishing homotopy equivalent but non-homeomorphic hyperplane arrangement complements.
method Analysis of twisted Alexander modules and polynomials.
result Distinguish non-homeomorphic homotopy equivalent arrangement complements.
Bing doubling is an operation which gives a satellite of a knot. It is also applied to a link by specifying a component of the link. We give a formula to compute the reduced colored Jones polynomial of a Bing double by using that of the companion. This formula enables us to compute a lot of examples of the reduced colo…
A new proof of an extension theorem with bounded generators.
problem Extension theorems in complex analysis.
method Skoda-type L2 division theorem with bounded generators. result The new division theorem allows α to be 1 in the norm of the datum. Unique convex divisible domain found in Grassmannian.
problem Finding convex divisible domains in flag manifolds.
method Analyzing projective isomorphism and Lie groups.
result Only one convex divisible domain in Grassmannian.
Solves division problem for L. Hörmander's systems.
problem Division problem for L. Hörmander's overdetermined systems.
method Formulates and proves divisibility criterion, coherence theorem.
result Establishes effective divisibility criterion and extends coherence theorem.
Uniform convexity in divisible domains leads to hyperbolic geometry.
problem Understanding the geometry of divisible convex sets in Finsler manifolds.
method Proving β-uniform convexity of a specific Finsler metric. result A strictly convex divisible domain induces a β-uniformly convex Finsler metric. Spectral methods learn flexible topic models with topic correlations.
problem Learning topic models with arbitrary topic correlations.
method Flexible topic model using Normalized Infinitely Divisible (NID) distributions, learned via spectral methods.
result Improved perplexity on real datasets compared to baseline.
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
A link L is called Brunnian if every proper sublink of L is trivial. Similarly, a bottom tangle T is called Brunnian if every proper subtangle of T is trivial. In this paper, we give a small subalgebra of the n-fold completed tensor power of U_h(sl_2) in which the universal sl_2 invariant of n-component Brunnian bottom…
Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …
Division algorithm for surface group rings yields standard complexes and cohomological dimensions.
problem Understanding cohomological dimensions of surface group actions.
method Division algorithm for group rings of surface groups.
result Some 2-complexes with surface fundamental groups are standard.
Geometrically explains divisibility of Euler classes for spin modules.
problem Divisibility of KO-theoretical Euler classes for spin modules. method Geometric interpretation of divisibility using spin structures and Seiberg-Witten theory.
result Clarifies the role of reducibles in monopole equations.
The paper sets lower bounds on envy-free divisions in cake-cutting problems.
problem Finding the minimum number of envy-free divisions in cake-cutting problems.
method Analyzes two scenarios: classical and hybrid, with different constraints and allocations.
result Sharp bounds and examples for envy-free divisions in both scenarios.
New proof of divisibility property for certain algebraic varieties.
problem Divisibility property for LQEL varieties.
method Construction of Clifford algebra representations to Severi varieties.
result New proof of Russo's Divisibility Property for LQEL varieties.
The paper studies parabolic representations of 2-bridge links using symplectic quandles.
problem Parabolic representations of 2-bridge links.
method Convert conjugation quandle equations to symplectic quandle equations, using a polynomial PK(u) to find arc coloring vectors. result Explicit formulas for parabolic representations of 2-bridge links are derived, including complex volume and cusp shape.
The paper revisits Rokhlin's divisibility theorem and its significance.
problem Rokhlin's divisibility theorem on signatures of manifolds.
method Overview and retrace of Rokhlin's proof and further developments.
result Reaffirms the importance of Rokhlin's theorem in manifold theory.
Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.
problem Division Theorem in Skoda's context
method Degeneration approach inspired by B. Berndtsson and L. Lempert's L2 extension theorem result Simplified and extended proof of L2 extension theorem Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
problem Understanding the distinction between incidence theorems over division rings and fields.
method Extending the surface-graph approach to noncommutative settings, the paper analyzes the topological properties of graphs embedded on surfaces of different genera.
result Theorems associated with graphs on the sphere hold over any division ring, while those on surfaces of positive genus typically hold only if the ground ring is a field.
Constructs projective plane over octonions, proving no higher real division algebras.
problem Existence of higher-dimensional real division algebras.
method Using Adams' solution of the Hopf invariant 1 problem, constructs projective plane over octonions.
result No higher-dimensional real division algebras exist.
New findings on branched covers of quasipositive links and their L-space properties.
problem Understanding the conditions under which branched covers of quasipositive links are L-spaces.
method Analyzing Alexander polynomials and using properties of cyclic covers.
result Conditions for the L-space property of branched covers of quasipositive links, including specific cases for strongly quasipositive and quasipositive links.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
This paper develops a new method to model treatment effects that are heterogeneous across different quantiles.
problem Modeling treatment effects that vary across different quantiles of the outcome distribution.
method The paper combines quantile classification with local polynomial estimation to build a decision tree and forest.
result The proposed QLPRT and QLPRF methods provide a new way to estimate and infer heterogeneous treatment effects.
A new SBI framework for trawl processes efficiently estimates parameters from large datasets.
problem Challenges in estimating parameters of complex stochastic processes.
method Telescoping ratio estimation, Chebyshev polynomial approximations, amortized posterior inference.
result Accurate and efficient inference for intractable stochastic processes, even with limited data.
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
problem Geodesic connectedness of affine connections on statistical manifolds with divisible cubic forms.
method Analogy with Hopf-Rinow theorem in Riemannian geometry, establishing geodesic completeness.
result Geodesic connectedness established for statistical manifolds with divisible cubic forms.
Paper finds a divisibility property of first Pontrjagin classes for even-dimensional homotopy complex projective spaces.
problem Understanding the first Pontrjagin classes of homotopy complex projective spaces.
method Analyzing the difference of first Pontrjagin classes for even-dimensional manifolds homotopy equivalent to CP(n). result The difference of the first Pontrjagin classes is divisible by 16 for even n. Algorithm learns fair division from noisy feedback in uncertain markets.
problem Learning fair division in uncertain markets with noisy feedback.
method Wrapper algorithms using dual averaging to learn item and agent values from bandit feedback.
result Asymptotically achieves optimal Nash social welfare in linear Fisher markets.
Study of characteristic numbers in 24-dimensional String manifolds.
problem Characterizing and understanding characteristic numbers of 24-dimensional String manifolds.
method Using Pontryagin numbers, integral basis of String cobordism group, and divisibility results.
result Established 2- and 3-primary divisibilities of characteristic numbers.
An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have C1 boundary, and have word hyperbolic divid…
Predicts the number of polynomial additions in Buchberger's algorithm using machine learning.
problem Predict the number of polynomial additions in Buchberger's algorithm.
method Multiple linear regression and recursive neural network models trained on ideal generator statistics.
result Machine learning can predict the number of polynomial additions in Buchberger's algorithm.
We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natural 1-1 correspondence between simply connected hyper-Kaehler symmetric spaces of dimension 8m and orbits of the general linear group GL(m,H…
In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.
Investigates polynomial solutions to minimal surface equation, proving constraints and structure theorems.
problem Finding polynomial solutions to the minimal surface equation.
method Proves structure theorem, analyzes polynomial constraints, and uses eigenvalue estimates.
result Polynomial solutions must contain terms of both high and low degree, and have specific factorization properties.
Study of congestion in negative curvature manifolds using fair-division algorithms.
problem Estimating and predicting the size and location of congestion core in negative curvature manifolds.
method Introducing a novel fair-division algorithm to estimate congestion core.
result Demonstrated the effectiveness of fair-division algorithms in estimating congestion core.
Research shows how certain flat structures behave in specific convex domains.
problem Understanding the behavior of codimension-1 simplices in divisible convex domains.
method Analyzes the set of codimension-1 flats and their images in quotient manifolds.
result The set of codimension-1 flats forms a finite collection of disjoint virtual tori, leading to cusped convex projective manifolds.