Geography and distance impact financial dynamics in Chinese stock markets.
problem Investigate the impact of geography and distance on financial dynamics in Chinese stock markets.
method Daily data analysis of individual stocks in Shanghai and Shenzhen stock markets, focusing on geographical correlation and distance effect.
result Stock location impacts financial dynamics, except during financial crises. Short distance has higher probability than long distance, and correlation weakly decays with distance in Shanghai but remains stable in Shenzhen.
New findings restrict Heegaard Floer homology for certain rational homology spheres.
problem The L-space conjecture or Heegaard Floer homology geography. method Verification of a stronger geography restriction for rational homology spheres.
result Heegaard Floer homology satisfies a stronger geography restriction for a wide class of rational homology spheres.
The geography problem is usually stated for simply connected symplectic 4-manifolds. When the first cohomology is nontrivial, however, one can restate the problem taking into account how close the symplectic manifold is to satisfying the conclusion of the Hard Lefschetz Theorem, which is measured by a nonnegative integ…
New method detects financial clustering influenced by sector and geography.
problem Detecting overlapping clusters in financial networks with multiple factors.
method Robust regression to remove sector and geography influences.
result Geography became more important for clustering after the 2008 financial crisis.
Scoping review of EO-ML methods for causal inference in poverty geography.
problem Lack of thorough documentation and best practices for EO-ML methods in causal analysis.
method Comprehensive scoping review cataloging five principal approaches.
result Detailed protocol for integrating EO data into causal analysis.
The geography and botany of smooth/symplectic nonspin 4-manifolds with abelian fundamental group are addressed.
The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group are addressed.
In this note, the geography problem in dimension four is reviewed and then its extension to dimension six for the symplectic case is explained. Finally some examples in dimension six are provided.
Geography problem for nonorientable surfaces bounded by knots.
problem Bounding and computing the nonorientable 4-genus of knots.
method Analysis of existing methods, relationships between Betti number and normal Euler class, exploration of families of torus knots, use of Ozsváth-Szabó d-invariant.
result Improvement on the bound for some knots using the Upsilon invariant.
Study on 4-manifolds with positive scalar curvature.
problem Characterizing 4-manifolds with positive scalar curvature.
method Geography problem approach focusing on four-dimensional case.
result Survey of mathematical work and strengthening of Carr's result.
Delisle's projection explained by Euler in 18th century.
problem Geographical projection issues.
method Analyzing Euler's work on Delisle's projection.
result Important mathematical points on metric geometry of surfaces.
In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds admitting several symplectic structures, inequivalent under deformation and sel…
This work aims to study the Portuguese regional agglomeration process, using the linear form the New Economic Geography models that emphasize the importance of spatial factors (distance, costs of transport and communication) in explaining of the concentration of economic activity in certain locations. In a theoretical …
Spin Lefschetz fibrations can represent any group and lattice point.
problem Representing groups and lattice points using Lefschetz fibrations.
method Proving any finitely presented group and admissible lattice point can be realized as a spin Lefschetz fibration.
result Spin Lefschetz fibrations can represent any group and lattice point.
Khovanov homology invariant under Conway mutation.
problem Invariance of Khovanov homology under specific transformations.
method Strong geography restrictions and homological mirror symmetry.
result Classification of components of a Khovanov multicurve invariant.
The study creates symplectic Lefschetz fibrations and rational blowdowns for new 4-manifolds.
problem Creating symplectic Lefschetz fibrations and rational blowdowns for new 4-manifolds.
method Producing simply connected, minimal, symplectic Lefschetz fibrations and rationally blowing down Lefschetz fibrations with clustered nodal fibers.
result New constructions of small symplectic exotic 4-manifolds.
Khovanov multicurves are restricted to linear components.
problem Khovanov multicurves are subject to strong geography restrictions.
method Applying ideas from homological mirror symmetry, we show that Khovanov multicurves are linear.
result Every component of the invariant is linear, homotopic to a straight line.
Lagrange's map construction ideas influenced later mathematicians.
problem Improving geographical map construction methods.
method Analyzing the impact of Lagrange's memoir on subsequent mathematical works.
result Lagrange's ideas were influential in later mathematical developments, particularly in geography.
We classify genus 2 Lefschetz fibrations on certain 4-manifolds.
problem Classify genus 2 Lefschetz fibrations on specific 4-manifolds.
method Positive factorization of type (10,10) and observations of restrictions.
result Positive factorizations describe genus 2 Lefschetz fibrations on various 4-manifolds.
Describes the Teichmüller stack and its variants, answering questions about orbifold points and local models.
problem Understanding the structure and properties of Teichmüller stacks and their variants.
method Analyzes the Teichmüller stack and its variants using the compactness of cycle spaces in the Kähler setting.
result Detailed answers to questions about orbifold points and local models in Teichmüller stacks and variants.
The study explores relations between various knot invariants.
problem Understanding the relationships between different knot invariants.
method Defined a relation between maps from knot types to sets X and Y, and determined specific relations for various knot invariants.
result Determined relations between crossing number, unknotting number, bridge number, braid index, genus, and canonical genus.
Waymo Open Dataset provides a large, diverse, and synchronized LiDAR and camera dataset for autonomous driving research.
problem Limited diversity and scale in existing self-driving datasets hinder real-world problem alignment.
method Developed a new large-scale, high-quality, diverse dataset with synchronized LiDAR and camera data.
result The dataset is 15x more diverse than the largest existing dataset based on a proposed diversity metric.
Paper proposes AI solutions for social problems in low-income areas.
problem Effective preventive measures against complex social problems in low-income regions.
method Design framework using data-driven machine learning for adaptive solutions.
result Illustrated design approach with survey data from India.
New methods predict ambulance demand with high accuracy.
problem Accurate prediction of ambulance demand in urban areas.
method Three methods based on Gaussian mixture models, kernel density estimation, and kernel warping.
result Significantly more accurate predictions for Toronto and Melbourne.
Enhances neural models with simple functions to improve language modeling.
problem Neural models struggle with certain spatial, temporal, or quantitative relationships.
method Integrates simple functions into neural architecture to form a hierarchical NSLM.
result NSLMs significantly reduce perplexity in small-corpus language modeling.
The paper characterizes Einstein 4-manifolds with semi-definite curvature and derives inequalities.
problem Characterizing Einstein 4-manifolds with semi-definite sectional curvature.
method Using pointwise inequalities involving scalar curvature and Weyl curvatures.
result Closed 4-dimensional Einstein metrics saturating the pointwise inequality are completely characterized.
In this paper, results of J. Park and of B.D Park and Szabo on simply connected symplectic 4-manifolds are re-proven and extended to non-simply connected manifolds using Luttinger surgeries.
Biotech startups are found to be similar to tech startups overall.
problem The uniqueness of biotech startups was previously overemphasized.
method Extensive research from new databases analyzed similarities and differences.
result Biotech startups share similarities in venture capital, exit time, and geography with tech startups.
Constructs symplectic surface bundles with positive signatures.
problem Symplectic surface bundles over surfaces with positive signatures.
method Constructs symplectic surface bundles with specific genera.
result Determines commutator lengths of new mapping classes.
The paper constructs exotic knotted surfaces and curves in 4-manifolds.
problem Understanding exotic knotted surfaces and curves in 4-manifolds.
method Local knotting and construction of surfaces and curves.
result First examples of exotically knotted complex curves and symplectic 2-spheres.
We show that there exist non-formal compact oriented manifolds of dimension n and with first Betti number b1=b≥0 if and only if n≥3 and b≥2, or n≥(7−2b) and 0≤b≤2. Moreover, we present explicit examples for each one of these cases.
We prove that if a contact manifold (M,ξ) is supported by a planar open book, then Euler characteristic and signature of any Stein filling of (M,ξ) is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal open books with planar pages. Moving beyond the geography of Stein filli…
In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points (χ,c) lying in 0≤c≤8.76χ. Furthermore, as a corollary, we prove that there exist infinitely many exotic smooth structures on (2n+1)(S2×S2)…
Researchers propose a new approach to the Hopf problem for aspherical varieties.
problem The Hopf problem for aspherical smooth projective varieties.
method An approach recently proposed by Liu, Maxim, and Wang in [LMW21].
result An intriguing conjecture regarding the geography of aspherical surfaces of general type.
Study shows non-trivial knot Floer homology for specific knots.
problem Proving non-triviality of knot Floer homology for certain knots.
method Analyzing Alexander grading and proving non-triviality in specific knots.
result Non-trivial knot Floer homology for certain knots, answering a question posed by Baldwin and Vela-Vick.
New method generates geolocated synthetic populations from real data.
problem Generating synthetic populations with explicit geographic coordinates.
method Mapping coordinates into a latent space using Normalizing Flows (NF), then combining with other features in a Variational Autoencoder (VAE).
result NF+VAE architecture outperforms existing methods in generating geolocated synthetic populations.
Paper constructs new symplectic 4-manifolds, improving previous results.
problem Symplectic 4-manifolds with nonnegative signature and nonspin structure.
method Combining complex surfaces and exotic symplectic manifolds.
result Infinitely many new homeomorphic but non-diffeomorphic symplectic manifolds.
New restrictions found on 4-manifolds with pinched curvature.
problem Restrictions on Euler characteristic and signature of 4-manifolds with pinched curvature.
method Proved new restrictions on Euler characteristic and signature of oriented 4-manifolds with pinched sectional curvature.
result Simply connected 4-manifolds with δ≤sec≤1 are homeomorphic to S4 or CP2. A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of b2+>1 are of superconformal simple type, and that the numerical invariants of 4-man…
The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example …
Paper proposes efficient multivariate spatial Fay-Herriot models using variational autoencoders.
problem Estimating population characteristics in small areas with limited data.
method Integrates multivariate spatial Fay-Herriot model with variational autoencoders to leverage spatial structure efficiently.
result Significant computational efficiency improvements for high-dimensional datasets.
This note shows every integer can be a signature of a hyperbolic 4-manifold.
problem Finding signatures of hyperbolic 4-manifolds.
method Using Long and Reid's theorem and explicit construction of a 24-cell manifold.
result Every integer is the signature of a non-compact, oriented, hyperbolic 4-manifold.
New method evaluates multiple social disparities using machine learning.
problem Reduction of educational disparities across multiple dimensions.
method Triply-Robust Machine Learning Approach for Causal Decomposition Analysis.
result Simultaneous interventions across multiple domains reduce disparities.
Study shows bounds on symplectic fillings for spinal open book decompositions.
problem Understanding symplectic fillings of contact 3-manifolds.
method Introduced spine removal surgery operation to prove universal bounds.
result Proves a universal bound on the Euler characteristic and signature of minimal symplectic fillings.
Study finds symplectic fillings' properties for specific contact covers.
problem Determining symplectic fillings' Euler characteristics and signatures.
method Analyzing exact symplectic fillings of contact branched covers.
result Identified links' symplectic fillings' properties.
With this work we try to analyse the agglomeration process in the Portuguese regions, using the New Economic Geography models. In these models the base idea is that where has increasing returns to scale in the manufactured industry and low transport costs, there is agglomeration. Of referring, as summary conclusion, th…
Study shows Conway mutation preserves a specific link invariant.
problem Investigating symmetry properties of peculiar modules.
method Analysis of Heegaard Floer invariants of 4-ended tangles.
result Conway mutation preserves the hat flavor of relatively δ-graded Heegaard Floer theory of links.
The aim of this paper is to analyze the relationship between inter-industry, intra-industry and inter-regional clustering and demand for labor by companies in Portugal. Is expected at the outset that there is more demand for work where the agglomeration is greater. It should be noted, as a summary conclusion, the resul…