Networks help map Roman economic complexity.
problem Mapping economic complexity in the Roman period.
method Using network models to visualize and quantify interactions.
result Network analysis reveals the complexity of Roman economic systems.
New Roman pipeline detects astronomical transients.
problem Automated detection of transients from Roman Space Telescope data.
method Machine learning model RuBR for distinguishing real from fake detections.
result Effective real-bogus classification in Roman era.
Let Σ be a closed surface, G a compact Lie group, not necessarily connected, with Lie algebra g, endowed with an adjoint action invariant scalar product, let ξ:P→Σ be a principal G-bundle, and pick a Riemannian metric and orientation on Σ, so that the corresponding Yang-Mills equations $$d_A*K_A =…
Let Y be a CW-complex with a single 0-cell, K its Kan group, a model for the loop space of Y, and let G be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant cohomology of the geometric realization of the cosimplicial manifold $\roman{Hom}(K,G)$ …
Let Y be a CW-complex with a single 0-cell, let K be its Kan group, a free simplicial group whose realization is a model for the space ΩY of based loops on Y, and let G be a Lie group, not necessarily connected. By means of simplicial techniques involving fundamental results of {\smc Kan's} and the standard $…
Let Σ be a closed surface, G a compact Lie group, with Lie algebra g, and ξ:P→Σ a principal G-bundle. In earlier work we have shown that the moduli space N(ξ) of central Yang- Mills connections, for appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yie…
Let Σ be a closed surface, G a compact Lie group, with Lie algebra g, ξ:P→Σ a principal G-bundle, let N(ξ) denote the moduli space of central Yang-Mills connections on ξ, for suitably chosen additional data, and let $\roman{Rep}_ξ(Γ,G)$ be the space of representations of the universal central ex…
A database of objects discovered in houses in the Roman city of Pompeii provides a unique view of ordinary life in an ancient city. Experts have used this collection to study the structure of Roman households, exploring the distribution and variability of tasks in architectural spaces, but such approaches are necessari…
Active learning reduces font classification data needs for historical documents.
problem Identifying fonts in historical documents for OCR accuracy.
method Active learning strategy using image features and bag-of-word representation.
result Combination of uncertainty and diversity sampling achieves 89% accuracy with 17% labeled data.
Let G be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let π be the fundamental group of an orientable (real) surface M with a finite number of punctures, and let C be a family of conjugacy classes in G, one for each puncture. A finite-dimensional construction…
Let G be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary infinite orientation preserving cocompact planar discrete group of euclidean or non-e…
We present an infinite sequence of smooth embeddings of a connected sum of 6 projective planes in the 4-sphere, which are all ambient homeomorphic, but pairwise ambient non-diffeomorphic. The double covers of the 4-sphere ramified along these surfaces form a family of the exotic $\Bbb CP^2#5\bar{\Bbb CP^2}$ constructed…
Hawksmoor's ceiling and Pantheon dome cofferings are explained using conformal mappings and Mercator's projection.
problem Understanding the design of curved ceiling cofferings using mathematical methods.
method Differential geometry and Mercator's projection of curved surfaces onto planes.
result The cofferings are conformal images of square tilings, ensuring right-angle intersections and square coffers.
In this work, we employ quantitative methods from the realm of statistics and machine learning to develop novel methodologies for author attribution and textual analysis. In particular, we develop techniques and software suitable for applications to Classical study, and we illustrate the efficacy of our approach in sev…
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
problem Identifying sundial design adjustments based on installation location.
method Shape analysis in a high-dimensional space, regression in shape space.
result Sundial design adjustments were latitude-dependent.
CNN identifies AGN host galaxies from Sloan Digital Sky Survey data.
problem Identifying AGN host galaxies using traditional methods is time-consuming.
method Trained a convolutional neural network on 210,000 galaxies.
result CNN can distinguish AGN host galaxies from non-active galaxies.
The paper relates curvature loci of different manifold types through projections and normal sections.
problem Understanding the geometry of manifolds and their curvature loci.
method Using normal sections and projections to relate curvature loci of different manifold types.
result A commutative diagram of projections and normal sections that relates the curvature loci of different types of manifolds.
New method speeds up galaxy analysis from hours to seconds.
problem Infeasibility of state-of-the-art SED analyses for large surveys.
method Amortized Neural Posterior Estimation (ANPE) for scalable Bayesian inference.
result Posterior distributions of 12 model parameters estimated in seconds per galaxy.
Virtual and welded periods of knots are equivalent to classical periods.
problem Understanding the equivalence of virtual and welded periods to classical periods.
method Direct demonstration of equivalence.
result Classical knots have only finitely many virtual or welded periods.
The paper proves periodic projections of alternating knots using Flyping theorem.
problem Proving the existence of periodic projections of alternating knots.
method Flyping theorem and symmetry analysis.
result Existence of q-periodic alternating projections of prime alternating q-periodic knots. Paper proposes a robust framework for detecting multiple periodic components in time series.
problem Detecting multiple periodic components in time series with interlaced patterns and external noise.
method Applying maximal overlap discrete wavelet transform to isolate periodic components, ranking them by wavelet variance, and detecting single periodicity robustly.
result The proposed algorithm outperforms other methods for both single and multiple periodicity detection.
The paper finds linked periodic orbits in disc homeomorphisms using braids.
problem Finding linked periodic orbits in disc homeomorphisms.
method Interpreting linking of orbits by induced braids and using forcing relations.
result New examples of linked orbits of periods at most 4 for pseudo-Anosov braid types.
Enhances financial time series forecasting with a multi-period learning framework.
problem Accurate financial time series forecasting requires considering both short-term and long-term trends.
method Proposes a Multi-period Learning Framework (MLF) with three modules: Inter-period Redundancy Filtering, Learnable Weighted-average Integration, and Multi-period self-Adaptive Patching.
result Improves financial time series forecasting accuracy and efficiency.
New prime amphicheiral knots found with a specific period.
problem Finding amphicheiral knots with a specific free period.
method Constructed new prime amphicheiral knots with free period 2.
result Solved an open question about amphicheiral knots and free periods.
The paper classifies orientation reversing periodic maps on surfaces.
problem Classifying orientation reversing periodic maps on closed surfaces.
method Developed a group of data for each map and criteria to judge conjugacy.
result Given orientation reversing periodic maps on Σ_g with period ≥ 3g are conjugate to specific types of maps.
Nonorientable spanning surfaces of periodic knots can have arbitrarily high first Betti number.
problem Periodic knots do not always have nonorientable spanning surfaces of high genus.
method Examples and calculations of nonorientable spanning surfaces of periodic knots.
result The first Betti number of nonorientable spanning surfaces can be arbitrarily large.
Model for multi-period carbon market pricing with allowances.
problem Carbon market pricing with multiple trading periods and compliance times.
method Singular forward-backward stochastic differential equations (SDEs).
result Value function convergence to infinite period model under certain conditions.
The study classifies isotopy types of 3-periodic nets and their embeddings.
problem Classifying isotopy types of 3-periodic nets and their embeddings.
method Definition of entangled embedded periodic nets, classification methodology using linear graph knots.
result Enumeration and classification of isotopy classes for various 3-periodic nets.
We give criteria for framed links and 3-manifolds to be periodic of prime order. As applications we show that the Poincare sphere is of periodicity 2, 3, 5 only and the Brieskorn sphere (2,3,7) is of periodicity 2, 3, 7 only.
We derive new obstructions to periodicity of classical knots by employing the Heegaard Floer correction terms of the finite cyclic branched covers of the knots. Applying our results to two fold covers, we demonstrate through numerous examples that our obstructions are successful where many existing periodicity obstruct…
Paper defines linking numbers for periodic tangles.
problem Defining invariant linking numbers for periodic tangles.
method Defined linking numbers using motifs and showed invariance.
result Linking numbers are well-defined and invariant.
Khovanov-Rozansky homology shows periodic links have group actions.
problem Understanding periodic links through homology.
method Showed Khovanov-Rozansky slN-homology has group actions on m-periodic links. result Proved an analog of periodicity criterion using slN-homology. Maps minimize periodic points for high periods, but not for low periods.
problem Understanding periodic points of maps on infinite type surfaces.
method Analysis of isotopic maps, spun pseudo-Anosov maps, and Handel-Miller maps.
result Spun pseudo-Anosov maps minimize periodic points for sufficiently high periods.
We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic points correspond to periodic orbits whose free homotopy classes are formed by it…
Study periodic monopoles via algebraic difference modules.
problem Classify periodic monopoles of GCK type.
method Relate geometric monopoles to algebraic difference modules.
result Established a Kobayashi-Hitchin correspondence for periodic monopoles.
Study on periodic knots, proving limitations on their Alexander polynomials.
problem Understanding Alexander polynomials of periodic knots.
method Polynomial factorization, number theory interpretation, computational methods.
result Alexander polynomials of freely periodic knots are restricted to products of cyclotomic polynomials.
Alexander invariants studied for periodic virtual knots.
problem Characterizing the periods of virtual knots.
method Realizing periodic virtual knots as closures of periodic braids, analyzing Alexander polynomials.
result Established congruence relating Alexander polynomials of periodic knots.
Derives an index formula for families of end-periodic Dirac operators.
problem Calculating the index of families of end-periodic Dirac operators.
method Using the renormalized Chern character and Fourier-Laplace transform of the Bismut superconnection.
result Establishes an index formula involving a new end-periodic eta form.
Paper disproves Wright's periodic map conjecture.
problem Existence of periodic maps on closed hyperbolic surfaces.
method Analyzes automorphisms and curve behavior on surfaces.
result No periodic map can fill every curve with its image.
Constructing new minimal surfaces of higher genus.
problem Creating minimal surfaces of higher genus.
method Weierstrass data construction and numerical solutions.
result Multiple new examples of higher genus minimal surfaces.
DEPTS learns to forecast periodic time series with improved accuracy.
problem Forecasting periodic time series is challenging due to complex dependencies and diverse periods.
method DEPTS uses a decoupled formulation with an expansion module and a periodicity module to handle these challenges.
result DEPTS significantly improves forecasting accuracy, reducing errors by up to 20%.
New minimal surfaces show stacking disorder in periodic structures.
problem Reproducing experimental twinning defects in periodic minimal surfaces.
method Constructing non-periodic minimal surfaces that lift to disordered stacking in 3D.
result Reproduced twinning defects in periodic minimal surfaces as stacking disorder.
Study periodic geodesics on contact 3D manifolds, proving existence and precise properties.
problem Existence and properties of periodic geodesics in contact sub-Riemannian metrics.
method Develops two independent subjects: existence of spiraling geodesics and precise study of geodesics on quotient of SL2(R).
result Proves existence and precise properties of periodic geodesics.
Paper introduces dynamic strategies for multi-period investment models.
problem Optimizing investment strategies over multiple periods with risk and return considerations.
method Developed a Bellman principle for discrete time multi-period mean-variance models, leading to dynamic optimal strategies and efficient frontiers.
result Dynamic optimal strategies can achieve higher returns with lower risk compared to the 1/n strategy.
We study the asymptotic behavior of the sequence of the Nielsen numbers {N(fk)}, the essential periodic orbits of f and the homotopy minimal periods of f by using the Nielsen theory of maps f on infra-solvmanifolds of type R. We give a linear lower bound for the number of essential periodic orbits of such …
The aim of this paper is to compare statistical properties of a bubble period with those of the anti-bubble period in stock markets. We investigate the statistical properties of daily data for the Nikkei 225 index in the 28-year period from January 1975 to April 2003, corresponded to the periods of bubbles and anti-bub…
Classifies periodic diffeomorphisms and hyperelliptic involutions on surfaces.
problem Classifying periodic diffeomorphisms and involutions on surfaces.
method Refinement of Ishizaka's result using Dehn twist presentations.
result Dehn twist presentations of hyperelliptic periodic mapping classes.
It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criteri…