cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.15468/dl.jrqyv9
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Apus apus (Linnaeus, 1758)",
 "Year is 52",
 "Country is Netherlands"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0008169-241107131044228/datasets/export for details.
DOI: 10.15468/dl.ysy8pa
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Haematopus ostralegus Linnaeus, 1758",
 "Year is 52",
 "Country is Netherlands"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0008170-241107131044228/datasets/export for details.
DOI: 10.5281/zenodo.14063009
title: M2851-PR1-¿Cómo podemos capturar los datos de la web?
DOI: 10.5281/zenodo.14063010
title: M2851-PR1-¿Cómo podemos capturar los datos de la web?
DOI: 10.15468/dl.tdntp7
title: Occurrence Download

description: A dataset containing 30917 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is Vascular plants of south-central China"
 ]
}

 The dataset includes 30917 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0008171-241107131044228/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.cxgjkt
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Vanessa atalanta (Linnaeus, 1758)",
 "Year is 52",
 "Country is Netherlands"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0008172-241107131044228/datasets/export for details.
DOI: 10.5281/zenodo.14076796
title: Minimal dataset for study, Spatiotemporal patterns of individual and multiple simultaneous severe weather events co-occurring with power outages in the United States, 2018-2020

description: These datasets are the minimal datasets for the study, Spatiotemporal patterns of individual and multiple simultaneous severe weather events co-occurring with power outages in the United States, 2018-2020.

Study DOI: https://doi.org/10.21203/rs.3.rs-4752336/v1
DOI: 10.5281/zenodo.14076797
title: Minimal dataset for study, Spatiotemporal patterns of individual and multiple simultaneous severe weather events co-occurring with power outages in the United States, 2018-2020

description: These datasets are the minimal datasets for the study, Spatiotemporal patterns of individual and multiple simultaneous severe weather events co-occurring with power outages in the United States, 2018-2020.

Study DOI: https://doi.org/10.21203/rs.3.rs-4752336/v1
DOI: 10.5281/zenodo.14041760
title: Swimming world records

description: This dataset contains the swimming world records for both men and women in long and short course.

LCM - long course (50m) men

SCM - short course (25m) men

LCW - long course (50m) women

SCW - short course (25m) women
DOI: 10.5281/zenodo.14041761
title: Swimming world records

description: This dataset contains the swimming world records for both men and women in long and short course.

LCM - long course (50m) men

SCM - short course (25m) men

LCW - long course (50m) women

SCW - short course (25m) women
DOI: 10.7274/25527781
title: Evolution of the Radius of Spatial Analyticity for the Dispersion Modified Degasperis-Procesi Equation

description: Here, the local well-posedness of the Cauchy problem for the dispersion modified <strong>b</strong>-equation with data in Sobolev spaces <em>H</em><sup>s</sup>(R) and analytic Gevrey spaces <em>G</em><sup>d,s</sup>(R) is proved for any <em>s</em> &gt; 1/4. However, for <strong>b</strong> = 3, which is the modified Degasperis-Procesi equation, a sharper result is established. In this case, the equation behaves as a nonlocal perturbation of the Kordeweg-de Vries (KdV) equation and well-posedness is shown for s &gt; -3/4. Furthermore, for <strong>b</strong> = 3, this equation possesses a twisted-<em>L</em><sup>2 </sup>conservation law. This yields an almost conservation law in the analytic Gevrey spaces <em>G</em><sup>d,0</sup>. Using this almost conservation law, global solutions are established and a lower bound, given by c/t <sup>4</sup>/<sup>3 + </sup>, for their radius of spatial analyticity is proved. Key ingredients in the proof of this result are the Paley-Wiener Theorem and bilinear estimates for the nonlinearity of the modified Degasperis-Procesi equation.
DOI: 10.7274/25537246
title: Asymptotic Expansions at Infinity for Solutions of Some Nonlinear Geometric PDE in Exterior Domains

description: We study asymptotic behaviors of solutions of a family of fully nonlinear elliptic equations in R<sup>n</sup> \<em>B</em><sub>1</sub> and establish expansions at infinity up to arbitrary order. We then prove the existence of solutions with prescribed asymptotic behavior at infinity and an arbitrarily high order of approximation. We also prove a similar existence result for solutions of the minimal surface equation in R<sup>n</sup> \<em>B</em><sub>1</sub> whose gradient vanishes at infinity.
DOI: 10.7274/25537246.v1
title: Asymptotic Expansions at Infinity for Solutions of Some Nonlinear Geometric PDE in Exterior Domains

description: We study asymptotic behaviors of solutions of a family of fully nonlinear elliptic equations in R<sup>n</sup> \<em>B</em><sub>1</sub> and establish expansions at infinity up to arbitrary order. We then prove the existence of solutions with prescribed asymptotic behavior at infinity and an arbitrarily high order of approximation. We also prove a similar existence result for solutions of the minimal surface equation in R<sup>n</sup> \<em>B</em><sub>1</sub> whose gradient vanishes at infinity.
DOI: 10.7274/25551114
title: Some Results on Operads and Configuration Spaces

description: The little <em>n</em>-disk operad <em>E</em>_n is constructed geometrically as the collection of configuration spaces of n-disks. This is not an isolated example of an interaction between operads and geometry: geometric objects often are either acted upon by operads, form operads, or have associated moduli spaces which form operads. One major area of study in geometric topology is the configuration spaces of nonoverlapping points in M, and more generally, embedding spaces of one manifold into another. In this thesis, we study these spaces from the perspective of operads in spectra. The category of spectra is the "linearization'' of the category of spaces, and as such it has a rich algebraic structure which parallels that of the category of chain complexes. As a result, many classical techniques from from the homological algebra of chain complexes can be used. One such technique is Koszul duality for operads, modules, and algebras.
 
 We initially study the stabilization of configuration space as an object in spectra, computing its Spanier-Whitehead dual and deducing the homotopy invariance of stabilized configuration space. For a framed manifold <em>M</em> of dimension <em>n</em>, the collection of all configuration spaces Conf(<em>M,i</em>) has a right module action of the E_n operad. We study the E_n operad action on the collection of configuration spaces and deduce results about Browder brackets in the homology of configuration spaces. We also deduce homotopy invariance results concerning the associated graded of filtrations of stabilized embedding spaces. Ultimately, we prove that the stabilized configuration spaces of a framed manifold are a fixed point of Koszul duality for right modules. In other words, the collection of stabilized configuration spaces of a framed manifold is Koszul self dual. This statement generalizes Atiyah duality to include the action of the E_n operad and has applications to spaces of embeddings and configuration spaces with labels in an E_n-algebra.
DOI: 10.7274/25551114.v1
title: Some Results on Operads and Configuration Spaces

description: The little <em>n</em>-disk operad <em>E</em>_n is constructed geometrically as the collection of configuration spaces of n-disks. This is not an isolated example of an interaction between operads and geometry: geometric objects often are either acted upon by operads, form operads, or have associated moduli spaces which form operads. One major area of study in geometric topology is the configuration spaces of nonoverlapping points in M, and more generally, embedding spaces of one manifold into another. In this thesis, we study these spaces from the perspective of operads in spectra. The category of spectra is the "linearization'' of the category of spaces, and as such it has a rich algebraic structure which parallels that of the category of chain complexes. As a result, many classical techniques from from the homological algebra of chain complexes can be used. One such technique is Koszul duality for operads, modules, and algebras.
 
 We initially study the stabilization of configuration space as an object in spectra, computing its Spanier-Whitehead dual and deducing the homotopy invariance of stabilized configuration space. For a framed manifold <em>M</em> of dimension <em>n</em>, the collection of all configuration spaces Conf(<em>M,i</em>) has a right module action of the E_n operad. We study the E_n operad action on the collection of configuration spaces and deduce results about Browder brackets in the homology of configuration spaces. We also deduce homotopy invariance results concerning the associated graded of filtrations of stabilized embedding spaces. Ultimately, we prove that the stabilized configuration spaces of a framed manifold are a fixed point of Koszul duality for right modules. In other words, the collection of stabilized configuration spaces of a framed manifold is Koszul self dual. This statement generalizes Atiyah duality to include the action of the E_n operad and has applications to spaces of embeddings and configuration spaces with labels in an E_n-algebra.
DOI: 10.7274/25562970
title: Packing Integral Tori in Del Pezzo Surfaces

description: We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in S^2 x S^2 to the Del Pezzo surfaces D<sub>n</sub>, <em>omega</em><sub>Dn </sub>for <em>n </em>= 1,...,5. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection {<em>L</em><sub>i</sub>} of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collection must intersect at least one of the <em>L</em><sub>i</sub>. We show that one can always find such a packing consisting of only the Clifford torus.<sub><br></sub>
DOI: 10.7274/25562970.v1
title: Packing Integral Tori in Del Pezzo Surfaces

description: We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in S^2 x S^2 to the Del Pezzo surfaces D<sub>n</sub>, <em>omega</em><sub>Dn </sub>for <em>n </em>= 1,...,5. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection {<em>L</em><sub>i</sub>} of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collection must intersect at least one of the <em>L</em><sub>i</sub>. We show that one can always find such a packing consisting of only the Clifford torus.<sub><br></sub>
DOI: 10.7274/25591224
title: Support of the Brown Measure of Free Multiplicative Brownian Motions with Non-Negative Initial Condition and Its Three-Parameter Family

description: We study a family of free multiplicative Brownian motions parameterized by a real variance and a complex covariance. In the case variance and covariance are the same, we identify a region such that the Brown measure is vanishing outside of the closure of this region except possibly at the origin. In the general case, we construct a mapping and define the support as the complement of the image of the complement of the first region under the mapping. Then the Brown measure is again zero outside this support except possibly at the origin.
DOI: 10.7274/25591224.v1
title: Support of the Brown Measure of Free Multiplicative Brownian Motions with Non-Negative Initial Condition and Its Three-Parameter Family

description: We study a family of free multiplicative Brownian motions parameterized by a real variance and a complex covariance. In the case variance and covariance are the same, we identify a region such that the Brown measure is vanishing outside of the closure of this region except possibly at the origin. In the general case, we construct a mapping and define the support as the complement of the image of the complement of the first region under the mapping. Then the Brown measure is again zero outside this support except possibly at the origin.
DOI: 10.7274/25596297
title: Some Results in NIP Theories

description: We give a proof using model-theoretic techniques and substitution that the Erdos-Hajnal property holds for graphs with VC-dimension at most 2. We also show that the family of graphs with bounded VC-minimal complexity, a notion that arises from VC-minimal theory, has the strong Erdos-Hajnal property. And we prove a lemma about combs and pure pairs that the author found when attempting to prove the Erdos-Hajnal property for dp-minimal graphs.
DOI: 10.7274/25596297.v1
title: Some Results in NIP Theories

description: We give a proof using model-theoretic techniques and substitution that the Erdos-Hajnal property holds for graphs with VC-dimension at most 2. We also show that the family of graphs with bounded VC-minimal complexity, a notion that arises from VC-minimal theory, has the strong Erdos-Hajnal property. And we prove a lemma about combs and pure pairs that the author found when attempting to prove the Erdos-Hajnal property for dp-minimal graphs.
DOI: 10.7274/25602501
title: The Non-Lefschetz Locus of Lines and Conics

description: A graded Artinian algebra A has the Weak Lefschetz Property if there exists a linear form l such that the multiplication map by l has maximum rank in every degree. The linear forms satisfying this property form a Zariski-open set; its complement is called the non-Lefschetz locus of A.
The study of the non-Lefschetz locus started with Boij--Migliore--Miró-Roig--Nagel, who proved that the non-Lefschetz locus of a general complete intersection of height 3 has the expected codimension.
This thesis aims to generalize this result in two main directions. The first concerns the non-Lefschetz locus of the first-cohomology module of rank 2 vector bundles E over P^2. This is motivated by Failla--Flores--Peterson who proved the WLP for such modules. The natural question is whether the non-Lefschetz locus has the expected codimension.
We first prove that the non-Lefschetz locus in this context is the set of jumping lines of E. Using this classification, we show that, assuming generality, the non-Lefschetz locus has the expected codimension. It is a hypersurface if E is unstable or its first Chern class is even, and it is a finite set otherwise.
In the second direction, we investigate analogous questions for degree-two forms rather than lines. The main result shows that the non-Lefschetz locus of conics for a general complete intersection of height 3 has the expected codimension in P^5. The hypothesis of generality is necessary: we include examples in which the non-Lefschetz locus has different codimension. 
To extend a similar result to the first cohomology modules of rank 2 vector bundles over P^2, we explore the connection between non-Lefschetz conics and jumping conics, defined first by Vitter. The non-Lefschetz locus of conics is a subset of the jumping conics, that can be proper when E is semistable with first Chern class even.
DOI: 10.7274/25602501.v1
title: The Non-Lefschetz Locus of Lines and Conics

description: A graded Artinian algebra A has the Weak Lefschetz Property if there exists a linear form l such that the multiplication map by l has maximum rank in every degree. The linear forms satisfying this property form a Zariski-open set; its complement is called the non-Lefschetz locus of A.
The study of the non-Lefschetz locus started with Boij--Migliore--Miró-Roig--Nagel, who proved that the non-Lefschetz locus of a general complete intersection of height 3 has the expected codimension.
This thesis aims to generalize this result in two main directions. The first concerns the non-Lefschetz locus of the first-cohomology module of rank 2 vector bundles E over P^2. This is motivated by Failla--Flores--Peterson who proved the WLP for such modules. The natural question is whether the non-Lefschetz locus has the expected codimension.
We first prove that the non-Lefschetz locus in this context is the set of jumping lines of E. Using this classification, we show that, assuming generality, the non-Lefschetz locus has the expected codimension. It is a hypersurface if E is unstable or its first Chern class is even, and it is a finite set otherwise.
In the second direction, we investigate analogous questions for degree-two forms rather than lines. The main result shows that the non-Lefschetz locus of conics for a general complete intersection of height 3 has the expected codimension in P^5. The hypothesis of generality is necessary: we include examples in which the non-Lefschetz locus has different codimension. 
To extend a similar result to the first cohomology modules of rank 2 vector bundles over P^2, we explore the connection between non-Lefschetz conics and jumping conics, defined first by Vitter. The non-Lefschetz locus of conics is a subset of the jumping conics, that can be proper when E is semistable with first Chern class even.
DOI: 10.7274/25604622
title: An HKR Theorem for Factorization Homology

description: We prove a Hochschild-Kostant-Rosenberg theorem (``the HKR theorem'') which computes the factorization homology of certain smooth commutative ring spectra. In doing so we fix and generalize a THH computation which was first conceived as the brainchild of McCarthy-Minasian. Included also is a direct application of our revised HKR theorem to the higher THH of rational $KU$.
DOI: 10.7274/25604622.v1
title: An HKR Theorem for Factorization Homology

description: We prove a Hochschild-Kostant-Rosenberg theorem (``the HKR theorem'') which computes the factorization homology of certain smooth commutative ring spectra. In doing so we fix and generalize a THH computation which was first conceived as the brainchild of McCarthy-Minasian. Included also is a direct application of our revised HKR theorem to the higher THH of rational $KU$.
DOI: 10.7274/25607832
title: Some Generalizations in Nonparametric Function Estimation for Temporal Spatial Multidimensional Data

description: This thesis presents a comprehensive examination of cutting-edge statistical methods for analyzing multidimensional data focusing on nonparametric function estimation through the popular technique called Trend Filtering. It delves into the application of this approach within temporal and spatial datasets, thereby enhancing statistical analysis across various domains including climatology, finance, neuroscience, agriculture, among others. Central to these explorations are two entwined main themes: the development of computationally efficient algorithms and the establishment of strong statistical guarantees for estimators across a broad array of frameworks.

In the first chapter, we outline the motivation, theoretical background, and critical challenges addressed by this thesis, providing a cohesive framework for the rest of the thesis. This introductory chapter sets the stage for a detailed exploration of innovative statistical methods, preparing the reader for the in-depth studies that follow.

The second chapter focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. In such a context, we study the Trend Filtering, a nonparametric estimator introduced by [33] and [41]. To the best of our knowledge, this estimator has not previously been examined in a similar context. For univariate settings, the signals we consider are assumed to have a kth weak derivative with bounded total variation, allowing for a general degree of smoothness. In the multivariate scenario, we study a K-Nearest Neighbor fused lasso estimator as in [35], employing an ADMM algorithm, suitable for signals with bounded variation that adhere to a piecewise Lipschitz continuity criterion. By aligning with lower bounds, the minimax optimality of our univariate and multivariate estimators is validated. A unique phase transition phenomenon, previously uncharted in Trend Filtering studies, emerges through our analysis. Both simulation studies and real data applications underscore the superior performance of our method when compared with established techniques in the existing literature.

Finally, the third chapter summarizes the contributions of this thesis and provides possible directions for future work.
DOI: 10.7274/25607832.v1
title: Some Generalizations in Nonparametric Function Estimation for Temporal Spatial Multidimensional Data

description: This thesis presents a comprehensive examination of cutting-edge statistical methods for analyzing multidimensional data focusing on nonparametric function estimation through the popular technique called Trend Filtering. It delves into the application of this approach within temporal and spatial datasets, thereby enhancing statistical analysis across various domains including climatology, finance, neuroscience, agriculture, among others. Central to these explorations are two entwined main themes: the development of computationally efficient algorithms and the establishment of strong statistical guarantees for estimators across a broad array of frameworks.

In the first chapter, we outline the motivation, theoretical background, and critical challenges addressed by this thesis, providing a cohesive framework for the rest of the thesis. This introductory chapter sets the stage for a detailed exploration of innovative statistical methods, preparing the reader for the in-depth studies that follow.

The second chapter focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. In such a context, we study the Trend Filtering, a nonparametric estimator introduced by [33] and [41]. To the best of our knowledge, this estimator has not previously been examined in a similar context. For univariate settings, the signals we consider are assumed to have a kth weak derivative with bounded total variation, allowing for a general degree of smoothness. In the multivariate scenario, we study a K-Nearest Neighbor fused lasso estimator as in [35], employing an ADMM algorithm, suitable for signals with bounded variation that adhere to a piecewise Lipschitz continuity criterion. By aligning with lower bounds, the minimax optimality of our univariate and multivariate estimators is validated. A unique phase transition phenomenon, previously uncharted in Trend Filtering studies, emerges through our analysis. Both simulation studies and real data applications underscore the superior performance of our method when compared with established techniques in the existing literature.

Finally, the third chapter summarizes the contributions of this thesis and provides possible directions for future work.