Semi-coarse Spaces, Homotopy and Homology

October 5, 2022

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Mathematics
Algebraic Topology
General Topology
Geometric Topology
We begin the study the algebraic topology of semi-coarse spaces, which are generalizations of coarse spaces that enable one to endow non-trivial `coarse-like' structures to compact metric spaces, something which is impossible in coarse geom...

On the Statistical Complexity of Estimation and Testing under Privacy Constraints

October 5, 2022

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Computer Science
Machine Learning
Cryptography and Security
The challenge of producing accurate statistics while respecting the privacy of the individuals in a sample is an important area of research. We study minimax lower bounds for classes of differentially private estimators. In particular, we s...

The tropical nn-gonal construction

October 5, 2022

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Mathematics
Combinatorics
Algebraic Geometry
We give a purely tropical analogue of Donagi's nn-gonal construction and investigate its combinatorial properties. The input of the construction is a harmonic double cover of an nn-gonal tropical curve. For n=2n = 2 and a dilated double co...

Large-scale power loss in ground-based CMB mapmaking

October 5, 2022

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Physics
Instrumentation and Methods for Astrophysics
Cosmology and Nongalactic Astrophysics
CMB mapmaking relies on a data model to solve for the sky map, and this process is vulnerable to bias if the data model cannot capture the full behavior of the signal. We demonstrate that this bias is not just limited to small-scale effects...

A Road To Compactness Through Guessing Models

October 5, 2022

Mathematics
Logic
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that ...

Nonconvex quasi-variational inequalities: stability analysis and application to numerical optimization

October 5, 2022

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Mathematics
Optimization and Control
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of \emph{optimal value function}, we transform the problem into that of solving a nonsmooth system of inequalities. Based on thi...

Modelling tree survival for investigating climate change effects

October 5, 2022

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Statistics
Applications
Computation
Using German forest health monitoring data we investigate the main drivers leading to tree mortality and the association between defoliation and mortality; in particular (a) whether defoliation is a proxy for other covariates (climate, soil...

Faster parameterized algorithms for modification problems to minor-closed classes

October 5, 2022

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Computer Science
Mathematics
Data Structures and Algorithms
Computational Complexity
Combinatorics
Data Structures and Algorithms
Computational Complexity
Combinatorics
Let G{\cal G} be a minor-closed graph class and let GG be an nn-vertex graph. We say that GG is a kk-apex of G{\cal G} if GG contains a set SS of at most kk vertices such that GSG\setminus S belongs to G{\cal G}. Our first result ...

Systematizing Cellular Complexity: A Hilbertian Approach To Biological Problems

October 5, 2022

Quantitative Biology
Physics
Other Quantitative Biology
Biological Physics
Examining individual components of cellular systems has been successful in uncovering molecular reactions and interactions. However, the challenge lies in integrating these components into a comprehensive system-scale map. This difficulty a...

Orphan Calabi-Yau threefold with arithmetic monodromy group

October 5, 2022

Mathematics
Algebraic Geometry
We study monodromy groups of Picard-Fuchs operators of one-parameter families of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy (\emph{orphan operators}). We construct rational symplectic bases for the monodromy action...