Tootfinder

Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
Ophelia Evelyn Sommer, Xueda Wen, Ashvin Vishwanath
https://arxiv.org/abs/2405.05316

Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically HBC captures the flow of local Berry curvature in a system. Here we provide a simple formula for computing the HBC for extended $d = 1$ systems at the level of wave functions using the Schmidt decomposition. We also find a corresponding formula for matrix product states (MPS), and show that for translationally invariant MPS this gives rise to a quantized invariant. We dem…

Bohr radius for invariant families of bounded analytic functions and certain Integral transforms
Molla Basir Ahamed, Partha Pratim Roy, Sabir Ahammed
https://arxiv.org/abs/2405.04040

Bohr radius for invariant families of bounded analytic functions and certain Integral transforms
In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $ \mathbb{D} $. Then, we obtain Bohr inequality for certain integral transforms, namely Fourier (discrete) and Laplace (discrete) transforms of bounded analytic functions $ f(z)=\sum_{n=0}^{\infty}a_nz^n $, in a simply connected domain \begin{align*} Ω_γ=\biggl\{z\in\mathbb{C}: \bigg|z+\dfracγ{1-γ}\bigg|<\dfrac{1}{1-γ}\;\mbox{for}\; 0\leq γ<1\biggr\}, \end{a…

This https://arxiv.org/abs/2403.01636 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sample Efficient Myopic Exploration Through Multitask Reinforcement Learning with Diverse Tasks
Multitask Reinforcement Learning (MTRL) approaches have gained increasing attention for its wide applications in many important Reinforcement Learning (RL) tasks. However, while recent advancements in MTRL theory have focused on the improved statistical efficiency by assuming a shared structure across tasks, exploration--a crucial aspect of RL--has been largely overlooked. This paper addresses this gap by showing that when an agent is trained on a sufficiently diverse set of tasks, a generic po…

This https://arxiv.org/abs/2303.12654 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Informational Rescaling of PCA Maps with Application to Genetic Distance
We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component analysis (PCA) (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Rescaling Principal Component based distances using MI allows a representation of relative statistical associations when,…

Assessing light pollution in vast areas: zenith sky brightness maps of Catalonia
Hector Linares, Eduard Masana Salvador J Ribas, Manuel Garc\'ia-Gil, Martin Aub\'e, Alejandro S\'anchez de Miguel, Alexandre Simoneau
https://arxiv.org/abs/2403.00112

Assessing light pollution in vast areas: zenith sky brightness maps of Catalonia
Zenith sky brightness maps in the V and B bands of the region of Catalonia are presented in this paper. For creating them we have used the light pollution numerical model Illumina v2. The maps have a sampling of 5x5 km for the whole region with an improved resolution of 1x1 km for one of the provinces within Catalonia, Tarragona. Before creating the final maps, the methodology was tested successfully by comparing the computed values to measurements in nineteen different locations spread out thr…

This https://arxiv.org/abs/2403.01636 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sample Efficient Myopic Exploration Through Multitask Reinforcement Learning with Diverse Tasks
Multitask Reinforcement Learning (MTRL) approaches have gained increasing attention for its wide applications in many important Reinforcement Learning (RL) tasks. However, while recent advancements in MTRL theory have focused on the improved statistical efficiency by assuming a shared structure across tasks, exploration--a crucial aspect of RL--has been largely overlooked. This paper addresses this gap by showing that when an agent is trained on a sufficiently diverse set of tasks, a generic po…

Crowdsourcing public attitudes toward local services through the lens of Google Maps reviews: An urban density-based perspective
Lingyao Li, Songhua Hu, Atiyya Shaw, Libby Hemphill
https://arxiv.org/abs/2404.13156

Crowdsourcing public attitudes toward local services through the lens of Google Maps reviews: An urban density-based perspective
Understanding how urban density impacts public perceptions of urban service is important for informing livable, accessible, and equitable urban planning. Conventional methods such as surveys are limited by their sampling scope, time efficiency, and expense. On the other hand, crowdsourcing through online platforms presents an opportunity for decision-makers to tap into a user-generated source of information that is widely available and cost-effective. To demonstrate such potential, we collect G…

This https://arxiv.org/abs/2304.10529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The first step towards symplectic homotopy theory
We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are pseudoholomorphic maps. We define new homotopy theories for these categories. In particular, we give definitions of homotopy equivalent symplectic manifolds and define new cohomology theories. Theses cohomology theories are functorial, homotopy invarian…

Sequential transport maps using SoS density estimation and $\alpha$-divergences
Benjamin Zanger, Tiangang Cui, Martin Schreiber, Olivier Zahm
https://arxiv.org/abs/2402.17943

Sequential transport maps using SoS density estimation and $α$-divergences
Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further invertigate the sequential transport maps framework proposed from arXiv:2106.04170 arXiv:2303.02554, which builds on a sequence of composed Knothe-Rosenblatt (KR) maps. Each of those maps are built by first estimating an intermediate density of moderate complexity, and then by computing the exact KR map from a reference dens…

This https://arxiv.org/abs/2212.08345 has been replaced.
link: https://scholar.google.com/scholar?q=a

Open Gromov-Witten invariants from the Fukaya category
This paper proposes a framework to show that the Fukaya category of a symplectic manifold $X$ determines the open Gromov-Witten invariants of Lagrangians $L \subset X$. We associate to an object in an $A_\infty$-category an extension of the negative cyclic homology, called \emph{relative cyclic homology}. We extend the Getzler-Gauss-Manin connection to relative cyclic homology. Then, we construct (under simplifying technical assumptions) a relative cyclic open-closed map, which maps the relativ…