Tootfinder

This https://arxiv.org/abs/2310.02204 has been replaced.
link: https://scholar.google.com/scholar?q=a

Determinisation and Unambiguisation of Polynomially-Ambiguous Rational Weighted Automata
We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted automaton? Recent results by Bell and Smertnig show that the problem is decidable, however they do not provide any complexity bounds. We show that both problems are in PSPACE for polynomially-ambiguous weighted automata.

game_thrones: Game of Thrones coappearances
Network of coappearances of characters in the Game of Thrones series, by George R. R. Martin, and in particular coappearances in the book "A Storm of Swords." Nodes are unique characters, and edges are weighted by the number of times the two characters' names appeared within 15 words of each other in the text.
This network has 107 nodes and 352 edges.
Tags: Social, Fictional, Weighted

What Are Weighted Keys and Why You Need (or Don't Need) Them?
#DigitalPiano #MusicianTips
https://m…

What Are Weighted Keys and Why You Need (or Don't Need) Them?
Stan Stewart - @muz4now

Weighted least squares subdivision schemes for noisy data on triangular meshes
Costanza Conti, Sergio L\'opez-Ure\~na, Dionisio F. Y\'a\~nez
https://arxiv.org/abs/2507.18976

Weighted least squares subdivision schemes for noisy data on triangular meshes
This paper presents and analyses a new family of linear subdivision schemes to refine noisy data given on triangular meshes. The subdivision rules consist of locally fitting and evaluating a weighted least squares approximating first-degree polynomial. This type of rules, applicable to any type of triangular grid, including finite grids or grids containing extraordinary vertices, are geometry-dependent which may result in non-uniform schemes. For these new subdivision schemes, we are able to pr…

Edge-weighted Matching in the Dark
Zhiyi Huang, Enze Sun, Xiaowei Wu, Jiahao Zhao
https://arxiv.org/abs/2507.19366 https://arxiv.org/pdf/2507.19366

Edge-weighted Matching in the Dark
We present a $0.659$-competitive Quadratic Ranking algorithm for the Oblivious Bipartite Matching problem, a distribution-free version of Query-Commit Matching. This result breaks the $1-\frac{1}{e}$ barrier, addressing an open question raised by Tang, Wu, and Zhang (JACM 2023). Moreover, the competitive ratio of this distribution-free algorithm improves the best existing $0.641$ ratio for Query-Commit Matching achieved by the distribution-dependent algorithm of Chen, Huang, Li, and Tang (SODA …

Leveraging Relational Evidence: Population Size Estimation on Tree-Structured Data with the Weighted Multiplier Method
Mallory J Flynn, Paul Gustafson
https://arxiv.org/abs/2506.21020

Leveraging Relational Evidence: Population Size Estimation on Tree-Structured Data with the Weighted Multiplier Method
Populations of interest are often hidden from data for a variety of reasons, though their magnitude remains important in determining resource allocation and appropriate policy. One popular approach to population size estimation, the multiplier method, is a back-calculation tool requiring only a marginal subpopulation size and an estimate of the proportion belonging to this subgroup. Another approach is to use Bayesian methods, which are inherently well-suited to incorporating multiple data sour…

Detecting weighted hidden cliques
Urmisha Chatterjee, Karissa Huang, Ritabrata Karmakar, B. R. Vinay Kumar, G\'abor Lugosi, Nandan Malhotra, Anirban Mandal, Maruf Alam Tarafdar
https://arxiv.org/abs/2506.21543

Detecting weighted hidden cliques
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated with independent and identically distributed edge weights from a distribution $P$. Under the alternate hypothesis, $k$ vertices are chosen at random and the edge weights between them are drawn from a distribution $Q$, while the remaining are sampled from $P$.…

$\mathbb{G}$-uniform weighted K-stability for models on klt varieties
Jiyuan Han, Yaxiong Liu
https://arxiv.org/abs/2506.18039 https://

$\mathbb{G}$-uniform weighted K-stability for models on klt varieties
In this paper, we make a generalization of the results in \cite{Li22a} to the singular and weighted setting. In particular, we show that on a polarized projective klt variety, the $\mathbb{G}$-uniform weighted K-stability for models implies the $\mathbb{G}$-coercivity of the weighted Mabuchi functional. In the toric case, we further show that the $(\mathbb{C}^{\times})^n$-uniform $(\mathrm{v},\mathrm{w}\cdot\ell_{\mathrm{ext}})$-weighted K-stability is preserved when perturbing the polarization…

psi: Plant Photosystem I excitation energy transfer network (2020)
Weighted directed network of the light-harvesting Photosystem Ι (PSI) of the plant Pisum sativum. The nodes represent chromophores with different identities (i.e. chlorophyll a, chlorophyll b, β-carotene and derivates, lutein, violaxanthin), while edges represent FRET transfer between chromophores. The link directionality connecting nodes in the PSI network depends on the energy levels of the connected chromophores. The…

New results on universal Taylor series via weighted polynomial approximation
St\'ephane Charpentier (I2M), Konstantinos Maronikolakis
https://arxiv.org/abs/2506.20224

New results on universal Taylor series via weighted polynomial approximation
We use weighted polynomial approximation to prove the existence of a compact set K with non-empty interior and a function f is dense in the space A(K) of all continuous functions on K that are holomorphic in the interior of K, endowed with the sup norm, while the set This improves a result of Mouze. The main ideas of the proof also allows us to construct a holomorphic function while the modulus of its non-zero Taylor coecients go to $\infty$. In passing, we complement a result by Pritsker a…

Weighted four-dimensional Fano hypersurfaces of K3 type
Valeria Bertini, Francesco Antonio Denisi, Enrico Fatighenti, Annalisa Grossi
https://arxiv.org/abs/2506.18014

Weighted four-dimensional Fano hypersurfaces of K3 type
We study weighted Fano fourfolds of K3 type realized as hypersurfaces in weighted projective spaces. Under the additional assumption that the singular locus has dimension at most one, we prove that only finitely many such families exist. We provide the complete list and analyze their rationality properties, as well as their singularities.

Papanicolaou Stain Unmixing for RGB Image Using Weighted Nucleus Sparsity and Total Variation Regularization
Nanxin Gong, Saori Takeyama, Masahiro Yamaguchi, Takumi Urata, Fumikazu Kimura, Keiko Ishii
https://arxiv.org/abs/2506.20450

Papanicolaou Stain Unmixing for RGB Image Using Weighted Nucleus Sparsity and Total Variation Regularization
The Papanicolaou stain, consisting of eosin Y, hematoxylin, light Green SF yellowish, orange G, and Bismarck brown Y, provides extensive color information essential for cervical cancer screening in cytopathology. However, the visual observation of these colors is subjective and difficult to characterize. In digital image analysis, the RGB intensities are affected by staining and imaging variations, hindering direct quantification of color in Papanicolaou-stained samples. Stain unmixing is a pro…

Weighted Assumption Based Argumentation to reason about ethical principles and actions
Paolo Baldi, Fabio Aurelio D'Asaro, Abeer Dyoub, Francesca Alessandra Lisi
https://arxiv.org/abs/2506.18056

Weighted Assumption Based Argumentation to reason about ethical principles and actions
We augment Assumption Based Argumentation (ABA for short) with weighted argumentation. In a nutshell, we assign weights to arguments and then derive the weight of attacks between ABA arguments. We illustrate our proposal through running examples in the field of ethical reasoning, and present an implementation based on Answer Set Programming.

Perpetua: Multi-Hypothesis Persistence Modeling for Semi-Static Environments
Miguel Saavedra-Ruiz, Samer B. Nashed, Charlie Gauthier, Liam Paull
https://arxiv.org/abs/2507.18808

Perpetua: Multi-Hypothesis Persistence Modeling for Semi-Static Environments
Many robotic systems require extended deployments in complex, dynamic environments. In such deployments, parts of the environment may change between subsequent robot observations. Most robotic mapping or environment modeling algorithms are incapable of representing dynamic features in a way that enables predicting their future state. Instead, they opt to filter certain state observations, either by removing them or some form of weighted averaging. This paper introduces Perpetua, a method for mo…

There’s a small difference between MacDonald and many other social media starlets.
She is 79.
“I was 70 when I started [working out],” MacDonald says on a video call from her home in Ontario,
white hair elegantly coiffed.
“I keep thinking I’m in my 30s.”
MacDonald’s workouts are intense,
whether you’re 30 or 70.
She does deadlifts, weighted planks and kettlebell swings,
and casually lifts dumbbells the size of fire extinguishers over her head.

On Uniform Weighted Deep Polynomial approximation
Kingsley Yeon, Steven B. Damelin
https://arxiv.org/abs/2506.21306 https://arxiv.org…

On Uniform Weighted Deep Polynomial approximation
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of degrees of freedom \cite{Sta, GN}. In contrast, polynomial approximations admit only algebraic convergence by Jackson's theorem \cite{Lub2}. Recent work shows that composite polynomial architectures can recover exponential approximation rates even with…

The Laplacian matrix of weighted threshold graphs
Yingyue Ke, Willem H. Haemers, Piet Van Mieghem
https://arxiv.org/abs/2506.16839 https://

The Laplacian matrix of weighted threshold graphs
Threshold graphs are generated from one node by repeatedly adding a node that links to all existing nodes or adding a node without links. In the weighted threshold graph, we add a new node in step $i$, which is linked to all existing nodes by a link of weight $w_i$. In this work, we consider the set ${\cal A}_N$ that contains all Laplacian matrices of weighted threshold graphs of order $N$. We show that ${\cal A}_N$ forms a commutative algebra. Using this, we find a common basis of eigenvectors…

Weighted nonlocal area functionals without the triangle inequality
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
https://arxiv.org/abs/2506.19048 https:/…

Weighted nonlocal area functionals without the triangle inequality
We consider a weighted nonlocal area functional in which the coefficients do not satisfy the triangle inequality. In the context of three phase transitions, this means that one of the weights is larger than the sum of the other two, say $$σ_{-1,1} > σ_{-1,0} + σ_{0,1}.$$ We show that the energy can be reduced by covering interfaces between phases $-1$ and $1$ with a thin strip of phase $0$. Moreover, as the fractional parameter $s\nearrow1$, we prove that the nonlocal energies $Γ$-converg…

copenhagen: Copenhagen Networks Study
A network of social interactions among university students within the Copenhagen Networks Study, over a period of four weeks, sampled every 5 minutes. Interactions include physical proximity (undirected), phone calls (directed, weighted), text messages (directed), and information about Facebook friendships (undirected). Nodes include some metadata, including gender.
This network has 692 nodes and 2426279 edges.
Tags: Social, Offline, Un…

Spectrum Estimation through Kirchhoff Random Forests
Simon Barthelm\'e, Fabienne Castell, Alexandre Gaudilli\`ere, Clothilde M\'elot, Matteo Quattropani, Nicolas Tremblay
https://arxiv.org/abs/2507.19164

Spectrum Estimation through Kirchhoff Random Forests
Given a non-oriented edge-weighted graph, we show how to make some estimation of the associated Laplacian eigenvalues through Monte Carlo evaluation of spectral quantities computed along Kirchhoff random rooted spanning forest trajectories. The sampling cost of this estimation is only linear in the node number, up to a logarithmic factor. By associating a double cover of such a graph with any symmetric real matrix, we can then perform spectral estimation in the same way for the latter.

On weighted multilinear polynomial averages in finite fields
Guo-Dong Hong
https://arxiv.org/abs/2507.14414 https://arxiv.org/pdf/250…

On weighted multilinear polynomial averages in finite fields
We study the weighted multilinear polynomial averages in finite fields. The essential ingredient is the $u^s$-norm control of the corresponding weighted multilinear polynomial averages in finite fields, which is motivated by Teräväinen \cite{T24}. As an application, we prove an asymptotic formula for the number of the following multidimensional rational function progressions in the subsets of $\mathbb{F}_p^D$: \[ \textbf{x}, \textbf{x}+ P_1(φ(y))v_1,\cdots, \textbf{x}+ P_k(φ(y))v_k, \] wher…

This https://arxiv.org/abs/2505.07292 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Weyl laws for exponentially small singular values of the $\overline{\partial}$ operator
We study the number of exponentially small singular values of the semiclassical $\overline{\partial}$ operator on exponentially weighted $L^2$ spaces on the two-dimensional torus. Accurate upper and lower bounds on the number of such singular values are established with the help of auxiliary notions of upper and lower bound weights. Assuming that the Laplacian of the exponential weight changes sign along a curve, we construct optimal such weights by solving a free boundary problem, which yields…

100 calf raises at 69, also with some shoulder mobility work. #calisthenics #fitness

Weighted superposition operators on Fock spaces
Tesfa Mengestie
https://arxiv.org/abs/2506.16152 https://arxiv.org/pdf/2506.16152

Weighted superposition operators on Fock spaces
We characterize all pairs of entire functions $(u,ψ)$ for which the induced weighted superposition operator $S_{(u,ψ)}$ transforms one Fock space into another Fock space.Further analytical structures like boundedness and Lipschitz continuity of $S_{(u,ψ)}$ are described. We, in particular, show the Fock spaces support no compact weighted superposition operator.

Properties and applications of partial multiple weights for fractional integrals
Wang Dinghuai, Yin Huicheng
https://arxiv.org/abs/2505.21007 https://

Properties and applications of partial multiple weights for fractional integrals
In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation theorem for two types of off-diagonal estimates. Secondly, we establish some weighted estimates for fractional integrals associated with partial Muckenhoupt weights. As applications, several basic inequalities (including the Fefferman-Phong inequality, the de…

Frequency-Weighted Training Losses for Phoneme-Level DNN-based Speech Enhancement
Nasser-Eddine Monir, Paul Magron, Romain Serizel
https://arxiv.org/abs/2506.18714

Frequency-Weighted Training Losses for Phoneme-Level DNN-based Speech Enhancement
Recent advances in deep learning have significantly improved multichannel speech enhancement algorithms, yet conventional training loss functions such as the scale-invariant signal-to-distortion ratio (SDR) may fail to preserve fine-grained spectral cues essential for phoneme intelligibility. In this work, we propose perceptually-informed variants of the SDR loss, formulated in the time-frequency domain and modulated by frequency-dependent weighting schemes. These weights are designed to emphas…

Bridging Equilibrium and Kinetics Prediction with a Data-Weighted Neural Network Model of Methane Steam Reforming
Zofia Pizo\'n, Shinji Kimijima, Grzegorz Brus
https://arxiv.org/abs/2506.17224

Bridging Equilibrium and Kinetics Prediction with a Data-Weighted Neural Network Model of Methane Steam Reforming
Hydrogen's role is growing as an energy carrier, increasing the need for efficient production, with methane steam reforming being the most widely used technique. This process is crucial for applications like fuel cells, where hydrogen is converted into electricity, pushing for reactor miniaturization and optimized process control through numerical simulations. Existing models typically address either kinetic or equilibrium regimes, limiting their applicability. Here we show a surrogate model ca…

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis
Emmanuel Russ (I2M), Herv\'e Pajot (IF)
https://arxiv.org/abs/2507.19235

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis
Let G = (V, p, $μ$) be a (finite or infinite) weighted graph with bounded geometry. Assuming that G satisfies the classical curvaturedimension condition of Bakry-Emery CD(K, n) with K $\ge$ 0 (for the usual Laplacian), we prove that the doubling volume property holds. One of the key points is to establish the existence and uniqueness of solutions of a modified non linear heat equation which replaces the standard one usually used in the case of Riemannian manifolds. Li-Yau and Harnack estimates…

Efficient Feedback Design for Unsourced Random Access with Integrated Sensing and Communication
Mohammad Javad Ahmadi, Mohammad Kazemi, Rafael F. Schaefer
https://arxiv.org/abs/2506.20262

Efficient Feedback Design for Unsourced Random Access with Integrated Sensing and Communication
We consider an unsourced random access (URA) system enhanced with a feedback mechanism that serves both communication and sensing tasks. While traditional URA systems do not incorporate feedback, we propose a novel feedback signal design that announces the decoding status of users and simultaneously enables target sensing. To design this dual-purpose feedback, we introduce a modified projected gradient descent algorithm that minimizes a weighted combination of communication and sensing errors. …

DRWKV: Focusing on Object Edges for Low-Light Image Enhancement
Xuecheng Bai, Yuxiang Wang, Boyu Hu, Qinyuan Jie, Chuanzhi Xu, Hongru Xiao, Kechen Li, Vera Chung
https://arxiv.org/abs/2507.18594

DRWKV: Focusing on Object Edges for Low-Light Image Enhancement
Low-light image enhancement remains a challenging task, particularly in preserving object edge continuity and fine structural details under extreme illumination degradation. In this paper, we propose a novel model, DRWKV (Detailed Receptance Weighted Key Value), which integrates our proposed Global Edge Retinex (GER) theory, enabling effective decoupling of illumination and edge structures for enhanced edge fidelity. Secondly, we introduce Evolving WKV Attention, a spiral-scanning mechanism tha…

All-Pairs Shortest Paths with Few Weights per Node
Amir Abboud, Nick Fischer, Ce Jin, Virginia Vassilevska Williams, Zoe Xi
https://arxiv.org/abs/2506.20017

All-Pairs Shortest Paths with Few Weights per Node
We study the central All-Pairs Shortest Paths (APSP) problem under the restriction that there are at most $d$ distinct weights on the outgoing edges from every node. For $d=n$ this is the classical (unrestricted) APSP problem that is hypothesized to require cubic time $n^{3-o(1)}$, and at the other extreme, for $d=1$, it is equivalent to the Node-Weighted APSP problem. We present new algorithms that achieve the following results: 1. Node-Weighted APSP can be solved in time $\tilde{O}(n^{(3+ω…

This https://arxiv.org/abs/2504.06248 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs
The partial integrability of the Kuramoto model is often thought to be restricted to identically connected oscillators or groups thereof. Yet, the exact connectivity prerequisites for having constants of motion on more general graphs have remained elusive. Using spectral properties of the Koopman generator, we derive necessary and sufficient conditions for the existence of distinct constants of motion in the Kuramoto model with heterogeneous phase lags on any weighted, directed, signed graph. T…

Automorphisms of prime power order of weighted hypersurfaces
Alvaro Liendo, Ana Julisa Palomino
https://arxiv.org/abs/2507.13538 https://

Automorphisms of prime power order of weighted hypersurfaces
We study automorphisms of quasi-smooth hypersurfaces in weighted projective spaces, extending classical results for smooth hypersurfaces in projective space to the weighted setting. We establish effective criteria for when a power of a prime number can occur as the order of an automorphism, and we derive explicit bounds on the possible prime orders. A key role is played by a weighted analogue of the classical Klein hypersurface, which we show realizes the maximal prime order of an automorphism …

Weighted Parameter Estimators of the Generalized Extreme Value Distribution in the Presence of Missing Observations
James H. McVittie, Orla A. Murphy
https://arxiv.org/abs/2506.15964

Weighted Parameter Estimators of the Generalized Extreme Value Distribution in the Presence of Missing Observations
Missing data occur in a variety of applications of extreme value analysis. In the block maxima approach to an extreme value analysis, missingness is often handled by either ignoring missing observations or dropping a block of observations from the analysis. However, in some cases, missingness may occur due to equipment failure during an extreme event, which can lead to bias in estimation. In this work, we propose weighted maximum likelihood and weighted moment-based estimators for the generaliz…

Self-Supervised Joint Reconstruction and Denoising of T2-Weighted PROPELLER MRI of the Lungs at 0.55T
Jingjia Chen, Haoyang Pei, Christoph Maier, Mary Bruno, Qiuting Wen, Seon-Hi Shin, William Moore, Hersh Chandarana, Li Feng
https://arxiv.org/abs/2507.14308

Self-Supervised Joint Reconstruction and Denoising of T2-Weighted PROPELLER MRI of the Lungs at 0.55T
Purpose: This study aims to improve 0.55T T2-weighted PROPELLER lung MRI through a self-supervised joint reconstruction and denoising model. Methods: T2-weighted 0.55T lung MRI dataset including 44 patients with previous covid infection were used. A self-supervised learning framework was developed, where each blade of the PROPELLER acquisition was split along the readout direction into two partitions. One subset trains the unrolled reconstruction network, while the other subset is used for lo…

Enhancing POI Recommendation through Global Graph Disentanglement with POI Weighted Module
Pei-Xuan Li, Wei-Yun Liang, Fandel Lin, Hsun-Ping Hsieh
https://arxiv.org/abs/2507.14612

Enhancing POI Recommendation through Global Graph Disentanglement with POI Weighted Module
Next point of interest (POI) recommendation primarily predicts future activities based on users' past check-in data and current status, providing significant value to users and service providers. We observed that the popular check-in times for different POI categories vary. For example, coffee shops are crowded in the afternoon because people like to have coffee to refresh after meals, while bars are busy late at night. However, existing methods rarely explore the relationship between POI categ…

celegansneural: C. elegans neurons (1986)
A network representing the neural connections of the Caenorhabditis elegans nematode.
This network has 297 nodes and 2359 edges.
Tags: Biological, Connectome, Weighted
https://networks.skewed.de/net/celegansneural
Rid…

A Weighted Likelihood Approach Based on Statistical Data Depths
Claudio Agostinelli, Ayanendranath Basu, Giulia Bertagnolli, Arun Kumar Kuchibhotla
https://arxiv.org/abs/2507.16998

A Weighted Likelihood Approach Based on Statistical Data Depths
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical depth of each data point relative to the model, as opposed to the sample. An observation is considered regular when the corresponding difference of these two depths is close to zero. When this difference is large the observation score contribution is downweight…

The Bivariate regular variation of randomly weighted sums revisited in the presence of interdependence
Dimitrios G. Konstantinides, Charalampos D. Passalidis
https://arxiv.org/abs/2506.17895

The Bivariate regular variation of randomly weighted sums revisited in the presence of interdependence
We study the closure properties of the class of Bivariate Regular Variation, symbolically BRV , in standard and nonstandard cases, with respect to the randomly weighted sums. However, we take into consideration a weak dependence structure among the random weights and the main random variables, providing more flexibility in applications. In the first main result, under the condition that the main random variables belong to BRV , we provide a dependent bivariate extension of Breiman's theorem, un…

Generalized Hilbert operators acting from Hardy spaces to weighted Bergman spaces
Liyi Wang, Shanli Ye
https://arxiv.org/abs/2506.19338 https://

Generalized Hilbert operators acting from Hardy spaces to weighted Bergman spaces
Let $μ$ be a positive Borel measure on the interval $[0,1)$. For $α>0$, the generalized Hankel matrix $\mathcal{H}_{μ, α}=(μ_{n, k, α})_{n, k \geq 0}$ with entries $μ_{n, k, α}=\int_{[0,1)} \frac{Γ(n+α)}{n ! Γ(α)} t^{n+k} \mathrm{d}μ(t)$ induces formally the operator \begin{equation*} \mathcal{H}_{μ, α}(f)(z)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} μ_{n, k, α} a_k\right) z^n \end{equation*} on the space of all analytic function $f(z)=\sum_{k=0}^{\infty} a_{k} z^{k}$ in the…

Weighted $L^2$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions
Zhenbin Cao, Jingyue Li, Changxing Miao, Yixuan Pang
https://arxiv.org/abs/2506.18657

Weighted $L^2$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions
We systematically study weighted $L^2$ restriction for quadratic manifolds of arbitrary codimensions by sharp uniform Fourier decay estimates and a refinement of the Du-Zhang method. Comparison with prior results is also discussed. In addition,we obtain an almost complete relation diagram for all existing nondegeneracy conditions for quadratic manifolds of arbitrary codimensions. These conditions come from various topics in harmonic analysis related to "curvature": Fourier restriction, decoupli…

sp_office: Workplace contacts (2013)
A temporal network of contacts between individuals, measured in an office building in France, from June 24 to July 3, 2013.
This network has 92 nodes and 9827 edges.
Tags: Social, Offline, Weighted, Temporal, Metadata
https://networks.skewed.de/net/sp_offi

The norms for symmetric and antisymmetric tensor products of the weighted shift operators
Xiance Tian, Penghui Wang, Zeyou Zhu
https://arxiv.org/abs/2507.17181

The norms for symmetric and antisymmetric tensor products of the weighted shift operators
In the present paper, we study the norms for symmetric and antisymmetric tensor products of weighted shift operators. By proving that for $n\geq 2$, $$\|S_α^{l_1}\odot\cdots \odot S_α^{l_k}\odot S_α^{*l_{k+1}}\odot\cdots \odot S_α^{*l_{n}}\| =\mathop{\prod}_{i=1}^n\left \| S_α^{l_{i}}\right\|, \text{ for any} \ (l_1,l_2\cdots l_n)\in\mathbb N^n$$ if and only if the weight satisfies the regularity condition, we partially solve \cite[Problem 6 and Problem 7]{GA}. It wil…

Correlations of error terms for weighted prime counting functions
Shubhrajit Bhattacharya, Greg Martin, Reginald M. Simpson
https://arxiv.org/abs/2507.13504

Correlations of error terms for weighted prime counting functions
Standard prime-number counting functions, such as $ψ(x)$, $θ(x)$, and $π(x)$, have error terms with limiting logarithmic distributions once suitably normalized. The same is true of weighted versions of those sums, like $π_r(x) = \sum_{p\le x} \frac1p$ and $π_\ell(x) = \sum_{p\le x} \log(1-\frac1p)^{-1}$, that were studied by Mertens. These limiting distributions are all identical, but passing to the limit loses information about how these error terms are correlated with one another. In t…

On Weighted Entropy Generating Function
Smitha S., Mary Andrewsa, Sudheesh K. Kattumannil
https://arxiv.org/abs/2507.15057 https://ar…

On Weighted Entropy Generating Function
In this paper, we study the properties of the weighted entropy generating function (WEGF). We also introduce the weighted residual entropy generating function (WREGF) and establish some characterization results based on its connections with the hazard rate and the mean residual life function. Furthermore, we propose two new classes of life distributions derived from WREGF. We also study the non-parametric estimation of WREGF. A non-parametric test for the Pareto type I distribution is developed…

macaques: Japanese macaques (1976)
Dominance interactions among a group of adult female Japanese macaques (Macaca fuscata fuscata), observed during a non-mating season in 1976. Edge weights represent the frequency of interaction.
This network has 62 nodes and 1187 edges.
Tags: Social, Animal, Weighted
https://networks.s…

Study of higher-order interactions in unweighted, undirected networks using persistent homology
Udit Raj, Slobodan Maleti\'c, Sudeepto Bhattacharya
https://arxiv.org/abs/2506.19448

Study of higher-order interactions in unweighted, undirected networks using persistent homology
Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions in a network. Studying of higher-order interactions (HoIs) of a system provides a more comprehensive understanding of the complex system; moreover, it is a more precise depiction of the system as many complex systems, such as ecological systems and biologica…

Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains
Nick Lindemulder, Emiel Lorist, Floris Roodenburg, Mark Veraar
https://arxiv.org/abs/2507.13478

Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains
We study the Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the distance to the boundary. Our analysis applies to bounded $C^{1,λ}$-domains with $λ\in[0,1]$, revealing a crucial trade-off: lower domain regularity can be compensated by enlarging the weight exponent. As a primary consequence, we establish maximal regularity f…

bible_nouns: Bible noun phrases
A network of noun phrases (places and names) in the King James Version of the Bible. Each node is a noun phrase, and an edge exists if the noun phrases co-occur in a Bible verse. Edge weight denotes how often the two words co-occur.
This network has 1773 nodes and 9131 edges.
Tags: Informational, Language, Weighted

Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
Pierre Matalon, Nicole Spillane
https://arxiv.org/abs/2506.17193

Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
The convergence of the GMRES linear solver is notoriously hard to predict. A particularly enlightening result by [Greenbaum, Pták, Strakoš, 1996] is that, given any convergence curve, one can build a linear system for which GMRES realizes that convergence curve. What is even more extraordinary is that the eigenvalues of the problem matrix can be chosen arbitrarily. We build upon this idea to derive novel results about weighted GMRES. We prove that for any linear system and any prescribed conv…

Projection Cascades of models of log del Pezzo surfaces
Muhammad Imran Qureshi
https://arxiv.org/abs/2506.19970 https://arxiv.org/pdf…

Projection Cascades of models of log del Pezzo surfaces
We introduce the notion of type-I projection cascade for a biregular model (infinite series) of log del Pezzo surfaces. We study the existence of type-I projection cascades for known classes of models of log del Pezzo surfaces, such that their images under their anti-canonical embeddings in some weighted projective space, can be described as codimension 4 and codimension 3 varieties. We obtain two cascades of length three and four cascades of length two, where each projection gives rise to a we…

Rate estimates for weighted total variation norm in terms of Wasserstein distances
Iv\'an Ivkovic, Mikl\'os R\'asonyi
https://arxiv.org/abs/2506.16088

Rate estimates for weighted total variation norm in terms of Wasserstein distances
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment conditions. We apply our results to convergence of functionals in Malliavin calculus.

Converting T1-weighted MRI from 3T to 7T quality using deep learning
Malo Gicquel, Ruoyi Zhao, Anika Wuestefeld, Nicola Spotorno, Olof Strandberg, Kalle {\AA}str\"om, Yu Xiao, Laura EM Wisse, Danielle van Westen, Rik Ossenkoppele, Niklas Mattsson-Carlgren, David Berron, Oskar Hansson, Gabrielle Flood, Jacob Vogel
https://ar…

Converting T1-weighted MRI from 3T to 7T quality using deep learning
Ultra-high resolution 7 tesla (7T) magnetic resonance imaging (MRI) provides detailed anatomical views, offering better signal-to-noise ratio, resolution and tissue contrast than 3T MRI, though at the cost of accessibility. We present an advanced deep learning model for synthesizing 7T brain MRI from 3T brain MRI. Paired 7T and 3T T1-weighted images were acquired from 172 participants (124 cognitively unimpaired, 48 impaired) from the Swedish BioFINDER-2 study. To synthesize 7T MRI from 3T imag…

Estimating Multiple Weighted Networks with Node-Sparse Differences and Shared Low-Rank Structure
Hao Yan, Keith Levin
https://arxiv.org/abs/2506.15915 http…

Estimating Multiple Weighted Networks with Node-Sparse Differences and Shared Low-Rank Structure
We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared low-rank structure and a node-sparse matrix that captures the differences between conditions. This formulation is motivated by practical scenarios, such as in connectomics, where most nodes share a global connectivity structure while only a few exhibit condit…

epinions: Epinions product ratings (2005)
A bipartite network of users and the products they rated on the website Epinions.com. A user connects to all products on which that user entered a rating. Edge weight represents the rating score, and edges are timestamped.
This network has 876252 nodes and 13668320 edges.
Tags: Economic, Preferences, Timestamps, Weighted

Improved girth approximation in weighted undirected graphs
Avi Kadria, Liam Roditty, Aaron Sidford, Virginia Vassilevska Williams, Uri Zwick
https://arxiv.org/abs/2507.13869

Improved girth approximation in weighted undirected graphs
Let $G = (V,E,\ell)$ be a $n$-node $m$-edge weighted undirected graph, where $\ell: E \rightarrow (0,\infty)$ is a real \emph{length} function defined on its edges, and let $g$ denote the girth of $G$, i.e., the length of its shortest cycle. We present an algorithm that, for any input, integer $k \geq 1$, in $O(kn^{1+1/k}\log{n} + m(k+\log{n}))$ expected time finds a cycle of length at most $\frac{4k}{3}g$. This algorithm nearly matches a $O(n^{1+1/k}\log{n})$-time algorithm of \cite{KadriaRSWZ…

Concavity principles for weighted marginals
Dario Cordero-Erausquin, Alexandros Eskenazis
https://arxiv.org/abs/2506.16941 https://ar…

Concavity principles for weighted marginals
We develop a general framework to study concavity properties of weighted marginals of $β$-concave functions on $\mathbb{R}^n$ via local methods. As a concrete implementation of our approach, we obtain a functional version of the dimensional Brunn-Minkowski inequality for rotationally invariant log-concave measures. Moreover, we derive a Prékopa-type concavity principle with rotationally invariant weights for even log-concave functions which encompasses the B-inequality.

bitcoin_alpha: Bitcoin Alpha trust network (2017)
A network of who-trusts-whom relationships among users of the Bitcoin Alpha platform. Each directed edge (i,j,w) represents the rating of user j by user i, in which i assigns j a weight w on a scale of -10 (total distrust) to 10 (total trust) in steps of 1.
This network has 3783 nodes and 24186 edges.
Tags: Social, Online, Weighted, Signed, Timestamps

celegans_2019: Complete C. elegans neurons (2019)
Networks among neurons of both the adult male and adult hermaphrodite worms C. elegans, constructed from electron microscopy series, to include directed edges (chemical) and undirected (gap junction), and spanning including nodes for muscle and non-muscle end organs.
This network has 586 nodes and 1758 edges.
Tags: Biological, Connectome, Weighted

On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians
Pascal Auscher, Khalid Baadi
https://arxiv.org/abs/2506.20368 https://

On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians
We establish norm inequalities for fractional powers of degenerate Laplacians, with degeneracy being determined by weights in the Muckenhoupt class $A_2(\mathbb{R}^n)$, accompanied by specific additional reverse Hölder assumptions. This extends the known results for classical Riesz potentials. The approach is based on size estimates for the degenerate heat kernels. The approach also applies to more general weighted degenerate operators.

foodweb_baywet: Florida cypress wetlands food web (1998)
Networks of carbon exchanges among species in the cypress wetlands of South Florida. One network covers the wet and the other the dry season. Each node represents a taxon (similar to a species), and a directed edge indicates that one taxon uses another as food.
This network has 128 nodes and 2106 edges.
Tags: Biological, Food web, Weighted

Supercyclic weighted composition operators on the space of smooth functions
J. Bes, C. Foster
https://arxiv.org/abs/2507.16425 https://

Supercyclic weighted composition operators on the space of smooth functions
A weighted composition operator on the space of scalar-valued smooth functions on an open set of d-dimensional Euclidean space is supercyclic if and only if it is weakly mixing, and it is strongly supercyclic if and only if it is mixing. Every mixing such operator is chaotic. In the one-dimensional case, it is supercyclic if and only if it is mixing and if and only if it is chaotic.

windsurfers: Windsurfers network (1986)
A network of interpersonal contacts among windsurfers in southern California during the Fall of 1986. The edge weights indicate the perception of social affiliations majored by the tasks in which each individual was asked​ to sort cards with other surfer’s name in the order of closeness.
This network has 43 nodes and 336 edges.
Tags: Social, Offline, Weighted

Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
Saida Mancer, Abdelhakim Necir, Djamel Meraghni
https://arxiv.org/abs/2507.15744

Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These estimators can be viewed as a robust generalization of both weighted least squares and kernel-based tail index estimators. We establish the consistency and asymptotic normality of the proposed class. A simulation study is conducted to assess their finite-sample p…

Weighted $k$-Server Admits an Exponentially Competitive Algorithm
Adithya Bijoy, Ankit Mondal, Ashish Chiplunkar
https://arxiv.org/abs/2507.12130 https://

Weighted $k$-Server Admits an Exponentially Competitive Algorithm
The weighted $k$-server is a variant of the $k$-server problem, where the cost of moving a server is the server's weight times the distance through which it moves. The problem is famous for its intriguing properties and for evading standard techniques for designing and analyzing online algorithms. Even on uniform metric spaces with sufficiently many points, the deterministic competitive ratio of weighted $k$-server is known to increase doubly exponentially with respect to $k$, while the behavio…

ReCoGNet: Recurrent Context-Guided Network for 3D MRI Prostate Segmentation
Ahmad Mustafa, Reza Rastegar, Ghassan AlRegib
https://arxiv.org/abs/2506.19687 …

ReCoGNet: Recurrent Context-Guided Network for 3D MRI Prostate Segmentation
Prostate gland segmentation from T2-weighted MRI is a critical yet challenging task in clinical prostate cancer assessment. While deep learning-based methods have significantly advanced automated segmentation, most conventional approaches-particularly 2D convolutional neural networks (CNNs)-fail to leverage inter-slice anatomical continuity, limiting their accuracy and robustness. Fully 3D models offer improved spatial coherence but require large amounts of annotated data, which is often imprac…

foldoc: FOLDOC entries (2002)
A network of hyperlinks among entries in the Free On-line Dictionary of Computing (FOLDOC, www.foldoc.org), an online dictionary of acronyms and technical terms for computers. An edge points from i to j if the term j is referred to in the entry for term i. Edge weight denotes number of uses of the same term.
This network has 13356 nodes and 120238 edges.
Tags: Informational, Web graph, Weighted

foldoc: FOLDOC entries (2002)
A network of hyperlinks among entries in the Free On-line Dictionary of Computing (FOLDOC, www.foldoc.org), an online dictionary of acronyms and technical terms for computers. An edge points from i to j if the term j is referred to in the entry for term i. Edge weight denotes number of uses of the same term.
This network has 13356 nodes and 120238 edges.
Tags: Informational, Web graph, Weighted

Dynamics for affine composition operators on weighted Bergman space of a half plane
Artur Blois, Osmar R. Severiano
https://arxiv.org/abs/2506.15822 https:…

Dynamics for affine composition operators on weighted Bergman space of a half plane
In this article, we completely characterize the positive expansive and absolutely Cesàro composition operators $C_ϕf=f\circ ϕ$ induced by affine self-maps $ϕ$ of the right half-plane $\mathbb{C}_+$ on the weighted Bergman space $\mathcal{A}^2_α(\mathbb{C}_+)$. Furthermore, we characterize which of these operators have the positive shadowing property.

advogato: Advogato trust network (2009)
A network of trust relationships among users on Advogato, an online community of open source software developers. Edge direction indicates that node i trusts node j, and edge weight denotes one of four increasing levels of declared trust from i to j: observer (0.4), apprentice (0.6), journeyer (0.8), and master (1.0).
This network has 6541 nodes and 51127 edges.
Tags: Social, Online, Weighted

dom: Animal dominance archive (2022)
Animal dominance interaction data published over a century of research. The archive contains 434 agonistic interaction datasets, totaling over 241,000 interactions. A directed edge (i,j) corresponds to an antagonist interaction between i (winner) and j (loser). If a 'weight' edge property map exists, it counts the number of such interactions.
This network has 12 nodes and 52 edges.
Tags: Social, Animal, Weighted

Vector valued weighted analogue of converse of Wiener-L\'evy theorem and applications to modulation spaces
Divyang G. Bhimani, Karishman B. Solanki
https://arxiv.org/abs/2507.16516

Vector valued weighted analogue of converse of Wiener-Lévy theorem and applications to modulation spaces
We shall prove a strong converse of the Wiener-Lévy theorem in weighted setting for Banach algebra valued functions. In fact, it is shown that if $ω$ is a weight on a discrete abelian group $G$, $\mathcal X$ is a unital commutative Banach algebra and if $F$ is a $\mathcal X-$valued function defined on $\mathbb C$ such that $T_F(f)=F\circ f \in A^q(Γ,\mathcal X)$ for all $f\in A^1_ω(Γ,\mathcal X)$, then $F$ must be real analytic. Its multivariate analogue and analogue for locally compact ab…

train_terrorists: Madrid train bombing terrorists (2004)
A network of associations among the terrorists involved in the 2004 Madrid train bombing, as reconstructed from press stories after-the-fact. Edge weights encode four levels of connection strength: friendships, ties to Al Qaeda and Osama Bin Laden, co-participants in wars, and co-participants in previous terrorist attacks.
This network has 64 nodes and 243 edges.
Tags: Social, Offline, Weighted

Toeplitz operators and weighted composition operators on variable exponent Bergman spaces
Cezhong Tong, Zicong Yang, Zehua Zhou
https://arxiv.org/abs/2507.13675

Toeplitz operators and weighted composition operators on variable exponent Bergman spaces
In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson measures. Then they extended the results to the ball setting. In this paper, we further generalize those results to variable exponent Bergman spaces over the unit ball. Our proofs, when restricted to the case of constant variable, are new and simpler. Moreov…

unicodelang: Languages spoken by country (2015)
A bipartite network of languages and the countries in which they are spoken, as estimated by Unicode. Edges are weighted by the proportion of the given country's population that is literate in a particular language.
This network has 868 nodes and 1255 edges.
Tags: Informational, Relatedness, Weighted

game_thrones: Game of Thrones coappearances
Network of coappearances of characters in the Game of Thrones series, by George R. R. Martin, and in particular coappearances in the book "A Storm of Swords." Nodes are unique characters, and edges are weighted by the number of times the two characters' names appeared within 15 words of each other in the text.
This network has 107 nodes and 352 edges.
Tags: Social, Fictional, Weighted

celegansneural: C. elegans neurons (1986)
A network representing the neural connections of the Caenorhabditis elegans nematode.
This network has 297 nodes and 2359 edges.
Tags: Biological, Connectome, Weighted
https://networks.skewed.de/net/celegansneural
Rid…

unicodelang: Languages spoken by country (2015)
A bipartite network of languages and the countries in which they are spoken, as estimated by Unicode. Edges are weighted by the proportion of the given country's population that is literate in a particular language.
This network has 868 nodes and 1255 edges.
Tags: Informational, Relatedness, Weighted

libimseti: Libimseti.cz social network (2012)
A network of ratings given between users at Libimseti.cz, a Czech online dating website. A directed edge (i,j) means that user i rate user j, and the corresponding edge weight is the given rating, on a scale of 1-10.
This network has 220970 nodes and 17359346 edges.
Tags: Social, Online, Weighted

libimseti: Libimseti.cz social network (2012)
A network of ratings given between users at Libimseti.cz, a Czech online dating website. A directed edge (i,j) means that user i rate user j, and the corresponding edge weight is the given rating, on a scale of 1-10.
This network has 220970 nodes and 17359346 edges.
Tags: Social, Online, Weighted

game_thrones: Game of Thrones coappearances
Network of coappearances of characters in the Game of Thrones series, by George R. R. Martin, and in particular coappearances in the book "A Storm of Swords." Nodes are unique characters, and edges are weighted by the number of times the two characters' names appeared within 15 words of each other in the text.
This network has 107 nodes and 352 edges.
Tags: Social, Fictional, Weighted

packet_delays: Internet packet delays (2002)
A network representing the difference in delay observed by packet probes sent from a computer at Rice University to similar machines at different universities, in c.2002. The edge weight denotes the difference in delay of the packet in milliseconds.
This network has 10 nodes and 9567 edges.
Tags: Technological, Communication, Weighted

bitcoin_alpha: Bitcoin Alpha trust network (2017)
A network of who-trusts-whom relationships among users of the Bitcoin Alpha platform. Each directed edge (i,j,w) represents the rating of user j by user i, in which i assigns j a weight w on a scale of -10 (total distrust) to 10 (total trust) in steps of 1.
This network has 3783 nodes and 24186 edges.
Tags: Social, Online, Weighted, Signed, Timestamps

sp_primary_school: Primary school dynamic contacts (2009)
Two temporal networks of contacts among students and teachers at a primary school in Lyon, France, on consecutive days of in October 2009. Each network accumulates all contacts over the course of a single day; contacts were sampled at 20-second intervals.
This network has 242 nodes and 125773 edges.
Tags: Social, Offline, Weighted, Temporal, Metadata

foodweb_baywet: Florida cypress wetlands food web (1998)
Networks of carbon exchanges among species in the cypress wetlands of South Florida. One network covers the wet and the other the dry season. Each node represents a taxon (similar to a species), and a directed edge indicates that one taxon uses another as food.
This network has 128 nodes and 2106 edges.
Tags: Biological, Food web, Weighted

moviegalaxies: Moviegalaxies, movies 410-466 (2018)
Social graphs for over 700 movies from the moviegalaxies.com website. Each node represents a character in a movie and each edge is a same-scene appearance between two characters in that movie. The weight gives the number of same-scene appearances. Networks are extracted from movie scripts automatically.
This network has 58 nodes and 201 edges.
Tags: Social, Fictional, Weighted

game_thrones: Game of Thrones coappearances
Network of coappearances of characters in the Game of Thrones series, by George R. R. Martin, and in particular coappearances in the book "A Storm of Swords." Nodes are unique characters, and edges are weighted by the number of times the two characters' names appeared within 15 words of each other in the text.
This network has 107 nodes and 352 edges.
Tags: Social, Fictional, Weighted

celegansneural: C. elegans neurons (1986)
A network representing the neural connections of the Caenorhabditis elegans nematode.
This network has 297 nodes and 2359 edges.
Tags: Biological, Connectome, Weighted
https://networks.skewed.de/net/celegansneural
Rid…

spanish_highschools: Spanish high schools (2023)
Directed networks of friendships obtained through a social survey of spanish high school students.
This network has 515 nodes and 6379 edges.
Tags: Social, Offline, Weighted, Metadata
https://networks.skewed.de/net/spanish

spanish_highschools: Spanish high schools (2023)
Directed networks of friendships obtained through a social survey of spanish high school students.
This network has 409 nodes and 8557 edges.
Tags: Social, Offline, Weighted, Metadata
https://networks.skewed.de/net/spanish

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

plant_pol_kato: Kato plant-pollinator web
A bipartite network of plants and pollinators from Kyoto University Forest of Ashu, Japan, from 1984 to 1987. Edge weights represent frequency of interactions.
This network has 772 nodes and 1206 edges.
Tags: Biological, Food web, Weighted
https://networks.skewed.d…

netscience: Scientific collaborations in network science (2006)
A coauthorship network among scientists working on network science, from 2006. This network is a one-mode projection from the bipartite graph of authors and their scientific publications.
This network has 1589 nodes and 2742 edges.
Tags: Social, Collaboration, Weighted, Projection

bible_nouns: Bible noun phrases
A network of noun phrases (places and names) in the King James Version of the Bible. Each node is a noun phrase, and an edge exists if the noun phrases co-occur in a Bible verse. Edge weight denotes how often the two words co-occur.
This network has 1773 nodes and 9131 edges.
Tags: Informational, Language, Weighted

twitter_higgs: Twitter, Higgs boson (2012)
Data on tweets related to the announcement of the discovery of a new fundamental particle with the features of the Higgs boson on 4th July 2012. Data covers 1-7 July 2012, and includes four types of networks: followers, retweets, replies, and mentions.
This network has 256491 nodes and 328132 edges.
Tags: Social, Online, Weighted, Multilayer

twitter_higgs: Twitter, Higgs boson (2012)
Data on tweets related to the announcement of the discovery of a new fundamental particle with the features of the Higgs boson on 4th July 2012. Data covers 1-7 July 2012, and includes four types of networks: followers, retweets, replies, and mentions.
This network has 456626 nodes and 14855842 edges.
Tags: Social, Online, Weighted, Multilayer

bitcoin_trust: Bitcoin OTC trust network (2017)
A network of who-trusts-whom relationships among users of the Bitcoin OTC platform. Each directed edge (i,j,w) represents the rating of user j by user i, in which i assigns j a weight w on a scale of -10 (total distrust) to 10 (total trust) in steps of 1.
This network has 5881 nodes and 35592 edges.
Tags: Social, Online, Weighted, Signed, Timestamps

residence_hall: ANU Residence Hall network
A network of friendships among students living in a residence hall at Australian National University (date unknown). Edge direction indicates that resident i named resident j as a friend, and edge weight indicates the level of friendship: 5 (best friend), 4 (close friend), 3 (friend), 2, 1.
This network has 217 nodes and 2672 edges.
Tags: Social, Offline, Weighted

advogato: Advogato trust network (2009)
A network of trust relationships among users on Advogato, an online community of open source software developers. Edge direction indicates that node i trusts node j, and edge weight denotes one of four increasing levels of declared trust from i to j: observer (0.4), apprentice (0.6), journeyer (0.8), and master (1.0).
This network has 6541 nodes and 51127 edges.
Tags: Social, Online, Weighted

advogato: Advogato trust network (2009)
A network of trust relationships among users on Advogato, an online community of open source software developers. Edge direction indicates that node i trusts node j, and edge weight denotes one of four increasing levels of declared trust from i to j: observer (0.4), apprentice (0.6), journeyer (0.8), and master (1.0).
This network has 6541 nodes and 51127 edges.
Tags: Social, Online, Weighted