Miracle-dz/UniFAR-FTUs huggingface dataset:
A Probabilistic Position Bias Model for Short-Video Recommendation Feeds

Modern web-based platforms often show ranked lists of recommendations to users, in an attempt to maximise user satisfaction or business metrics. Typically, the goal of such systems boils down to maximising the exposure probability —conversely, minimising the rank— for items that are deemed “reward-maximising” according to some metric of interest. This general framing comprises music or movie streaming applications, as well as e-commerce, restaurant or job recommendations, and even web search. Position bias or user models can be used to estimate exposure probabilities for each use-case, specifically tailored to how users interact with the presented rankings. A unifying factor in these diverse problem settings is that typically only one or several items will be engaged with (clicked, streamed, purchased, et cetera) before a user leaves the ranked list. Short-video feeds on social media platforms diverge from this general framing in several ways, most notably that users do not tend to leave the feed after, for example, liking a post. Indeed, seemingly infinite feeds invite users to scroll further down the ranked list. For this reason, existing position bias or user models tend to fall short in such settings, as they do not accurately capture users’ interaction modalities. In this work, we propose a novel and probabilistically sound personalised position bias model for feed recommendations. We focus on a 1st-level feed in a hierarchical structure, where users may enter a 2nd-level feed via any given 1st-level item. We posit that users come to the platform with a given scrolling budget that is drawn according to a discrete power-law distribution, and show how the survival function of said distribution can be used to obtain closed-form estimates for personalised exposure probabilities. Empirical insights gained through data from a large-scale social media platform show how our probabilistic position bias model more accurately captures empirical exposure than existing models, and paves the way for improved unbiased evaluation and learning-to-rank.
Distributed Certification for Classes of Dense Graphs

A proof-labeling scheme (PLS) for a boolean predicate $\Pi$ on labeled graphs is a mechanism used for certifying the legality with respect to $\Pi$ of global network states in a distributed manner. In a PLS, a certificate is assigned to each processing node of the network, and the nodes are in charge of checking that the collection of certificates forms a global proof that the system is in a correct state, by exchanging the certificates once, between neighbors only. The main measure of complexity is the size of the certificates. Many PLSs have been designed for certifying specific predicates, including cycle-freeness, minimum-weight spanning tree, planarity, etc. In 2021, a breakthrough has been obtained, as a meta-theorem stating that a large set of properties have compact PLSs in a large class of networks. Namely, for every $\mathrm{MSO}_2$ property $\Pi$ on labeled graphs, there exists a PLS for $\Pi$ with $O(\log n)$-bit certificates for all graphs of bounded tree-depth. This result has been extended to the larger class of graphs with bounded {tree-width}, using certificates on $O(\log^2 n)$ bits. We extend this result even further, to the larger class of graphs with bounded clique-width, which, as opposed to the other two aforementioned classes, includes dense graphs. We show that, for every $\mathrm{MSO}_1$ property $\Pi$ on labeled graphs, there exists a PLS for $\Pi$ with $O(\log^2 n)$ bit certificates for all graphs of bounded clique-width.
Solitons to Mean Curvature Flow in the hyperbolic 3-space

We consider {translators} (i.e., initial condition of translating solitons) to mean curvature flow (MCF) in the hyperbolic $3$-space $\mathbb H^3$, providing existence and classification results. More specifically, we show the existence and uniqueness of two distinct one-parameter families of complete rotational translators in $\mathbb H^3$, one containing catenoid-type translators, and the other parabolic cylindrical ones. We establish a tangency principle for translators in $\mathbb H^3$ and apply it to prove that properly immersed translators to MCF in $\mathbb H^3$ are not cylindrically bounded. As a further application of the tangency principle, we prove that any horoconvex translator which is complete or transversal to the $x_3$-axis is necessarily an open set of a horizontal horosphere. In addition, we classify all translators in $\mathbb H^3$ which have constant mean curvature. We also consider rotators (i.e., initial condition of rotating solitons) to MCF in $\mathbb H^3$ and, after classifying the rotators of constant mean curvature, we show that there exists a one-parameter family of complete rotators which are all helicoidal, bringing to the hyperbolic context a distinguished result by Halldorsson, set in $\mathbb R^3$.
It's Not Always the Leader's Fault: How Informed Followers Can Undermine Efficient Leadership

Coordination facilitation and efficient decision-making are two essential components of successful leadership. In this paper, we take an informational approach and investigate how followers' information impacts coordination and efficient leadership in a model featuring a leader and a team of followers. We show that efficiency is achieved as the unique rationalizable outcome of the game when followers possess sufficiently imprecise information. In contrast, if followers have accurate information, the leader may fail to coordinate them toward the desired outcome or even take an inefficient action herself. We discuss the implications of the results for the role of leaders in the context of financial fragility and crises.
Minor Merger Growth in Action: JWST Detects Faint Blue Companions around Massive Quiescent Galaxies at 0.5 ≤ z ≤ 3.0

Minor mergers are thought to drive the structural evolution of massive quiescent galaxies; however, existing Hubble Space Telescope (HST) imaging is primarily sensitive to stellar mass ratios ≳1:10. Here, we report the discovery of a large population of low-mass companions within 35 kpc of known logM*/M⊙≳10.5 quiescent galaxies at 0.5 ≤ z ≤ 3. While massive companions like those identified by HST are rare, JWST imaging from the JWST Advanced Deep Extragalactic Survey reveals that the average massive quiescent galaxy hosts approximately five nearby companions with stellar mass ratios <1:10. Despite a median stellar mass ratio of just 1:900, these tiny companions are so numerous that they represent at least 30% of the total mass being added to quiescent galaxies via minor mergers. While relatively massive companions have colors similar to their hosts, companions with mass ratios <1:10 typically have bluer colors and lower mass-to-light ratios than their host galaxies at similar radii. The accretion of these tiny companions is likely to drive evolution in the color gradients and stellar population properties of the host galaxies. Our results suggest that the well-established “minor merger growth” model for quiescent galaxies extends down to very low mass ratios of ≲1:100, and demonstrates the power of JWST to constrain both the spatially resolved properties of massive galaxies and the properties of low-mass companions beyond the local Universe.
Removing induced powers of cycles from a graph via fewest edits

What is the minimum proportion of edges which must be added to or removed from a graph of density $p$ to eliminate all induced cycles of length $h$? The maximum of this quantity over all graphs of density $p$ is measured by the edit distance function, $\text{ed}_{\text{Forb}(C_h)}(p)$, a function which provides a natural metric between graphs and hereditary properties. Martin determined $\text{ed}_{\text{Forb}(C_h)}(p)$ for all $p \in [0,1]$ when $h \in \{3, \ldots, 9\}$ and determined $\text{ed}_{\text{Forb}(C_{10})}(p)$ for $p \in [1/7, 1]$. Peck determined $\text{ed}_{\text{Forb}(C_h)}(p)$ for all $p \in [0,1]$ for odd cycles, and for $p \in [ 1/\lceil h/3 \rceil, 1]$ for even cycles. In this paper, we fully determine the edit distance function for $C_{10}$ and $C_{12}$. Furthermore, we improve on the result of Peck for even cycles, by determining $\text{ed}_{\text{Forb}(C_h)}(p)$ for all $p \in [p_0, 1/\lceil h/3 \rceil ]$, where $p_0 \leq c/h^2$ for a constant $c$. More generally, if $C_h^t$ is the $t$-th power of the cycle $C_h$, we determine $\text{ed}_{\text{Forb}(C_h^t)}(p)$ for all $p \geq p_0$ in the case when $(t+1) \mid h$, thus improving on earlier work of Berikkyzy, Martin and Peck.
Multi 3 WOZ: A Multilingual, Multi-Domain, Multi-Parallel Dataset for Training and Evaluating Culturally Adapted Task-Oriented Dialog Systems

Abstract Creating high-quality annotated data for task-oriented dialog (ToD) is known to be notoriously difficult, and the challenges are amplified when the goal is to create equitable, culturally adapted, and large-scale ToD datasets for multiple languages. Therefore, the current datasets are still very scarce and suffer from limitations such as translation-based non-native dialogs with translation artefacts, small scale, or lack of cultural adaptation, among others. In this work, we first take stock of the current landscape of multilingual ToD datasets, offering a systematic overview of their properties and limitations. Aiming to reduce all the detected limitations, we then introduce Multi3WOZ, a novel multilingual, multi-domain, multi-parallel ToD dataset. It is large-scale and offers culturally adapted dialogs in 4 languages to enable training and evaluation of multilingual and cross-lingual ToD systems. We describe a complex bottom–up data collection process that yielded the final dataset, and offer the first sets of baseline scores across different ToD-related tasks for future reference, also highlighting its challenging nature.
Geometric quantum complexity of bosonic oscillator systems

According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the original concept of complexity based on the minimal number of gates required to construct the desired operation as a product, this geometrical approach amounts to a more concrete and computable definition, but its evaluation is nontrivial in systems with a high-dimensional Hilbert space. The geometrical formulation can more easily be evaluated by considering the geometry associated with a suitable finite-dimensional group generated by a small number of relevant operators of the system. In this way, the method has been applied in particular to the harmonic oscillator, which is also of interest in the present paper. However, subtle and previously unrecognized issues of group theory can lead to unforeseen complications, motivating a new formulation that remains on the level of the underlying Lie algebras for most of the required steps. Novel insights about complexity can thereby be found in a low-dimensional setting, with the potential of systematic extensions to higher dimensions as well as interactions. Specific examples include the quantum complexity of various target unitary operators associated with a harmonic oscillator, inverted harmonic oscillator, and coupled harmonic oscillators. The generality of this approach is demonstrated by an application to an anharmonic oscillator with a cubic term.
A visit generation process for human mobility random graphs with location-specific latent-variables: from land use to travel demand

This research introduces a mathematical framework to comprehending human mobility patterns, integrating mathematical modeling and economic analysis. The study focuses on latent-variable networks, investigating the dynamics of human mobility using stochastic models. By examining actual origin-destination data, the research reveals scaling relations and uncovers the economic implications of mobility patterns, such as the income elasticity of travel demand. The mathematical analysis commences with the development of a stochastic model based on inhomogeneous random graphs to construct a visitation model with multipurpose drivers for travel demand. A directed multigraph with weighted edges is considered, incorporating trip costs and labels to represent factors like distance traveled and travel time. The study gains insights into the structural properties and dynamic correlations of human mobility networks, to derive analytical and computational solutions for key network metrics, including scale-free behavior of the strength and degree distribution, together with the estimation of assortativity and clustering coefficient. Additionally, the model's validity is assessed through a real-world case study of the New York metropolitan area. The analysis of this data exposes clear scaling relations in commuting patterns, confirming theoretical predictions and validating the efficacy of the mathematical model. The model further explains a series of scaling behaviors in origin-destination flows among areas of a region, successfully reproducing statistical regularities observed in real-world cases using extensive human mobility datasets. In particular, the model's application to estimating income elasticity of travel demand bears significant implications for urban and transport economics.
Memory-Efficient Graph Convolutional Networks for Object Classification and Detection with Event Cameras

Recent advances in event camera research emphasize processing data in its original sparse form, which allows the use of its unique features such as high temporal resolution, high dynamic range, low latency, and resistance to image blur. One promising approach for analyzing event data is through graph convolutional networks (GCNs). However, current research in this domain primarily focuses on optimizing computational costs, neglecting the associated memory costs. In this paper, we consider both factors together in order to achieve satisfying results and relatively low model complexity. For this purpose, we performed a comparative analysis of different graph convolution operations, considering factors such as execution time, the number of trainable model parameters, data format requirements, and training outcomes. Our results show a 450-fold reduction in the number of parameters for the feature extraction module and a 4.5-fold reduction in the size of the data representation while maintaining a classification accuracy of 52.3%, which is 6.3% higher compared to the operation used in state-of-the-art approaches. To further evaluate performance, we implemented the object detection architecture and evaluated its performance on the N-Caltech101 dataset. The results showed an accuracy of 53.7% mAP@0.5 and reached an execution rate of 82 graphs per second.
On nonlinear Landau damping and Gevrey regularity

In this article we study the problem of nonlinear Landau damping for the Vlasov-Poisson equations on the torus. As our main result we show that for perturbations initially of size $\epsilon>0$ and time intervals $(0,\epsilon^{-N})$ one obtains nonlinear stability in regularity classes larger than Gevrey $3$, uniformly in $\epsilon$. As a complementary result we construct families of Sobolev regular initial data which exhibit nonlinear Landau damping. Our proof is based on the methods of Grenier, Nguyen and Rodnianski.
Multi-Model Subset Selection

The two primary approaches for high-dimensional regression problems are sparse methods (e.g. best subset selection which uses the L0-norm in the penalty) and ensemble methods (e.g. random forests). Although sparse methods typically yield interpretable models, they are often outperformed in terms of prediction accuracy by"blackbox"multi-model ensemble methods. We propose an algorithm to optimize an ensemble of L0-penalized regression models by extending recent developments in L0-optimization for sparse methods to multi-model regression ensembles. The sparse and diverse models in the ensemble are learned simultaneously from the data. Each of these models provides an explanation for the relationship between a subset of predictors and the response variable. We show how the ensembles achieve excellent prediction accuracy by exploiting the accuracy-diversity tradeoff of ensembles and investigate the effect of the number of models. In prediction tasks the ensembles can outperform state-of-the-art competitors on both simulated and real data. Forward stepwise regression is also generalized to multi-model regression ensembles and used to obtain an initial solution for our algorithm. The optimization algorithms are implemented in publicly available software packages.
Submodular Hypergraph Partitioning: Metric Relaxations and Fast Algorithms via an Improved Cut-Matching Game

Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning objectives beyond this. This work proposes algorithms for a general model of hypergraph partitioning that unifies both undirected and directed versions of many well-studied partitioning objectives. The first contribution of this paper introduces polymatroidal cut functions, a large class of cut functions amenable to approximation algorithms via metric embeddings and routing multicommodity flows. We demonstrate an $O(\sqrt{\log n})$-approximation, where $n$ is the number of vertices in the hypergraph, for these problems by rounding relaxations to metrics of negative-type. The second contribution of this paper generalizes the cut-matching game framework of Khandekar et. al. to tackle polymatroidal cut functions. This yields the first almost-linear time $O(\log n)$-approximation algorithm for standard versions of undirected and directed hypergraph partitioning. A technical consequence of our construction is that a cut-matching game which greatly relaxes the set of allowed actions for both players can be used to partition hypergraphs with negligible impact on the approximation ratio. We believe this to be of independent interest.
Perturbation analysis on T-eigenvalues of third-order tensors

Perturbation analysis has emerged as a significant concern across multiple disciplines, with notable advancements being achieved, particularly in the realm of matrices. This study centers on specific aspects pertaining to tensor T-eigenvalues within the context of the tensor-tensor multiplication. Initially, an analytical perturbation analysis is introduced to explore the sensitivity of T-eigenvalues. In the case of third-order tensors featuring square frontal slices, we extend the classical Gershgorin disc theorem and show that all T-eigenvalues are located inside a union of Gershgorin discs. Additionally, we extend the Bauer-Fike theorem to encompass F-diagonalizable tensors and present two modified versions applicable to more general scenarios. The tensor case of the Kahan theorem, which accounts for general perturbations on Hermite tensors, is also investigated. Furthermore, we propose the concept of pseudospectra for third-order tensors based on tensor-tensor multiplication. We develop four definitions that are equivalent under the spectral norm to characterize tensor $\varepsilon$-pseudospectra. Additionally, we present several pseudospectral properties. To provide visualizations, several numerical examples are also provided to illustrate the $\varepsilon$-pseudospectra of specific tensors at different levels.
Evidence against a strong first-order phase transition in neutron star cores: Impact of new data

With the aim of exploring the evidence for or against phase transitions in cold and dense baryonic matter, the inference of the sound speed and equation-of-state for dense matter in neutron stars is extended in view of recent new observational data. The impact of the heavy (2.35 $M_\odot$) black widow pulsar PSR J0952-0607 and of the unusually light supernova remnant HESS J1731-347 is inspected. In addition a detailed re-analysis is performed of the low-density constraint based on chiral effective field theory and of the perturbative QCD constraint at asymptotically high densities, in order to clarify the influence of these constraints on the inference procedure. The trace anomaly measure, $\Delta = 1/3 - P/\varepsilon$, is also computed and discussed. A systematic Bayes factor assessment quantifies the evidence (or non-evidence) of low averaged sound speeds $(c_s^2 \leq 0.1)$, a prerequisite for a phase transition, within the range of densities realized in the core of neutron stars. One of the consequences of including PSR J0952-0607 in the data base is a further stiffening of the equation-of-state, resulting for a 2.1 solar-mass neutron star in a reduced central density of less than five times the equilibrium density of normal nuclear matter at the 68\% level. The evidence against small sound speeds in neutron star cores is further strengthened. Within the inferred 68\% posterior credible bands, only a weak first-order phase transition with a coexistence density interval $\Delta n/n \lesssim 0.2$ would be compatible with the observed data.
#Cyberbullying in the digital age: People's perspective and information sharing behavior on Twitter

Few studies have used social networking sites to understand people's perspectives on cyberbullying. The current study investigated people's insights and information sharing behavior about cyberbullying through the text mining of tweets. English language tweets were collected and analyzed in RStudio. Findings indicated that people shared quite a lot of informative information on Twitter such as online articles about how to deal with the different aspects of cyberbullying. Analyzing cyberbullying tweets revealed some of the major actions that needed to be taken into consideration (e.g., educating parents and teachers about cyberbullying), as well as some certain events (e.g., the Michigan cyberbullying law) that had drawn people's attention. Parents, and teachers seem to be having an important role in educating, informing, warning, preventing, and protecting cyberbullying behaviors. Strong correlation was found among girl, photo and shared, which may represent that girls are more likely to experience appearance-related cyberbullying than boys.
New Properties of the Zeros of Certain Nonclassical Orthogonal Polynomials

We propose new and remarkable algebraic identities satisfied by the zeros of certain nonclassical orthogonal polynomials. To prove the identities, we generalize the notion of spectral and pseudospectral matrix representations of linear differential operators. The identities hold for every polynomial family {p_n(x)} orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family are generalized eigenfunctions of some linear differential operator D, in the sense that D p_n(x) =q_n(x) p_n(x), where each q_n(x) is a polynomial of degree at most n_0 and n_0 does not depend on n. We illustrate the general result by proving remarkable algebraic relations satisfied by the zeros of the Sonin-Markov orthogonal polynomials.