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The digitization of historical documents is crucial for preserving the cultural heritage of the society. An important step in this process is converting scanned images to text using Optical Character Recognition (OCR), which can enable further search, information extraction, etc. Unfortunately, this is a hard problem as standard OCR tools are not tailored to deal with historical orthography as well as with challenging layouts. Thus, it is standard to apply an additional text correction step on the OCR output when dealing with such documents. In this work, we focus on Bulgarian, and we create the first benchmark dataset for evaluating the OCR text correction for historical Bulgarian documents written in the first standardized Bulgarian orthography: the Drinov orthography from the 19th century. We further develop a method for automatically generating synthetic data in this orthography, as well as in the subsequent Ivanchev orthography, by leveraging vast amounts of contemporary literature Bulgarian texts. We then use state-of-the-art LLMs and encoder-decoder framework which we augment with diagonal attention loss and copy and coverage mechanisms to improve the post-OCR text correction. The proposed method reduces the errors introduced during recognition and improves the quality of the documents by 25\%, which is an increase of 16\% compared to the state-of-the-art on the ICDAR 2019 Bulgarian dataset. We release our data and code at \url{https://github.com/angelbeshirov/post-ocr-text-correction}.}, Comment: Accepted for publication in the International Journal on Digital Libraries

A key challenge of quantum programming is uncomputation: the reversible deallocation of qubits. And while there has been much recent progress on automating uncomputation, state-of-the-art methods are insufficient for handling today's expressive quantum programming languages. A core reason is that they operate on primitive quantum circuits, while quantum programs express computations beyond circuits, for instance, they can capture families of circuits defined recursively in terms of uncomputation and adjoints. In this paper, we introduce the first modular automatic approach to synthesize correct and efficient uncomputation for expressive quantum programs. Our method is based on two core technical contributions: (i) an intermediate representation (IR) that can capture expressive quantum programs and comes with support for uncomputation, and (ii) modular algorithms over that IR for synthesizing uncomputation and adjoints. We have built a complete end-to-end implementation of our method, including an implementation of the IR and the synthesis algorithms, as well as a translation from an expressive fragment of the Silq programming language to our IR and circuit generation from the IR. Our experimental evaluation demonstrates that we can handle programs beyond the capabilities of existing uncomputation approaches, while being competitive on the benchmarks they can handle. More broadly, we show that it is possible to benefit from the greater expressivity and safety offered by high-level quantum languages without sacrificing efficiency., Comment: 25 pages, 9 figures

Federated learning works by aggregating locally computed gradients from multiple clients, thus enabling collaborative training without sharing private client data. However, prior work has shown that the data can actually be recovered by the server using so-called gradient inversion attacks. While these attacks perform well when applied on images, they are limited in the text domain and only permit approximate reconstruction of small batches and short input sequences. In this work, we propose DAGER, the first algorithm to recover whole batches of input text exactly. DAGER leverages the low-rank structure of self-attention layer gradients and the discrete nature of token embeddings to efficiently check if a given token sequence is part of the client data. We use this check to exactly recover full batches in the honest-but-curious setting without any prior on the data for both encoder- and decoder-based architectures using exhaustive heuristic search and a greedy approach, respectively. We provide an efficient GPU implementation of DAGER and show experimentally that it recovers full batches of size up to 128 on large language models (LLMs), beating prior attacks in speed (20x at same batch size), scalability (10x larger batches), and reconstruction quality (ROUGE-1/2 > 0.99).

Pre-trained Language Models (PLMs) are known to contain various kinds of knowledge. One method to infer relational knowledge is through the use of cloze-style prompts, where a model is tasked to predict missing subjects or objects. Typically, designing these prompts is a tedious task because small differences in syntax or semantics can have a substantial impact on knowledge retrieval performance. Simultaneously, evaluating the impact of either prompt syntax or information is challenging due to their interdependence. We designed CONPARE-LAMA - a dedicated probe, consisting of 34 million distinct prompts that facilitate comparison across minimal paraphrases. These paraphrases follow a unified meta-template enabling the controlled variation of syntax and semantics across arbitrary relations. CONPARE-LAMA enables insights into the independent impact of either syntactical form or semantic information of paraphrases on the knowledge retrieval performance of PLMs. Extensive knowledge retrieval experiments using our probe reveal that prompts following clausal syntax have several desirable properties in comparison to appositive syntax: i) they are more useful when querying PLMs with a combination of supplementary information, ii) knowledge is more consistently recalled across different combinations of supplementary information, and iii) they decrease response uncertainty when retrieving known facts. In addition, range information can boost knowledge retrieval performance more than domain information, even though domain information is more reliably helpful across syntactic forms., Comment: Accepted for NAACL 2024

We introduce EXAMS-V, a new challenging multi-discipline multimodal multilingual exam benchmark for evaluating vision language models. It consists of 20,932 multiple-choice questions across 20 school disciplines covering natural science, social science, and other miscellaneous studies, e.g., religion, fine arts, business, etc. EXAMS-V includes a variety of multimodal features such as text, images, tables, figures, diagrams, maps, scientific symbols, and equations. The questions come in 11 languages from 7 language families. Unlike existing benchmarks, EXAMS-V is uniquely curated by gathering school exam questions from various countries, with a variety of education systems. This distinctive approach calls for intricate reasoning across diverse languages and relies on region-specific knowledge. Solving the problems in the dataset requires advanced perception and joint reasoning over the text and the visual content of the image. Our evaluation results demonstrate that this is a challenging dataset, which is difficult even for advanced vision-text models such as GPT-4V and Gemini; this underscores the inherent complexity of the dataset and its significance as a future benchmark.

Federated learning is a framework for collaborative machine learning where clients only share gradient updates and not their private data with a server. However, it was recently shown that gradient inversion attacks can reconstruct this data from the shared gradients. In the important honest-but-curious setting, existing attacks enable exact reconstruction only for a batch size of $b=1$, with larger batches permitting only approximate reconstruction. In this work, we propose SPEAR, the first algorithm reconstructing whole batches with $b >1$ exactly. SPEAR combines insights into the explicit low-rank structure of gradients with a sampling-based algorithm. Crucially, we leverage ReLU-induced gradient sparsity to precisely filter out large numbers of incorrect samples, making a final reconstruction step tractable. We provide an efficient GPU implementation for fully connected networks and show that it recovers high-dimensional ImageNet inputs in batches of up to $b \lesssim 25$ exactly while scaling to large networks. Finally, we show theoretically that much larger batches can be reconstructed with high probability given exponential time.

The wide-spread use of social networks has given rise to subjective, misleading, and even false information on the Internet. Thus, subjectivity detection can play an important role in ensuring the objectiveness and the quality of a piece of information. This paper presents the solution built by the Gpachov team for the CLEF-2023 CheckThat! lab Task~2 on subjectivity detection. Three different research directions are explored. The first one is based on fine-tuning a sentence embeddings encoder model and dimensionality reduction. The second one explores a sample-efficient few-shot learning model. The third one evaluates fine-tuning a multilingual transformer on an altered dataset, using data from multiple languages. Finally, the three approaches are combined in a simple majority voting ensemble, resulting in 0.77 macro F1 on the test set and achieving 2nd place on the English subtask.

We study the behavior of the smallest possible constants $d(a,b)$ and $d_n$ in Hardy's inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^2\,dx\leq d(a,b)\,\int_a^b [f(x)]^2 dx $$ and $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2. $$ The exact constant $d(a,b)$ and the precise rate of convergence of $d_n$ are established and the extremal function and the ``almost extremal'' sequence are found., Comment: 10 pages

Malicious server (MS) attacks have enabled the scaling of data stealing in federated learning to large batch sizes and secure aggregation, settings previously considered private. However, many concerns regarding the client-side detectability of MS attacks were raised, questioning their practicality. In this work, for the first time, we thoroughly study client-side detectability. We first demonstrate that all prior MS attacks are detectable by principled checks, and formulate a necessary set of requirements that a practical MS attack must satisfy. Next, we propose SEER, a novel attack framework that satisfies these requirements. The key insight of SEER is the use of a secret decoder, jointly trained with the shared model. We show that SEER can steal user data from gradients of realistic networks, even for large batch sizes of up to 512 and under secure aggregation. Our work is a promising step towards assessing the true vulnerability of federated learning in real-world settings.

We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath\'eodory--Fej\'er--Tur\'an problem. The first variation imposes the additional requirement that the function is radially decreasing while the second one is a generalization which involves derivatives of the entire function. Various interesting inequalities, inspired by results due to Duffin and Schaeffer, Landau, and Hardy and Littlewood, are also established., Comment: 18 pages, 4 figures

Fair representation learning (FRL) is a popular class of methods aiming to produce fair classifiers via data preprocessing. Recent regulatory directives stress the need for FRL methods that provide practical certificates, i.e., provable upper bounds on the unfairness of any downstream classifier trained on preprocessed data, which directly provides assurance in a practical scenario. Creating such FRL methods is an important challenge that remains unsolved. In this work, we address that challenge and introduce FARE (Fairness with Restricted Encoders), the first FRL method with practical fairness certificates. FARE is based on our key insight that restricting the representation space of the encoder enables the derivation of practical guarantees, while still permitting favorable accuracy-fairness tradeoffs for suitable instantiations, such as one we propose based on fair trees. To produce a practical certificate, we develop and apply a statistical procedure that computes a finite sample high-confidence upper bound on the unfairness of any downstream classifier trained on FARE embeddings. In our comprehensive experimental evaluation, we demonstrate that FARE produces practical certificates that are tight and often even comparable with purely empirical results obtained by prior methods, which establishes the practical value of our approach., Comment: ICML 2023

While federated learning (FL) promises to preserve privacy, recent works in the image and text domains have shown that training updates leak private client data. However, most high-stakes applications of FL (e.g., in healthcare and finance) use tabular data, where the risk of data leakage has not yet been explored. A successful attack for tabular data must address two key challenges unique to the domain: (i) obtaining a solution to a high-variance mixed discrete-continuous optimization problem, and (ii) enabling human assessment of the reconstruction as unlike for image and text data, direct human inspection is not possible. In this work we address these challenges and propose TabLeak, the first comprehensive reconstruction attack on tabular data. TabLeak is based on two key contributions: (i) a method which leverages a softmax relaxation and pooled ensembling to solve the optimization problem, and (ii) an entropy-based uncertainty quantification scheme to enable human assessment. We evaluate TabLeak on four tabular datasets for both FedSGD and FedAvg training protocols, and show that it successfully breaks several settings previously deemed safe. For instance, we extract large subsets of private data at >90% accuracy even at the large batch size of 128. Our findings demonstrate that current high-stakes tabular FL is excessively vulnerable to leakage attacks.

Recent attacks have shown that user data can be recovered from FedSGD updates, thus breaking privacy. However, these attacks are of limited practical relevance as federated learning typically uses the FedAvg algorithm. Compared to FedSGD, recovering data from FedAvg updates is much harder as: (i) the updates are computed at unobserved intermediate network weights, (ii) a large number of batches are used, and (iii) labels and network weights vary simultaneously across client steps. In this work, we propose a new optimization-based attack which successfully attacks FedAvg by addressing the above challenges. First, we solve the optimization problem using automatic differentiation that forces a simulation of the client's update that generates the unobserved parameters for the recovered labels and inputs to match the received client update. Second, we address the large number of batches by relating images from different epochs with a permutation invariant prior. Third, we recover the labels by estimating the parameters of existing FedSGD attacks at every FedAvg step. On the popular FEMNIST dataset, we demonstrate that on average we successfully recover >45% of the client's images from realistic FedAvg updates computed on 10 local epochs of 10 batches each with 5 images, compared to only <10% using the baseline. Our findings show many real-world federated learning implementations based on FedAvg are vulnerable.

The automatic identification of harmful content online is of major concern for social media platforms, policymakers, and society. Researchers have studied textual, visual, and audio content, but typically in isolation. Yet, harmful content often combines multiple modalities, as in the case of memes, which are of particular interest due to their viral nature. With this in mind, here we offer a comprehensive survey with a focus on harmful memes. Based on a systematic analysis of recent literature, we first propose a new typology of harmful memes, and then we highlight and summarize the relevant state of the art. One interesting finding is that many types of harmful memes are not really studied, e.g., such featuring self-harm and extremism, partly due to the lack of suitable datasets. We further find that existing datasets mostly capture multi-class scenarios, which are not inclusive of the affective spectrum that memes can represent. Another observation is that memes can propagate globally through repackaging in different languages and that they can also be multilingual, blending different cultures. We conclude by highlighting several challenges related to multimodal semiotics, technological constraints, and non-trivial social engagement, and we present several open-ended aspects such as delineating online harm and empirically examining related frameworks and assistive interventions, which we believe will motivate and drive future research., Comment: Accepted at IJCAI-ECAI 2022 (Survey Track) - Editorial Feedback Revised, 9 pages (7 main + 2 reference pages)

Recent work shows that sensitive user data can be reconstructed from gradient updates, breaking the key privacy promise of federated learning. While success was demonstrated primarily on image data, these methods do not directly transfer to other domains such as text. In this work, we propose LAMP, a novel attack tailored to textual data, that successfully reconstructs original text from gradients. Our attack is based on two key insights: (i) modeling prior text probability with an auxiliary language model, guiding the search towards more natural text, and (ii) alternating continuous and discrete optimization, which minimizes reconstruction loss on embeddings, while avoiding local minima by applying discrete text transformations. Our experiments demonstrate that LAMP is significantly more effective than prior work: it reconstructs 5x more bigrams and 23% longer subsequences on average. Moreover, we are the first to recover inputs from batch sizes larger than 1 for textual models. These findings indicate that gradient updates of models operating on textual data leak more information than previously thought.

Federated learning is an established method for training machine learning models without sharing training data. However, recent work has shown that it cannot guarantee data privacy as shared gradients can still leak sensitive information. To formalize the problem of gradient leakage, we propose a theoretical framework that enables, for the first time, analysis of the Bayes optimal adversary phrased as an optimization problem. We demonstrate that existing leakage attacks can be seen as approximations of this optimal adversary with different assumptions on the probability distributions of the input data and gradients. Our experiments confirm the effectiveness of the Bayes optimal adversary when it has knowledge of the underlying distribution. Further, our experimental evaluation shows that several existing heuristic defenses are not effective against stronger attacks, especially early in the training process. Thus, our findings indicate that the construction of more effective defenses and their evaluation remains an open problem.

Among the various modes of communication in social media, the use of Internet memes has emerged as a powerful means to convey political, psychological, and socio-cultural opinions. Although memes are typically humorous in nature, recent days have witnessed a proliferation of harmful memes targeted to abuse various social entities. As most harmful memes are highly satirical and abstruse without appropriate contexts, off-the-shelf multimodal models may not be adequate to understand their underlying semantics. In this work, we propose two novel problem formulations: detecting harmful memes and the social entities that these harmful memes target. To this end, we present HarMeme, the first benchmark dataset, containing 3,544 memes related to COVID-19. Each meme went through a rigorous two-stage annotation process. In the first stage, we labeled a meme as very harmful, partially harmful, or harmless; in the second stage, we further annotated the type of target(s) that each harmful meme points to: individual, organization, community, or society/general public/other. The evaluation results using ten unimodal and multimodal models highlight the importance of using multimodal signals for both tasks. We further discuss the limitations of these models and we argue that more research is needed to address these problems., Comment: harmful memes, multimodality, social media

Internet memes have become powerful means to transmit political, psychological, and socio-cultural ideas. Although memes are typically humorous, recent days have witnessed an escalation of harmful memes used for trolling, cyberbullying, and abuse. Detecting such memes is challenging as they can be highly satirical and cryptic. Moreover, while previous work has focused on specific aspects of memes such as hate speech and propaganda, there has been little work on harm in general. Here, we aim to bridge this gap. We focus on two tasks: (i)detecting harmful memes, and (ii)identifying the social entities they target. We further extend a recently released HarMeme dataset, which covered COVID-19, with additional memes and a new topic: US politics. To solve these tasks, we propose MOMENTA (MultimOdal framework for detecting harmful MemEs aNd Their tArgets), a novel multimodal deep neural network that uses global and local perspectives to detect harmful memes. MOMENTA systematically analyzes the local and the global perspective of the input meme (in both modalities) and relates it to the background context. MOMENTA is interpretable and generalizable, and our experiments show that it outperforms several strong rivaling approaches., Comment: The paper has been accepted in the Findings of Empirical Methods in Natural Language Processing (EMNLP), 2021

Existing neural network verifiers compute a proof that each input is handled correctly under a given perturbation by propagating a symbolic abstraction of reachable values at each layer. This process is repeated from scratch independently for each input (e.g., image) and perturbation (e.g., rotation), leading to an expensive overall proof effort when handling an entire dataset. In this work, we introduce a new method for reducing this verification cost without losing precision based on a key insight that abstractions obtained at intermediate layers for different inputs and perturbations can overlap or contain each other. Leveraging our insight, we introduce the general concept of shared certificates, enabling proof effort reuse across multiple inputs to reduce overall verification costs. We perform an extensive experimental evaluation to demonstrate the effectiveness of shared certificates in reducing the verification cost on a range of datasets and attack specifications on image classifiers including the popular patch and geometric perturbations. We release our implementation at https://github.com/eth-sri/proof-sharing., Comment: Extended version of our CAV'22 paper

Propaganda can be defined as a form of communication that aims to influence the opinions or the actions of people towards a specific goal; this is achieved by means of well-defined rhetorical and psychological devices. Propaganda, in the form we know it today, can be dated back to the beginning of the 17th century. However, it is with the advent of the Internet and the social media that it has started to spread on a much larger scale than before, thus becoming major societal and political issue. Nowadays, a large fraction of propaganda in social media is multimodal, mixing textual with visual content. With this in mind, here we propose a new multi-label multimodal task: detecting the type of propaganda techniques used in memes. We further create and release a new corpus of 950 memes, carefully annotated with 22 propaganda techniques, which can appear in the text, in the image, or in both. Our analysis of the corpus shows that understanding both modalities together is essential for detecting these techniques. This is further confirmed in our experiments with several state-of-the-art multimodal models., Comment: propaganda, disinformation, fake news, memes, multimodality. arXiv admin note: text overlap with arXiv:2105.09284

We describe SemEval-2021 task 6 on Detection of Persuasion Techniques in Texts and Images: the data, the annotation guidelines, the evaluation setup, the results, and the participating systems. The task focused on memes and had three subtasks: (i) detecting the techniques in the text, (ii) detecting the text spans where the techniques are used, and (iii) detecting techniques in the entire meme, i.e., both in the text and in the image. It was a popular task, attracting 71 registrations, and 22 teams that eventually made an official submission on the test set. The evaluation results for the third subtask confirmed the importance of both modalities, the text and the image. Moreover, some teams reported benefits when not just combining the two modalities, e.g., by using early or late fusion, but rather modeling the interaction between them in a joint model., Comment: propaganda, disinformation, misinformation, fake news, memes, multimodality

We introduce the concept of provably robust adversarial examples for deep neural networks - connected input regions constructed from standard adversarial examples which are guaranteed to be robust to a set of real-world perturbations (such as changes in pixel intensity and geometric transformations). We present a novel method called PARADE for generating these regions in a scalable manner which works by iteratively refining the region initially obtained via sampling until a refined region is certified to be adversarial with existing state-of-the-art verifiers. At each step, a novel optimization procedure is applied to maximize the region's volume under the constraint that the convex relaxation of the network behavior with respect to the region implies a chosen bound on the certification objective. Our experimental evaluation shows the effectiveness of PARADE: it successfully finds large provably robust regions including ones containing $\approx 10^{573}$ adversarial examples for pixel intensity and $\approx 10^{599}$ for geometric perturbations. The provability enables our robust examples to be significantly more effective against state-of-the-art defenses based on randomized smoothing than the individual attacks used to construct the regions.

We study the behaviour of the smallest possible constants $d_n$ and $c_n$ in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2, \qquad (a_1,\ldots,a_n) \in \mathbb{R}^n $$ and $$ \int_{0}^{\infty}\Bigg(\frac{1}{x}\int\limits_{0}^{x}f(t)\,dt\Bigg)^2 dx \leq c_n \int_{0}^{\infty} f^2(x)\,dx, \ \ f\in \mathcal{H}_n, $$ for the finite dimensional spaces $\mathbb{R}^n$ and $\mathcal{H}_n:=\{f\,:\, \int_0^x f(t) dt =e^{-x/2}\,p(x)\ :\ p\in \mathcal{P}_n, p(0)=0\}$, where $\mathcal{P}_n$ is the set of real-valued algebraic polynomials of degree not exceeding $n$. The constants $d_n$ and $c_n$ are identified as the smallest eigenvalues of certain Jacobi matrices and the two-sided estimates for $d_n$ and $c_n$ of the form $$ 4-\frac{c}{\ln n}< d_n, c_n<4-\frac{c}{\ln^2 n}\,,\qquad c>0\, $$ are established.

For parameters $\,c\in(0,1)\,$ and $\,\beta>0$, let $\,\ell_{2}(c,\beta)\,$ be the Hilbert space of real functions defined on $\,\mathbb{N}\,$ (i.e., real sequences), for which $$ \| f \|_{c,\beta}^2 := \sum_{k=0}^{\infty}\frac{(\beta)_k}{k!}\,c^k\,[f(k)]^2<\infty\,. $$ We study the best (i.e., the smallest possible) constant $\,\gamma_n(c,\beta)\,$ in the discrete Markov-Bernstein inequality $$ \|\Delta P\|_{c,\beta}\leq \gamma_n(c,\beta)\,\|P\|_{c,\beta}\,,\quad P\in\mathcal{P}_n\,, $$ where $\,\mathcal{P}_n\,$ is the set of real algebraic polynomials of degree at most $\,n\,$ and $\,\Delta f(x):=f(x+1)-f(x)\,$. We prove that: (i) $\displaystyle \gamma_n(c,1)\leq 1+\frac{1}{\sqrt{c}}\,$ for every $\,n\in \mathbb{N}\,$ and $\displaystyle \lim_{n\to\infty}\gamma_n(c,1)= 1+\frac{1}{\sqrt{c}}\,$. (ii) For every fixed $\,c\in (0,1)\,$, $\,\gamma_n(c,\beta)\,$ is a monotonically decreasing function of $\,\beta\,$ in $\,(0,\infty)\,$. (iii) For every fixed $\,c\in (0,1)\,$ and $\,\beta>0\,$, the best Markov-Bernstein constants $\,\gamma_n(c,\beta)\,$ are bounded uniformly with respect to $\,n$. A similar Markov-Bernstein unequality is proved for sequences in $\,\ell_{2}(c,\beta)\,$. We also establish a relation between the best Markov-Bernstein constants $\,\gamma_n(c,\beta)\,$ and the smallest eigenvalues of certain explicitly given Jacobi matrices., Comment: 15 pages

Publicly available social media archives facilitate research in the social sciences and provide corpora for training and testing a wide range of machine learning and natural language processing methods. With respect to the recent outbreak of the Coronavirus disease 2019 (COVID-19), online discourse on Twitter reflects public opinion and perception related to the pandemic itself as well as mitigating measures and their societal impact. Understanding such discourse, its evolution, and interdependencies with real-world events or (mis)information can foster valuable insights. On the other hand, such corpora are crucial facilitators for computational methods addressing tasks such as sentiment analysis, event detection, or entity recognition. However, obtaining, archiving, and semantically annotating large amounts of tweets is costly. In this paper, we describe TweetsCOV19, a publicly available knowledge base of currently more than 8 million tweets, spanning October 2019 - April 2020. Metadata about the tweets as well as extracted entities, hashtags, user mentions, sentiments, and URLs are exposed using established RDF/S vocabularies, providing an unprecedented knowledge base for a range of knowledge discovery tasks. Next to a description of the dataset and its extraction and annotation process, we present an initial analysis and use cases of the corpus.

Semantic Web technologies offer the prospect of significantly reducing the amount of effort required to integrate existing enterprise functionality in support of new composite processes; whether within a given organization or across multiple ones. A significant body of work in this area has aimed to fully automate this process, while assuming that all functionality has already been encapsulated in the form of semantic web services with rich and accurate annotations. In this article, we argue that this assumption is often unrealistic. Instead, we describe a mixed initiative framework for semantic web service discovery and composition that aims at flexibly interleaving human decision making and automated functionality in environments where annotations may be incomplete and even inconsistent.

In this note we extend the classical relation between the equilibrium configurations of unit movable point charges in a plane electrostatic field created by these charges together with some fixed point charges and the polynomial solutions of a corresponding Lam\'e differential equation. Namely, we find similar relation between the equilibrium configurations of unit movable charges subject to a certain type of rational or polynomial constraint and polynomial solutions of a corresponding degenerate Lam\'e equation, see details below. In particular, the standard linear differential equations satisfied by the classical Hermite and Laguerre polynomials belong to this class. Besides these two classical cases, we present a number of other examples including some relativistic orthogonal polynomials and linear differential equations satisfied by those., Comment: 15 pages, 1 figure

As one of the richest sources of encyclopedic information on the Web, Wikipedia generates an enormous amount of traffic. In this paper, we study large-scale article access data of the English Wikipedia in order to compare articles with respect to the two main paradigms of information seeking, i.e., search by formulating a query, and navigation by following hyperlinks. To this end, we propose and employ two main metrics, namely (i) searchshare -- the relative amount of views an article received by search --, and (ii) resistance -- the ability of an article to relay traffic to other Wikipedia articles -- to characterize articles. We demonstrate how articles in distinct topical categories differ substantially in terms of these properties. For example, architecture-related articles are often accessed through search and are simultaneously a "dead end" for traffic, whereas historical articles about military events are mainly navigated. We further link traffic differences to varying network, content, and editing activity features. Lastly, we measure the impact of the article properties by modeling access behavior on articles with a gradient boosting approach. The results of this paper constitute a step towards understanding human information seeking behavior on the Web.