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Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPS) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPS, as well as further relevant examples of MPS including the W state and the Dicke states in an approximate sense. Our findings motivate the usage of ans\"atze simpler than tensor networks in systems whose structure is invariant under permutations., Comment: 15 pages

The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical introduction, we first explain the necessary results about undecidability in mathematics and computer science. Then we briefly review the first results about undecidability in physics which emerged mostly in the 80s and early 90s. Finally we focus on the most recent contributions, which we divide in two main categories: many body systems and quantum information problems., Comment: 77 pages, v1

This paper proposes temporally aligned Large Language Models (LLMs) as a tool for longitudinal analysis of social media data. We fine-tune Temporal Adapters for Llama 3 8B on full timelines from a panel of British Twitter users, and extract longitudinal aggregates of emotions and attitudes with established questionnaires. We validate our estimates against representative British survey data and find strong positive, significant correlations for several collective emotions. The obtained estimates are robust across multiple training seeds and prompt formulations, and in line with collective emotions extracted using a traditional classification model trained on labeled data. To the best of our knowledge, this is the first work to extend the analysis of affect in LLMs to a longitudinal setting through Temporal Adapters. Our work enables new approaches towards the longitudinal analysis of social media data., Comment: Code available at https://github.com/dess-mannheim/temporal-adapters

We study noisy calcium imaging data, with a focus on the classification of spike traces. As raw traces obscure the true temporal structure of neuron's activity, we performed a tuned filtering of the calcium concentration using two methods: a biophysical model and a kernel mapping. The former characterizes spike trains related to a particular triggering event, while the latter filters out the signal and refines the selection of the underlying neuronal response. Transitioning from traditional time series analysis to point process theory, the study explores spike-time distance metrics and point pattern prototypes to describe repeated observations. We assume that the analyzed neuron's firing events, i.e. spike occurrences, are temporal point process events. In particular, the study aims to categorize 47 point patterns by depth, assuming the similarity of spike occurrences within specific depth categories. The results highlight the pivotal roles of depth and stimuli in discerning diverse temporal structures of neuron firing events, confirming the point process approach based on prototype analysis is largely useful in the classification of spike traces., Comment: 12 pages, 8 figures

The applications of Large Language Models (LLMs) are going towards collaborative tasks where several agents interact with each other like in an LLM society. In such a setting, large groups of LLMs could reach consensus about arbitrary norms for which there is no information supporting one option over another, regulating their own behavior in a self-organized way. In human societies, the ability to reach consensus without institutions has a limit in the cognitive capacities of humans. To understand if a similar phenomenon characterizes also LLMs, we apply methods from complexity science and principles from behavioral sciences in a new approach of AI anthropology. We find that LLMs are able to reach consensus in groups and that the opinion dynamics of LLMs can be understood with a function parametrized by a majority force coefficient that determines whether consensus is possible. This majority force is stronger for models with higher language understanding capabilities and decreases for larger groups, leading to a critical group size beyond which, for a given LLM, consensus is unfeasible. This critical group size grows exponentially with the language understanding capabilities of models and for the most advanced models, it can reach an order of magnitude beyond the typical size of informal human groups.

We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood as the superposition of all the words in a regular language and encompass physically relevant states such as the GHZ-, W- or Dicke-states. By leveraging the theory of regular languages, we develop a theoretical framework to describe them. First, we express them in terms of matrix product states, providing efficient criteria to recognize them. We then develop a canonical form which allows us to formulate a fundamental theorem for the equivalence of regular language states, including under local unitary operations. We also exploit the theory of tensor networks to find an efficient criterion to determine when regular languages are shift-invariant., Comment: 12 pages, 1 figure

Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single repeated tensor are known to coincide with 1D quantum cellular automata (QCA), i.e., unitaries with an exact light cone. However, this correspondence breaks down for MPU with open boundary conditions, even if the resulting operator is translation-invariant. Such unitaries can turn short- to long-range correlations and thus alter the underlying phase of matter. Here we make the first steps towards a theory of MPU with uniform bulk but arbitrary boundary. In particular, we study the structure of a subclass with a direct-sum form which maximally violates the QCA property. We also consider the general case of MPU formed by site-dependent (nonuniform) tensors and show a correspondence between MPU and locally maximally entanglable states.

Pursuit of honest and truthful decision-making is crucial for governance and accountability in democracies. However, people sometimes take different perspectives of what it means to be honest and how to pursue truthfulness. Here we explore a continuum of perspectives from evidence-based reasoning, rooted in ascertainable facts and data, at one end, to intuitive decisions that are driven by feelings and subjective interpretations, at the other. We analyze the linguistic traces of those contrasting perspectives in Congressional speeches from 1879 to 2022. We find that evidence-based language has continued to decline since the mid-1970s, together with a decline in legislative productivity. The decline was accompanied by increasing partisan polarization in Congress and rising income inequality in society. Results highlight the importance of evidence-based language in political decision-making.

The accessibility of the Hawking-Page transition in AdS$_5$ through a 1d Heisenberg spin chain is demonstrated. We use the random matrix formulation of the Loschmidt echo for a set of spin chains, and randomize the ferromagnetic spin interaction. It is shown that the thermal Loschmidt echo, when averaged, detects the predicted increase in entropy across the Hawking-Page transition. This suggests that a 1d spin chain exhibits characteristics of black hole physics in 4+1 dimensions. We show that this approach is equally applicable to free fermion systems with a general dispersion relation., Comment: 5+13 pages, 2+3 figures. v2: minor improvements, references added, published version

We investigate the link between quantum position-verification (QPV) and holography established in [MPS19] using holographic quantum error correcting codes as toy models. By inserting the "temporal" scaling of the AdS metric by hand via the bulk Hamiltonian interaction strength, we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based verification is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another., Comment: (v2: updated presentation)

Scale-free networks are one of the most famous examples of emergent behavior and are ubiquitous in social systems, especially online social media in which users can follow each other. By analyzing the interactions of multiple generative agents using GPT3.5-turbo as a language model, we demonstrate their ability to not only mimic individual human linguistic behavior but also exhibit collective phenomena intrinsic to human societies, in particular the emergence of scale-free networks. We discovered that this process is disrupted by a skewed token prior distribution of GPT3.5-turbo, which can lead to networks with extreme centralization as a kind of alignment. We show how renaming agents removes these token priors and allows the model to generate a range of networks from random networks to more realistic scale-free networks.

Schizophrenia (SZ) is a prevalent mental disorder characterized by cognitive, emotional, and behavioral changes. Symptoms of SZ include hallucinations, illusions, delusions, lack of motivation, and difficulties in concentration. Diagnosing SZ involves employing various tools, including clinical interviews, physical examinations, psychological evaluations, the Diagnostic and Statistical Manual of Mental Disorders (DSM), and neuroimaging techniques. Electroencephalography (EEG) recording is a significant functional neuroimaging modality that provides valuable insights into brain function during SZ. However, EEG signal analysis poses challenges for neurologists and scientists due to the presence of artifacts, long-term recordings, and the utilization of multiple channels. To address these challenges, researchers have introduced artificial intelligence (AI) techniques, encompassing conventional machine learning (ML) and deep learning (DL) methods, to aid in SZ diagnosis. This study reviews papers focused on SZ diagnosis utilizing EEG signals and AI methods. The introduction section provides a comprehensive explanation of SZ diagnosis methods and intervention techniques. Subsequently, review papers in this field are discussed, followed by an introduction to the AI methods employed for SZ diagnosis and a summary of relevant papers presented in tabular form. Additionally, this study reports on the most significant challenges encountered in SZ diagnosis, as identified through a review of papers in this field. Future directions to overcome these challenges are also addressed. The discussion section examines the specific details of each paper, culminating in the presentation of conclusions and findings.

Political conflict is an essential element of democratic systems, but can also threaten their existence if it becomes too intense. This happens particularly when most political issues become aligned along the same major fault line, splitting society into two antagonistic camps. In the 20th century, major fault lines were formed by structural conflicts, like owners vs workers, center vs periphery, etc. But these classical cleavages have since lost their explanatory power. Instead of theorizing new cleavages, we present the FAULTANA (FAULT-line Alignment Network Analysis) pipeline, a computational method to uncover major fault lines in data of signed online interactions. Our method makes it possible to quantify the degree of antagonism prevalent in different online debates, as well as how aligned each debate is to the major fault line. This makes it possible to identify the wedge issues driving polarization, characterized by both intense antagonism and alignment. We apply our approach to large-scale data sets of Birdwatch, a US-based Twitter fact-checking community and the discussion forums of DerStandard, an Austrian online newspaper. We find that both online communities are divided into two large groups and that their separation follows political identities and topics. In addition, for DerStandard, we pinpoint issues that reinforce societal fault lines and thus drive polarization. We also identify issues that trigger online conflict without strictly aligning with those dividing lines (e.g. COVID-19). Our methods allow us to construct a time-resolved picture of affective polarization that shows the separate contributions of cohesiveness and divisiveness to the dynamics of alignment during contentious elections and events.

Tensor networks are factorizations of high-dimensional tensors into networks of smaller tensors. They have applications in physics and mathematics, and recently have been proposed as promising machine learning architectures. To ease the integration of tensor networks in machine learning pipelines, we introduce TensorKrowch, an open source Python library built on top of PyTorch. Providing a user-friendly interface, TensorKrowch allows users to construct any tensor network, train it, and integrate it as a layer in more intricate deep learning models. In this paper, we describe the main functionality and basic usage of TensorKrowch, and provide technical details on its building blocks and the optimizations performed to achieve efficient operation., Comment: 20 pages, 2 figures. The TensorKrowch GitHub repository is in https://github.com/joserapa98/tensorkrowch and the TensorKrowch documentation is in https://joserapa98.github.io/tensorkrowch. V3: Accepted version, corrected acknowledgments

The wealth of text data generated by social media has enabled new kinds of analysis of emotions with language models. These models are often trained on small and costly datasets of text annotations produced by readers who guess the emotions expressed by others in social media posts. This affects the quality of emotion identification methods due to training data size limitations and noise in the production of labels used in model development. We present LEIA, a model for emotion identification in text that has been trained on a dataset of more than 6 million posts with self-annotated emotion labels for happiness, affection, sadness, anger, and fear. LEIA is based on a word masking method that enhances the learning of emotion words during model pre-training. LEIA achieves macro-F1 values of approximately 73 on three in-domain test datasets, outperforming other supervised and unsupervised methods in a strong benchmark that shows that LEIA generalizes across posts, users, and time periods. We further perform an out-of-domain evaluation on five different datasets of social media and other sources, showing LEIA's robust performance across media, data collection methods, and annotation schemes. Our results show that LEIA generalizes its classification of anger, happiness, and sadness beyond the domain it was trained on. LEIA can be applied in future research to provide better identification of emotions in text from the perspective of the writer. The models produced for this article are publicly available at https://huggingface.co/LEIA

Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a lumped element or its associated physics may be unknown, modeling tasks may be restricted to full-fidelity simulations of the physics of a system. In this work, we consider data-driven modeling tasks with limited point-wise measurements of otherwise continuous systems. We build upon the notion of the Universal Differential Equation (UDE) to construct data-driven models for reducing dynamics to that of a lumped parameter and inferring its properties. The flexibility of UDEs allow for composing various known physical priors suitable for application-specific modeling tasks, including lumped parameter methods. The motivating example for this work is the plunge and dwell stages for friction-stir welding; specifically, (i) mapping power input into the tool to a point-measurement of temperature and (ii) using this learned mapping for process control.

How can citizens address hate in online discourse? We analyze a large corpus of more than 130,000 discussions on Twitter over four years. With the help of human annotators, language models and machine learning classifiers, we identify different dimensions of discourse that might be related to the probability of hate speech in subsequent tweets. We use a matching approach and longitudinal statistical analyses to discern the effectiveness of different counter speech strategies on the micro-level (individual tweet pairs), meso-level (discussion trees) and macro-level (days) of discourse. We find that expressing simple opinions, not necessarily supported by facts, but without insults, relates to the least hate in subsequent discussions. Sarcasm can be helpful as well, in particular in the presence of organized extreme groups. Mentioning either outgroups or ingroups is typically related to a deterioration of discourse. A pronounced emotional tone, either negative such as anger or fear, or positive such as enthusiasm and pride, also leads to worse discourse quality. We obtain similar results for other measures of quality of discourse beyond hate speech, including toxicity, extremity of speech, and the presence of extreme speakers. Going beyond one-shot analyses on smaller samples of discourse, our findings have implications for the successful management of online commons through collective civic moderation.

Understanding couple instability is a topic of social and economic relevance. This paper investigates how the risk of dissolution relates to efforts to solve disagreements. We study whether the prevalence of relationship instability in the past among couples is associated with marital locus of control. This is a noncognitive trait that captures individuals perception of control over problems within the couple. We implement a list experiment using the count-item technique to a sample of current real-life couples to elicit truthful answers about couple break-up intentions in the past at the individual level. We find that around 44 per cent of our sample has considered to end their relationship with their partner in the past. The intention to break-up is more prevalent among those who score low in marital locus of control, males, low-income earners, individuals with university studies and couples without children.

At the end of October 2022, Elon Musk concluded his acquisition of Twitter. In the weeks and months before that, several questions were publicly discussed that were not only of interest to the platform's future buyers, but also of high relevance to the Computational Social Science research community. For example, how many active users does the platform have? What percentage of accounts on the site are bots? And, what are the dominating topics and sub-topical spheres on the platform? In a globally coordinated effort of 80 scholars to shed light on these questions, and to offer a dataset that will equip other researchers to do the same, we have collected all 375 million tweets published within a 24-hour time period starting on September 21, 2022. To the best of our knowledge, this is the first complete 24-hour Twitter dataset that is available for the research community. With it, the present work aims to accomplish two goals. First, we seek to answer the aforementioned questions and provide descriptive metrics about Twitter that can serve as references for other researchers. Second, we create a baseline dataset for future research that can be used to study the potential impact of the platform's ownership change.

Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean field reduction, which gives rise to next generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favours the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry: namely, chimera-like solutions in the inhibitory case and anti-phase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic time scale and the slow adaptation one, ranging from anti-phase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the $\theta$-$\gamma$ range has revealed that a reduction of SFA leads to an increase of the $\theta$ frequency joined to a decrease of the $\gamma$ one. This is analogous to what reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, that is known to reduce SFA.

Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool, both for theoretical and numerical purposes. On the other hand, for tensor networks in dimension two or greater there is only limited understanding of the gauge symmetry. Here we introduce a new canonical form, the minimal canonical form, which applies to projected entangled pair states (PEPS) in any dimension, and prove a corresponding fundamental theorem. Already for matrix product states this gives a new canonical form, while in higher dimensions it is the first rigorous definition of a canonical form valid for any choice of tensor. We show that two tensors have the same minimal canonical forms if and only if they are gauge equivalent up to taking limits; moreover, this is the case if and only if they give the same quantum state for any geometry. In particular, this implies that the latter problem is decidable - in contrast to the well-known undecidability for PEPS on grids. We also provide rigorous algorithms for computing minimal canonical forms. To achieve this we draw on geometric invariant theory and recent progress in theoretical computer science in non-commutative group optimization., Comment: 51 pages, more than 8 figures

The spread of online misinformation on social media is increasingly perceived as a problem for societal cohesion and democracy. The role of political leaders in this process has attracted less research attention, even though politicians who "speak their mind" are perceived by segments of the public as authentic and honest even if their statements are unsupported by evidence. Analyzing communications by members of the U.S. Congress on Twitter between 2011 and 2022, we show that politicians' conception of honesty has undergone a distinct shift, with authentic belief-speaking that may be decoupled from evidence becoming more prominent and more differentiated from explicitly evidence-based truth seeking. We show that for Republicans - but not Democrats - an increase of belief-speaking of 10% is associated with a decrease of 12.8 points of quality (NewsGuard scoring system) in the sources shared in a tweet. Conversely, an increase in truth-seeking language is associated with an increase in quality of sources for both parties. The results support the hypothesis that the current dissemination of misinformation in political discourse is in part driven by an alternative understanding of truth and honesty that emphasizes invocation of subjective belief at the expense of reliance on evidence.

We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the Loschmidt echo. This leads to the study of a random matrix ensemble with a complex weight, whose analysis requires novel technical considerations, that we develop. We obtain three main results: 1) There is a third order phase transition at a rescaled critical time, that we determine. 2) The third order phase transition persists away from the thermodynamic limit. 3) For times below the critical value, the difference between the thermodynamic limit and a finite chain decreases exponentially with the system size. All these results depend in a rich manner on the parity of the number of flipped spins of the quantum state conforming the fidelity., Comment: v2: 60 pages, 18 figures, published version

Increased sharing of untrustworthy information on social media platforms is one of the main challenges of our modern information society. Because information disseminated by political elites is known to shape citizen and media discourse, it is particularly important to examine the quality of information shared by politicians. Here we show that from 2016 onward, members of the Republican party in the U.S. Congress have been increasingly sharing links to untrustworthy sources. The proportion of untrustworthy information posted by Republicans versus Democrats is diverging at an accelerating rate, and this divergence has worsened since president Biden was elected. This divergence between parties seems to be unique to the U.S. as it cannot be observed in other western democracies such as Germany and the United Kingdom, where left-right disparities are smaller and have remained largely constant.

Coral reef science is a fast-growing field propelled by the need to better understand coral health and resilience to devise strategies to slow reef loss resulting from environmental stresses. Key to coral resilience are the symbiotic interactions established within a complex holobiont, i.e. the multipartite assemblages comprising the host coral organism, endosymbiotic dinoflagellates, bacteria, archaea, fungi, and viruses. Tara Pacific is an ambitious project built upon the experience of previous Tara Oceans expeditions, and leveraging state-of-the-art sequencing technologies and analyses to dissect the biodiversity and biocomplexity of the coral holobiont screened across most archipelagos spread throughout the entire Pacific Ocean. Here we detail the Tara Pacific workflow for multi-omics data generation, from sample handling to nucleotide sequence data generation and deposition. This unique multidimensional framework also includes a large amount of concomitant metadata collected side-by-side that provide new assessments of coral reef biodiversity including micro-biodiversity and shape future investigations of coral reef dynamics and their fate in the Anthropocene.