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Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is ultimately constrained by the intrinsic properties of datasets, independently of computational power or model complexity. In this work, we introduce a formal entropy-based measure of classificability, which quantifies the inherent difficulty of a classification problem by assessing the uncertainty in class assignments given feature representations. This measure captures the degree of class overlap and aligns with human intuition, serving as an upper bound on classification performance for classification problems. Our results establish a theoretical limit beyond which no classifier can improve the classification accuracy, regardless of the architecture or amount of data, in a given problem. Our approach provides a principled framework for understanding when classification is inherently fallible and fundamentally ambiguous.

This paper investigates how teachers learn about race in the school context, with a particular focus on teachers' development of racial competency. Using in-depth, semi-structured interviews we find that teachers learn through three sources: from their peers, from years of experience, and from teacher preparation and in-service experiences. Furthermore, we find that learning occurs both informally and formally and that these sources of learning are moderated by three contextual factors: career status, school culture, and out-of-school factors We find that teachers rely most on informal avenues and encounters to develop racial competency.

Local teacher recruitment through "grow-your-own" programs is a prominent strategy to address workforce shortages and ensure that incoming teachers resemble, understand, and have strong connections to their communities. We exploit the staggered rollout of the Teacher Academy of Maryland career and technical education certificate program across public high schools, finding that exposed students were more likely to become teachers by 0.6 percentage points (pp), or 47%. Effects are concentrated among White girls (1.4pp/39%) and Black girls (0.7pp/80%). We also identify positive impacts on wages (5% on average/18% for Black girls), countering a prevailing narrative that teaching leaves one worse off financially relative to other labor market opportunities.

Mounting evidence supporting the advantages of a diverse teacher workforce prompts policymakers to scrutinize existing recruitment pathways. Following four cohorts of Maryland public high-school students over 12 years reveals several insights. Early barriers require timely interventions, aiding students of color in achieving educational milestones that are prerequisites for teacher candidacy (high school graduation, college enrollment). While alternative pathways that bypass traditional undergraduate teacher preparation may help, current approaches still show persistent racial disparities. Data simulations underscore the need for race-conscious policies specifically targeting or differentially benefiting students of color, as race-neutral strategies have minimal impact. Ultimately, multiple race-conscious policy solutions addressing various educational milestones must demonstrate significant effects--approximately 30% increases--to reshape the teacher workforce to align with student body demographics.

The United Nations 2030 Agenda for Sustainable Development outlines 17 goals to address global challenges. However, progress has been slower than expected and, consequently, there is a need to investigate the reasons behind this fact. In this study, we used a novel data-driven methodology to analyze data from 107 countries (2000$-$2022) using unsupervised machine learning techniques. Our analysis reveals strong positive and negative correlations between certain SDGs. The findings show that progress toward the SDGs is heavily influenced by geographical, cultural and socioeconomic factors, with no country on track to achieve all goals by 2030. This highlights the need for a region specific, systemic approach to sustainable development that acknowledges the complex interdependencies of the goals and the diverse capacities of nations. Our approach provides a robust framework for developing efficient and data-informed strategies, to promote cooperative and targeted initiatives for sustainable progress.

In recent years, several models using Quaternion-Valued Convolutional Neural Networks (QCNNs) for different problems have been proposed. Although the definition of the quaternion convolution layer is the same, there are different adaptations of other atomic components to the quaternion domain, e.g., pooling layers, activation functions, fully connected layers, etc. However, the effect of selecting a specific type of these components and the way in which their interactions affect the performance of the model still unclear. Understanding the impact of these choices on model performance is vital for effectively utilizing QCNNs. This paper presents a statistical analysis carried out on experimental data to compare the performance of existing components for the image classification problem. In addition, we introduce a novel Fully Quaternion ReLU activation function, which exploits the unique properties of quaternion algebra to improve model performance., Comment: 17 pages, 6 figures

Understanding the emergence and evolution of information handling is essential for unraveling the origins of life. Traditional genetic-first and metabolism-first models fall short in explaining how instructional information control systems naturally arise from molecular dynamics. To address this gap, we adopt an information-first approach, integrating Hofmeyr's (F, A)-systems -- an extension of Rosen's (M, R)-systems -- with temporal parametrization and multiscale causality. These models, which embody closure to efficient causation while remaining open to formal causation, provide a robust framework for primitive autopoiesis, anticipation, and adaptation. We establish a formal equivalence between extended (F, A)-systems and communicating X-machines, resolving self-referential challenges and demonstrating the hypercomputational nature of life processes. Our stepwise model traces the evolution of information handling from simple reaction networks that recognize regular languages to self-replicating chemical systems with memory and anticipatory capabilities. This transition from analog to digital architectures enhances evolutionary robustness and aligns with experimental evidence suggesting that chemical computation does not require life-specific chemistry. Furthermore, we incorporate open-ended evolutionary dynamics driven by computational undecidability and irreducibility, reinforcing the necessity of unconventional computing frameworks. This computational enactivist perspective provides a cohesive theoretical basis for a recently proposed trialectic between autopoiesis, anticipation and adaptation in order to solve the problem of relevance. By highlighting the critical role of hypercomputational processes in life's emergence and evolution, our framework offers new insights into the fundamental principles underlying biological information processing., Comment: 12 pages

The US teaching force remains disproportionately white while the student body grows more diverse. It is therefore important to understand how and under what conditions white teachers learn racial competency. This study applies a mixed-methods approach to investigate the hypothesis that Black peers improve white teachers' effectiveness when teaching Black students. The quantitative portion of this study relies on longitudinal data from North Carolina to show that having a Black same-grade peer significantly improves the achievement and reduces the suspension rates of white teachers' Black students. These effects are persistent over time and largest for novice teachers. Qualitative evidence from open-ended interviews of North Carolina public school teachers reaffirms these findings. Broadly, our findings suggest that the positive impact of Black teachers' ability to successfully teach Black students is not limited to their direct interaction with Black students but is augmented by spillover effects on early-career white teachers, likely through peer learning.

Now that the most acute phase of the COVID-19 crisis is over, public conversation has turned to the millions of students who are still struggling academically and emotionally--and how the nation's schools ought to respond. Decisions that education leaders make right now will determine whether this generation of students recovers or continues to lose ground. That's why policies that lower expectations--such as rescinding "third-grade reading guarantees" or keeping pandemic-era no-grading policies in effect--are so troubling. This study uses nationally representative survey data to explore how teacher expectations differ by sector, and how they affect achievement, attainment, and other outcomes. [Foreword by Amber M. Northern and David Griffith.]

The performance of various superconducting devices operating at ultra-low temperatures is impaired by the presence of non-equilibrium quasiparticles. Inelastic quasiparticle (QP) tunneling across Josephson junctions in superconducting qubits results in decoherence and spurious excitations and, notably, can trigger correlated errors that severely impede quantum error correction. In this work, we use "gap engineering" to suppress the tunneling of low-energy quasiparticles in Al-based transmon qubits, a leading building block for superconducting quantum processors. By implementing potential barriers for QP, we strongly suppress QP tunneling across the junction and preserve charge parity for over $10^3$ seconds. The suppression of QP tunneling also results in a reduction in the qubit energy relaxation rates. The demonstrated approach to gap engineering can be easily implemented in all Al-based circuits with Josephson junctions., Comment: 10 pages, 6 figures, 2 tables; Added references for the supplementary information and updated an author's preferred initials; Revised version in response to referee comments

Since their first applications, Convolutional Neural Networks (CNNs) have solved problems that have advanced the state-of-the-art in several domains. CNNs represent information using real numbers. Despite encouraging results, theoretical analysis shows that representations such as hyper-complex numbers can achieve richer representational capacities than real numbers, and that Hamilton products can capture intrinsic interchannel relationships. Moreover, in the last few years, experimental research has shown that Quaternion-Valued CNNs (QCNNs) can achieve similar performance with fewer parameters than their real-valued counterparts. This paper condenses research in the development of QCNNs from its very beginnings. We propose a conceptual organization of current trends and analyze the main building blocks used in the design of QCNN models. Based on this conceptual organization, we propose future directions of research.

A recent increase in data availability has allowed the possibility to perform different statistical linguistic studies. Here we use the Google Books Ngram dataset to analyze word flow among English, French, German, Italian, and Spanish. We study what we define as ``migrant words'', a type of loanwords that do not change their spelling. We quantify migrant words from one language to another for different decades, and notice that most migrant words can be aggregated in semantic fields and associated to historic events. We also study the statistical properties of accumulated migrant words and their rank dynamics. We propose a measure of use of migrant words that could be used as a proxy of cultural influence. Our methodology is not exempt of caveats, but our results are encouraging to promote further studies in this direction., Comment: 13 pages

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality -- a balance between change and stability, order and chaos -- is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks -- a general model of discrete dynamical systems -- we show that heterogeneity -- in time, structure, and function -- can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.

Statistical linguistics has advanced considerably in recent decades as data has become available. This has allowed researchers to study how statistical properties of languages change over time. In this work, we use data from Twitter to explore English and Spanish considering the rank diversity at different scales: temporal (from 3 to 96 hour intervals), spatial (from 3km to 3000+km radii), and grammatical (from monograms to pentagrams). We find that all three scales are relevant. However, the greatest changes come from variations in the grammatical scale. At the lowest grammatical scale (monograms), the rank diversity curves are most similar, independently on the values of other scales, languages, and countries. As the grammatical scale grows, the rank diversity curves vary more depending on the temporal and spatial scales, as well as on the language and country. We also study the statistics of Twitter-specific tokens: emojis, hashtags, and user mentions. These particular type of tokens show a sigmoid kind of behaviour as a rank diversity function. Our results are helpful to quantify aspects of language statistics that seem universal and what may lead to variations.

Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are considered homogeneous, criticality is restricted to phase transitions, leading either to robust (ordered) or adaptive (chaotic) phases in most of the parameter space. Many real-world complex systems, however, are not homogeneous. Some elements change in time faster than others, with slower elements (usually the most relevant) providing robustness, and faster ones being adaptive. Structural patterns of connectivity are also typically heterogeneous, characterized by few elements with many interactions and most elements with only a few. Here we take a few traditionally homogeneous dynamical models and explore their heterogeneous versions, finding evidence that heterogeneity extends criticality. Thus, parameter fine-tuning is not necessary to reach a phase transition and obtain the benefits of (homogeneous) criticality. Simply adding heterogeneity can extend criticality, making the search/evolution of complex systems faster and more reliable. Our results add theoretical support for the ubiquitous presence of heterogeneity in physical, social, and technological systems, as natural selection can exploit heterogeneity to evolve complexity "for free". In artificial systems and biological design, heterogeneity may also be used to extend the parameter range that allows for criticality., Comment: 17 pages, 3 figures

The COVID-19 pandemic has forced school leaders to make difficult decisions about how to balance students' educational needs with the health, safety, and social-emotional well-being of students and teachers. The American Rescue Plan Act of 2021 (Rescue Plan) recently enacted by Congress offers unprecedented amounts of potentially transformative funding to elementary and secondary schools. The Rescue Plan has the potential to simultaneously spur post-pandemic learning recovery efforts and address long-standing socio-demographic gaps in academic achievement and opportunity. This brief is intended to help state and local education leaders consider how to approach this opportunity to meet a persistent problem: the need for more educators of color to serve students. To do this, the authors encourage local education agencies (LEAs) to act strategically by leveraging the findings and evidence-based practices (EBP) of two distinct research bases: (1) High-dosage tutoring, extended-day programs, and summer learning programs are effective options for learning recovery; and (2) Students benefit from exposure to a diverse, representative educator workforce.

Genetic algorithms have been used in recent decades to solve a broad variety of search problems. These algorithms simulate natural selection to explore a parameter space in search of solutions for a broad variety of problems. In this paper, we explore the effects of introducing temporal heterogeneity in genetic algorithms. In particular, we set the crossover probability to be inversely proportional to the individual's fitness, i.e., better solutions change slower than those with a lower fitness. As case studies, we apply heterogeneity to solve the $N$-Queens and Traveling Salesperson problems. We find that temporal heterogeneity consistently improves search without having prior knowledge of the parameter space., Comment: Draft from November 2020

Josephson junctions (JJs) with Josephson energy $E_J \lesssim 1K$ are widely employed as non-linear elements in superconducting circuits for quantum computing, operating at milli-Kelvin temperatures. Here we experimentally study incoherent phase slips (IPS) in low-$E_J$ Aluminum-based JJs at $T<0.2K$, where the IPS become the dominant source of dissipation. We observed strong suppression of the critical (switching) current and a very rapid growth of the zero-bias resistance with decreasing Josephson energy below $E_J \sim 1K$. This behavior is attributed to the IPSs whose rate exponentially increases with decreasing the ratio $E_J/T$. Our observations are in line with other data reported in literature. With further improvement of coherence of superconducting qubits, the observed dissipation from IPS might limit the performance of qubits based on low-$E_J$ junctions., Comment: 10 pages, 6 figures

Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a variety of fields. More recently, data availability has allowed us to study rank dynamics: how elements of a ranking change in time. Here, we study the rank distributions and rank dynamics of twelve datasets from different sports and games. To study rank dynamics, we consider measures we have defined previously: rank diversity, change probability, rank entropy, and rank complexity. We also introduce a new measure that we call ``system closure'' that reflects how many elements enter or leave the rankings in time. We use a random walk model to reproduce the observed rank dynamics, showing that a simple mechanism can generate similar statistical properties as the ones observed in the datasets. Our results show that, while rank distributions vary considerably for different rankings, rank dynamics have similar behaviors, independently of the nature and competitiveness of the sport or game and its ranking method. Our results also suggest that our measures of rank dynamics are general and applicable for complex systems of different natures., Comment: 15 pages

There is no agreed definition of intelligence, so it is problematic to simply ask whether brains, swarms, computers, or other systems are intelligent or not. To compare the potential intelligence exhibited by different cognitive systems, I use the common approach used by artificial intelligence and artificial life: Instead of studying the substrate of systems, let us focus on their organization. This organization can be measured with information. Thus, I apply an informationist epistemology to describe cognitive systems, including brains and computers. This allows me to frame the usefulness and limitations of the brain-computer analogy in different contexts. I also use this perspective to discuss the evolution and ecology of intelligence., Comment: 11 pages

In the study of oscillatory electron transport in high-mobility Si MOSFETs at low temperatures we observed two correlated effects in weak in-plane magnetic fields: a steep decrease of the renormalized magnetic susceptibility $\chi^*(H)$ and an increase of the concentration of mobile carriers $n(H)$. We suggest a phenomenological model of the magnetic field driven redistribution between the extended and localized electronic states that qualitatively explains both effects. We argue that the redistribution is mainly caused by magnetization of the large-spin localized states with energies close to the Fermi energy $E_F$, coexisting with the majority Fermi liquid state. Our findings also resolve a long-standing disagreement between the experimental data on $\chi^*$ obtained in weak ($H \sim k_BT/\mu_B$) and strong ($H \sim E_F/g\mu_B$) magnetic fields., Comment: 11 pages, 8 figures

A study of the dynamical formation of networks of friends and enemies in social media, in this case Twitter, is presented. We characterise the single node properties of such networks, as the clustering coefficient and the degree, to investigate the structure of links. The results indicate that the network is made from three kinds of nodes: one with high clustering coefficient but very small degree, a second group has zero clustering coefficient with variable degree, and finally, a third group in which the clustering coefficient as a function of the degree decays as a power law. This third group represents $\sim2\%$ of the nodes and is characteristic of dynamical networks with feedback. This part of the lattice seemingly represents strongly interacting friends in a real social network.

Nature has found one method of organizing living matter, but maybe other options exist -- not yet discovered -- on how to create life. To study the life "as it could be" is the objective of an interdisciplinary field called Artificial Life (commonly abbreviated as ALife). The word "artificial" refers to the fact that humans are involved in the creation process. The artificial life forms might be completely unlike natural forms of life, with different chemical compositions, and even computer programs exhibiting life-like behaviours., Comment: Short review chapter, to be included in EPS Grand Challenges 2050 book

Even when concepts similar to emergence have been used since antiquity, we lack an agreed definition. However, emergence has been identified as one of the main features of complex systems. Most would agree on the statement ``life is complex''. Thus, understanding emergence and complexity should benefit the study of living systems. It can be said that life emerges from the interactions of complex molecules. But how useful is this to understand living systems? Artificial life (ALife) has been developed in recent decades to study life using a synthetic approach: build it to understand it. ALife systems are not so complex, be them soft (simulations), hard (robots), or wet (protocells). Then, we can aim at first understanding emergence in ALife, for then using this knowledge in biology. I argue that to understand emergence and life, it becomes useful to use information as a framework. In a general sense, I define emergence as information that is not present at one scale but is present at another scale. This perspective avoids problems of studying emergence from a materialist framework, and can be also useful in the study of self-organization and complexity., Comment: 28 pages, 1 figure

Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from socioeconomic policy to knowledge extraction. A century of research has found regularities when temporal rank data is aggregated. Far less is known, however, about how rankings change in time. Here we explore the dynamics of 30 rankings in natural, social, economic, and infrastructural systems, comprising millions of elements and timescales from minutes to centuries. We find that the flux of new elements determines the stability of a ranking: for high flux only the top of the list is stable, otherwise top and bottom are equally stable. We show that two basic mechanisms - displacement and replacement of elements - capture empirical ranking dynamics. The model uncovers two regimes of behavior; fast and large rank changes, or slow diffusion. Our results indicate that the balance between robustness and adaptability in ranked systems might be governed by simple random processes irrespective of system details., Comment: 12 pages, 3 figures. SI: 40 pages, 22 figures

Mexico has kept electronic records of all taxable transactions since 2014. Anonymized data collected by the Mexican federal government comprises more than 80 million contributors (individuals and companies) and almost 7 billion monthly-aggregations of invoices among contributors between January 2015 and December 2018. This data includes a list of almost ten thousand contributors already identified as tax evaders, due to their activities fabricating invoices for non-existing products or services so that recipients can evade taxes. Harnessing this extensive dataset, we build monthly and yearly temporal networks where nodes are contributors and directed links are invoices produced in a given time slice. Exploring the properties of the network neighborhoods around tax evaders, we show that their interaction patterns differ from those of the majority of contributors. In particular, invoicing loops between tax evaders and their clients are over-represented. With this insight, we use two machine-learning methods to classify other contributors as suspects of tax evasion: deep neural networks and random forests. We train each method with a portion of the tax evader list and test it with the rest, obtaining more than 0.9 accuracy with both methods. By using the complete dataset of contributors, each method classifies more than 100 thousand suspects of tax evasion, with more than 40 thousand suspects classified by both methods. We further reduce the number of suspects by focusing on those with a short network distance from known tax evaders. We thus obtain a list of highly suspicious contributors sorted by the amount of evaded tax, valuable information for the authorities to further investigate illegal tax activity in Mexico. With our methods, we estimate previously undetected tax evasion in the order of \$10 billion USD per year by about 10 thousand contributors., Comment: 26 pages, 12 figures

We know from previous survey research that teachers who hold high expectations for all of their students significantly increase the odds that those young people will go on to complete high school and college. One indicator of teachers' expectations is their approach to grading--specifically, whether they subject students to more or less rigorous grading practices. Unfortunately, "grade inflation" is pervasive in U.S. high schools, as evidenced by rising GPAs even as SAT scores and other measures of academic performance have held stable or fallen. The result is that a "good" grade is no longer a clear marker of knowledge and skills. Authored by American University's Seth Gershenson, "Great Expectations: The Impact of Rigorous Grading Practices on Student Achievement" examines to what extent teachers' grading standards affect student success. Specifically, this report investigates the following questions: (1) How do the grading standards of an Algebra I teacher affect content mastery, as measured by student performance on the end-of-course Algebra I exam? (2) Do the grading standards of an Algebra I teacher impact students' longer-term performance in subsequent math courses like geometry and Algebra II, and their likelihood of graduating from high school? and (3) Does the impact of an Algebra I teacher's grading standards vary by student, school, or teacher characteristics? Likewise, what school and teacher characteristics predict teachers' grading standards? To address these questions, Gershenson analyzed administrative data for all eighth and ninth grade Algebra I students in North Carolina's public schools from 2006 to 2016. The analysis yielded six major findings. Among them: Students of all racial/ethnic groups learn more from teachers with high grading standards, and these standards tend to be higher in schools serving more advantaged students. Moreover, the impact of rigorous grading practices can improve student performance in subsequent math classes up to two years later. [Foreword and Executive Summary by Amber M. Northern and Michael J. Petrilli.]

There's mounting evidence that, for children of color especially, having one or more teachers of the same race over the course of students' educational careers seems to make a positive difference. But to what extent, if any, do the benefits of having a same-race teacher vary by type of school? Existing "race-match" studies fail to distinguish among the traditional district and charter school sectors. Knowing whether differences exist across school types could improve how we recruit and develop educators, as well as shed light on whether the success of urban charter schools is due in part to their greater success in recruiting a diverse teaching staff--an explanation that's received short shrift in research and policy circles. "Student-Teacher Race Match in Charter and Traditional Public Schools," authored by Dr. Seth Gershenson of American University, uses student-level data for all public school students in North Carolina from grades three to five between 2006 and 2013. The analysis yielded five findings: (1) Traditional public schools and charter schools serve the same proportion of black students, but charter schools have about 35 percent more black teachers; (2) Black students in charter schools are about 50 percent more likely to have a black teacher than their traditional public school counterparts, but white students are equally likely to have a white teacher across the two sectors; (3) Race-match effects are nearly twice as large in the charter school sector as in traditional public schools, though these differences are statistically insignificant, likely due to small sample sizes; (4) In charter schools, race-match effects are twice as large for nonwhite as for white students, while no such difference exists in traditional public schools; and (5) Race-match effects are relatively constant across school locales, enrollments, and compositions. Since the effects of having a same-race teacher appear stronger in charter schools than in the district sector--and stronger still for nonwhite students--it's encouraging that the charter sector has more of these matches between black students and teachers, due largely to having more black teachers in the first place. This is clearly an overlooked dimension of charter effectiveness. Moreover, traditional public schools might seek to emulate their charter school counterparts when it comes to boosting the number of teachers of color they hire, though there remains room for improving teacher diversity, not to mention academic achievement, in both sectors. [Foreword by Amber M. Northern and Michael J. Petrilli.]

The area of Smart Power Grids needs to constantly improve its efficiency and resilience, to pro-vide high quality electrical power, in a resistant grid, managing faults and avoiding failures. Achieving this requires high component reliability, adequate maintenance, and a studied failure occurrence. Correct system operation involves those activities, and novel methodologies to detect, classify, and isolate faults and failures, model and simulate processes with predictive algorithms and analytics (using data analysis and asset condition to plan and perform activities). We show-case the application of a complex-adaptive, self-organizing modeling method, Probabilistic Boolean Networks (PBN), as a way towards the understanding of the dynamics of smart grid devices, and to model and characterize their behavior. This work demonstrates that PBNs are is equivalent to the standard Reinforcement Learning Cycle, in which the agent/model has an inter-action with its environment and receives feedback from it in the form of a reward signal. Differ-ent reward structures were created in order to characterize preferred behavior. This information can be used to guide the PBN to avoid fault conditions and failures.