In response to the low representation of Latinx adults in STEM occupations, this community-based participatory action research study aims to increase the number of middle school youths developing STEM career identities and entering high school with the intention to pursue STEM careers. The students were provided with summer and after-school activities focusing on network science and career development curricula. Using a quasi-experimental pretest–posttest design and career narratives, this study examined the changes in STEM and career self-efficacy, as well as career identity. The results show improvements in self-efficacy, an increased number of youths with intentions of pursuing future STEM career opportunities, and deeper reflections on their talents and skills after program participation. This paper also describes the program development and implementation in detail, as well as the adaptations that resulted from COVID-19, for scholars and educators designing similar programs. This study provides promising evidence for the quality of STEM and career development lessons in supporting the emergence of a STEM career identity and self-efficacy.

This is the first of two sequential papers describing the design and first-year implementation of a collaborative participatory action research effort between Sociedad Latina, a youth serving organization in Boston, Massachusetts, and Boston University. The collaboration aimed to develop and deliver a combined STEM and career development set of lessons for middle school Latinx youth. In the first paper, life design and the U.N. Sustainable Development Goals are described in relation to the rationale and the design of the career development intervention strategy that aims to help middle school youth discover the ways that learning advanced-STEM skills expand future decent work opportunities both within STEM and outside STEM, ultimately leading to an outcome of well-being and sustainable communities. In addition to providing evidence of career development intervention strategies, a qualitative analysis of the collaboration is described. The second paper will discuss two additional frameworks that guided the design and implementation of our work. As an example of translational research, the paper will provide larger national and regional contexts by describing system level career development interventions underway using Bronfenbrenner’s bioecological and person–process–context–time frameworks.

Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behaviour. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.

In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic. This property, called disorder, is usually associated with contact times between individuals and can be modeled by a weighted network, where the weights are related to normalized contact times ω. In this paper, we study the SIR model for disease spreading when both close and distant types of interactions are present. We develop a mitigation strategy that reduces only the time duration of distant contacts, which are easier to alter in practice. Using branching theory, supported by simulations, we found that the effectiveness of the strategy increases when the density f1 of close contacts decreases. Moreover, we found a threshold f̃1=Tc∕β below which the strategy can bring the system from an epidemic to a non-epidemic phase, even when close contacts have the longest time durations.

Human survival depends on our ability to predict future outcomes so that we can make informed decisions. Human cognition and perception are optimized for local, short-term decision-making, such as deciding when to fight or flight, whom to mate, or what to eat. For more elaborate decisions (e.g., when to harvest, when to go to war or not, and whom to marry), people used to consult oracles—prophetic predictions of the future inspired by the gods. Over time, oracles were replaced by models of the structure and dynamics of natural, technological, and social systems. In the 21st century, computational models and visualizations of model results inform much of our decision-making: near real-time weather forecasts help us decide when to take an umbrella, plant, or harvest; where to ground airplanes; or when to evacuate inhabitants in the path of a hurricane, tornado, or flood (1). Long-term weather and climate forecasts predict a future with increasing torrential rains, stronger winds, and more frequent drought, landslides, and forest fires as well as rising sea levels, enabling decision makers to prepare for these changes by building dikes, moving cities and roads, and building larger water reservoirs and better storm sewers (2).Computational models are particularly useful if they are combined with high-quality data and if they are widely used and understood. As early as 1960, Buckminster Fuller proposed the “World Game” to address the world’s problems through a holistic and anticipatory systems approach (3, 4). The game used Fuller's Dymaxion Map to visualize resources, trends, and scenarios. It was meant to be accessible to everyone (not just experts); therefore, decisions could be made collectively, and results could be used by anyone. In the 1970s, “The limits to growth: A report to the club of Rome” (5) used simulations to forecast future states of the … [↵][1]1To whom correspondence should be addressed. Email: katy{at}indiana.edu. [1]: #xref-corresp-1-1

We present NetSci High, our NSF-funded educational outreach program that connects high school students who are underrepresented in STEM (Science Technology Engineering and Mathematics), and their teachers, with regional university research labs and provides them with the opportunity to work with researchers and graduate students on team-based, year-long network science research projects, culminating in a formal presentation at a network science conference. This short paper reports the content and materials that we have developed to date, including lesson plans and tools for introducing high school students and teachers to network science; empirical evaluation data on the effect of participation on students' motivation and interest in pursuing STEM careers; the application of professional development materials for teachers that are intended to encourage them to use network science concepts in their lesson plans and curriculum; promoting district-level interest and engagement; best practices gained from our experiences; and the future goals for this project and its subsequent outgrowth.

The goal of this symposium is to present and discuss how advances in computer hardware, scientific visualization, and computational methods of visualization, has enabled multiple conceptual and visual representations of atomic and molecular concepts. These advances in molecular modeling and visualization enable students to manipulate a variety of visual representations of abstract concepts, explore these concepts, and, therefore, bring the study of science closer to the doing of science. We will present several projects funded by the National Science Foundation (NSF) to create research-oriented, user-friendly, molecular modeling education tools that facilitate multiple visual representations.

The number of distinct sites visited by a random walker after t steps is of great interest, as it provides a direct measure of the territory covered by a diffusing particle. We review the analytical solution to the problem of calculating SN(t), the mean number of distinct sites visited by N random walkers on a d-dimensional lattice, for d=1, 2, 3 in the limit of large N. There are three distinct time regimes for SN(t). A remarkable transition, for dimension ≥2, in the geometry of the set of visited sites is found. This set initially grows as a disk with a relatively smooth surface until it reaches a certain size, after which the surface becomes increasingly rough. We also review the results for a model for migration and spreading of populations and diseases. The model is based on N diffusing species, where each species has a probability α- of dying (or recovery from a disease) and a probability α+ to give birth (or to infect another species). It is found analytically that when α+ ≈ α- ≠ 0, after a crossover time t× ~ N/2α-, the territory covered by the population is localized around its center of mass while the center of mass diffuses regularly. When α+ > α-, the localization breaks down after a second crossover time and the species diffuse and spread around their center of mass. These results may explain the phenomena of migration and spreading of diseases and population appearing in nature.

We review recent developments in the study of the diffusion reaction systems of the type A + B → C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x > 0 and x < 0, respectively. We find that whereas for d ⩾ 2 the mean field exponent characterizes the width of the reaction zone, fluctuations are relevant in the one-dimensional system. We present analytical and numerical results for the reaction rate on fractals and percolation systems at criticality.We also study the case where the particles are Lévy flights in d = 1. Finally, we consider experimentally, analytically, and numerically the reaction A + Bstatic → C, where species A diffuses from a localized source.

We review recent developments in the study of the diffusion reaction systems of the type A + B → C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at χ > 0 and χ < 0 respectively. We find that whereas for d ≥ 2 the mean field exponent characterizes the width of the reaction zone, fluctuations are relevant in the one-dimensional system. We also present analytical and numerical results for the reaction rate on fractals and percolation systems.

The dynamics of diffusion controlled reactions of the type A + B → C has been studied extensively since the pioneering work of Smoluchowski [1,2]. Most studies have focused on homogeneous systems, i.e., when both reactants are initially uniformly mixed in a d-dimensional space, and interesting theoretical results have been obtained. When the concentrations of the A and B reactants are initially equal, i.e., c A (0) = c B (0) = c(0), the concentration of both species is found to decay with time as, c(t) ~ t -d/4 for Euclidean d ≤ 4-dimensional systems [3–10] and as for fractals [5,6] with fracton dimension d s ≤ 2. Also, self-segregated regions of A and B in low dimensions (d ≤ 3) [4] and in fractals [9] have been found. Quantities such as the distributions of domain sizes of segregated regions and interparticle distances between species of the same type and different types have been calculated [11–13]. These systems were also studied theoretically and numerically under steady state conditions and interesting predictions have been obtained [14–17]. However, the above numerical and theoretical predictions have not been observed in experiments, in part because of difficulties to implement the initially uniformly-mixed distributions of reactants.

We compare results of two different educational projects in which high school students manipulate computer models of physical systems derived from current science research. The first project developed a complete set of educational materials from scratch (software, hands‐on activities, experiments, and complete manuals) with which students study the growth of random fractal forms in nature. The result is a set of self‐contained educational modules whose software runs on standard personal computers of the early 1990s. The second project added graphics visualization interfaces to actual computation programs used in research on molecular networks, programs that originally ran only on high‐speed workstations (but now can run on recent personal computers). High school students used these workstation programs as supplements in conventional honors and regular high school chemistry classes, thus requiring us to develop fewer supporting and background materials. Both uses of computer models contributed to a change in method of instruction, toward independent student investigations, with the teacher acting as mentor and advisor. The authors are grateful to the National Science Foundation for support under the following grants: MDR 89‐54628 (Applications of Advanced Technology—OGAF), MDR 91‐50079 (Applications of Advanced Technology—WAMNet), MDR 91‐50079 (Research in Teaching and Learning), ESI 93‐53900 (Instructional Materials Development), and ESI 93‐53500 (Teacher Enhancement).

We study a system in which diffusing particles (species A) are injected into a reactive d-dimensional substrate (species B) at rate lambda, with the rule that A+B--> C(inert). The amount of species C, C(t), and the number of surviving A particles, A(t), are calculated for substrate dimensions d = 1, 2, and 3. We find the surprising results A(t) is similar to t2/3 for d = 3 and C(t) is similar to square-root t ln t for d = 1. We confirm our predictions by performing Monte Carlo simulations for d = 1, 2, and 3 and experiments for the reaction I2(gas) + 2Ag(solid) --> 2AgI(solid) for d = 2.

This article is based upon the Thirtieth Saha Memorial Lecture (delivered on 4 January 1992) and the Fourth Bose Memorial Lecture (delivered on 5 January 1992). I felt deeply touched to have been so honored by invitations to deliver these lectures, especially in view of the list of illustrious predecessors who have held this honor. At the outset I wish to acknowledge that almost all of my work is connected in one way or another to random walks, a topic about which I learned most from the classic 1943 review of the great Indian physicist S. Chandrasekar. I also wish to acknowledge my personal debt to the great culture and music of India, and to the many Indian scholars who have taught me their unique insights into the mysteries of physics. In particular, I wish to dedicate this work to the late Bengali genius Satyajit Ray, whose recent passing has left the world immeasurably poorer. It was my dream while in Calcutta to have the opportunity of meeting this hero of mine, but his ill health at that time prevented our meeting.

THE number of distinct sites visited by a random walker after t steps is of great interest 1-21, as it provides a direct measure of the territory covered by a diffusing particle. Thus, this quantity appears in the description of many phenomena of interest in ecology 13-16, metallurgy 5-7, chemistry 17,18 and physics 19-22. Previous analyses have been limited to the number of distinct sites visited by a single random walker 19-22, but the (nontrivial) generalization to the number of distinct sites visited by N walkers is particularly relevant to a range of problems-for example, the classic problem in mathematical ecology of defining the territory covered by N members of a given species 13-16. Here we present an analytical solution to the problem of calculating S(N)(t), the mean number of distinct sites visited by N random walkers on a d-dimensional lattice, for d = 1, 2, 3 in the limit of large N. We confirm the analytical arguments by Monte Carlo and exact enumeration methods. We find that there are three distinct time regimes, and we determine SN(t) in each regime. Moreover, we also find a remarkable transition, for dimensions greater-than-or-equal-to 2, in the geometry of the set of visited sites. This set initially grows as a disk with a relatively smooth surface until it reaches a certain size, after which the surface becomes increasingly rough.

Science research professionals originated an education innovation project that adapts the mentoring model of graduate study in science to the high school, closely coupling experiment and computer visualization models devised originally for science research in natural or random fractals. Educational researchers who joined the project helped to interpret the effort in terms of “cognitive apprenticeship,” a teaching paradigm already known in the cognitive research literature. This article traces the evolution of the materials informed by this paradigm and the results of two sequential trials of a fractal dimension unit in a suburban high school. In the 2nd‐year trial, students began to act as independent investigators and the teacher gradually and spontaneously adopted the role of mentor.