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from
Part I
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Basics: Foundational Material, Elementary Aspects, and Examples
Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig,Raffaella Mulas, Vrije Universiteit Amsterdam,Dong Zhang, Peking University
This chapter provides an overview of the spectral theory of the Laplacian on functions and differential forms. It also introduces the p-Laplacian for functions. We emphasize variational aspects of eigenvalues and Cheeger's inequality.
from
Part I
-
Basics: Foundational Material, Elementary Aspects, and Examples
Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig,Raffaella Mulas, Vrije Universiteit Amsterdam,Dong Zhang, Peking University
This chapter discusses the elementary properties of Laplace operators on graphs and hypergraphs. Many interesting examples will illustrate how special eigenvalues emerge. We also introduce discrete Pólya–Cheeger constants and their dual versions and provide the initial steps relating spectral clustering, spectra of neighborhood graphs, signed Laplacians, and spectra of simplicial complexes and hypergraphs.
Accurate prediction of bridge crack evolution is essential for infrastructure safety assurance and maintenance optimization. This study develops an interpretable machine learning framework to predict the expansion of cracks on the main beam in small- and medium-span highway beam bridges and identify the underlying mechanisms of structural deterioration. A comprehensive database was constructed from inspection and monitoring records of over 100 bridges, featuring critical degradation indicators, including crack density (CD) and maximum crack width (MCW). Following data preprocessing and feature selection through correlation analysis, three machine learning algorithms, that is, support vector regression (SVR), random forest (RF), and extreme gradient boosting (XGBoost), were implemented and evaluated using statistical metrics (R2, RMSE, and MAE). The XGBoost model demonstrated superior predictive performance with R2 values of 0.9433 and 0.9413 for MCW and CD, respectively, reducing RMSE by up to 66.8% and MAE by up to 72% compared to alternative models. SHAP (SHapley Additive exPlanations) analysis revealed that four factors, namely, vehicle load (VL), annual average daily truck traffic (ADTT), bridge age (BA), and annual average daily traffic (ADT), collectively contributed 61.45 ± 2.35% to crack development, with VL (19.7%) being the most influential factor. These findings identify excessive traffic loading and aging as the dominant drivers of crack propagation in beam bridges, providing valuable insights for targeted maintenance strategies and bridge management.
We perform direct numerical simulations of continuously growing broadband surface waves forced by a turbulent atmospheric boundary layer coupled with a developing underwater current. We resolve and analyse the multiscale space–time evolution of the waves by considering the wave spectrum in frequency and wavenumber space and describe the kinematics of nonlinear gravity–capillary waves under a current initially described by a viscous boundary layer and transitioning to turbulence at later times under the wind-wave forcing. The wave speed experiences a scale-dependent Doppler shift, with shorter waves shifted by currents closer to the surface, in agreement with the framework from Stewart & Joy (1974 Deep Sea Res. Oceanogr. Abstracts 21(12), 1039–1049). At low wave slopes, the wave energy concentrates along the linear dispersion relation. When the wave slope is high enough, we observe wave energy located in multiple branches associated with nonlinear bound harmonics travelling at the speed of a carrier mode. These nonlinear branches are well described by a generalized nonlinear dispersion relation that links each harmonic to the effective velocity of the carrier mode to which they are bound, and are found to be Doppler shifted with the carrier mode. The generalized Doppler-shifted nonlinear dispersion relation remains valid as the underwater current becomes turbulent, and the depth-varying mean current profile can be systematically reconstructed from the measured phase velocities from waves at different scales.
Previous studies document links between early-life exposures and life-cycle outcomes, but fewer examine how local labor market shocks during early life affect old-age male mortality. This article studies this relationship using a large-scale deindustrialization shock: the decline of New England’s textile industry during the 1920s and 1930s. Consistent with prior work, we find small effects on migration and limited changes in counties’ sociodemographic composition after deindustrialization. Using Social Security Administration death records linked to the 1900–1940 historical censuses and difference-in-differences event studies, we find reduced longevity among men born in highly exposed counties, especially among non-migrant families and those in non-urban areas. The estimates imply intent-to-treat effects of about 3.6 months, while treatment-on-the-treated calculations suggest longevity reductions of about 4.2 years for children of affected families. Using 1950–1960 census data, we also find reductions in schooling, high school completion, and socioeconomic standing.
This paper explores the implications of Jīva Gosvāmī’s (sixteenth century) Bhedābheda Vedānta for the contemporary philosophical debate on consciousness, thereby contributing to the broader and growing interest in the insights that Indian traditions may bring to current discussions in the philosophy of mind. More specifically, I develop here a metaphysical, coarse-grained partial reconstruction of Jīva’s thought, arguing that it can be interpreted as a distinctive form of priority cosmopsychism, which I term śakti-based Vedānta cosmopsychism. Needless to say, this involves both a terminological and a taxonomical task, as I seek to clarify how key aspects of Jīva’s thought can be articulated through the conceptual framework and vocabulary of contemporary metaphysics and philosophy of mind. In the final part of the paper, I turn to a more fine-grained analysis, examining the implications of śakti-based Vedānta cosmopsychism for central issues in the philosophy of consciousness, including the causal exclusion problem and the explanatory gap problem, here framed as the individuation problem. I also address some few objections, among them a cosmopsychist formulation of the Vedāntic problem of imperfection.
Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig,Raffaella Mulas, Vrije Universiteit Amsterdam,Dong Zhang, Peking University
In recent years, proposals for legislatures composed of ordinary citizens have attracted renewed attention. Political theorists have advanced diverse arguments for transferring legislative powers traditionally reserved for elected officials to randomly selected citizens, appealing to fairness, equality, and protection against corruption, as well as to improved representation and collective problem-solving. Yet these arguments hinge on a contested assumption: that citizens can competently legislate and resist capture by experts or interest groups. This paper examines the 2019–2020 French Citizens’ Convention for Climate (CCC) as a proof of concept for citizen lawmaking. Drawing on firsthand observations we argue that the CCC’s design effectively transformed its 150 members into de facto legislators. We develop the concept of the “citizen-legislator,” refining Mark Warren’s (2009) notion of the “citizen-representative,” and propose criteria for evaluating the quality of citizens’ legislative outputs. Finally, we identify the normative principle “citizens on top, experts on tap” as crucial to the Convention’s ability to preserve citizen autonomy and prevent capture. The CCC, we conclude, demonstrates the feasibility of involving ordinary citizens qua legislators in more inclusive and participatory forms of democratic governance.
This article focuses on outlining formalized Native American Graves Protection and Repatriation Act (NAGPRA) training efforts at the undergraduate level. Since 2022, the Center for Archaeology and Society Repository (CASR) at Arizona State University has offered a four-semester NAGPRA learning track designed to prepare students for careers in NAGPRA. Recognizing the shortage of trained practitioners entering the field and the limited incorporation of NAGPRA education in anthropology curricula, the learning track integrates classroom learning, intensive mentorship, and hands-on experience with active repatriation work. Each semester builds progressively from a foundation of collections care and NAGPRA principles, to advanced repatriation tasks, then project management, and finally implementing repatriation in a setting outside of CASR. The program emphasizes a respectful approach to skills competency within a supportive environment that interweaves student needs with repatriation goals. Lessons learned highlight the need for planning, dedicated supervision, and a repatriation process tailored to student integration to ensure meaningful student learning, professional readiness, and NAGPRA project advancement. The CASR NAGPRA learning track serves as a model for other institutions seeking to implement a NAGPRA educational program. The combination of experiential learning, direct participation in compliance processes, and discussion topics prepares students for a career in repatriation and fields beyond.
The objective of this study was to characterise chronic stress in gestating sows (n = 66; parity 0–6) housed within the same facility, assigned to gestation stalls or group pens (25 sows per pen) within two days of breeding until day 111 (± 1.4) of gestation using hair cortisol concentrations (HCC) as a biological marker of longer-term stress. Hair was shaved from the right hip at day 6.0 (± 3.8), day 37, day 74, and day 111 of gestation; day 37 and day 111 samples were analysed for cortisol. Housing system, parity class (0–1 [n = 23], 2–3 [n = 17], and 4–6 [n = 26]), and their interactions were explored. Stall-housed parity 0–1 females had higher HCC than all other females regardless of housing system, suggesting that gilts and parity 1 females in stall housing may experience greater chronic stress during gestation.
Acquiring morphology poses a considerable challenge in second language acquisition (SLA), highlighting the need to explore methods that facilitate this task for L2 learners. One potential facilitator is salience, which is theorized to aid language acquisition by directing learners’ attention to certain linguistic elements. To empirically investigate the impact of one type of salience, perceptual salience, a text-based eye-tracking experiment was conducted with 68 L1 Dutch speakers who read 240 sentences in Englishti, an English-based semi-artificial language featuring perceptually high-salient (-ulp) and low-salient (-o) morphemes according to length. Learning context was manipulated with participants being either assigned to an intentional or an incidental paradigm. The task consisted of two phases: a learning phase involving input flooding of the target morphemes followed by content-related questions, and a testing phase where participants completed a grammaticality judgment task on Englishti sentences, half of which were familiar from the learning phase and half of which were new. The results revealed a significant influence of salience, mediated by learning context and English proficiency, on fixation durations, thus empirically confirming the effect of perceptual salience on attention allocation in L2 morphology acquisition.
This chapter discusses the importance of the audience in research on forensic performance. “Forensic performance” is taken here to include the dramaturgical techniques that inform Erving Goffman’s account of “the presentation of self in everyday life,” extending not only to ways of affirming one’s own position but also to ways of portraying the various figures or propositions in a legal dispute. These practices include the use of speech, gesture, and ritual to convey arguments, embody or criticize legal authority, and impersonate a party, witness, or any other participant in an actual or imagined scenario. The audience includes those in the courtroom and imagined observers in the larger public. The chapter begins by examining criticisms of forensic performance in the early modern period and then turns to the use of cross-examination in the nineteenth century. Finally, the discussion considers judges’ behavior, particularly when they encourage the audience to laugh in response to their questions. By doing so, judges merge the role of an impartial interlocutor attending to policy questions and the role of an individual to whom the law might apply.
Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig,Raffaella Mulas, Vrije Universiteit Amsterdam,Dong Zhang, Peking University
We investigate thermal boundary layer (BL) asymmetry in turbulent Rayleigh–Bénard convection (RBC) under both spherical and annular geometries using different BL theories. Unlike planar RBC, the spherical and annular configurations exhibit asymmetric thermal BLs near the inner and outer boundaries due to boundary curvature and non-uniform radial gravity. We generalise three BL frameworks – the Prandtl–Blasius BL model, the steady free-convective model and the fluctuating BL model – and apply them to both geometries. Direct numerical simulations (DNSs), based on the Oberbeck–Boussinesq equations, are performed in three-dimensional spherical RBC and three-dimensional annular RBC for various radius ratios ($\eta$), gravity profiles and also Prandtl numbers ($ \textit{Pr}$), to compare with the predictions of the extended BL models. We find that the BL asymmetries predicted by both the extended steady free-convective BL and the fluctuating BL agree well with DNS results, with the fluctuating BL model providing the best agreement for the mean temperature profiles. A force-balance analysis further shows that this better performance is consistent with the DNS observation that, in the wall-normal direction within the thermal BL, buoyancy is balanced primarily by the pressure-gradient force. This is consistent with the assumption underlying the steady free-convective and fluctuating BL models. Moreover, the fluctuating BL model explicitly accounts for the contribution of turbulent fluctuations to the heat flux, which further improves its agreement with the DNS mean temperature profiles. We derive analytical expressions for the bulk temperature and the thermal BL thickness ratio as functions of the radius ratio and gravity profile across different Prandtl-number regimes. These expressions are obtained by integrating the similarity thermal equation for both the inner and outer BLs using an approximate similarity streamfunction, and by closing the solutions through a heat-flux matching condition. The resulting leading-order expressions obtained from both the steady free-convective and fluctuating BL models are shown to be the same, and they agree well with DNS data. This analytical result provides a robust and practical tool for quantifying BL asymmetry in curved RBC systems.
Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig,Raffaella Mulas, Vrije Universiteit Amsterdam,Dong Zhang, Peking University
Polysubstance use is increasingly the norm among adolescents who use substances, yet research and clinical frameworks remain concentrated in single-substance models. This narrative conceptual editorial highlights key emerging literature on the conceptual inconsistencies and methodological challenges in polysubstance use research, particularly in the context of shifting cannabis legislation and adolescent vulnerability. A lack of definitional consensus, regarding the number of substances, timing of engagement, and intent of substances used, undermines the comparability of findings and the effectiveness of interventions. Adolescent polysubstance use is shaped by developmental, social, and structural factors, with cannabis and nicotine frequently overlooked despite their prevalence. This editorial addresses three linked gaps: definitional inconsistencies, insufficient attention to timing and intent of co-use, and the continued dominance of single-substance research frameworks. Therefore, we argue for clearer definitions, inclusive research designs, and interdisciplinary approaches.
From 1948 until 1967, Israel banned German language films, plays, and vocal music. Largely forgotten today, this article unravels the shifting contours of the ban—the only formal ban ever instituted by Israel on Germany—and unearths its rationales. It does so by focusing on the government agency in charge of formulating and administering the ban, the Film and Theatre Review Board. The article makes four arguments. First, the ban sought to protect the feelings of Holocaust survivors specifically, and Israeli society generally. Traumatized by the Holocaust, Israeli censors wished to remove any reminders of Germany from the public sphere. Second, the fluctuations of the ban tracked diplomatic developments with Germany and the changing sentiments in Israel toward postwar Germany. Third, the ban contributed to a discourse of national dignity and honor, bolstering the argument in favor of an independent Jewish state. Finally, the ban positioned the Board as an entity that claimed to speak for Jews, downplaying demands by Israeli Jews who wanted to consume German culture. As such, the ban should be viewed as an act of nation building and as an important component in the construction of a new Israeli identity, distinct from and independent of the diaspora Jew.