Analytical Arguments Research Articles

SIR model on one dimensional small world networks

We study the nonequilibrium phase transition for the model of epidemic spreading, Susceptible–Infected–Refractory (SIR), on one dimensional small world networks. This model belongs to the universality class of dynamical percolation class (DyP) and the upper critical dimension corresponding to this class is dc=6. One dimensional case is special case of this class in which the percolation threshold goes to one (boundary value) in thermodynamic limit. This behavior resembles slightly the behavior of equilibrium phase transition in a one dimensional Ising and XY models where the critical thresholds for both models go to zero temperature (boundary value) in thermodynamic limit. By analytical arguments and numerical simulations we demonstrate that, increasing the connectivity (2k) of this model on regular one dimensional lattice does not alter the criticality of the model. However the phase transition study shows that, this model crosses from a one dimensional structure to mean field like for any finite value of the rewiring probability (p). This behavior is similar to what happened in the equilibrium phase transition for the Ising and XY models on small world networks. Thus, this model is a one of nonequilibrium models which behaves similarly to the equilibrium systems on small world networks. Unlike of many nonequilibrium systems on small world networks which have been found to display a mean field like behavior only at finite values of p or even show critical exponents depend on p. Furthermore, we calculate the critical exponents and the full critical phase space of this model on small world network. We also introduce the crossover scaling function of this model from one dimensional behavior to mean field behavior and reveal the similarity between this model and the equilibrium models on the small world networks.

Was It a “Fatal Error”? Sraffa and Samuelson on Marshall's Partial Equilibria Method

Sraffa's “On the Relations between Cost and Quantity Produced” (1925) and Samuelson's “An Exact Hume-Ricardo-Marshall Model of International Trade” (1971) presented a strikingly similar analytical argument regarding the theoretical domain of Marshallian partial equilibrium models. Yet they reached radically different conclusions from their analyses. This article addresses this theoretical puzzle and proposes a plausible solution. To this end, the article reconstructs the evolution of Sraffa's and Samuelson's thinking on Marshallian partial equilibrium analysis and the evolution of Samuelson's thinking regarding Sraffa's 1926 critique of Marshallian economics. Sraffa's unpublished manuscripts to which Samuelson did not have access during his lifetime are carefully examined. A change in Sraffa's assessment of Marshallian partial equilibrium methodology that occurred in the second half of the 1920s is highlighted. This leads to new insights into Sraffa's thinking on the role and significance of the case of constant costs within Marshallian economics.

Artificial intelligence (AI) and the 21st Century University: Discussion on a New University Scenary

Introduction: The vertiginous growth of Artificial Intelligence (AI) is present in all fields including the University, implying a rethinking of pedagogical processes that has to be seen from the technoetic to give way to new ways of learning and personalizing learning. Method: this research is of qualitative perspective from the Grounded Theory of systematic design. For the analysis, AI was established as the central category, then open coding was established to give way to axial coding. Phases: 1) theoretical sampling, 2) constant comparison based on axial coding, 3) synthesis and paradigmatic reinterpretation. Results: After the review of the scientific literature reaching theoretical saturation, 3 elements were identified that should accompany the current critical and analytical debate: 1) AI and pedagogy, 2) AI in university educational practice, 3) AI and technoethics. Discussion: there is a need to create knowledge about application, possible impact and effects of AI in the university. Any review on AI should be done from the technoethical to give way to a technodidactics that allows progress towards digital transformation and the promotion of technological humanization. The University must respond to the new scenario presented by AI.

Collective effects in flow-driven cell migration.

Autologous chemotaxis is the process in which cells secrete and detect molecules to determine the direction of fluid flow. Experiments and theory suggest that autologous chemotaxis fails at high cell densities because molecules from other cells interfere with a given cell's signal. We investigate autologous chemotaxis using a three-dimensional Monte Carlo-based motility simulation that couples spatial and temporal gradient sensing with cell-cell repulsion. Surprisingly, we find that when temporal gradient sensing dominates, high-density clusters chemotax faster than individual cells. To explain this observation, we propose a mechanism by which temporal gradient sensing allows cells to form a collective sensory unit. We demonstrate using computational fluid mechanics that that this mechanism indeed allows a cluster of cells to outperform single cells in terms of the detected anisotropy of the signal, a finding that we demonstrate with analytic scaling arguments. Our work suggests that collective autologous chemotaxis at high cell densities is possible and requires only known, ubiquitous cell capabilities.

Different glassy characteristics are related to either caging or dynamical heterogeneity.

Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.

Tipping in a low-dimensional model of a tropical cyclone

A presumed impact of global climate change is the increase in frequency and intensity of tropical cyclones. Due to the possible destruction that occurs when tropical cyclones make landfall, understanding their formation should be of mass interest. In 2017, Kerry Emanuel modeled tropical cyclone formation by developing a low-dimensional dynamical system which couples tangential wind speed of the eye-wall with the inner-core moisture. For physically relevant parameters, this dynamical system always contains three fixed points: a stable fixed point at the origin corresponding to a non-storm state, an additional asymptotically stable fixed point corresponding to a stable storm state, and a saddle corresponding to an unstable storm state. The goal of this work is to provide insight into the underlying mechanisms that govern the formation and suppression of tropical cyclones through both analytical arguments and numerical experiments. We present a case study of both rate and noise-induced tipping between the stable states, relating to the destabilization or formation of a tropical cyclone. While the stochastic system exhibits transitions both to and from the non-storm state, noise-induced tipping is more likely to form a storm, whereas rate-induced tipping is more likely to cause the storm to destabilize. In fact, rate-induced tipping can never lead to the formation of a storm when acting alone. When rate-induced tipping causes the storm to destabilize, a striking result is that both wind shear and maximal potential velocity have to increase at a substantial rate in order to affect tipping away from the active hurricane state. For storm formation through noise-induced tipping, we identify a specific direction along which the non-storm state is most likely to get activated.

Coupled dynamics of endemic disease transmission and gradual awareness diffusion in multiplex networks

Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired behavioral responses during an outbreak have often been neglected or oversimplified in earlier models. Combining the microscopic Markov chain approach with the law of total probability, we herein institute a mathematical model describing the dynamic interplay between stage-based progression of awareness diffusion and endemic disease transmission in multiplex networks. We analytically derived the epidemic thresholds for both discrete-time and continuous-time versions of our model, and we numerically demonstrated the accuracy of our analytic arguments in capturing the time course and the steady state of the coupled disease-awareness dynamics. We found that our model is exact for arbitrary unclustered multiplex networks, outperforming a widely adopted probability-tree-based method, both in the prediction of the time-evolution of a contagion and in the final epidemic size. Our findings show that informing the unaware individuals about the circulating disease will not be sufficient for the prevention of an outbreak unless the distributed information triggers strong awareness of infection risks with adequate protective measures, and that the immunity of highly-aware individuals can elevate the epidemic threshold, but only if the rate of transition from weak to strong awareness is sufficiently high. Our study thus reveals that awareness diffusion and other behavioral parameters can nontrivially interact when producing their effects on epidemiological dynamics of an infectious disease, suggesting that future public health measures should not ignore this complex behavioral interplay and its influence on contagion transmission in multilayered networked systems.

The Inhomogeneity Effect. III. Weather Impacts on the Heat Flow of Hot Jupiters

The interior flux of a giant planet impacts atmospheric motion, and the atmosphere dictates the interior’s cooling. Here we use a non-hydrostatic general circulation model (Simulating Non-hydrostatic Atmospheres on Planets) coupled with a multi-stream multi-scattering radiative module (High-performance Atmospheric Radiation Package) to simulate the weather impacts on the heat flow of hot Jupiters. We found that the vertical heat flux is primarily transported by convection in the lower atmosphere and regulated by dynamics and radiation in the overlying radiation-circulation zone. The temperature inversion occurs on the dayside and reduces the upward radiative flux. The atmospheric dynamics relay the vertical heat transport until the radiation becomes efficient in the upper atmosphere. The cooling flux increases with atmospheric drag due to increased day–night contrast and spatial inhomogeneity. The temperature dependence of the infrared opacity greatly amplifies the opacity inhomogeneity. Although atmospheric circulation could transport heat downward in a narrow region above the radiative-convective boundary, the opacity inhomogeneity effect overcomes the dynamical effect and leads to a larger overall interior cooling than the local simulations with the same interior entropy and stellar flux. The enhancement depends critically on the equilibrium temperature, drag, and atmospheric opacity. In a strong-drag atmosphere hotter than 1600 K, a significant inhomogeneity effect in three-dimensional (3D) models can boost interior cooling several-fold compared to the 1D radiative-convective equilibrium models. This study confirms the analytical argument of the inhomogeneity effect in the companion papers by Zhang. It highlights the importance of using 3D atmospheric models in understanding the inflation mechanisms of hot Jupiters and giant planet evolution in general.

Relating the Ramsay Quotient Model to the Classical D-Scoring Rule

In a series of papers, Dimitrov suggested the classical D-scoring rule for scoring items that give difficult items a higher weight while easier items receive a lower weight. The latent D-scoring model has been proposed to serve as a latent mirror of the classical D-scoring model. However, the item weights implied by this latent D-scoring model are typically only weakly related to the weights in the classical D-scoring model. To this end, this article proposes an alternative item response model, the modified Ramsay quotient model, that is better-suited as a latent mirror of the classical D-scoring model. The reasoning is based on analytical arguments and numerical illustrations.

Understanding Substantive Representation of Women in Consociational Post-Conflict Political Systems

Feminist critics of power-sharing argue that consociational structures privilege ethnic groups and that power-sharing is “bad for women.” This article identifies a gap in the relatively new field of research on gender equality and ethno-national power-sharing, as the focus so far has been mainly on women’s political exclusion, with limited attention on the representation of women’s needs and interests through policy. In bringing together power-sharing literature, representation theory and a gendered understanding of institutions and change, this article issues a call for further research. The article proposes an analytical framework, to be applied in empirical research on: Where, why, and how substantive representation of women in post-conflict consociational political systems occurs? An initial examination of a case from Bosnia and Herzegovina is presented, demonstrating how the analytical framework can be applied on violence against women policy research. Even though Bosnia and Herzegovina was a lead in the Istanbul Convention ratification, in the implementation, the consociational conditions in decision-making have led to disparate directions. The article makes a contribution to existing analytical debates at the intersection of consociationalism and women’s representation and has a practical goal: drawing the attention of scholars to the study of substantive representation of women.

Reviving product states in the disordered Heisenberg chain

When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception is localized systems that are non-ergodic and do not thermalize; however, local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states that feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current phenomenology of many-body localization, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision.

Exploring the angular momentum – atomic gas content connection with eagle and IllustrisTNG

ABSTRACT We use the Evolution and Assembly of GaLaxies and their Environments (eagle) and IllustrisTNG (The Next Generation) cosmological simulations to investigate the properties of the baryonic specific angular momentum (j), baryonic mass (M), and atomic gas fraction (fatm) plane for nearby galaxies. We find EAGLE and TNG to be in excellent agreement with each other. These simulations are also consistent with the results obtained with eXtended GALEX Arecibo SDSS Survey (xGASS) for gas fractions greater than 0.01. This implies that the disagreements previously identified between xGASS and predictions from simple analytical disc stability arguments also holds true for eagle and tng. For lower gas fraction (the regime currently unconstrained by observations), both simulations deviate from the plane but still maintain good agreement with each other. Despite the challenges posed by resolution limits at low gas fractions, our findings suggest a potential disconnect between angular momentum and gas fraction in the gas-poor regime, implying that not all gas-poor galaxies have low specific angular momentum.

Do We Really Not Know What Toulmin’s Analytic Arguments Are?

The aim of this paper is to challenge the idea that Toulmin’s main focus in The Uses of Argument is to critique formal deductive logic. I first try to challenge the argument that, on the basis of what Toulmin says about analytic arguments, it is impossible to determine exactly what they are. I will then attempt to determine the basic contours of analytic arguments. Finally, I will conclude that the concept of an analytic argument involves epistemological assumptions to which formal logicians are in no way committed by the nature of their discipline.

Resolving the physics of quasar Ly α nebulae (RePhyNe): I. Constraining quasar host halo masses through circumgalactic medium kinematics

ABSTRACT Ly α nebulae ubiquitously found around z > 2 quasars can supply unique constraints on the properties of the circumgalactic medium, such as its density distribution, provided the quasar halo mass is known. We present a new method to constrain quasar halo masses based on the line-of-sight velocity dispersion maps of Ly α nebulae. By using MUSE-like mock observations obtained from cosmological hydrodynamic simulations under the assumption of maximal quasar fluorescence, we show that the velocity dispersion radial profiles of Ly α emitting gas are strongly determined by gravity and that they are thus self-similar with respect to halo mass when rescaled by the virial radius. Through simple analytical arguments and by exploiting the kinematics of He ii1640 Å emission for a set of observed nebulae, we show that Ly α radiative transfer effects plausibly do not change the shape of the velocity dispersion profiles but only their normalization without breaking their self-similarity. Taking advantage of these results, we define the variable $\eta ^{140-200}_{40-100}$ as the ratio of the median velocity dispersion in two specifically selected annuli and derive an analytical relation between $\eta ^{140-200}_{40-100}$ and the halo mass which can be directly applied to observations. We apply our method to 37 observed quasar Ly α nebulae at 3 < z < 4.7 and find that their associated quasars are typically hosted by ∼1012.16 ± 0.14M⊙ haloes independent of redshift within the explored range. This measurement, which is completely independent of clustering methods, is consistent with the lowest mass estimates based on quasar autocorrelation clustering at z∼3 and with quasar-galaxies cross-correlation results.

Emergence of rigidity percolation in flowing granular systems.

Jammed granular media and glasses exhibit spatial long-range correlations as a result of mechanical equilibrium. However, the existence of such correlations in the flowing matter, where the mechanical equilibrium is unattainable, has remained elusive. Here, we investigate this problem in the context of the percolation of interparticle forces in flowing granular media. We find that the flow rate introduces an effective long-range correlation, which plays the role of a relevant perturbation giving rise to a spectrum of varying exponents on a critical line as a function of the flow rate. Our numerical simulations along with analytical arguments predict a crossover flow rate [Formula: see text] below which the effect of induced disorder is weak and the universality of the force chain structure is shown to be given by the standard rigidity percolation. We also find a power-law behavior for the critical exponents with the flow rate [Formula: see text].

Social Assistance and Social Development: regression of social assistance rights?

The Social Development as a broader field than Social Assistance policy, in this case reduced to the condition of guardianship action, has been an issue that is persistently present in the neoliberal orientation. The issue was present in debates during the transition process of the new Government Luís Inácio Lula da Silva (2023-2025), which sought to build a model of concertation aimed at democratic restoration. Governments from 2016-2022 removed the status of the State as guarantor of social rights. They illusorily presented the logic of offering emancipation and citizenship through insertion into work, in a context of high unemployment and an increase in social disprotections. Social protection policies were rejected, deprived of resources, social participation, and inter-federal coordination. It is the duty of the Social State and the Fiscal State to rescue and strengthen the Unified Social Assistance System and guarantee constitutional rights. This text aims to stress the understanding of the elements that distinguish the direction of social development from social assistance policy, understanding that they are neither synonyms nor antonyms. Historical and analytical arguments are brought about such understanding, situating current and future challenges for SUAS.

Towards Tolerance Specifications for the Elastic Buckling Design of Axially Loaded Cylinders

Abstract The quest for safe lower bounds to the elastic buckling of axially loaded circular cylindrical shells has exercised researchers for the past 100 years. Recent work bringing together the capabilities of nonlinear numerical simulation, interpreted within the context of extended linear classical theory, has come close to achieving this goal of defining safe lower bounds. This paper briefly summarizes some of the important predictions emerging from previous work and presents new simulation results that confirm these earlier predictions. In particular, we show that for a specified maximum amplitude of the most sensitive, eigenmode-based geometric imperfections, normalized with respect to the shell thickness, lower bounds to the buckling loads remain constant beyond a well-defined value of the Batdorf parameter. Furthermore, we demonstrate how this convenient means of presenting the imperfection-sensitive buckling loads can be reinterpreted to develop practical design curves which provide safe, but not overly conservative, design loads for monocoque cylinders with a given maximum permitted tolerance of geometric imperfection. Hence, once the allowable manufacturing tolerance is specified during design or is measured post-manufacturing, the greatest expected knockdown factor for a shell of any geometry is defined. With the recent research interest in localized imperfections, we also attempt to reconcile their relation to the more classical, periodic, and eigenmode-based imperfections. Overall, this paper provides analytical and computational arguments that motivate a shift in focus in defect-tolerant design of thin-walled cylinders—away from the knockdown experienced for a specific geometric imperfection and towards the worst possible knockdown expected for a specified manufacturing tolerance.

On unitarity of the Coon amplitude

The Coon amplitude is a one-parameter deformation of the Veneziano amplitude. We explore the unitarity of the Coon amplitude through its partial wave expansion using tools from q-calculus. Our analysis establishes manifest positivity on the leading and sub-leading Regge trajectories in arbitrary spacetime dimensions D, while revealing a violation of unitarity in a certain region of (q, D) parameter space starting at the sub-sub-leading Regge order. A combination of numerical studies and analytic arguments allows us to argue for the manifest positivity of the partial wave coefficients in fixed spin and Regge asymptotics.

Tidal Truncation of Circumplanetary Disks Fails above a Critical Disk Aspect Ratio

We use numerical simulations of circumplanetary disks to determine the boundary between disks that are radially truncated by the tidal potential and those where gas escapes the Hill sphere. We consider a model problem, in which a coplanar circumplanetary disk is resupplied with gas at an injection radius smaller than the Hill radius. We evolve the disk using the Phantom smoothed particle hydrodynamics code until a steady state is reached. We find that the most significant dependence of the truncation boundary is on the disk aspect ratio H/R. Circumplanetary disks are efficiently truncated for H/R ≲ 0.2. For H/R ≃ 0.3, up to about half of the injected mass, depending on the injection radius, flows outward through the decretion disk and escapes. As expected from analytic arguments, the conditions (H/R and Shakura–Sunyaev α) required for tidal truncation are independent of planet mass. A simulation with larger α = 0.1 shows stronger outflow than one with α = 0.01, but the dependence on transport efficiency is less important than variations of H/R. Our results suggest two distinct classes of circumplanetary disks: tidally truncated thin disks with dust-poor outer regions, and thicker actively decreting disks with enhanced dust-to-gas ratios. Applying our results to the PDS 70 c system, we predict a largely truncated circumplanetary disk, but it is possible that enough mass escapes to support an outward flow of dust that could explain the observed disk size.

Polynomial Volume Growth of Quasi-Unipotent Automorphisms of Abelian Varieties (with an Appendix in Collaboration with Chen Jiang)

Abstract Let $X$ be an abelian variety over an algebraically closed field $\textbf{k}$ and $f$ a quasi-unipotent automorphism of $X$. When $\textbf{k}$ is the field of complex numbers, Lin, Oguiso, and D.-Q. Zhang provide an explicit formula for the polynomial volume growth of (or equivalently, for the Gelfand–Kirillov dimension of the twisted homogeneous coordinate ring associated with) the pair $(X, f)$, by an analytic argument. We give an algebraic proof of this formula that works in arbitrary characteristic. In the course of the proof, we obtain the following: (1) a new description of the action of endomorphisms on the $\ell $-adic Tate spaces, in comparison with recent results of Zarhin and Poonen–Rybakov; (2) a partial converse to a result of Reichstein, Rogalski, and J.J. Zhang on quasi-unipotency of endomorphisms and their pullback action on the rational Néron–Severi space $\textsf{N}^{1}(X)_{\textbf{Q}}$ of $\textbf{Q}$-divisors modulo numerical equivalence; and (3) the maximum size of Jordan blocks of (the Jordan canonical form of) $f^{*}|_{\textsf{N}^{1}(X)_{\textbf{Q}}}$ in terms of the action of $f$ on the Tate space $V_{\ell }(X)$.