Tulane University is a private research university in New Orleans, Louisiana. It was founded as a public medical college in 1834 and became a comprehensive university in 1847. The institution was made private under the endowments of Paul Tulane and Josephine Louise Newcomb in 1884. Tulane is the 9th oldest private university in the Association of American Universities, which consists of major research universities in the United States and Canada. The Tulane University Law School and Tulane University Medical School are, respectively, the 12th oldest law school and 15th oldest medical school in the United States.Alumni include the former President of Costa Rica; twelve governors of Louisiana; one Chief Justice of the United States Supreme Court; various members of Congress, including one Speaker of the House; two Surgeons General of the United States; 23 Marshall Scholars; 18 Rhodes Scholars; 12 Truman Scholars; 155 Fulbright Scholars; and four living billionaires. Two Nobel laureates have been affiliated with the university.
Peter Lax's 1968 discovery that certain nonlinear wave equations possess operator pairs (Lax pairs) opened the theory of completely integrable systems, yielding exact solutions, infinite conservation hierarchies, and perfectly elastic soliton collisions. When a nonlinear dispersive equation is provably non-integrable (admitting no Lax pair and only finitely many conservation laws), what mathematical structure governs its dynamics? The K(m,m) compacton equations, u_t + (u^m)_x + (u^m)_xxx = 0 for m >= 2, provide a testing ground: they support traveling waves with compact support, yet fail every known integrability test. We prove universal algebraic formulas determining the shape, width, and speed of every K(m,m) compacton. We develop a constraint-deficit mechanism explaining how the five independent conservation laws constrain emergent amplitudes and suppress the fundamental Fourier mode of the collision debris, while higher radiation modes remain unconstrained. The mechanism's conclusions rest on explicit hypotheses supported by numerical evidence. A phase-plane analysis reveals the compacton as a singular limit of smooth solitary waves through simultaneous regularity loss and support compactification. These results delineate intermediate territory between integrable order and generic nonlinear dynamics, organized by scaling universality and by the constraint deficit of a finite conservation structure.
Flood risk is increasingly shaped by intensifying rainfall extremes interacting with complex catchment processes under a changing climate. This chapter brings together advances in modelling frameworks that link extreme rainfall to flood generation and risk assessment. It reviews recent developments in hydrological and hydraulic modelling, including machine learning and physics-informed approaches that improve prediction across diverse catchments, alongside efficient two-dimensional hydrodynamic models that enable large-scale flood mapping. The chapter also discusses methods such as statistical downscaling and weather generators that translate climate-scale information into local flood impacts. Despite these advances, challenges remain in representing non-stationarity, parameter uncertainty, and model structural limitations under evolving climate conditions. Together, these modelling approaches improve our ability to simulate flood risk across scales, while also highlighting key uncertainties that must be addressed to support robust climate adaptation and risk-informed decision-making.
Extreme rainfall and flooding are intensifying worldwide, reshaping risks to agriculture, rural livelihoods, and watershed systems in ways that demand both scientific insight and practical responses. This chapter brings together advances in observing, understanding, and modelling these hazards, linking rainfall extremes, flood dynamics, and risk assessment into a unified framework. It reviews key climate data and tools used to study these changes, including ground observations, satellite products, reanalysis datasets, and high-resolution convection-permitting models, alongside statistical methods for identifying extremes and vulnerability hotspots. The chapter also highlights progress in hydrological and hydraulic modelling, from machine learning and physics-informed approaches that improve predictions across diverse catchments to efficient two-dimensional models for large-scale flood mapping. In addition, it discusses techniques such as statistical downscaling and weather generators that translate climate-scale information into local impacts. Together, these developments show how observations and models can generate actionable insights for flood risk management and climate adaptation.
Let (X-1, d(1)), ... , (X-N, d(N)) be metric spaces with d(i) : X-i & times; Xi -> [0,1] and let X = Pi(N)(i=1) X-i. Let G be a directed graph with vertex set [N] = {1,. .., N} and edge set E(G). Given edge weights P = {p(ij) is an element of (0, 1] : (i, j) E E(G)}, define the closed in-neighborhood Bj(G) := { j} boolean OR {i: (i, j) E E(G)} and put p(jj) = 1. Define, for g, h is an element of X, d(X,G,P)(g,h) := 1- 1/N Sigma(j=1) Pi(i is an element of Bj(G)) (1-d(i)(g(i),h(i)))(1/pij). We prove that d(X,G,P) is a metric and analyze its behavior under graph operations (disjoint unions, Cartesian products). Two quantitative principles govern this family: (i) edge densification (adding edges) increases the distance pointwise and in expectation, with an exact single-edge increment formula and a uniform 1/N sensitivity bound; and (ii) weight monotonicity: increasing an edge weight pij decreases the metric. When the coordinate pairs are independent across coordinates, we obtain a closed-form factorization of the mean distance. In the discrete specialization X = F-q(N) with d(i) is an element of {0, 1} and G acyclic, after replacing G by the oriented reflexive transitive closure G(<=) of Corollary 1.4, the unnormalized distance D-X,D-G <=,D-P := Nd-X,Nd-G <=,Nd-P coincides with the size of the hereditary closure of the support, yielding a poset/digraph sphere-packing bound via the counting of lower ideals. Finally, we give a continuous analog of the construction, yielding a metric on C([0, 1], & Copf;) through an explicit integral formula. These results unify and generalize several graph-based metrics used in coding theory while providing new design levers for mean-distance control. (c) 2026 Published by Elsevier B.V.
In response to peripheral inflammation, such as the intraperitoneal administration of lipopolysaccharide (LPS), inflammatory cytokines recruit afferent neurons that communicate the inflammation to the brain and, in addition, cytokines are released to the bloodstream and reach circumventricular organs in the brain, such as the area postrema (AP). The nucleus of the solitary tract (NTS) perceives peripheral inflammatory stimuli both directly from afferent peripheral nerves and indirectly through its bidirectional connection to the AP. Norepinephrine (NE) neurons within the NTS are known to mediate behavioral and physiological responses to stress, especially stress related to inflammatory challenges in the periphery. However, the restrictions of traditional pain assays limit the understanding of the influence of NTS NE neurons on pain. Here, we used the Blackbox, a machine-learning assisted behavioral analysis apparatus that was developed specifically for the study of pain in rodents. First, we determined the Blackbox variables that correlate to allodynia in mice submitted to intraperitoneal injection of LPS. IP injection of LPS caused several changes to behavior and posture. Most notably, the distance travelled, hind paw toe spread and hind paw distance significantly decreased in response to LPS and strongly correlated with decreased von Frey mechanosensitivity threshold. Selective chemogenetic activation of NTS NE neurons caused similar pain-related behaviors, while inhibition of NTS NE neurons partially reversed the impact of LPS on pain-related behaviors. Taken together, these data show that the NE neurons within the NTS mediate allodynia in response to peripheral inflammation, contributing to the nociception aspect of sickness behaviors.
