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A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world's leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.

The use of violent coercion to repress unarmed protests, such as that seen during the Arab Spring, sometimes backfires on the government – an outcome called 'political jiu-jitsu'. Examining unique global data covering extreme violence used by governments against unarmed protests from 1989 to 2011 (drawn from UCDP) and the Nonviolent and Violent Campaigns and Outcomes (NAVCO) data, this study aims to explain the conditions under which this outcome occurs. This study contributes to both the nonviolent action and one-sided violence literatures by further disaggregating this effect into both domestic and international outcomes, a distinction that has not previously been made in empirical studies. We find evidence that a pre-existing campaign infrastructure increases the likelihood of increased domestic mobilization and security defections after violent repression, but is unrelated to international backlash. Within ongoing NAVCO campaigns we find that parallel media institutions increase the likelihood of increased domestic mobilization and international repercussions after repression, and that this effect holds true for both traditional media and 'new' (i.e. internet-based) media. One of the novel contributions of this study is that we identify an important selection effect in the NAVCO data and the critical role of organizational infrastructure, especially communications infrastructure, in generating preference changes that create the conditions where killing unarmed civilians becomes costly for repressive governments. We conclude with a discussion of the potential implications of this study and avenues for future research.

Mindful of the growing interest in non-Western and pre-modern political systems, we propose a framework for the analysis of states, state systems, and international orders. We provide a culturally neutral definition of the state and outline a method for assessing variation in political organization both within and above the state. Our framework cleanly delineates hierarchy from anarchy and can be applied to a diverse set of state systems. We then show how the content of international order inter-relates with system structure and the local density (interaction capacity) of a region. We argue that our framework captures similarities—and exposes differences—between different systems and orders over time and space. It strikes a balance between the traditional focus on the Western experience and the current trend toward regional studies in which it is difficult to accumulate knowledge in a rigorous manner.

We present what is, to the best of our knowledge, the first published set of annual out-of-sample forecasts of genocide and politicide based on a global dataset. Our goal is to produce a prototype for a real-time model capable of forecasting one year into the future. Building on the current literature, we take several important steps forward. We implement an unconditional two-stage model encompassing both instability and genocide, allowing our sample to be the available global data, rather than using conditional case selection or a case-control approach. We explore factors exhibiting considerable variance over time to improve yearly forecasting performance. And we produce annual lists of at-risk states in a format that should be of use to policymakers seeking to prevent such mass atrocities. Our out-of-sample forecasts for 1988—2003 predict 90.9% of genocide onsets correctly while also predicting 79.2% of non-onset years correctly, an improvement over a previous study using a case-control in-sample approach. We produce 16 annual forecasts based only on previous years' data, which identify six of 11 cases of genocide/politicide onset within the top 5% of at-risk countries per year. We believe this represents substantial progress towards useful real-time forecasting of such rare events. We conclude by suggesting ways to further enhance predictive performance.

A growing research field examines the conditions under which major nonviolent resistance campaigns—that is, popular nonviolent uprisings for regime or territorial change—are successful. Why these campaigns emerge in the first place is less well understood. We argue that extensive social networks that are economically interdependent with the state make strategic nonviolence more feasible. These networks are larger and more powerful in states whose economies rely upon organized labor. Global quantitative analysis of the onset of violent and nonviolent campaigns from 1960 to 2006 (NAVCO), and major protest events in Africa from 1990 to 2009 (SCAD) shows that the likelihood of nonviolent conflict onset increases with the proportion of manufacturing to gross domestic product. This study points to a link between modernization and social conflict, a link that has been often hypothesized, but, hitherto, unsupported by empirical studies.

This paper reports the results of the first cross-national examination of the impact of the geography of nonviolent contention on regime transitions. Nonviolent tactics 'work' in part by signalling the preferences of non-participants through the symbolism of participants, unlike violent tactics. This opens the way for nonviolent campaigns to exploit variations in social-spatial meaning to enhance the informativeness of dissent. Capital cities are one such symbolic place and the main prediction of this study is a positive relationship between large protests and regime transitions in the capital, but not elsewhere. I also predict a strong direct relationship between the proximity to the capital of fighting in civil wars, and regime transitions; no relationship to the proximity of nonviolent contention; and that the intensity of violent conflict impacts regime transitions in a way that is largely independent of location. Results from an analysis of episodes of violent and nonviolent conflict from 1990 to 2014 generally support these contentions.

BackgroundAtrial fibrillation (AF)-induced cardiomyopathy (AIC) is characterised by reversible left ventricular (LV) dysfunction after restoration of sinus rhythm (SR). The need for continued guideline-directed medical therapy (GDMT) for heart failure after LV ejection fraction (LVEF) recovery in AIC after catheter ablation (CA) is unclear.MethodsThis multicentre cohort study across 12 UK centres included adults undergoing index AF ablation (June 2019–June 2024) with LVEF <50% preablation and recovery to ≥50% at three timepoints: preablation; early postablation (≥4 weeks) and late postablation (≥3 months or ≥3 months post-GDMT withdrawal). Patients were stratified post recovery of LVEF after CA. The primary outcome was mean LVEF at late follow-up; secondary outcomes included absolute change in LVEF, LV end-diastolic diameter (LVEDD) and SR maintenance.Results88 patients met inclusion enrolment criteria (61.7±10.6 years old; 91% male), of which 50 (56.8%) continued full-dose GDMT and 38 (43.2%) withdrew ≥50% of GDMT. In the GDMT-withdrawn group, mean GDMT classes decreased from 2.97±0.88 to 1.03±0.79 (p<0.001). At late follow-up, mean LVEF was comparable (56.3%±3.8% GDMT-continued vs 56.8%±5.5% GDMT-withdrawn; p=0.59), as was LVEF change (1.2% vs 0.4%; p=0.48). One relapse occurred in each group secondary to an acute coronary syndrome (2.0% vs 2.6%; p=1). LVEDD remained stable (p>0.8). SR was maintained in 82.0% vs 92.1% of patients; p=0.17.ConclusionsSelective GDMT withdrawal after sustained LVEF recovery and rhythm control did not compromise LV systolic function, remodelling or rhythm maintenance. This supports the study of personalised de-escalation strategies in AIC in prospective trials.

Aims We present a single‐centre retrospective experience using oral milrinone in patients with a left ventricular assist device (LVAD) and concurrent refractory right ventricular failure. Methods and results All patients implanted with LVAD between January 2013 and July 2021 from a high‐volume advanced heart failure service were reviewed. Eight patients were initiated on oral milrinone during this period. Oral milrinone was started 1.5 [inter‐quartile range (IQR) 1–2.3] years after LVAD implantation and continued for 1.2 (IQR 0.5–2.8) years. Therapeutic milrinone levels were achieved (232.2 ± 153.4 ng/mL) with 62.4 ± 18% of time within the therapeutic range. Two patients had adverse events (non‐sustained ventricular tachycardia and ventricular fibrillation effectively treated by internal cardioverter defibrillator) but did not require milrinone discontinuation. Four deaths occurred, one after transplant and three from disease progression determined to be unrelated to oral milrinone use. Three patients continue oral milrinone therapy in the community. There was no significant difference found after the initiation of oral milrinone on any of the physiological measures; however, there were trends in reduction of New York Heart Association class from 3.4 ± 0.5 to 3.0 ± 0.8 (P = 0.08), reduction of right atrial/wedge pressure from 0.9 ± 0.3 to 0.5 ± 0.2 (P = 0.08), and improvement of right ventricular stroke work index from 3.8 ± 2 to 5.8 ± 2.7 (P = 0.16). Conclusions Oral milrinone appears safe for long‐term use in the outpatient setting when combined with therapeutic monitoring in this complex medical cohort with limited management options. Further study is needed to ascertain whether this treatment is effective in reducing heart failure symptoms and admissions.

Civil wars show substantial variation in where they are fought. One dimension of this variation is the proximity of fighting to the capital city. While some wars are fought in the periphery, others devastate capital cities, often for months, or years, on end. What explains this? This article approaches the puzzle from a bargaining perspective and argues that wars with evenly balanced belligerents (bipolar conflicts) should be less likely to see fighting in the capital while wars with multiple, evenly matched belligerents (multipolar conflicts) should be more likely to do so. Empirical analysis of new conflict-year data on the location of fighting in civil war and measures of conflict actor 'fractionalization' and 'polarization' from 1975 to 2011 support these claims. Highly asymmetric conflicts are fought furthest from the capital city. Bipolar conflicts are fought closer to the capital, but only modestly so. The transition from a bipolar to a multipolar conflict sharply increases the risk of fighting within 10 km of the capital and decreases the expected distance of conflict from the capital. In general, this article points to the utility of bargaining theory to help explain spatial patterns in violent conflict, in addition to questions of onset, duration, and termination, to which this theory has been traditionally applied.

How have the structures of state systems varied over time and space? We outline a game theoretic model of the decision by political units to accept offers of graded sovereignty from imperial centers. We conceptualize four types of sovereign bargains – tributary, informal extractive, suzerain, and departmental – as a function of whether a polity has external sovereignty and whether resources flow from the subordinate polity to the imperial center through transfers or direct extraction. We then specify the payoffs for these bargains and theorize how increasing interaction capacity and international competition shape the structure of state systems. We show how increasing interaction capacity is related to the transition from transfers to extraction while international competition plays a role only when interaction capacity is already high. We demonstrate the applicability of our model with case studies from low- and high-density environments during the early modern period, respectively: (1) The Oyo Empire of western Africa; (2) Mysore of south Asia.