Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms

In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.Comment: journal versio

Importance sampling in path space for diffusion processes with slow-fast variables

Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton-Jacobi-Bellmann equation. We focus on certain diffu- sions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.Comment: 41 page

Writing the Script? ECOWAS’ Military Intervention Mechanism

Introduction: In 1999, the Economic Community of West African States (ECOWAS) adopted an innovative protocol. The ECOWAS Protocol relating to the Mechanism for Conflict Prevention, Management, Resolution, Peace-Keeping, and Security (Protocol-Mechanism) established a nine member state Mediation and Security Council (MSC) deciding with majority rule upon military interventions in member states against the will of target countries in cases of, among others, violation of human rights, the rule of law, or democratic principles. Up until then the United Nations Security Council (UNSC) had been the sole organization to have this right, and so far no other regional organization had followed suit. An additional Protocol on Democracy and Good Governance from 2001 complemented the first protocol by providing a more explicit framework of reference for appropriate governance standards within member states. In a region mostly known for countries with weak statehood and military coup d’états the Protocols of 1999 and 2001 represent a strong commitment to liberal democracy combined with a mandate by the regional organization to defend these principles by force if necessary

Theory and Algorithms

The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated. View Full-Tex

Application to light-induced control of open quantum systems

In linear control, balanced truncation is known as a powerful technique to reduce the state-space dimension of a system. Its basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace without changing the overall response of the system. This work deals with a first application of balanced truncation to the control of open quantum systems which are modeled by the Liouville-von Neumann equation within the Lindblad formalism. Generalization of the linear theory has been proposed to cope with the bilinear terms arising from the coupling between the control field and the quantum system. As an example we choose the dissipative quantum dynamics of a particle in an asymmetric double well potential driven by an external control field, monitoring population transfer between the potential wells as a control target. The accuracy of dimension reduction is investigated by comparing the populations obtained for the truncated system versus those for the original system. The dimension of the model system can be reduced very efficiently where the degree of reduction depends on temperature and relaxation rate

Building a participatory national consensus on wastewater reclamation and reuse in Palestine

Water scarcity is a major constraint for economic and social development and sustainability of the agricultural sector in Palestine. Rapid population growth and increasing dominance of Israeli occupation over the Palestinian water and land resources exacerbate this problem. Wastewater reuse in agriculture is a potential non-conventional water resource that needs better utilization. Our research studied the enabling environment and the political economy of wastewater reclamation and reuse in Palestine. The research team adopted participatory approach that was based on active involvement of all stakeholders in the various phases and activities of this project. The team organized large number of public meetings and national workshops that gathered policy makers as well as representatives of the stakeholder community. The team also implemented a questionnaire survey to study the public perceptions toward wastewater reuse. The research was concluded by a national symposium that gathered more than 200 persons from this community. The major research findings show a national consensus on the importance of wastewater reclamation and reuse in irrigated agriculture. The results show positive knowledge and perceptions of all stakeholders towards reuse of reclaimed wastewater. It also shows that there is a big gap between various institutions related to the subject. It also shows poor collaboration between the academic/research institutions and policy making. The research also emphasizes the importance of onsite systems, especially grey water, for wastewater treatment and reuse as they are low cost and do not require permission of Israeli occupation. The research has a substantial policy impact as it opened opportunities for participatory approaches and dialogue between policy makers and the entire stakeholders’ communit

ECOWAS and the Restoration of Democracy in The Gambia

Nach den umstrittenen Präsidentschaftswahlen in Gambia im Dezember 2016 konnte die westafrikanischen Regionalorganisation ECOWAS die Demokratie im Land wiederherstellen, indem sie eine militärische Intervention androhte, ohne dass es tatsächlich zu Gewaltmaßnahmen kam. Sowohl die Afrikanische Union als auch der Sicherheitsrat der Vereinten Nationen hatten die Entscheidung der Regionalorganisation unterstützt und damit zur Legitimation dieser "afrikanischen Lösung für afrikanische Probleme" beigetragen. Die gambische Regierung räumte ihre Wahlniederlage erst in dem Moment ein, als das Szenario einer Militärinvasion glaubhaft erschien. Vier Hauptfaktoren erklären das Vorgehen von ECOWAS und den Erfolg: Die Regionalorganisation verfügte über ein rechtlich eindeutiges Mandat, die Demokratie in einem ihrer Mitgliedsländer durch Androhung von Gewalt zu schützen; es bestand Konsens, dass die relativ kleine gambische Armee einer ECOWAS-Eingreiftruppe nicht gewachsen wäre; der gambische Präsident konnte weder auf befreundete Regierungen im regionalen Umfeld noch auf mächtige Alliierte außerhalb des afrikanischen Kontinents setzen; regionale Führungsmächte wie Nigeria und Senegal erklärten ihre Unterstützung einer regionalen Intervention. Die ECOWAS-Intervention in Gambia ist ein erfolgreiches Beispiel für einen aktiven demokratischen Regionalismus; ihr Erfolg beruht allerdings auf den spezifischen Bedingungen in Westafrika und es ist wenig wahrscheinlich, dass sie zum Modell für regionale Interventionen in anderen Teilen Afrikas wird.Following the disputed December 2016 presidential elections in The Gambia, ECOWAS managed to "restore democracy" in the country by using the threat of force, but without any use of direct physical violence. Both the African Union and the United Nations Security Council backed ECOWAS, which also gave ECOWAS legitimacy, for what was essentially ECOWAS's policy, and indeed an African solution to African problems. Only when the scenario of military invasion became credible did the Gambian regime accept the defeat. Four main factors explain the behaviour of ECOWAS and its success: ECOWAS had a clear legal mandate to threaten the use of force in order to protect democracy in one of its member states; there was consensus that ECOWAS forces could have coped with the relatively small Gambian army; the Gambian president could not rely on friends among his regional peers or some powerful ally from outside Africa; and regional leaders such as Nigeria and Senegal made a credible commitment to the regional intervention. While the intervention was a victory for pro-democratic activist regionalism, the specific West African conditions make a diffusion of the model to other parts of Africa unlikely