Modern Homotopy Methods in Optimization

Probability-one homotopy methods are a class of algorithms for solving nonlinear systems of equations that are accurate, robust, and converge from an arbitrary starting point almost surely. These new techniques have been successfully applied to solve Brouwer faced point problems, polynomial systems of equations, and discretizations of nonlinear two-point boundary value problems based on shooting, finite differences, collocation, and finite elements. This paper summarizes the theory of globally convergent homotopy algorithms for unconstrained and constrained optimization, and gives some examples of actual application of homotopy techniques to engineering optimization problems

Multi-Objective Control-Structures Optimization Via Homotopy Methods

A recently developed active set algorithm for tracking parametrized optima is adapted to multi-objective optimization. The algorithm traces a path of Kuhn-Tucker points using homotopy curve tracking techniques, and is based on identifying and maintaining the set of active constraints. Second order necessary optimality conditions are used to determine nonoptimal stationary points on the path. In the bi-objective optimization case the algoritm is used to trace the curve efficient solutions (Pareto optima). As an example, the algorithm is applied to the simultaneous minimization of the weight and control force of a ten-bar truss with two collocated sensors and actuators, with some interesting results

Linear Perturbations in Brane Gas Cosmology

We consider the effect of string inhomogeneities on the time dependent background of Brane Gas Cosmology. We derive the equations governing the linear perturbations of the dilaton-gravity background in the presence of string matter sources. We focus on long wavelength fluctuations and find that there are no instabilities. Thus, the predictions of Brane Gas Cosmology are robust against the introduction of linear perturbations. In particular, we find that the stabilization of the extra dimensions (moduli) remains valid in the presence of dilaton and string perturbations.Comment: 17 pages, 1 figur

Threats and Changes Affecting Human Relationships with Wilderness: Implications for Management

For wilderness managers, the ability to recognize threats and changing conditions is vital. While these threats are typically associated with resource and social conditions, they can also be investigated relative to wilderness relationships. This paper explores how threats and changes may be affecting human relationships with wilderness and the possible implications for management. Previously, threats have been conceptualized as affecting ecosystem integrity or stakeholder values. This paper suggests these conceptualizations should be expanded to also consider the meanings and relationships attributed to wilderness. From such a lens, threats such as global climate change, wildland fire, and invasive species can dramatically influence both the wilderness landscape and the meanings associated with its character. They fundamentally alter the place in ways that conflict with personal histories and previous experiences. Thus, managers must be charged with finding ways to protect and foster these human relationships. Addressing threats to these relationships may also require managers to develop approaches that mitigate or adapt to these relationships over time. These approaches need to proactively define and protect a diversity of meanings and values to ensure ongoing human relationships with wilderness

Moduli Stabilization with Long Winding Strings

Stabilizing all of the modulus fields coming from compactifications of string theory on internal manifolds is one of the outstanding challenges for string cosmology. Here, in a simple example of toroidal compactification, we study the dynamics of the moduli fields corresponding to the size and shape of the torus along with the ambient flux and long strings winding both internal directions. It is known that a string gas containing states with non-vanishing winding and momentum number in one internal direction can stabilize the radius of this internal circle to be at self-dual radius. We show that a gas of long strings winding all internal directions can stabilize all moduli, except the dilaton which is stabilized by hand, in this simple example.Comment: title changed, improved presentation; reference added. 18 pages, JHEP styl

Using nestedness and species-accumulation analyses to strengthen a conservation plan for littoral forest birds in south-eastern Madagascar

The littoral forests of south-eastern Madagascar are among the most threatened ecosystems on the island. A conservation plan has been developed for the region due to a proposed mining venture. Here, we provide a novel methodology to assess if the planned conservation measures would effectively conserve the bird diversity inhabiting these forests. Bird community composition within 30 littoral forest fragments was quantified with each fragment characterized by measures of fragment area, isolation, and internal habitat complexity. A nestedness and cumulative species–area analysis was conducted to ascertain the contribution of forest fragments of different sizes in capturing the overall bird species richness. Datasets representing the overall and forest-dependent bird assemblages were found to be significantly nested. The pattern of nestedness appeared to be driven by fragment size. However, cumulative species–area analyses showed that the assemblages were imperfectly nested with ten species displaying idiosyncratic distribution patterns. When a modest conservation target was set (the occurrence of a bird species in three or more fragments), the proposed conservation plan would only protect approximately half the species found in the littoral forests. We show that protecting an additional four large patches would mean that the proportion of forest-birds captured in three or more patches would increase to 70%

Social Justice in the Borderlands: How Agenda-setting Theory Might Be Used to Reduce Health Disparities along the U.S./Mexico Border

Background and Purpose: Along the U.S./Mexico border, poverty, unemployment, and no to low access to health care is the norm. A primary goal of this article was to discuss a framework based on agendasetting theory to aid community members in getting relevant health care issues on the community “agenda.” To accomplish this, we aimed to better understand the demographics of influential people, or agenda-setters, in the area. Methods: We identified and interviewed 30 agenda-setters in communities on both sides of the U.S./ Mexico border. Health promotion agenda-setting (HPA-S) theories guided our study, and primarily qualitative research methods were utilized to analyzed transcripts taken from individual interviews with. Results: Participants indicated that community members can best advocate for health care resources by creating a shared vision among community members prior to asking for resources- by understanding the priorities of those holding the purse-strings, by framing the community wants within the bounds of those priorities, and by fostering strategic partnerships with influential agenda-setters in their communities. Conclusion: Through application of this framework, community members can increase their social justice by becoming better able to advocate for and obtain needed health care resources

Renewing the Exploration Approach for Mid-Enthalpy Systems: Examples from Northern England and Scotland

After a promising start in the 1970s and 80s, the UK rather fell behind other countries in the search for viable mid-enthalpy geothermal resources. This situation began to turn around in 2004, when the first of three deep geothermal exploration boreholes were drilled in northern England. What distinguished these from earlier drilling in Cornwall was the deliberate search for naturallyhigh permeability associated with major faults, especially those that have undergone strike-slip reactivation during the Cenozoic. Boreholes at Eastgate in the North Pennines targeted buried radiothermal granite, whereas the 1,821m-deep Science Central Borehole in Newcastle upon Tyne targeted a postulated deep sedimentary aquifer (the Fell Sandstones), which were inferred to be connected laterally to the granitic heat source by a major fault (the reactivation of the Iapetus geo-suture). The drilling was in both cases rewarded with impressive heat flows, and in the case of Eastgate with what is believed to be the highest permeability yet found in a deep granite batholith anywhere in the world. In parallel with these developments, a re-assessment was made of the preexisting geothermal heat flow database for the UK, applying newly-standardised correction protocols for palaeoclimatic and topographic distortions, which were found to be particularly marked in Scotland (where only shallow boreholes had been used to establish geothermal gradients in the original 1980s analysis), Similar prospects in northern England (similar to that drilled at Science Central) are now the focus of commercial exploration efforts. Appraisal of fault dispositions relative to the present-day maximum compressive stress azimuth are being used to identify the most promising areas for intersecting fault-related permeability at depth. New geophysical tools – most notably atomic dielectric resonance scanning – are also being appraised for their ability to directly detect features (such as hot brines) which are indicative of localised convection in target fault zones and aquifers

Supersymmetry Breaking and Dilaton Stabilization in String Gas Cosmology

In this Note we study supersymmetry breaking via gaugino condensation in string gas cosmology. We show that the same gaugino condensate which is introduced to stabilize the dilaton breaks supersymmetry. We study the constraints on the scale of supersymmetry breaking which this mechanism leads to.Comment: 11 page