A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example

A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Feeling Healthy? A Survey of Physical and Psychological Wellbeing of Students from Seven Universities in the UK

University students’ physical and psychological health and wellbeing are important and comprise many variables. This study assessed perceived health status in addition to a range of physical and psychological wellbeing indicators of 3,706 undergraduate students from seven universities in England, Wales and Northern Ireland. We compared differences in these variables across males and females, and across the participating universities. The data was collected in 2007–2008. A self-administered questionnaire assessed socio-demographic information (e.g., gender, age), self-reported physical and psychological health data, as well as questions on health awareness, health service use, social support, burdens and stressors and university study related questions. While females generally reported more health problems and psychological burdens, male students felt that they received/had fewer persons to depend on for social support. The comparisons of health and wellbeing variables across the different universities suggested some evidence of ‘clustering’ of the variables under study, whereby favourable situations would be exhibited by a cluster of the variables that is encountered at some universities; and conversely, the clustering of less favourable variables as exhibited at other universities. We conclude that the level of health complaints and psychological problems/burdens is relatively high and calls for increased awareness of university administrators, leaders and policy makers to the health and well-being needs of their students. The observed clustering effects also indicated the need for local (university-specific) health and wellbeing profiles as basis and guidance for relevant health promotion programmes at universities

A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v

Polyhedra Circuits and Their Applications

To better compute the volume and count the lattice points in geometric objects, we propose polyhedral circuits. Each polyhedral circuit characterizes a geometric region in Rd . They can be applied to represent a rich class of geometric objects, which include all polyhedra and the union of a finite number of polyhedron. They can be also used to approximate a large class of d-dimensional manifolds in Rd . Barvinok [3] developed polynomial time algorithms to compute the volume of a rational polyhedron, and to count the number of lattice points in a rational polyhedron in Rd with a fixed dimensional number d. Let d be a fixed dimensional number, TV(d,n) be polynomial time in n to compute the volume of a rational polyhedron, TL(d,n) be polynomial time in n to count the number of lattice points in a rational polyhedron, where n is the total number of linear inequalities from input polyhedra, and TI(d,n) be polynomial time in n to solve integer linear programming problem with n be the total number of input linear inequalities. We develop algorithms to count the number of lattice points in geometric region determined by a polyhedral circuit in O(nd⋅rd(n)⋅TV(d,n)) time and to compute the volume of geometric region determined by a polyhedral circuit in O(n⋅rd(n)⋅TI(d,n)+rd(n)TL(d,n)) time, where rd(n) is the maximum number of atomic regions that n hyperplanes partition Rd . The applications to continuous polyhedra maximum coverage problem, polyhedra maximum lattice coverage problem, polyhedra (1−β) -lattice set cover problem, and (1−β) -continuous polyhedra set cover problem are discussed. We also show the NP-hardness of the geometric version of maximum coverage problem and set cover problem when each set is represented as union of polyhedra

Sframe: An Efficient System for Detailed DC Simulation of Bipolar Analog Integrated Circuits Using Continuation Methods

In this paper we describe an experimental system called sframe which is being incorporated into the design for manufacturability initiative at the Reading Works of AT&T Bell Laboratories. Our system is able to perform detailed and accurate DC analyses of integrated circuits containing several hundred transistors to be fabricated in a relatively complex junction isolated complementary technology