The Teaching Space Allocation Problem with splitting

A standard problem within universities is that of teaching space allocation which can be thought of as the assignment of rooms and times to various teaching activities. The focus is usually on courses that are expected to fit into one room. However, it can also happen that the course will need to be broken up, or ‘split’, into multiple sections. A lecture might be too large to fit into any one room. Another common example is that of seminars or tutorials. Although hundreds of students may be enrolled on a course, it is often subdivided into particular types and sizes of events dependent on the pedagogic requirements of that particular course. Typically, decisions as to how to split courses need to be made within the context of limited space requirements. Institutions do not have an unlimited number of teaching rooms, and need to effectively use those that they do have. The efficiency of space usage is usually measured by the overall ‘utilisation’ which is basically the fraction of the available seat-hours that are actually used. A multi-objective optimisation problem naturally arises; with a trade-off between satisfying preferences on splitting, a desire to increase utilisation, and also to satisfy other constraints such as those based on event location and timetabling conflicts. In this paper, we explore such trade-offs. The explorations themselves are based on a local search method that attempts to optimise the space utilisation by means of a ‘dynamic splitting’ strategy. The local moves are designed to improve utilisation and satisfy the other constraints, but are also allowed to split, and un-split, courses so as to simultaneously meet the splitting objectives.

Threshold effects in the Teaching Space Allocation Problem with Splitting

Universities aim for good “Space Management” so as to use the teaching space efficiently. Part of this task is to assign rooms and time-slots to teaching activities with limited numbers and capacities of lecture theaters, seminar rooms, etc. It is also common that some teaching activities require splitting into multiple events. For example, lectures can be too large to fit in one room or good teaching practice requires that seminars/tutorials are taught in small groups. Then, space management involves decisions on splitting as well as the assignments to rooms and time-slots. These decisions must be made whilst satisfying the pedagogic requirements of the institution and constraints on space resources. The efficiency of such management can be measured by the “utilisation”: the percentage of available seat-hours actually used. In many institutions, the observed utilisation is unacceptably low, and this provides our underlying motivation: to study the factors that affect teaching space utilisation, with the goal of improving it. We give a brief introduction to our work in this area, and then introduce a specific model for splitting. We present experimental results that show threshold phenomena and associated easy-hard-easy patterns of computational difficulty. We discuss why such behaviour is of importance for space management.

Impaired functioning of thermolabile methylenetetrahydrofolate reductase is dependent on riboflavin status: implications for riboflavin requirements.

BACKGROUND: Methylenetetrahydrofolate reductase (MTHFR; EC 1.7.99.5) supplies the folate needed for the metabolism of homocysteine. A reduction in MTHFR activity, as occurs in the homozygous state for the 677C-->T (so-called thermolabile) enzyme variant (TT genotype), is associated with an increase in plasma total homocysteine (tHcy). OBJECTIVE: In vitro studies suggest that the reduced activity of thermolabile MTHFR is due to the inappropriate loss of its riboflavin cofactor. We investigated the hypothesis that MTHFR activity in the TT genotype group is particularly sensitive to riboflavin status. DESIGN: We studied tHcy and relevant B-vitamin status by MTHFR genotype in a cross-sectional study of 286 healthy subjects aged 19-63 y (median: 27 y). The effect of riboflavin status was examined by dividing the sample into tertiles of erythrocyte glutathionine reductase activation coefficient, a functional index of riboflavin status. RESULTS: Lower red blood cell folate (P = 0.0001) and higher tHcy (P = 0.0082) concentrations were found in the TT group than in the heterozygous (CT) or wild-type (CC) groups. However, these expected relations in the total sample were driven by the TT group with the lowest riboflavin status, whose mean tHcy concentration (18.09 micromol/L) was almost twice that of the CC or CT group. By contrast, adequate riboflavin status rendered the TT group neutral with respect to tHcy metabolism. CONCLUSIONS: The high tHcy concentration typically associated with homozygosity for the 677C-->T variant of MTHFR occurs only with poor riboflavin status. This may have important implications for governments considering new fortification policies aimed at the prevention of diseases for which this genotype is associated with increased risk.

Dynamical and steady-state requirements for effective entanglement transfer

Entanglement transfer processes from a continuous-variable (CV) to a qubit system have primary importance in quantum information processing due to some practical implications in the realization of a quantum network. A CV system can propagate entanglement while a qubit system is easy to manipulate. We study conditions to entangle two atomic qubits with a two-mode squeezed field driving two cavities containing the atoms.