Nexus 2012: Relationships Between Architecture and Mathematics

The ninth edition of the biennial conference series “Nexus: Relationships Between Architecture and Mathematics” took place at the Politecnico di Milan in June 2012. There are many connections between architecture and mathematics: mathematic principles may be used as a basis for an architectural design, or as a tool for analyzing an existing monument; architecture may be a concrete expression of mathematical ideas, becoming, in a sense, “visual mathematics”. The purpose of the Nexus conference series is to bring together all those working with ideas related to both architecture and mathematics, and to allow researchers to exchange ideas first-hand. Papers presented at the conference are published in the Nexus Network Journal, providing a permanent archive of studies in architecture and mathematics, and in 2012 a special volume of papers from the Ph.D. Day and the poster session was published.     

Allocation and scheduling of Conditional Task Graphs

We propose an original, complete and efficient approach to the allocation and scheduling of Conditional Task Graphs (CTGs). In CTGs, nodes represent activities, some of them are branches and are labeled with a condition, arcs rooted in branch nodes are labeled with condition outcomes and a corresponding probability. A task is executed at run time if the condition outcomes that label the arcs in the path to the task hold at schedule execution time; this can be captured off-line by adopting a stochastic model. Tasks need for their execution either unary or cumulative resources and some tasks can be executed on alternative resources. The solution to the problem is a single assignment of a resource and of a start time to each task so that the allocation and schedule is feasible in each scenario and the expected value of a given objective function is optimized. For this problem we need to extend traditional constraint-based scheduling techniques in two directions: (i) compute the probability of sets of scenarios in polynomial time, in order to get the expected value of the objective function; (ii) define conditional constraints that ensure feasibility in all scenarios. We show the application of this framework on problems with objective functions depending either on the allocation of resources to tasks or on the scheduling part. Also, we present the conditional extension to the timetable global constraint. Experimental results show the effectiveness of the approach on a set of benchmarks taken from the field of embedded system design. Comparing our solver with a scenario based solver proposed in the literature, we show the advantages of our approach both in terms of execution time and solution quality.     

Amygdala Central Nucleus Function Is Necessary for Learning, but Not Expression, of Conditioned Auditory Orienting.

In Pavlovian appetitive conditioning, rats often acquire 2 classes of conditioned responses: those whose form is determined by the reinforcer, and those whose form is determined by characteristics of the conditioned stimulus (CS). Consistent with the results of previous lesion studies, reversible inactivation of amygdala central nucleus function during pairings of an auditory CS with food prevented the acquisition of conditioned orienting responses specific to auditory CSs, whereas food-related conditioned behaviors were acquired normally. Neither inactivation nor posttraining neurotoxic lesions of the central nucleus affected the expression of previously acquired conditioned orienting. Thus, although the central nucleus is critical to the acquisition of information required for conditioned orienting to auditory cues, it is not needed for maintaining this information for later use. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How to monitor the modulus of elasticity of concrete,automatically since the earliest age?

Monitoring the evolution of an early age set of parameters on concrete is necessary to predict the early age behaviour of structures. The difficulty lies in the fact that this monitoring must be automatic because the concrete hardening process takes place over a long period after the casting. This paper presents a new methodology and an apparatus, specifically designed at IFSTTAR, to monitor the hardening process of a concrete. Mainly, the Young’s modulus can be monitored in compression. Measurements start soon after having cast the concrete and the sample temperature is completely controlled so that the concrete maturity is well mastered. The performances of this apparatus, obtained on an ordinary concrete, are compared to more classical measurements using an extensometer mounted on the sample just after the setting time and to ultrasonic measurements. In these cases, the temperatures were not controlled and results have to be expressed in equivalent time. A comparison with another method developed and used at ULB by using the same concrete, in the frame of a joined cooperation between our two laboratories is achieved. This test set up is based on the so called Temperature Stress Testing Machine (TSTM). This device has been specifically designed with a control of the concrete maturity by the use of a dummy specimen only submitted to free deformations (thermal, shrinkage). The TSTM allows compressive and tensile testing starting just after the setting time. In addition, concrete properties, such as compressive and tensile strength, have been characterized at early age. These values have been used for the design of the loading histories applied in the automatic tests. The heat released by the cement hydration has also been measured in order to express the results on a maturity scale.