The Equiprobability Bias from a Mathematical and Psychological Perspective

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.

Mathematical modelling of quantum yield enhancements of methyl orange photooxidation in aqueous TiO2 suspensions under controlled periodic UV LED illumination

Quantum yields of the photocatalytic degradation of methyl orange under controlled periodic illumination (CPI) have been modelled using existing models. A modified Langmuir-Hinshelwood (L-H) rate equation was used to predict the degradation reaction rates of methyl orange at various duty cycles and a simple photocatalytic model was applied in modelling quantum yield enhancement of the photocatalytic process due to the CPI effect. A good agreement between the modelled and experimental data was observed for quantum yield modelling. The modified L-H model, however, did not accurately predict the photocatalytic decomposition of the dye under periodic illumination.

Bdellovibrio predation in the presence of decoys:Three-way bacterial interactions revealed by mathematical and experimental analyses

Bdellovibrio bacteriovorus is a small, gram-negative, motile bacterium that preys upon other gram-negative bacteria, including several known human pathogens. Its predation efficiency is usually studied in pure cultures containing solely B. bacteriovorus and a suitable prey. However, in natural environments, as well as in any possible biomedical uses as an antimicrobial, Bdellovibrio is predatory in the presence of diverse decoys, including live nonsusceptible bacteria, eukaryotic cells, and cell debris. Here we gathered and mathematically modeled data from three-member cultures containing predator, prey, and nonsusceptible bacterial decoys. Specifically, we studied the rate of predation of planktonic late-log-phase Escherichia coli S17-1 prey by B. bacteriovorus HD100, both in the presence and in the absence of Bacillus subtilis nonsporulating strain 671, which acted as a live bacterial decoy. Interestingly, we found that although addition of the live Bacillus decoy did decrease the rate of Bdellovibrio predation in liquid cultures, this addition also resulted in a partially compensatory enhancement of the availability of prey for predation. This effect resulted in a higher final yield of Bdellovibrio than would be predicted for a simple inert decoy. Our mathematical model accounts for both negative and positive effects of predator-prey-decoy interactions in the closed batch environment. In addition, it informs considerations for predator dosing in any future therapeutic applications and sheds some light on considerations for modeling the massively complex interactions of real mixed bacterial populations in nature.

MNI: Motorway Notation Network

In his essay, Anti-Object, Kengo Kuma proposes that architecture cannot and should not be understood as object alone but instead always as series of networks and connections, relationships within space and through form. Some of these relationships are tangible, others are invisible. Stan Allen and James Corner have also called for an architecture that is more performative and operative – ‘less concerned with what buildings look like and more concerned with what they do’ – as means of effecting a more intimate and promiscuous relationship between infrastructure, urbanism and buildings. According to Allen this expanding filed offers a reclamation of some of the areas ceded by architecture following disciplinary specialization:

‘Territory, communication and speed are properly infrastructural problems and architecture as a discipline has developed specific technical means to deal with these variables. Mapping, projection, calculation, notation and visualization are among architecture’s traditional tools for operating at the very large scale’.

The motorway may not look like it – partly because we are no longer accustomed to think about it as such – but it is a site for and of architecture, a territory where architecture can be critical and active. If the limits of the discipline have narrowed, then one of the functions of a school of architecture must be an attempt occupy those areas of the built environment where architecture is no longer, or has yet to reach. If this is a project about reclamation of a landscape, it is also a challenge to some of the boundaries that surround architecture and often confine it, as Kuma suggests, to the appreciation of isolated objects.

M:NI 2014-15
We tend to think of the motorway as a thing or an object, something that has a singular function. Historically this is how it has been seen, with engineers designing bridges and embankments and suchlike with zeal … These objects like the M3 Urban Motorway, Belfast’s own Westway, are beautiful of course, but they have caused considerable damage to the city they were inflicted upon.

Actually, it’s the fact that we have seen the motorway as a solid object that has caused this problem. The motorway actually is a fluid and dynamic thing, and it should be seen as such: in fact it’s not an organ at all but actually tissue – something that connects rather than is. Once we start to see the motorway as tissue, it opens up new propositions about what the motorway is, is used for and does. This new dynamic and connective view unlocks the stasis of the motorway as edifice, and allows adaptation to happen: adaptation to old contexts that were ignored by the planners, and adaptation to new contexts that have arisen because of or in spite of our best efforts.

Motorways as tissue are more than just infrastructures: they are landscapes. These landscapes can be seen as surfaces on which flows take place, not only of cars, buses and lorries, but also of the globalized goods carried and the lifestyles and mobilities enabled. Here the infinite speed of urban change of thought transcends the declared speed limit [70 mph] of the motorway, in that a consignment of bananas can cause soil erosion in Equador, or the delivery of a new iphone can unlock connections and ideas the world over.

So what is this new landscape to be like? It may be a parallax-shifting, cognitive looking glass; a drone scape of energy transformation; a collective farm, or maybe part of a hospital. But what’s for sure, is that it is never fixed nor static: it pulses like a heartbeat through that most bland of landscapes, the countryside. It transmits forces like a Caribbean hurricane creating surf on an Atlantic Storm Beach: alien forces that mutate and re-form these places screaming into new, unclear and unintended futures.

And this future is clear: the future is urban. In this small rural country, motorways as tissue have made the whole of it: countryside, mountain, sea and town, into one singular, homogenous and hyper-connected, generic city.

Goodbye, place. Hello, surface!

Methodological aspects of a mathematical programming model to evaluate soil tillage technologies in a risky environment

In this work we develop a methodology for the economic evaluation of soil tillage technologies, in a risky environment, and to capture the influence of farmer behaviour on his technology choice. The model has short-term activities, that change with the type of year, and long-term activities, in which sets of traction investment activities are included. Although these activities do not change with the type of year, they lead to different availability of resources for each type of year, since the same tractor has different available fieldwork days under different weather conditions. We prove that the model is sensitive to the greater income variability resulting from the use of alternative technologies and to the balance between income and risk, accounting for the probability of occurrence of each state of nature and giving an investment solution that considers the best production plan for each type of year. (c) 2005 Elsevier B.V. All rights reserved.

O contributo das representações numéricas básicas e da função executiva no desempenho de operações aritméticas : um estudo exploratório

Tese de mestrado, Psicologia (Secção de Cognição Social Aplicada), Universidade de Lisboa, Faculdade de Psicologia, 2014

Notation timelines and the aesthetics of disappearance

Contemporary cities are frequently surrounded by transitional landscapes: ambiguous lands, non-places on the urban edge, commonly experienced under the condition of speed. Although variously shaped by processes of urbanisation, logistics of road engineering, safety and ownership, and local people's lives, for travellers such landscapes are usually perceived in a state of disappearance. This condition presents a major challenge for the traditional methods used in architecture and urban design. For designers interested in the organisation and design of such mobility routes for the engagement of the traveller, a method of scripting based on notation timelines would provide a helpful supplement to traditional master plans. This paper explores the development of such a method and its roots in time-based arts, such as dance, music and film, as well as in the recent history of architecture and urban design. It does so through the presentation of an experimental study based on a real route, the train journey from London to Stansted airport.

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

Fuzzy Monte Carlo mathematical model for load curtailment minimization in transmission power systems

This paper presents a methodology which is based on statistical failure and repair data of the transmission power system components and uses fuzzyprobabilistic modeling for system component outage parameters. Using statistical records allows developing the fuzzy membership functions of system component outage parameters. The proposed hybrid method of fuzzy set and Monte Carlo simulation based on the fuzzy-probabilistic models allows catching both randomness and fuzziness of component outage parameters. A network contingency analysis to identify any overloading or voltage violation in the network is performed once obtained the system states by Monte Carlo simulation. This is followed by a remedial action algorithm, based on optimal power flow, to reschedule generations and alleviate constraint violations and, at the same time, to avoid any load curtailment, if possible, or, otherwise, to minimize the total load curtailment, for the states identified by the contingency analysis. In order to illustrate the application of the proposed methodology to a practical case, the paper will include a case study for the Reliability Test System (RTS) 1996 IEEE 24 BUS.

Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.

Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints

On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.