Schukajlow's three categories of mathematical problems were applied to identify the types of problems the ML teachers used. The strategies used by the teachers in facilitating the mathematisation process were analysed using a framework in which a real-life problem is explored, a model is ...
4.1.3Mathematical model integrated in the problem Inna decided to measure various cartons herself [returned to the situation]. She was surprised to discover that according to the measurements, the cartons did not contain an entire liter.
This is called a mathematical model. (b) Solve the mathematical problem by moving from one statement to an equivalent statement justifying each stage by using relevant mathematical knowledge. (c) Check the mathematical solution(s) by substituting them into the original formulation of the mathematical...
As a basis for comparison for their eye model results, Phan et al. first examined drug release from the contact lens submerged in a large fluid volume in a vial configuration. The volume of fluid in the vial was reported to be \(V_{\textrm{vial}} = 2\) mL. Assuming spatial uniformit...
To model an optimization problem, mathematical programming formulations represent the main goal as objective function, which is the output (a single score) to maximize or minimize. In addition,mathematical programsrepresent problem choices as decision variables that influence the objective function with co...
This means that the input model requires some understanding of the underlying mathematics. This is a key difference 42 | Math input and layout between computer typesetting of mathematics and a purely visual composition as practised in the days of metal type. It is not enough to look at a ...
that they are unable to understand and interpret the evidence modellers provide [111,112,113,115,116], and often additionally shared in formats that are difficult to decipher [112,116]. The value of the model evidence may also not be well understood [111,112]. Overall, these barriers are...
Model selection criteria Criteria used to select the best model among a set of candidate models estimated by ML Likelihood ratio test A test of hypothesis involving both restricted and unrestricted ML estimates EM algorithm Recursive algorithm used for ML estimation of latent-variable models ...
In the models discussed above, independent, single binding sites are assumed such that protein-protein interactions and cooperative effects are considered insignificant. To investigate this assumption, Angioletti-Uberti et al. developed a model based on the dynamic density functional theory (DDFT) which...
Large language models (LLMs) have demonstrated significant capabilities in mathematical reasoning, particularly with text-based mathematical problems. However, current multi-modal large language models (MLLMs), especially those specialized in mathematics, tend to focus predominantly on solving geometric probl...