12

Very many references may easily be found with a Google search for "mathematical model memory". Probably the most classic and iconic reference is Atkinson and Shiffrin (1965), which is also described on Wikipedia. Its three components and their relationships are nicely encapsulated in this figure: Many other, lesser-known mathematical models of memory exist, ...


10

The question which of these two descriptions is correct? is perhaps natural in the context of, say, someone studying for an examination. Epistemologists might suggest that a better formulation would be is either of these correct? However, as stated here there are clear reasons for preferring the first formulation to the second. I shall first explain why, ...


9

To calculate $d'$ you need to know two things: the hit rate and the false alarm rate. The hit rate is the proportion of trials where the stimulus was present and the subject responded that the stimulus was present. The false alarm rate is the proportion of trials where the stimulus was not present, and the subject responded that the stimulus was present. ...


6

Thoughts on the paper The paper appears to provide a high level overview of the role of mathematics in cognitive science. I'm not a sufficient expert in the overall field of cognitive science where I'd feel comfortable to truly judge the accuracy of the overall synthesis that Andler (2012) provides. That said, much of the paper is about providing examples ...


6

For a review of how this question is debated in Cognitive Science, search for Searle's Chinese Room Thought Experiment. In the Chinese Room Thought Experiment, Searle argues there is something fundamentally meaningful (semantic-holding-preserving) about the internal state of a living being. Additionally, this meaning cannot be approximated by a computer. ...


6

I think the key concept to tackle this question is to consider the concept of abstraction. Abstract models are generalized models of some kind "reality" that we are interested in, with the aim to describe some behavior of the system in question reasonably well. Often the abstraction should also be relevant to many instances of the entity that we would like ...


6

Note: This is not intended to set a verbosity standard for answers, but to give a comprehensive example of what kind of information I am looking in order to further clarify the question. An answer including only a parallel of the principles of ecological psychology subsection would be sufficient, for example. Ecological psychology Ecological Psychology (EP)...


5

In my opinion as a computational neuroscience researcher, graph theory has not made major inroads into computational neuroscience because we don't have good evidence for what graphs characterise brains. For example, my research revolves around how patterns of connections between neurons within local cortical circuits relate to information processing ...


5

The R package diffIRT (http://www.dylanmolenaar.nl/jss1265.pdf) estimates both the Q and the D diffusion models (see his website for the van der Maas et al. paper discussing the differences between these models). R code for the EZ2 approach, which is much faster if that is important for your applications, is http://raoul.socsci.uva.nl/EZ2/.


5

I also like https://bayesmodels.com/. I posted the question on twitter, you could check out the responses. Joachim Vandekerckhove suggested: Lewandowsky, S., & Farrell, S. (2010). Computational modeling in cognition: Principles and practice. Sage Publications. https://www.amazon.com/Computational-Modeling-Cognition-Principles-Practice/dp/1412970768 ...


4

If you have a physics background, you may be particularly interested in Sparse Distributed Memory, a model that provides a number of psychologically plausible characteristics, and is also neuroscientifically plausible. The model and some of its characteristics are summarized in this paper. Many great references have been provided by Nick Stauner, but ...


4

I don't think anyone has ever bothered (though Ralph Miller might disagree), since many of the 'failures' are outside of the model's purview. The model expresses as simply as possible the profound insight that we learn most when our expectations are not met. Many features of learning won't conform to this general principle (spontaneous recovery) but it doesn'...


4

Thanks for sharing the article. I read the paper and what I take from it is a rather pessimistic view. He suggests that there is a crucial need for overarching proper mathematical modeling, but he makes it sound this is also a huge obsticle and we must wait (longer than a young persons academic career) to see the fruits of it. I'm coming from a theoretical ...


4

The index of sensitivity $d'$ is typically defined in terms of two equal variance normally distributed random variables with means $\mu_s$ and $\mu_n$ and standard deviation $\sigma$: $$d'=\frac{\mu_s-\mu_n}{\sigma}$$ In behavioural experiments, the probability that the subjects responded correctly (either saying 'yes' when the signal was present or saying ...


3

The final two paragraphs of that piece address this exact question. Although understanding how neurons communicate with each other contributes to our understanding of behaviour at the level of biology, behaviour cannot be reduced to biological explanations. In conclusion, the communication of neurons within the nervous system assists our understanding of ...


3

I hold a Bachelor's in Applied Mathematics and, for my Master's in Neuroscience, I have used mainly the classic one from Kandel Principles of Neural Science. With regard to Mathematical Psychology I would suggest Oxford Handbook on Computational and Mathematical Psychology


3

Semantic foraging in memory is another nice example: concepts in memory can be represented spatially as locations in multidimensional space, and the route we travel in that 'space' has a lot in common with the optimal foraging movements animals adopt. http://www.indiana.edu/~clcl/Papers/HTJ_Foraging.pdf


3

Here are a few off the top of my head from neuroscience: neural activity may primarily exist on low dimensional attractors. reconstructing PET signal origins from emitted gamma rays It's widely believed our brains are gyrencephalic (wrinkly) to maximize surface area. Various distance metrics (Euclidean, Mahalanobis) are common tools for clustering data, for ...


3

There are some mentions of Evolutionary Game Theory in this Behavior & Brain Sciences (BBS) article by Andrew Colman (2003). The main article itself only has a brief section on EGT. However, like all BBS articles, there are short commentary articles after the main article. A few of these deal directly with EGT. I was able to find the relevant articles ...


3

In the subheading you also mention that you're interested in matlab / python implementations: I've personally used DMAT in matlab at that's a nice package. However, the python based HDDM package may be one of the best around at the moment (in my opinion) and it has a good user guide. http://ski.clps.brown.edu/hddm_docs/abstract.html and the paper ...


3

I really like https://bayesmodels.com/ There's also a lot of fun you can have at http://probmods.org/ that feeds into a bunch of current cognitive modeling work, see also http://agentmodels.org/ You might enjoy "Complex probabilistic inference: From cognition to neural computation" by Samuel Gershman and Jeffery Beck. With the background you describe, you ...


2

The R package rtdists is another great option: Provides response time distributions (density/PDF, distribution function/CDF, quantile function, and random generation): (a) Ratcliff diffusion model based on C code by Andreas and Jochen Voss and (b) linear ballistic accumulator (LBA) with different distributions underlying the drift rate.


2

Here is the illustrate of both equation To make them visible at same time, I changed 100 to 1 and set memory strength as 1. They look alike.


2

Come read some cognition! It's a wide open field with angles on all kinds of psychology stuff, and we're having a great time throwing greek letters around like confetti. I think you might like it! One of my favorite recent pro-model rants is this one psyarxiv.com/rybh9/ Although, to be fair they do argue for 'computational' rather than 'mathematical'. I ...


1

According to the author, in this maze-category the objects are memories (or mental objects). The author references to chapter 3, when discussing the maze-category. Chapter 3 of the book, gives an application to Memory Evolutive Neuronal Systems (MENS). There, a morphism represents a way of relating mental objects. This is a general description. The ...


1

See my comment above, but it is possible to assume that B acquires the same reward value as the original reward, so B can then be treated as a reward, which in turn brings A closer to the reward event (now at time B). Does that make sense? In other words, the addition of B allows the reward value to accrue to B and thus brings A closer to reward.


1

Graph theory and complex networks are central to many works involving fMRI (1, 2), whole brain models (3, 4), protein interaction graphs (5, 6), and some EEG studies of consciousness (7, 8, 9). The problem is that neuroscience is a very wide field that emcompases many different specific questions, most of which are pointed at small features that dont envolve ...


1

I don't exactly what it is you are after, but if you are looking for other analyzing techniques, you should try Independent Component Analysis (ICA). I have heard (but I do not have references) that ICA is better than PCA analyses. A very neat (and free) Matlab toolbox that has this function is FieldTrip (http://www.fieldtriptoolbox.org/). It is a nicely ...


1

Firstly lets define criteria for what difficult learning material is. My interpretation of the matter states that the task of developing mastery or competency in understanding and applying difficult content: Takes an increased amount of time or Demands increased cognitive effort It's relevant to keep in mind The 2 systems that occur in the brain The ...


1

Part of it has to do with the ability to construct a model of reality. Every developer can relate to that. Visible, concrete things are easy to deconstruct in pragmatic terms. But once you get into abstract concepts, it gets harder and harder to bind it with your existing view of the world. Some concepts are also very difficult to grasp if you can't connect ...


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