Biomathematics - Science topic

Bifurcation is a fascinating concept found in various fields, including mathematics, physics, and biology.

The framework of economics today draws largely from post-War scholarship. And here, we remember the use of biomathematics by Paul Samuelson and contemporaries of the sixties and seventies. Now, that framework has been challenged and partly because of its finite dimensions. Hark back the 2007/8 crisis. Take ‘forward guidance’. It terrified the central banker. The models could not handle the realities of strongly nonlinear dynamical systems. Another crisis is here, Covid. Looking ahead, economics might have to draw more from the data-driven linearisation of engineering. And the Koopman world comes to mind. So we must ask, why can’t engineering and economics merge? And the question is more relevant in the most strongly nonlinear spaces of the lower income countries. Do you see the joy in dropping on a university hill of Africa and being welcomed by a department of engineering and economics? We just have to overcome a few institutional issues (norms and values). And the jolt of Covid should help us overcome the institutional challenges.

The wisdom of the early twentieth century established institutes of advanced studies for deep interdisciplinary work. The lower income countries don’t have those institutes. And it seems institutes in the advanced economies have lost their original fervour. So, the merger seems the most feasible solution for economics.

PS: And to Koopman people in their corner, this note provokes augmentation for transients.

A  phase transition of order k is mathematically characterized by a loss of regularity of free energy f: f is k-1 differentiable but not k differentiable. There are many examples of first and second order phase transitions in experiments and in models. There are also cases where f is C^{\infty} but not analytic (Griffith singularities).

But are their known example of phase transition of order k, k>2 ?

A third order phase transition would mean that quantities like susceptibility or heat capacity are not differentiable with respect to parameters variations. But I have no idea of what this means physically.

In the context of complexity, it is well known that each change that is given to nodes or relationships in a network will give emergent properties, and I am looking for a way to model these effects.

For reference I am attaching paper.

I would like to calculate dissociation constant (Kd) using fluorescence anisotropy.

Dear all,

I am staining two adjacent cellular structures solids with fluorescent antibodies (Alexa-488 and 555). I want to calculate the coverage of the small solid respect to the big one.

In disease state, they both reduce their volume although is more dramatic in the small one.

I know volume ratio is not enough nor surface area.

Could you suggest me any help?

Best regards,

Alan

I have some individual interest to understand a little bit more these two phenomena, because the apparent mathematical similarities between them, and because some particularities, too. The overview to direct possible concerned researchers to solve this question can be seen in the attached link. Thanks for you interest.

I am calculating the correlation values between two data sets of size 257. I want to know what is the critical value of correlation for a sample size of 257. I tried searching on the web, but critical values corresponding to 100, 200 and 500 are seen but not 257 specifically.

So, what is the formula to calculate the correlation critical value? There are a few online tools to calculate that, but I would like to know the formula so that I can integrate it into the code I am using so as to get correlation values along with the critical values.

Which tool is best for data plotting for scientific documents, journals, etc. In MATLAB, I did some plots with very low step size like the plot in the attachment, If I change different features like *, ^, v instead of '-' I am getting only thick lines (because of very low time steps). If I print in black and white printer, we cannot find the difference. How to overcome this issue. Can anyone suggest me a plotting tool to show the difference in black and white print out (we have to keep it in mind that we have to use very low time steps like 0.0005 also).

I want to know the method that determines the stability of dde for all situations.

Organisation, its omni-presence, preservation and dependence, is possible the distinctive aspect of biological phenomena. Achieving a consensus about what is organisation and how can it be used to generate biological explanations would greatly benefit the development of (theoretical) biology.