## interaction design – How can I keep up-to-date with the latest thinking about designing complex, rich applications?

If you agree that on some level complex systems go hand-in-hand with complex problems (or complex problem domains), then perhaps it makes sense to tap into the research and development community to see what they are up to. From your description, you may be specifically interested in the Visual Analytics community.

From a recent call-for-papers for the IEEE VAST Conference, Visual Analytics is defined as:

Visual Analytics is the science of analytical reasoning supported by
highly interactive visual interfaces. People use visual analytics
tools and techniques in all aspects of science, engineering, business,
and government to synthesize information into knowledge; derive
insight from massive, dynamic, and often conflicting data; detect the
expected and discover the unexpected; provide timely, defensible, and
understandable assessments; and communicate assessments effectively
for action. The issues stimulating this body of research provide a
grand challenge in science: turning information overload into the
opportunity of the decade. Visual analytics requires interdisciplinary
science, going beyond traditional scientific and information
visualization to include statistics, mathematics, knowledge
representation, management and discovery technologies, cognitive and
perceptual sciences, decision sciences, and more.

As a starting point, look at the annual VAST conference competition to see the scale/complexity of the problems that are currently “interesting” to the research community. Maybe even consider attending one of the conferences, and interacting with some of the sponsoring companies (maybe pick up trial versions of software etc).

I think half the battle is figuring out who is actually developing software solutions in these often highly niche product areas. Conferences (IEEE VisWeek as one example) and user groups can help to bridge that gap. Blogs will mainly try to condense information, which may not always be what you want.

Lastly, if you want a completely different point of view, a book was published recently (August 2012) that focuses on the interaction techniques and interfaces used in science fiction films. It is titled “Make It So: Interaction Design Lessons from Science Fiction”. I haven’t personally read the book, so I can’t comment on its contents, but here is a short description from the publisher’s site:

Many designers enjoy the interfaces seen in science fiction films and
television shows. Freed from the rigorous constraints of designing for
real users, sci-fi production designers develop blue-sky interfaces
that are inspiring, humorous, and even instructive. By carefully
studying these “outsider” user interfaces, designers can derive
lessons that make their real-world designs more cutting edge and
successful.

So, my suggestion is to keep up with the latest complex problems, and see how people try to solve them, instead of trying to sift through hundreds of applications and blogs and distill some UI/UX trend. I would wager that every truly complex problem requires a unique solution.

## complex analysis – Magnus Effect – Coupled linear inhomogeneous ODE with variable coefficients

I am trying to derive the equations of motion for an object under influence of the Magnus Force (ball spinning in air). This gives me the following coupled ODE:
begin{align} begin{bmatrix} ddot{x}(t) \ ddot{y}(t) \ end{bmatrix} &= begin{bmatrix} -gamma & -comega (t) \ comega (t) & -gamma end{bmatrix} begin{bmatrix} dot{x}(t) \ dot{y}(t) end{bmatrix} – begin{bmatrix} 0\ g end{bmatrix}end{align}
Which is of the form: $$vec{Psi}’=A(t)vec{Psi}+vec{g}$$. Here $$gamma , c$$ and $$g$$ are constants, but $$x, y$$ and $$omega$$ are functions of time. As for initial conditions, one could probably choose $$x(0)=0, y(0)=0, dot{y}(0)=v_{y0}, dot{x}(0)=v_{x0}$$ This question is very much like System of ODE with non constant coefficients, with the difference being that it was possible to write $$A(t)=f(t)A$$ in their case, where I’ve been unsuccessful in getting the time dependent factors out of the coefficient matrix. My equation also contains an inhomogeneous term, but I know there a ways of getting the full solution if only one can find the homogeneous solutions. I tried following the second answer anyway, but without success (worked up until the answer made the reduction: $$AX_1=3X_1$$ and $$AX_2=−X_2$$).

So my question is, is it possible to solve this coupled ODE analytically, and if so, how?

I have also considered looking at an extended model which includes second order terms:
begin{align} begin{bmatrix} ddot{x}(t) \ ddot{y}(t) \ end{bmatrix} &= -gamma begin{bmatrix} dot{x}(t)^2\ dot{y}(t)^2 end{bmatrix} +comega (t) begin{bmatrix} dot{x}(t) \ dot{y}(t) end{bmatrix} – begin{bmatrix} 0\ g end{bmatrix}end{align}
But have assumed that it would be even more difficult that the first set of equations. Any confirmation or refusal of this would also be of great help.

Note: I know this question is about physics, but since the difficulties lie in the applied mathematics part, I assumed MSE was the right place to post. If this is not the case, please tell me and I will remove the post and instead post it at PSE.

## complex analysis – Extract the $0$-th coefficient from given series.

Let there be a function:
$$F:mathbb{R}rightarrowmathbb{C}$$
$$F(x)=sum_{nin mathbb{Z}}a_ne^{inx}$$

For some real-valued sequence $$(a_n)_{nin mathbb{Z}}$$

How to extract the zeroth coefficient ($$a_0$$) ?

I was considering the usage of derivatives in this case, but i didn’t figure out how to do this.

Thank you for help.

## complex analysis – Show that the function $Logfrac{z-a}{z-b}$, with $a Thanks for contributing an answer to Mathematics Stack Exchange! • Please be sure to answer the question. Provide details and share your research! But avoid • Asking for help, clarification, or responding to other answers. • Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. ## complex analysis – Riemann Xi Function$xi(s)\$

If $$xi(sigma+it_0)$$ denotes the Riemann Xi function for fixed $$t_0$$, If $$sigma>1/2$$ then, Prove that $$Re( xi(sigma+it_0) xi'(sigma-it_0) )>0$$ where $$xi'(sigma-it_0)$$ denotes derivative with respect to $$sigma$$.

My Attempt

$$s=sigma+it_0$$

$$sigma>1/2$$

To Prove
$$Re( xi(s) xi'(bar{s}) )>0$$.

## pathfinder 1e – Can a simulacrum be healed by any means other the ‘complex process’ outlined in the spell?

Thanks for contributing an answer to Role-playing Games Stack Exchange!

But avoid

• Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

## Complex Conjugate of a positive square root of a variable

I have a complex number: $$x=sqrt{a}+i$$, where $$a$$ is positive. I need to get the complex conjugate of $$x$$. How can I give a condition that my $$a$$ is positive while applying Conjugate?

Following is my code:

x= Sqrt(a)+ I;
ComplexExpand(Conjugate(x))



This is giving me the following result:

-I + (a^2)^(1/4) Exp(-1/2 I Arg(a))
$$$$


## complex geometry – What in Gods Green Earth is this?

I found quite possibly the strangest thing I have ever seen. I started with x^2+y^2=a with a being a variable I could set. I don’t know what persuaded me to do this, but I set a to 1.5 Root(x^3), which I don’t know the equivalent value of. I found out that when I plugged this into Desmos, the graph looked discontinuous. I decided to zoom in at the origin. I did this all the way down to a scale of 10^-108, at which I could see exactly what the shape was. Link: https://www.desmos.com/calculator/qyc3rfzidi. What caused this? is it a bug? What is the type of function called? It’s concentric circles sliced into exponential sections.

## import – Formatting Imported Complex Arrays from Python (csv. files)

Just a short question, I am trying to import a complex array (matrix) from Python to Mathematica by first writing to a csv. file. When I Import the csv. array to Mathematica it is in a form (matrix elements are wrapped in round brackets with imaginary part denoted with Python imaginary part symbol ‘j’) that is not compatible with Mathematica as indicated by the code example (2×2 matrix) below:
The matrix $$A$$ that I am importing as an example is:
$$begin{pmatrix} i &2 \ 3 & 4 end{pmatrix}$$

A = Import("C:\Users\JohnDoe\Documents\PycharmProjects\pythonProject\foo.csv", "Data")


where the output of imported array A in Mathematica is:

{{(0.00000000000000000e+00+1.00000000000000000e+00j),(2.00000000000000000e+00+0.00000000000000000e+00j)},
{(3.00000000000000000e+00+0.00000000000000000e+00j), (4.00000000000000000e+00+0.00000000000000000e+00j)}}
`

Can anyone advise on how to process the array after importing such that it is in a standard Mathematica form without brackets (and standard Mathematica imaginary part)?

Thanks for any assistance.

## integration – How to compute a complex integral of x dz?

I’m working through chapter 4 of Alfohrs, and the first exercise is computing the integral $$int_gamma x : dz$$ where $$gamma$$ is the directed line segment from $$0$$ to $$1+i$$. What, exactly, does this mean?

I know that by definition, $$int_gamma f(z):dz = int_a^b f(z(t)) z'(t) :dt$$; however, I’m not quite sure what to do with this definition here. One thing that seems to be the case is $$f$$ is probably implied to be in the form $$x + iy$$ (is this a fair assumption?) If so, I could use the expansion $$int_gamma f(z):dz = int_gamma (u dx – v dy) + i int_gamma (u dy + v dx)$$, which would after substitution become $$int_gamma x dx + i int_gamma x dy$$.

If I can indeed have it in this form, I need to somehow parametrize $$gamma$$, correct? My attempt here is saying that $$gamma(t) = t + it$$ for $$0 leq t leq 1$$. Then I get that $$int_gamma x dx + i int_gamma x dy = int_0^1 x(t)x'(t)dt + iint_0^1 x(t)y'(t)dt = int_0^1 t dt + iint_0^1 t dt = (t^2/2)mid_0^1 + (t^2/2)mid_0^1 = (t^2)mid_0^1 = 1^2=0^2=1$$.

Is any of this reasoning correct?