unity – How can I render 3D objects and particle systems in front of a Screen Space – Overlay Camera?

To render 3D objects on top of your canvas:

  1. Create a new Canvas in Screen Space – Overlay.
  2. Add a RawImage to that canvas.
  3. Create a new Render Texture.
  4. Add the Render Texture to the Raw Image.
  5. Create a new Camera.
  6. Set the camera to Solid Color background with an alpha of 0.
  7. Set the output texture of the camera to be the Render Texture you created.

You can now render 3D objects on top of your canvas; however, there are extra steps for particle systems:

  1. Create a material. Set its shader to Universal Render Pipeline/2D/Sprite-Lit-Default.
  2. Add your particle sprite to the Diffuse of your material.
  3. In the Renderer settings of your particle system, replace the material with the one you just created.

You should be good to go!

(If you have any problems, try going to your Render Settings and change the Anti Aliasing to 8x.)

Operating systems memory management: help understanding a question related to segmentation

There is this question in my textbook (Operating Systems: Internals and Design Principles by William Stallings):

Write the binary translation of the logical address 0011000000110011
under the following hypothetical memory management schemes, and
explain your answer:

a. A paging system with a 512-address page size,
using a page table in which the frame number happens to be half of the
page number.

b.
A segmentation system with a 2K-address maximum segment size, using a segment
table in which bases happen to be regularly placed at real addresses:
segment# + 20 + offset + 4,096.

I am having trouble with understanding part b. I’m not a native English speaker. Initially, I assumed that “using a segment table in which bases happen to be regularly placed at real addresses” means that the segment number in the logical address is the number of the physical segment, but then I read this “segment# + 20 + offset + 4,096”, and I am not sure what to make of it. So does this mean that the base number in the segment table contains segment# (in the logical address) + 20 + offset (in the logical address) + 4,096?

reference request – What is the state-of-the-art for solving polynomials systems over fields that are not algebraically closed?

I am not working in the field of algorithmic algebraic geometry – yet, for my current work, I need some results from it.

More specifically, what is the state-of-the-art when it comes to solving (whatever “solving” means in this case) system of polynomials of fields that are not algebraically closed, whose ideal has dimension $>0$?
Could you recommend a survey paper that summarizes what has been achieved so far?

For the case of $0$-dimensional ideals, there seems to exist many heavily cited papers, like “Solving Zero-dimensional Algebraic Systems” by D. Lazard, which seem mostly to be concerned with finding ways of to display the system of polynomials in a nice way (e.g. triangularly). Are these articles already superseded, or does it make sense to read them?

dynamic – Estimation of parameters of limit cycles for systems of high-order differential equations (n> = 3)

There is a system of differential equations:

enter image description here

Then, call the limit cycle the projection of the phase trajectory onto the plane in a pairwise combination of state variables ($x-y,y-z,x-z$).

where $x,y,z$ – state variables, $a,b,c$ – constants.

Is it possible to use Mathematica to estimate the amplitude and frequency of the limit cycle? (it is possible by approximate numerical methods, most importantly, not graphical).

ds.dynamical systems – Smoothening pseudo-Anosov flows

A topological Anosov flow on a closed 3-manifold can be replaced by a smooth Anosov flow using an argument of Fried: use Markov partitions to find a surface of section, put in other terms, one can blow up some closed orbits so that the flow is a suspension of a pseudo-Anosov map on a surface with boundary. Then take a smooth representative of this pseudo-Anosov map within its isotopy class, and blow down the orbits to get back the original manifold.

Is this statement (or some analogue of it) still true for pseudo-Anosov flows? The above argument doesn’t work anymore since the singular orbits cannot lie in the interior of a Markov rectangle, so one cannot find a surface of section near these singular orbits in the same way. Is an alternate way of thinking about all of this that generalizes more easily to pseudo-Anosov flows? Any help is appreciated!

ds.dynamical systems – Counting simple closed curves

I’m currently trying to understand how to count simple closed curves. I’ve been reading Alex Wright’s survey (https://arxiv.org/pdf/1905.01753.pdf). However, I don’t feel like I’m getting the big picture. All the surveys I can find on the subject try to show things in an explicit way, but I’d rather see an abstration. I feel the way dynamicist tacle this problem post Mirzakhani is by giving a flow on $M_{g,n}$, the Teichm├╝ller geodesic flow. By the work of Mirzakhani, this is a ergodic flow. My question is how does this help us understand the function
$$f_L:M_{g,n}rightarrow mathbb{R}, quad Xmapsto s_X(L):={ gamma mid ell(gamma)leq L}?$$
I feel that estimates of this function should be related to the Ergodic Theorem, but I can not find anything on that.

PS: I’m sorry for the tags, but I’m uncertain which tags I should use.

at.algebraic topology – Is the derived category of local systems equivalent to the derived category of sheaves of vector spaces with local system cohomology?

Let $k$ be a field and $X$ a topological space.

Write $mathrm{Sh}(X)$ for the category of sheaves of vector spaces on $X$, and $mathrm{Loc}(X)$ for the subcategory of local systems of finite dimensional $k$-vector spaces.

The category not local systems is an abelian category, so we can form the derived category $D(Loc(X))$. This is the category of complexes of local systems on $X$ with quasi-isomorphisms inverted.

We can also consider the subcategory $D_{mathrm{Loc}}(X)$ of $D(X):=D(mathrm{Sh}(X))$ consisting of complexes whose cohomology sheaves are local systems on $X$.

I have two questions:

  1. Is $D_{mathrm{Loc}}(X)$ a triangulated subcategory of $D(X)$? More precisely is it closed under taking mapping cones?
  2. Under what hypotheses (if any) are $D_{mathrm{Loc}}(X)$ and $D(mathrm{Loc}(X))$ equivalent?

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