٭٭٭٭٭ Report ٭٭٭٭٭

٭ User input
# 2021.12.16
# AmirHosein Sadeghimanesh
# 
# The goal is to apply Lemma 5.2 of the superlevel set paper to conclude
# that with probability one, the rectangle [2, 2.5] * [2.5, 3] in Figure
# 3c of the Kac-Rice paper (the arXiv version) which has average number
# of solutions equal to 2 is not a rectangle that almost all of it is
# inside the region with 2 solutions, but instead has non-zero measure 
# intersections with regions of different number of solutions.
#
# The first step is to generate the example using 
# MCKR generate example 
#
Task: MCKR generate example
Save_location: ./
Save_name: File_20211216_testing_Lemma_5_2_output_1
Example_name: Kac_Rice_Example_2_3_normal
Number_of_variables: 1
Number_of_parameters: 2
Determinant_expression: 100*(5*x1^4+4*(-k2-9/2)*x1^3+3*((9*k2)/2+21/4)*x1^2+2*(-(23*k2)/4+3/8)*x1+(15*k2)/8-23/8)
g_expression: 25/4-100*x1^5+100*x1^4*k2+450*x1^4-450*x1^3*k2-525*x1^3+575*x1^2*k2-75/2*x1^2-375/2*k2*x1+575/2*x1
summand_expression: s(x1,k2,B)+s(1/x1,k2,B)/x1^2
Distribution: Normal
Include cpu information
Include memory information
٭ End of input.

Example file Kac_Rice_Example_2_3_normal.jl is generated. You can find it in the Example_MCKR_bank folder.


٭ Information of cpus of the computing system.
This system has 12 cpus.
Base.Sys.CPUinfo[Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     460484            0      2375250     90988671       983875  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     249921            0       444578     93129718        32234  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    2844828            0      1098140     89881265        14703  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     612593            0       425546     92786093         5265  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1214078            0       778453     91831703        12218  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     252109            0       367281     93204828         2968  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     738250            0       660578     92425406         9375  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     520296            0      1317890     91986046         8859  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     581921            0      1327953     91914359         8125  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     554062            0       424062     92846093         6453  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     519406            0       664890     92639906         9671  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     244078            0       287250     93292875         3062  ticks]

٭ Information about the memory.
The total memory is 63.60728454589844 GB.
The free memory before compiling the task was 52.897884368896484 GB.
