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<p>Sea <script id="MathJax-Element-10368" type="math/tex">f:\mathbb{Z}[t]\to \mathbb{Z}[\sqrt 3]</script>, <script id="MathJax-Element-10369" type="math/tex">p(x)\mapsto p(\sqrt 3)</script>.</p> | |
<p>Claramente <script id="MathJax-Element-10370" type="math/tex">f</script> es sobreyectiva. Veamos que <script id="MathJax-Element-10371" type="math/tex">ker(f)=(t^2-3)</script>.</p> | |
<p>Claramente la inclusión <script id="MathJax-Element-10372" type="math/tex">\supset</script> se da.</p> | |
<p>Ahora, sea <script id="MathJax-Element-10373" type="math/tex">p\in ker f</script>. Por pseudodivisión, <script id="MathJax-Element-10374" type="math/tex">p(t)=(t^2-3)q(x)+r(x)</script>, con <script id="MathJax-Element-10375" type="math/tex">deg(r)<2</script>, y por tanto <script id="MathJax-Element-10376" type="math/tex">p(\sqrt 3)=r(\sqrt 3)=a+b\sqrt 3=0</script>. Como la suma de dos números racionales ha de ser racional, y <script id="MathJax-Element-10377" type="math/tex">\sqrt 3</script> es irracional, no queda más remedio |
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<p>The intuition behind the proof of Lób’s theorem invokes the formalization of the following argument:</p> | |
<p>Let <script id="MathJax-Element-27" type="math/tex">S</script> stand for the sentence “If <script id="MathJax-Element-28" type="math/tex">S</script> is provable, then I am Santa Claus”.</p> | |
<p>As it is standard, when trying to prove a If…then theorem we can start by supposing the antecedent and checking that the consequent follows. But if <script id="MathJax-Element-29" type="math/tex">S</script> is provable, then we can chain its proof to an application of modus ponens of <script id="MathJax-Element-30" type="math/tex">S</script> to itself in order to get a proof of the consequent “I am Santa Claus”. If we suppose that finding a proof of a sentence implies that the sentence is true, then “I am Santa Claus” is true.</p> | |
<p>Thus we have supposed that <script id="MathJax-Element-31" type="math/tex">S</script> is provably true then it follows that “I am Santa Claus”, which is a proof of what <script |
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# -*- coding: utf-8 -*- | |
""" | |
Created on Mon Apr 9 15:48:18 2018 | |
@author: jsevillamol | |
""" | |
# After the game, I get either $1000 or the value of C in dollars rounded to nearest cent | |
# You can ask the 3rd party to run the flip_n_times() function as many times as you want within the 2h | |
# If C overflows during the game, the game ends and I get $1000 dollars |
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# Create model | |
model = Sequential() | |
input_shape = (n_tel, img_w, img_h, n_channels) | |
# mask the inputs that correspond to padding | |
model.add(Masking(mask_value=0., input_shape=input_shape)) | |
# Add CNN feature extractor | |
model.add(TimeDistributed( | |
Conv2D( |
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import tensorflow as tf | |
from tensorflow.keras.layers import Layer | |
class ROIPoolingLayer(Layer): | |
""" Implements Region Of Interest Max Pooling | |
for channel-first images and relative bounding box coordinates | |
# Constructor parameters | |
pooled_height, pooled_width (int) -- | |
specify height and width of layer outputs |
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#!/usr/bin/env python3 | |
# -*- coding: utf-8 -*- | |
""" | |
Created on Sat Oct 27 10:22:03 2018 | |
@author: jsevillamol | |
""" | |
import yaml, argparse | |
from contextlib import redirect_stdout |
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# The data config section configures the data loader | |
data_config: | |
# file_list_fn: path to a txt file where each line is the absolute path | |
# to a .h5 file containing information from an event | |
file_list_fn: /data2/deeplearning/ctlearn/tests/prototype_files_class_balanced.txt | |
# channels: list of image-like features per image that will be loaded. Supports: | |
# image_charge: total charge received by pixel during the event | |
# peak_times: time in seconds when the peak of energy occured | |
# CAUTION: ctalearn assumes that image_charge is always the first channel |
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jsevillamol@jsevillamol-N551JK:~/Descargas/pgilinux-2019-194-x86-64$ sudo ./install | |
[sudo] password for jsevillamol: | |
Welcome to the PGI Linux installer! | |
You are installing PGI 2019 version 19.4 for Linux. | |
Please note that all Trademarks and Marks are the properties | |
of their respective owners. | |
Press enter to continue... |
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# Script to retrieve the characteristics of the available backends in IBM Quantum Experience | |
# by Jaime Sevilla, based on a script from Douglas T. McClure | |
# Importing standard Qiskit libraries and configuring account | |
from qiskit import QuantumCircuit, execute, Aer, IBMQ | |
from qiskit.compiler import transpile, assemble | |
from qiskit.tools.jupyter import * | |
from qiskit.visualization import * | |
# Loading your IBM Q account(s) | |
provider = IBMQ.load_account() |
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dag { | |
"Ethnic fractionalization" [pos="-0.656,0.548"] | |
"Historical population" [pos="-0.543,0.055"] | |
"Modern GPD per capita" [outcome,pos="0.182,0.314"] | |
"Population growth" [pos="-0.362,0.631"] | |
"Slave trade intensity" [exposure,pos="-0.886,0.266"] | |
"Spatial autocorrelation" [pos="-0.174,0.071"] | |
"State development" [pos="-0.033,0.566"] | |
"Ethnic fractionalization" -> "Modern GPD per capita" | |
"Historical population" -> "Ethnic fractionalization" |
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