text:
# Blog & News

## Part two of the differential cryptanalysis series

The design of block ciphers is usually seen as a specialist topic. Consequently, knowledge is mostly preserved in academic papers and there are only few introductory tutorials. We aim to fill this gap between the IT security practitioner and the block cipher designer. In this blog series we introduce differential cryptanalysis with a hands-on approach. Our target group are IT security practitioners and programmers without a deep knowledge of math.

The following list shows the topics of all scheduled blog posts. It will be updated with the corresponding links once new posts are being released.

• Part 3: Differential Cryptanalysis of a Multi-Round SPN

# Introduction

Differential cryptanalysis is a type of cryptographic attack on the design of a cipher. It was introduced by Biham and Shamir in the late 80s. However, later it was revealed that differential cryptanalysis was already known to IBM when they designed – the first public standardized algorithm for encrypting data.

Differential cryptanalysis is a chosen plaintext attack, i.e., the attacker can query encryptions of a plaintext and has to recover the key. This is formally modeled by querying a so-called chosen-plaintext oracle. In practice it does not matter how the oracle works exactly, but it somehow has to provide the ciphertext, given a plaintext. This setting is part of the attack scenario. The main idea of differential cryptanalysis is to trace differences of plaintexts through the encryption algorithm. In the ideal case, for a given difference of inputs each difference of outputs has the same probability of occurrence. However, due to mathematical reasons that ideal situation can never be the case. If the deviations from that ideal probability are too large they can be exploited and the key can be recovered.

In this blog post we introduce a toy cipher on which we demonstrate the principles of differential cryptanalysis. We implemented our attack in Python in order to raise the understanding of differential cryptanalysis.

# Our Toy Cipher

In this section we describe the design of our toy cipher which we attack below using differential cryptanalysis. Further, we give a short security discussion.

## Design

The toy cipher analyzed in this post follows the which we have already discussed in the . In some sense this is the simplest cipher which can be proven secure in some formal model.

The block size of our toy cipher is 4 bits. The key consists of 8 bits. This key is split into two halves, k0 and k1 of 4 bits each. Additionally the cipher contains an S-box. The S-box is basically a table lookup that maps a 4 bit input to a 4 bit output.

Encrypting an input block of 4 bit length requires the following steps:

1. Xor the plaintext input with the first key k0.
2. Feed the output of the previous step into the S-box.
3. Xor the output of the previous step with k1.

The output of the last step is the cipher text.

The image below shows the steps of the encryption routine as a circuit. As usual, the data flow is from top to the bottom.

Creating the concrete values for the S-box was done using a dice. This generally leads to an insecure S-box, which is perfect for illustrating differential cryptanalysis. In general, for modern ciphers the values of the S-boxes are chosen very carefully in order to impede attacks such as the differential cryptanalysis we show in this post.

Below is the Python code which implements encryption with our toy cipher.

sbox = [12, 2, 13, 14, 3, 10, 0, 9, 5, 8, 15, 11, 4, 7, 1, 6]

def round_function(input, key):
return sbox[key ^ input]

def encrypt(input, key0, key1):
return round_function(input, key0) ^ key1

## Security Discussion

A naive security analysis shows that it is possible to brute-force the key of the cipher. As the key consists of only 8 bits there are 256 possible keys in total.

This attack can be improved. If we have some plaintext/ciphertext pairs, then it is possible to speed up the encryption to only 16 guesses. If we guess k1, we can compute the value of k0 using the plaintext/ciphertext pair. For this, the given ciphertext can be traced back through the cipher: it is xored with the guessed k1 and the S-box is reversed. The result of this operation xor the given plaintext gives a guess for the key k0. This guess for the combined key (k0, k1) can be validated using an additional plaintext/ciphertext pair. Thus, it is necessary to only test each of the 16 possible 4 bit partial keys k1.

Consequently, for a differential attack to be considered effective, it has to require less than 16 guesses. Otherwise, a brute force attack is more efficient.

# Differential Attack

The main idea of differential cryptanalysis is to trace not single values but differences through each stage of the cipher.

In our case, we define a difference of two plaintexts p and p' as p⊕p', where ⊕ denotes the bitwise xor operation. There are other more exotic definitions of differences possible, which are more suitable for other ciphers. However, in our cipher defining the difference classically as bitwise xor is sufficient for a successful attack.

Notice that encrypting a value p for a fixed key yields some value c of ciphertext. As the encryption algorithm is deterministic, encrypting p again under the same key yields the same c. Consequently, two inputs with a difference of zero yield two outputs with a difference of zero. This behavior is independent of the key.

Let us now take a look at two inputs p and p' with a fixed input difference p⊕p' for a fixed key k. What are the output differences? Encrypting p yields some ciphertext c. Encrypting p' yields some other ciphertext c'. As c and c' should have no relationship, each output difference c⊕c' should have the same probability of occurrence.

Next, we trace the operation of xoring through the cipher in order to check whether for a fixed input difference each output difference has the same probability. When encrypting p, we first xor the key k_0 into the plaintext p. An important observation is, that this xor does not affect the differences at all. If we have p⊕p' as input difference, then after xoring with the key k_0, we get the same output difference as (p⊕k_0)⊕(p'⊕k_0) = p⊕p'⊕k_0⊕k_0 = p⊕p' due to the commutativity of the xor operation. The same holds for xoring with k_1. Consequently the relation of input differences and output differences is independent of the used key. In particular, the operation of the encryption on the differences depends only on the S-box. This action of the encryption on the differences is called the differential characteristic of the S-box. Formally, a differential characteristic is usually defined as an input difference, an output difference, and the conditional probability of occurrence of that output difference, given the input difference.

Next, for each fixed input difference, we iterate over all possible pairs of plaintext with that difference and count the frequency of occurrence of the output differences. As there are 4 bit of input this results in 2^4*2^4 = 256 operations.

Even for more realistic encryption algorithms, this can usually be done in a preprocessing phase. The resulting table is called difference distribution table, as it shows the distribution of differences.

def get_difference_distribution_table():
print("[*] Computing difference distribution table.")
diff_dist_table = [[0 for x in range(16)] for y in range(16)]
for in_diff in range(16):
for input0 in range(16):
input1 = input0 ^ in_diff
out_diff = sbox[input0] ^ sbox[input1]
diff_dist_table[in_diff][out_diff] = diff_dist_table[in_diff][out_diff] + 1
return diff_dist_table

def matrix_pretty_print(matrix):
# see https://stackoverflow.com/questions/13214809/pretty-print-2d-python-list
s = [[str(e) for e in row] for row in matrix]
lens = [max(map(len, col)) for col in zip(*s)]
fmt = '  '.join('{{:{}}}'.format(x) for x in lens)
table = [fmt.format(*row) for row in s]
print('\n'.join(table))

diff_dist_table = get_difference_distribution_table()
matrix_pretty_print(diff_dist_table)

The resulting difference distribution table is shown below. The first 16 means that an input difference of 0 leads to an output difference of 16 for all 16 possible inputs.

The entry in row a and column b means that an input difference of a-1 leads to an output difference of b-1 for that many differences, as we index starting with zero.

As a concrete example, the value of 4 in row 2 and column 4 means that an input difference of 1 leads to an output difference of 3 for 4 of the 16 tested differences.

Remember from above, that for a perfect cipher, each output difference should have the same probability of occurrence for a fixed input difference. If that was the case, all values in the table would be 1 even those in the first row and column. However, as this cannot be the case, as an input difference of 0 always leads to an output difference of 0, a perfect cipher in this sense cannot exist.

0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 4 2 0 0 2 0 4 0 0 0 2 2 0
0 4 0 6 0 2 0 0 0 0 2 0 2 0 0 0
0 0 4 0 0 0 2 2 0 0 4 0 0 0 2 2
0 2 0 0 0 0 0 2 2 0 0 0 0 4 2 4
0 2 2 0 2 0 2 0 0 2 2 0 2 0 2 0
0 0 0 0 4 0 0 0 0 0 0 4 4 0 4 0
0 0 2 2 0 2 0 2 2 2 0 0 0 2 0 2
0 2 2 0 0 2 0 2 0 2 2 0 0 2 0 2
0 2 0 0 4 0 4 2 2 0 0 0 0 0 2 0
0 0 2 2 2 0 2 0 2 2 0 0 2 0 2 0
0 0 0 0 0 4 0 4 0 0 0 4 0 4 0 0
0 0 4 0 0 2 2 0 4 0 0 0 2 0 0 2
0 0 0 0 0 0 4 0 0 0 0 8 0 0 0 4
0 4 0 0 2 2 0 0 0 4 0 0 2 2 0 0
0 0 0 2 0 2 0 0 4 0 6 0 2 0 0 0

There are some especially nasty values in the table. For example an input difference of 13 leads to an output difference of 11 with a probability of 1/2, or in 8 of the 16 possible cases. This is the differential characteristic which we are going to use in the remainder of this blog post.

Note that using this knowledge we can already create a distinguisher for the cipher. This is an algorithm that can distinguish our toy encryption algorithm from an ideal cipher. The distinguisher queries a chosen-plaintext oracle with two plaintexts with a difference of 13. If the output difference is 11, then there is a high probability of dealing with the toy cipher instead of an ideal cipher. Often, designing a distinguisher is a first step in attacking an algorithm. Even though distinguishing attacks are not relevant in practice they can sometimes be extended to allow for key-recovery.

In a next step, we expand our attack beyond a distinguishing attack to achieve key recovery.

# Key Recovery through Differential Cryptanalysis

In this section we expand our attack to recover the whole key.

Recall from the security discussion above, that the length of the key is 8 bits, thus brute-forcing naively needs 2^8=256 encryption operations. However, we can improve that by only brute-forcing the first half of the key k_0 and compute the remaining half k_1 using basic algebra as we know one plaintext/ciphertext pair. Key guesses can then be validated using a second known plaintext/ciphertext pair. Consequently, brute forcing like this needs 2^4=16 encryption operations.

For our attack using differential cryptanalysis to make sense it needs to execute less than 16 encryption operations. The main idea is to use a differential characteristic to narrow down the key space. As differential cryptanalysis is a chosen plaintext attack, we can access an encryption oracle to get a pair of plaintexts and corresponding ciphertexts satisfying a special difference. The remaining key space is then searched for the correct key. In the following, we provide a walk through of the attack.

As we have seen above, the differential characteristic (13,11) holds with a probability of 1/2. This is the characteristic we chose for performing our attack. Still as part of the preprocessing phase, all possible input values to the S-box for which the differential characteristic (13,11) holds are computed. Note that there are 8 of these values, as can be seen in the difference distribution table at the chosen differential characteristic.

Thus, for that differential there are 8 possible intermediate values in the encryption algorithm, i.e., values that are input to the S-box but after the xor operation with the key k_0. And when given an input difference of 13 the corresponding output difference is 11 with probability 1/2. On the other hand, if we would have chosen a differential with low probability of occurrence, then there are only few intermediate values (and thus a small space of possible keys) but the probability of findings pairs where the differential characteristic holds is low.

def gen_possible_intermediate_values(input_diff, output_diff):
good_pairs = []
for input0 in range(16):
input1 = input0 ^ input_diff
if sbox[input0] ^ sbox[input1] == output_diff:
good_pairs.append([input0, input1])
return good_pairs

intermediate_values = gen_possible_intermediate_values(13, 11)
print("[*] Possible intermediate values: " + str(intermediate_values))

Running the code yields the possible intermediate values [0, 13], [2, 15], [4, 9], [6, 11], [9, 4], [11, 6], [13, 0], [15, 2]. Note that there are duplicates due to symmetry. Without the duplicates we have the following pairs of input: [0, 13], [2, 15], [4, 9], [6, 11]. Each of these pairs has an xor difference of 13 (i.e., 0⊕13 = 2⊕15 = ... = 13), and leads to an output difference of 11 when processed with the S-box. Further, there are no more input pairs with this property. Consequently, if there is a pair of inputs p and p' with p⊕p' = 13 and corresponding outputs c and c' with c⊕c' = 11, then the values directly before the S-box are among these 8 values.

As differential cryptanalysis is a chosen plaintext attack, the attacker can query an oracle to generate pairs of plaintext with a fixed difference and get the corresponding ciphertexts. In the code below three pairs of plaintext with a fixed difference of 13 and their corresponding ciphertexts are created. As not all plaintexts with a fixed difference of 13 lead to a pair of ciphertexts with a difference of 11 (only with probability of 1/2), we are asking the oracle for multiple pairs. The number three has been chosen experimentally. Of course, more plaintext pairs increase the chance of a ciphertext pair with the sought difference of 11.

def gen_plain_cipher_pairs(input_diff, num):
# Generate num plaintext, ciphertext pairs with fixed input difference.
# Remember, this is a chosen plaintext attack
# random key which we want to recover
key = (random.randint(0, 15), random.randint(0, 15))
print("[*] Real key: %s %s" % (key[0], key[1]))
pairs = []
for input0 in random.sample(range(16), num):
input1 = input0 ^ input_diff
output0 = encrypt(input0, key[0], key[1])
output1 = encrypt(input1, key[0], key[1])
pairs.append(((input0, input1), (output0, output1)))
return pairs

plain_cipher_pairs = gen_plain_cipher_pairs(13, 3)

Next, the ciphertext pairs are sieved and the good pairs are kept. These are the pairs, where the differential characteristic holds, i.e., the difference of the plaintexts is 13 and the output difference is 11.

def find_good_pair(plain_cipher_pairs, output_diff):
print("[*] Searching for good pairs.")
for ((input0, input1), (output0, output1)) in plain_cipher_pairs:
if output0 ^ output1 == output_diff:
return ((input0, input1), (output0, output1))
raise Exception("No good pair found.")

((good_p0, good_p1), (good_c0, good_c1)) = find_good_pair(plain_cipher_pairs, 11)
print("[*] Found a good pair: " + str(((good_p0, good_p1), (good_c0, good_c1))))

If there are x plaintext/ciphertext pairs with an input difference of 13 then approximately x/2 of these are good pairs, i.e., they have the output difference 11. For such a good pair, the 8 possible intermediate values before and after the S-box are known, as these have been computed previously. As we know the plaintext and the possible inputs to the S-box the possible key k_0 can be computed using xor. Thus, each of these 8 intermediate values results in a guess for the key k_0. Given k_0 and the plaintext/ciphertext pair, k_1 can be computed and we receive the full key.

If a key is guessed, it can be validated using another plaintext/ciphertext pair. Note that a good pair is not necessary for validating a guess for the key. Any pair works.

def validate_key(guessed_k0, guessed_k1):
"""Checks a key against known plaintext/ciphertext pair and returns True if the key is correct."""
for ((input0, input1), (output0, output1)) in plain_cipher_pairs:
if encrypt(input0, guessed_k0, guessed_k1) != output0:
return False
if encrypt(input1, guessed_k0, guessed_k1) != output1:
return False
return True

All that is left to do is to compute the possible keys given the possible intermediate values before the S-box and check the guessed keys. The attacker still has to brute force multiple keys, but there are only 8 possible values instead of 16 values for a full brute-force attack.

def recover_key():
print("[*] Brute-Forcing remaining key space")
for (p0, p1) in intermediate_values:
guessed_k0 = p0 ^ good_p0
guessed_k1 = sbox[p0] ^ good_c0
if validate_key(guessed_k0, guessed_k1):
print("Recovered key --> %s %s" % (guessed_k0, guessed_k1))
else:
print("                  %s %s" % (guessed_k0, guessed_k1))

recover_key()

# Full code

The full code is shown below, and can be downloaded .

# Differential Cryptanalysis Toy Implementation

# Encryption is as follows: xor key0, then substitute, then xor key1
# So we have the simplest type of a sp-network (without the permutation)
# key sizes: key0=4bit, key1=4 bit, so key is 8 bit
# block length is 4 bit
# sbox width is 4 bit

import random

sbox = [12, 2, 13, 14, 3, 10, 0, 9, 5, 8, 15, 11, 4, 7, 1, 6]  # chosen by fair dice roll

# Note: fixed point of sbox[11]=11

def round_function(input, key):
return sbox[key ^ input]

def encrypt(input, key0, key1):
return round_function(input, key0) ^ key1

def get_difference_distribution_table():
print("[*] Computing difference distribution table.")
diff_dist_table = [[0 for x in range(16)] for y in range(16)]
for in_diff in range(16):
for input0 in range(16):
input1 = input0 ^ in_diff
out_diff = sbox[input0] ^ sbox[input1]
diff_dist_table[in_diff][out_diff] = diff_dist_table[in_diff][out_diff] + 1
return diff_dist_table

def matrix_pretty_print(matrix):
# https://stackoverflow.com/questions/13214809/pretty-print-2d-python-list
s = [[str(e) for e in row] for row in matrix]
lens = [max(map(len, col)) for col in zip(*s)]
fmt = '  '.join('{{:{}}}'.format(x) for x in lens)
table = [fmt.format(*row) for row in s]
print('\n'.join(table))

diff_dist_table = get_difference_distribution_table()
matrix_pretty_print(diff_dist_table)

# 16  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
# 0   0  0  4  2  0  0  2  0  4  0  0  0  2  2  0
# 0   4  0  6  0  2  0  0  0  0  2  0  2  0  0  0
# 0   0  4  0  0  0  2  2  0  0  4  0  0  0  2  2
# 0   2  0  0  0  0  0  2  2  0  0  0  0  4  2  4
# 0   2  2  0  2  0  2  0  0  2  2  0  2  0  2  0
# 0   0  0  0  4  0  0  0  0  0  0  4  4  0  4  0
# 0   0  2  2  0  2  0  2  2  2  0  0  0  2  0  2
# 0   2  2  0  0  2  0  2  0  2  2  0  0  2  0  2
# 0   2  0  0  4  0  4  2  2  0  0  0  0  0  2  0
# 0   0  2  2  2  0  2  0  2  2  0  0  2  0  2  0
# 0   0  0  0  0  4  0  4  0  0  0  4  0  4  0  0
# 0   0  4  0  0  2  2  0  4  0  0  0  2  0  0  2
# 0   0  0  0  0  0  4  0  0  0  0  8  0  0  0  4
# 0   4  0  0  2  2  0  0  0  4  0  0  2  2  0  0
# 0   0  0  2  0  2  0  0  4  0  6  0  2  0  0  0

# We see that an input difference of 13 leads to an output difference of 11
# with probability 1/2 (8/16)
# So we already built a distinguisher for the cipher.
print("[*] Choosing differential characteristic 13 -> 11")
# How? Well, we query a chosen-plaintext oracle with two plaintexts with
# difference 13. If the output difference is 11, then we probably deal
# with the cipher, instead of a random oracle.

# Next, we want to recover the key.
# Note that the key length is 8 bits, thus brute-forcing naively needs
# 2^8 steps. However, we brute-force only the first half of the key and
# compute the remaining half using basic algebra. Key guesses can then
# be validated using some known plaintext-ciphertext pair.
# Consequently, brute forcing needs 2^4=16 steps.

# Now, we use differential cryptanalysis and need less then 16
# steps. As differential cryptanalysis is a chosen-plaintext attack, we
# can access an encryption oracle.

# Now, let us compute all possible intermediate values for which the
# differential characteristic 13 -> 11 holds. This can be done in a
# pre-processing phase. Note that there are 8 intermediate values, as
# that is the probability of the differential characteristic. Thus, we
# have many intermediate values, but it is easy to find a
# plaintext-ciphertext pair for which the characteristic holds. On the
# other hand, if the probability of the differential is low, then there
# are only few possible intermediate values, but it is hard to find a
# plaintext-ciphertext pair for which the differential characteristic
# holds.

def gen_possible_intermediate_values(input_diff, output_diff):
good_pairs = []
for input0 in range(16):
input1 = input0 ^ input_diff
if sbox[input0] ^ sbox[input1] == output_diff:
good_pairs.append([input0, input1])
return good_pairs

intermediate_values = gen_possible_intermediate_values(13, 11)
print("[*] Possible intermediate values: " + str(intermediate_values))

def gen_plain_cipher_pairs(input_diff, num):
# Generate num plaintext, ciphertext pairs with fixed input difference.
# Remember, this is a chosen plaintext attack
# random key which we want to recover
key = (random.randint(0, 15), random.randint(0, 15))
print("[*] Real key: %s %s" % (key[0], key[1]))
pairs = []
for input0 in random.sample(range(16), num):
input1 = input0 ^ input_diff
output0 = encrypt(input0, key[0], key[1])
output1 = encrypt(input1, key[0], key[1])
pairs.append(((input0, input1), (output0, output1)))
return pairs

plain_cipher_pairs = gen_plain_cipher_pairs(13, 3)
# We are using three pairs. This should be enough, but of course more is better.

# Next, we want to only take a look at the good plaintext-ciphertext
# pairs. These are those pairs, where the differential characteristic
# holds.

def find_good_pair(plain_cipher_pairs, output_diff):
print("[*] Searching for good pairs.")
for ((input0, input1), (output0, output1)) in plain_cipher_pairs:
if output0 ^ output1 == output_diff:
return ((input0, input1), (output0, output1))
raise Exception("No good pair found.")

# If we have num plaintext-ciphertext pairs with the input difference
# 13, then approximately num/2 of these are good pairs, i.e., they
# have the output difference 11.

((good_p0, good_p1), (good_c0, good_c1)) = find_good_pair(plain_cipher_pairs, 11)

print("[*] Found a good pair: " + str(((good_p0, good_p1), (good_c0, good_c1))))

# For such a good pair, we know the 8 possible intermediate values
# before and after the sbox. Each of these intermediate values gives us
# a guess for the key.

# If we have guessed a key, we can validate it using the other (even
# bad) plaintext-ciphertext pair or some other known
# plaintext-ciphertext pair.

def validate_key(guessed_k0, guessed_k1):
"""Checks a key against known plaintext-ciphertext pair and returns True if the key is correct."""
for ((input0, input1), (output0, output1)) in plain_cipher_pairs:
if encrypt(input0, guessed_k0, guessed_k1) != output0:
return False
if encrypt(input1, guessed_k0, guessed_k1) != output1:
return False
return True

# All that is left is compute the possible keys, given the possible
# intermediate values before the sbox and check the keys. Note that
# we are still bruteforcing, but we are only bruteforcing 8 values,
# instead of 16.
def recover_key():
print("[*] Brute-Forcing remaining key space")
for (p0, p1) in intermediate_values:
guessed_k0 = p0 ^ good_p0
guessed_k1 = sbox[p0] ^ good_c0
if validate_key(guessed_k0, guessed_k1):
print("Recovered key --> %s %s" % (guessed_k0, guessed_k1))
else:
print("                  %s %s" % (guessed_k0, guessed_k1))

recover_key()

~ Dr. Henning Kopp


text:
Math Help - Ratio and Root Test series problem.

1. Ratio and Root Test series problem.

Here it is:

Show that the ratio test is inconclusive but the root test indicates convergence for the series:

(1/2) + 1/(3^2) + 1/(3^4) + 1/(2^5) + . . .

The problem I'm having here isn't necessarily the application of the ratio and root tests. Rather, I'm having trouble recognizing any sort of pattern in this series so I can get started! It should be pretty simple if I can somehow acquire an expression for the "nth" term in the series...

Any and all help is greatly appreciated.

2. Originally Posted by Tulki
Here it is:

Show that the ratio test is inconclusive but the root test indicates convergence for the series:

(1/2) + 1/(3^2) + 1/(3^4) + 1/(2^5) + . . .

The problem I'm having here isn't necessarily the application of the ratio and root tests. Rather, I'm having trouble recognizing any sort of pattern in this series so I can get started! It should be pretty simple if I can somehow acquire an expression for the "nth" term in the series...

Any and all help is greatly appreciated.

As far as I can see there is no recognizable pattern in those terms (it can be several things), so the question is impossible to solve.

Tonio

3. suggestion

Originally Posted by Tulki
Here it is:

Show that the ratio test is inconclusive but the root test indicates convergence for the series:

(1/2) + 1/(3^2) + 1/(3^4) + 1/(2^5) + . . .

The problem I'm having here isn't necessarily the application of the ratio and root tests. Rather, I'm having trouble recognizing any sort of pattern in this series so I can get started! It should be pretty simple if I can somehow acquire an expression for the "nth" term in the series...

Any and all help is greatly appreciated.
can something be done by rearranging the terms???say by grouping the powers of 2 together and those of 3 together then seperately doing something???Like (1/2+/(2^5)+....)+(1/(3^2)+1/(3^4)....).then for the series involving 2 we see that 1/(2^(2n+1)) where n begins from 0 could be a possible pattern. and for the series involving 3 we see that 1/(3^(2n)) could be a possible pattern.

4. Originally Posted by Tulki
Here it is:

Show that the ratio test is inconclusive but the root test indicates convergence for the series:

(1/2) + 1/(3^2) + 1/(3^4) + 1/(2^5) + . . .

The problem I'm having here isn't necessarily the application of the ratio and root tests. Rather, I'm having trouble recognizing any sort of pattern in this series so I can get started! It should be pretty simple if I can somehow acquire an expression for the "nth" term in the series...

Any and all help is greatly appreciated.
$\sum_{n=0}^{\infty} {\frac{1}{2^{4n+1}} + \frac{1}{3^{2n}}}$

5. Originally Posted by lilaziz1
$\sum_{n=0}^{\infty} {\frac{1}{2^{4n+1}} + \frac{1}{3^{2n}}}$
For the term where n=0, this will add an extra term equal to 1, so I'm not sure that works...

6. Originally Posted by Tulki
For the term where n=0, this will add an extra term equal to 1, so I'm not sure that works...
The finite sum does not affect the convergence of the series ..

7. $\sum_{n=0}^{\infty} {\frac{1}{2^{4n+1}} + \frac{1}{3^{2n}}}$

I found that the ratio test was inconclusive quite easily, but now I'm having trouble getting the "nth" term into the form (an)^n in order to apply the root test. I can get each of the individual sum terms into that form, but it doesn't seem as if that helps get me anywhere.

format: plain


text:
# Unstable sampled color in GLSL shader

It looks like that sampling the same exact color data from different areas of a texture atlas results in different vec4 in the GLSL fragment shader.

In other words, texture2D is directly dependent of the specified texture coordinates, and not only transitively because of the color of the texel at those coordinates.

To say that with an example, I am getting the impression that sampling a red pixel surrounded by blue pixels from, say, (0.1, 0.2) may give a different result than sampling the same shade of red surrounded by the same shade of blue at, say, (0.7, 0.3).

Is this non-deterministic behavior that I am observing likely to be real?

I have a atlas that we use to texture multiple screen-aligned quads. Each vertex has a xy position and uv texture coordinates. The allotted rectangles in the atlas do not overlap; furthermore, a 2 pixel margin exists between adjacent rectangles. We are using linear filtering and no mipmapping.

The atlas is populated dynamically using sprites downloaded from the web. Two different runs of the program may have the atlas populated in different orders, even if user input is exactly the same, due to the fact that some HTTP requests may complete before others.

So now imagine that on a run we have a Princess Peach sprite in the middle of the screen; the texture is coming from the upper left corner of the atlas, because Princess Peach was the first sprite added to the scene.

In another run, there have been a few sprites loaded but now their quads are not on the screen and again we have Princess Peach in the middle, in the same exact position as the first run. But this time the texture is coming from a different region of the atlas.

Problem: rendered images are not the same. The differences are imperceptible and usually consist of only a few pixels near the edges of the rendered sprites. The differences are detected by a screenshot testing framework. Where is the source of randomness?

# Even more details

• It's a WebGL project.
• It happens on both GeForce and Quadro cards.
• Using nearest neighbor sampling leads to more stable (and ugly) renderings but it does not fully eliminate the problem.
• Enforcing a strict order when copying the sprites to the atlas fully solves the problem, but it is not an acceptable solution.
• I inspected the GL state using an inspector and I found two frames that should have been the same in two different runs of the program; the state is the same in both cases, the only difference being a different arrangement of sprites in the atlas, and consequently different texture coordinates in the array buffer.
• I know that I could test using some sort of fuzzy/thresholded comparison but first I would like to rule out bugs on my side.
• This sounds exactly like texture compression. What pixel format is used to store the texture atlas that you build, and can you be sure that it isn't compressed with some DXT or other on the way to the screen? – Victor T. Apr 19 '17 at 23:31
• Including a lossless png example of the difference would help. – DMGregory Apr 20 '17 at 3:08
• I suggest you also check your driver control panel for any "optimizations", particularly any performance/quality tradeoffs. – Maximus Minimus Apr 20 '17 at 7:24

Two possibilities I can think of so far:

1. Contamination in transparent regions. You mention the artifacts show up mainly near the edges of the sprites. Depending on how you perform your atlas updates, it could be that when the sprites are placed in the atlas, only the texels with non-zero alpha are being replaced. Texels with zero alpha could, under some update methods, retain the RGB value of whatever was in that part of the atlas previously (eg. a previous sprite, or uninitialized video memory...). This can cause odd fringing at the edges of objects under bilinear texture filtering, as the RGB is tugged away from your sprite's value while the alpha is still ramping down.

2. Rounding/phase differences. Especially if your atlas packing uses a non-power-of-two grid of entries, or you're scaling your sprites as you copy them into the atlas. Factors like these introduce a multiplier into the texture coordinates used to read or write into the atlas, which could lead to a sub-pixel-sized offset that varies from entry to entry in your atlas with a period different than your entry spacing. So moving the same sprite over one slot causes the offset to hit it in a different phase, slightly nudging texel lookups away from where they landed in the original position.

I think we can rule out floating point differences. Most GPUs perform texture filtering using fixed-point arithmetic with 8 binary digits of sub-pixel precision, and 32-bit floating point texture coordinates have even more. Unless you're using a reduced-precision format for the UV coordinates, this shouldn't come into play.

To narrow this down further, it would help to see the methods you use to initialize & populate the atlas, and to produce your textured quads. Image examples of the effect would help too - particularly if you can construct clear-cut cases using eg. grid textures or other regular patterns that will help us isolate which pixels/cases contribute to the issue.

• Thank you for your help. We finally found the issue, I'll post the details soon. – damix911 May 19 '17 at 14:56

Texture coords (like pixel coords) go from the edges of pixels. So, imagine you have a 3x1 texture.

0.0                           1.0
|                             |
V                             V
+---------+---------+---------+
|         |         |         |
|         |         |         |
|         |         |         |
+---------+---------+---------+

So if you're trying to select a specific pixel the correct texture coordinate for that pixel is

 uv = (pixelCoord + 0.5) / size;

Plugging that into the example above the correct texcoords for each of the pixels are

 pixel 0 =  (0 + .5) / 3 = 0.16666
pixel 1 =  (1 + .5) / 3 = 0.5
pixel 2 =  (2 + .5) / 3 = 0.83333

That may or may not have anything to do with the issue you're seeing. I just know sometimes people think it's

 uv = pixelCoord / size

That ends up putting you exactly on the boundary between 2 pixels and so if your filtering is set to NEAREST you'll often get randomly one pixel or the other depending on various rounding issues and if you are using LINEAR you'll get the exact mix between 2 pixels.

For mapping textures to pixels it works because if your source is 3x1 and your dest is 3x1 then the grids overlap perfectly and GL will do what you expect. But as soon as you start trying to pick specific pixels out of the texture then it starts to get more complicated.

Being that it's WebGL it seems like it would be easy to post a simple example. Make a texture using canvas2d. Put a red block and and a blue block in the texture. Make another, put the red and blue blocks in different places that repo your issue. Render with those as your atlas. That would help narrow the issue down.

• Thank you for your help. We finally found the issue, I'll post the details soon. Your post makes a lot of sense, I find it weird that in our case adding 0.5 does not seem to influence the stability of the result. – damix911 May 19 '17 at 14:59

Our current understanding of the situation is:

The sampler will do whatever the heck he wants

The smallest code that can reproduce a similar looking issue is a quad rendering app that does texture mapping this way:

varying highp vec2 v_texcoord;

uniform highp sampler2D u_texture;
uniform highp float u_time;

void main(void) {
highp vec2 err = 10.0 * vec2(cos(u_time), sin(u_time));
highp vec2 iErr = floor(err);
mediump vec4 color = texture2D(u_texture, v_texcoord + iErr);
gl_FragColor = color;
}

The brick texture used in this test is taken from TextureX.com website.

If you use GL_REPEAT texture wrapping, this fragment shader should produce the same output every frame. There are no possible rounding errors issues/excuses. Every frame surely looks the same to the naked eye. But if you take a screenshot and enhance the difference in the RGB channels, you will see that there are a lot of mismatches. Probably imgur.com is doing a recopression of the image and they end up showing as vertical streaks of white blobs, but nevertheless, they are not part of the original texture.

There is also a https://www.shadertoy.com/view/XdfBzM that shows the problem in motion.

## Note for people that need to do screenshot testing

If your app dynamically populates a texture atlas, and the order to which sprites/glyphs/textures/whatever are added to the atlas is somewhat pseudo-random, you may want to provide also a deterministic path to use during testing, or simply accept the fact that results are going to be different every time and find a threshold value that works for you.


text:
# Is this proof that $\lfloor x \rfloor \geq n \left\lfloor \frac{x}{n} \right\rfloor$ correct?

In this text the fractional part of a real $x$ shall be denoted $\{x\}$, such that $x = \lfloor x \rfloor + \{x\}$.

Theorem:

$$\forall x \in \mathbb{R}_{\geq 0} \forall n \in \mathbb{N}_{\geq 1} : \left\lfloor x \right\rfloor \geq n \left\lfloor \frac{x}{n} \right\rfloor$$

Proof:

Let $n$ be a positive integer. Let $x$ be a nonnegative real number.

$$x = n \frac{x}{n} = n \left( \left\lfloor \frac{x}{n} \right\rfloor + \left\{\frac{x}{n}\right\} \right)$$

Keeping in mind that the floor function is increasing:

$$\lfloor x \rfloor = \left\lfloor n \left\lfloor \frac{x}{n} \right\rfloor + n \left\{\frac{x}{n}\right\} \right\rfloor \geq \left\lfloor n \left\lfloor \frac{x}{n} \right\rfloor \right\rfloor = n \left\lfloor \frac{x}{n} \right\rfloor$$

$$\square$$

Having just written it down it seems so clear (and unexpectedly short), but is this proof correct? What could be improved about it?

• Yes, it is correct. – Zarrax Sep 9 '14 at 17:19
• It is ok. Why do you say it is unexpectedly short? – Crostul Sep 9 '14 at 17:34
• @Crostul I suppose it has something to do with the theorem holding true only for integer $n$, a constraint I did not notice earlier. I am very new to this. – Homeward Sep 9 '14 at 17:42

A shorter proof would note that we always have $y \ge \lfloor y \rfloor$, hence ${x \over n} \ge \lfloor {x \over n} \rfloor$. Multiplying by $n$ gives $x \ge n\lfloor {x \over n} \rfloor$. Taking the floor of both sides gives the desired result (noting that the floor of an integer is the integer).


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Article Contents
Article Contents

# On the stability of $\vartheta$-methods for stochastic Volterra integral equations

• * Corresponding author

The work is supported by GNCS-Indam project

• The paper is focused on the analysis of stability properties of a family of numerical methods designed for the numerical solution of stochastic Volterra integral equations. Stability properties are provided with respect to the basic test equation, as well as to the convolution test equation. For each equation, stability properties are intended both in the mean-square and in the asymptotic sense. Stability regions are also provided for a selection of methods. Numerical experiments confirming the theoretical study are also given.

Mathematics Subject Classification: Primary: 65C30.

 Citation:

• Figure 1.  Mean-square stability regions in the ($x, y$)-plane with respect to the basic test equation (2).

Figure 2.  Asymptotic stability regions in the ($x, y$)-plane with respect to the basic test equation (2).

Figure 3.  Mean-square stability regions in the ($x, y$)-plane with respect to the basic test equation (2) for values of $\vartheta\geq 1$.

Figure 4.  Mean-square and asymptotic stability regions in the ($x, y$)-plane with respect to the convolution test equation (3) for the stochastic $\vartheta$-method (5) for several choices of $\vartheta$ and $z$.

Figure 5.  Mean-square and asymptotic stability regions in the ($x, y$)-plane with respect to the convolution test equation (3) for $z = -2$ and several choices of $\vartheta$.

Figure 6.  Mean-square of the numerical solution of problem (2), with $\lambda = -8$ and $\mu = 2\sqrt{2}$, obtained by applying methods (5) (blue), (9) (black), (10) (magenta) and (15) (red) with $\vartheta = 1/2$.

Figure 7.  Absolute value of the numerical solution of problem (2), with $\lambda = -8$ and $\mu = 4$, obtained by applying methods (5) (blue), (9) (black), (10) (magenta) and (15) (red) with $\vartheta = 1/2$.

Figure 8.  Mean-square of the numerical solution of problem (3), with $\lambda = -4$, $\mu = 2\sqrt{5}/5$ and $\sigma = -2/h^2$, obtained by applying methods (5) (blue), (9) (black), (10) (magenta) and (15) (red) with $\vartheta = 1$.

Figure 9.  Absolute value of the numerical solution of problem (3), with $\lambda = -1$, $\mu = \sqrt{6}$ and $\sigma = -2/h^2$, obtained by applying methods (5) (blue), (9) (black), (10) (magenta) and (15) (red) with $\vartheta = 1$.

•  H. Brunner and P. J. van der Houwen, The Numerical Solution of Volterra Equations, CWI Monographs 3. North-Holland, Amsterdam, 1986. A. Bryden  and  D. J. Higham , On the boundedness of asymptotic stability regions for the stochastic theta method, BIT, 43 (2003) , 1-6.  doi: 10.1023/A:1023659813269. E. Buckwar  and  T. Sickenberger , A comparative linear mean-square stability analysis of Maruyama-and Milstein-type methods, Math. Comput. Simul., 81 (2011) , 1110-1127.  doi: 10.1016/j.matcom.2010.09.015. D. Conte , Z. Jackiewicz  and  B. Paternoster , Two-step almost collocation methods for Volterra integral equations, Appl. Math. Comp., 204 (2008) , 839-853.  doi: 10.1016/j.amc.2008.07.026. D. Conte  and  B. Paternoster , Multistep collocation methods for Volterra integral equations, Appl. Numer. Math., 59 (2009) , 1721-1736.  doi: 10.1016/j.apnum.2009.01.001. D. Conte , R. D'Ambrosio  and  B. Paternoster , Two-step diagonally-implicit collocation based methods for Volterra integral equations, Appl. Numer. Math., 62 (2012) , 1312-1324.  doi: 10.1016/j.apnum.2012.06.007. X. Ding , Q. Ma  and  L. Zhang , Convergence and stability of the split-step-method for stochastic differential equations, Comput. Math. Appl., 60 (2010) , 1310-1321.  doi: 10.1016/j.camwa.2010.06.011. D. J. Higham , Mean-square and asymptotic stability of the stochastic theta method, SIAM J. Numer. Anal., 38 (2000) , 753-769.  doi: 10.1137/S003614299834736X. D. J. Higham , A-stability and stochastic mean-square stability, BIT, 40 (2000) , 404-409.  doi: 10.1023/A:1022355410570. D. J. Higham , An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001) , 525-546.  doi: 10.1137/S0036144500378302. P. Hu and C. Huang, The stochastic $\vartheta$-method for nonlinear stochastic Volterra integro-differential equations, Abs. Appl. Anal. , (2014), 583930, 13pp. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin Heidelberg, 1992. Y. Saito  and  T. Mitsui , Stability analysis of numerical schemes for stochastic differential equations, SIAM J. Numer. Anal., 33 (1996) , 2254-2267.  doi: 10.1137/S0036142992228409. C. Shi, Y. Xiao and C. Zhang, The convergence and MS stability of exponential Euler method for semilinear stochastic differential equations, Abs. Appl. Anal., 2012 (2012), Art. ID 350407, 19 pp. Z. Wang , Existence and uniqueness of solutions to stochastic Volterra equations with singular kernels and non-Lipschitz coefficients, Stat. Prob. Lett., 78 (2008) , 1062-1071.  doi: 10.1016/j.spl.2007.10.007. C. H. Wen  and  T. S. Zhang , Rectangular method on stochastic Volterra equations, Int. J. Appl. Math. Stat., 14 (2009) , 12-26. C. H. Wen  and  T. S. Zhang , Improved rectangular method on stochastic Volterra equations, J. Comput. Appl. Math., 235 (2011) , 2492-2501.  doi: 10.1016/j.cam.2010.11.002. X. Zhang , Euler schemes and large deviations for stochastic Volterra equations with singular kernels, J. Diff. Eq., 244 (2008) , 2226-2250.  doi: 10.1016/j.jde.2008.02.019.

Figures(9)


text:
Detail publikace

# A note on the comparison of topologies

KOVÁR, M.

Originální název

A note on the comparison of topologies

Anglický název

A note on the comparison of topologies

Jazyk

en

Originální abstrakt

A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is $RR$-pairwise paracompact its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom $\tau S_2 \sigma$ which is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly regarding the comparison of topologies.

Anglický abstrakt

A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is $RR$-pairwise paracompact its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom $\tau S_2 \sigma$ which is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly regarding the comparison of topologies.

Dokumenty

BibTex

@article{BUT40135,
author="Martin {Kovár}",
title="A note on the comparison of topologies",
annote="A considerable problem of some bitopological covering properties  is the bitopological unstability with
respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is
$RR$-pairwise paracompact its two topologies will collapse and revert to the unitopological case.
We introduce a new bitopological separation axiom $\tau S_2 \sigma$ which is appropriate for the study of the bitopological
collapse. We also show that the property that may cause the collapse is much weaker than some
modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly
regarding the comparison of topologies.",
chapter="40135",
number="4",
volume="26",
year="2001",
month="january",
pages="233",
type="journal article - other"
}


text:
News

# Industry, Academia, and Government Working to Extend Battery Life in EVs

August 05, 2012 by Jeff Shepard

In what could propel electric vehicles (EVs) miles down the road toward commercial viability, GE researchers, in partnership with Ford Motor Company</b< and the University of Michigan, will develop a smart, miniaturized sensing system that has the potential to significantly extend the life of car batteries over conventional battery systems used in electric vehicles today.

"The car battery remains the greatest barrier and most promising opportunity to bringing EVs mainstream." said Aaron Knobloch, principal investigator and mechanical engineer at GE Global Research. "Improvements in the range, cost and life of the battery will all be needed for EVs to be competitive. With better sensors and new battery analytics, we think we can make substantial progress at increasing battery life. This, in turn, could help bring down its overall cost and the cost entitlement of buying an electric car."

To improve the life and reduce the lifecycle cost of EV batteries, GE will combine a novel ultrathin battery sensor system with sophisticated modeling of cell behavior to control and optimize battery management systems. Today’s sensors on EVs and plug-in hybrid vehicles (PHEVs) measure the health of the battery by looking at factors such as its temperature, voltage, and current. However, these measurements provide a limited understanding of a battery’s operation and health. The goal of the ARPA-E project will be to develop small, cost effective sensors with new measurement capabilities. Due to their small size, these sensors will be placed in areas of the battery where existing sensor technologies cannot be currently located. The combination of small size and ability to measure new quantities will enable a much better understanding of battery performance and life.

A group of scientists from the University of Michigan, led by Anna Stefanopoulou, a professor of mechanical engineering, will use the data generated by GE sensors to verify advanced battery models. They will ultimately create schemes that use instantaneous sensor data to predict future battery-cell and battery-pack behavior.

"Ensuring a battery’s health over many cycles requires taking frequent snapshots of its condition as it ages. Control systems on cars have to be able to use this vast amount of data quickly and efficiently. Information provided by advanced sensors will allow us to create and verify finely resolved physical models to underpin battery management schemes," said Charles Monroe, a chemical engineering professor on the University of Michigan team. He added, "The big challenge is to make battery management programs adapt and work fast."

The use of sensors in conjunction with real-time models will enable novel algorithms that optimize how the battery system is managed to extend its life. To demonstrate the capabilities of the sensor system and analytics, Ford will integrate them into one of their vehicles for validation.

Tony Philips, Senior Technical Leader, Vehicle Controls, Research and Engineering, Ford Motor Company, said. "This collaboration brings together a diverse set of experts on sensor technology, controls and modeling, and automotive engineering to innovate on some of the most critical elements of battery technology. Ultimately, through this collaboration we anticipate being able to deliver more cost effective and durable battery system solutions to our customers."

The goal of this 3-year / $3.1 million program is to demonstrate a working sensing system in an actual electric vehicle. The Department of Energy (DOE) announced that a team of engineers at Washington University in St. Louis will receive$2 million to design a battery management system for lithium-ion batteries that will guarantee their longevity, safety and performance.

The project is one of 12 that won funding from the DOE’s Advanced Research Projects Agency-Energy (ARPA-E) under the new AMPED program that focuses on innovations in battery management and storage to advance electric vehicle technologies and to help improve the efficiency and reliability of the electrical grid.

"This initiative is part of a broader effort to strengthen the university’s expertise in energy-related technologies," says Pratim Biswas, PhD, chair of the Department of Energy, Environmental & Chemical Engineering in the School of Engineering & Applied Science. "While this grant targets car batteries," he says, "the technology is also directly applicable to intermittent sources of energy such as solar that produce energy that may need to be buffered rather than plugged directly into electrical grid."

The AMPED award goes to the Modeling, Analysis and Process-control Laboratory for Electrochemical systems (MAPLE) in the Department of Energy, Environmental & Chemical Engineering, led by Venkat Subramanian, PhD, associate professor.

Lithium-ion batteries are what are called secondary cells, because the electrochemical reactions that create a current are reversible and the battery can be recharged. The more familiar primary cells, in contrast are used once and thrown away. The lithium is stored in metallic (uncharged) form inside the particles of a graphic electrode, explained Subramanian. During discharge the lithium comes to the electrode’s surface, where it is ionized, creating a current that travels to the cathode. At the cathode, typically a lithium-based alloy, the ions are neutralized and enter electrode particles as metallic lithium. The battery is recharged by forcing a current to flow in the opposite direction, moving the lithium back into the anode.

Lithium-ion batteries hold great promise for applications such as electric vehicles because they have high energy density (energy stored per unit volume) and lose charge very slowly when not in use. No battery is perfect and lithium-ion batteries, like all batteries, have drawbacks. If the batteries are charged too fast, they can heat up and may explode. To avoid catastrophic failure, manufacturers overdesign the batteries and use only part of their energy capacity per cycle, Subramanian said.

"The goal of the AMPED program is to push the current technology to 100-percent efficiency, while making sure battery lifetime is not compromised," Subramanian said. This would ultimately reduce the weight of the car and improve its energy efficiency.

"If you can predict what will happen inside the battery, you can push the battery to do more per cycle," Subramanian says. "Currently empirical (experience based) models that have no predictive capability are used to manage the batteries. This is why manufacturers over-stack the material; they have no idea what’s happening inside."

There are physics-based models of lithium-ion batteries but they are computationally intensive and can’t be solved in real time by the usual methods. This is where the MAPLE lab comes in. The engineers plan to use a class of simulation techniques called spectral methods aided by mathematical analysis to solve a physics-based model’s differential equations. Spectral methods should allow them to cut down on the model’s computational demands so that it runs faster.

The Battery Management System (BMS), MAPLE lab develop will keep the battery operating optimally, enabling maximum utilization of energy at all times.

More news and information regarding the latest developments in Smart Grid electronics can be found at Darnell’s SmartGridElectronics.Net.


text:
Return is the financial gain or loss on an investment and is typically expressed as the change in dollar value of an investment over time. Return is also referred to as total return and expresses what an investor earned from an investment during a certain period. Total return includes interest, dividends, and capital gain, such as an increase in the share price. In other words, a return is retrospective, or backward-looking.

For example, if an investor bought a stock for $50 and sold it for$60, the return would be $10. If the company paid a dividend of$1 during the time the stock was held, the total return would be $11, including the capital gain and dividend. A positive return is a profit on an investment, and a negative return is a loss on an investment. Yield is the income returned on an investment, such as the interest received from holding a security. The yield is usually expressed as an annual percentage rate based on the investment's cost, current market value, or face value. Yield may be considered known or anticipated depending on the security in question, as certain securities may experience fluctuations in value. Yield is forward-looking. Furthermore, it measures the income, such as interest and dividends, that an investment earns and ignores capital gains. This income is taken in the context of a specific period and is then annualized with the assumption that the interest or dividends will continue to be received at the same rate. A bond yield can have multiple yield options depending on the exact nature of the investment. The coupon is the bond interest rate fixed at issuance, and the coupon rate is the yield paid by a fixed-income security. The coupon rate is the annual coupon payments paid by the issuer relative to the bond's face or par value. The current yield is the bond interest rate as a percentage of the current price of the bond. The yield to maturity is an estimate of what an investor will receive if the bond is held to its maturity date. ### Risk and Yield Risk is an important component of the yield paid on an investment. The higher the risk, the higher the associated yield potential. Some investments are less risky than others. For example, U.S. Treasuries carry less risk than stocks. Since stocks are considered to carry a higher risk than bonds, stocks typically have a higher yield potential to compensate investors for the added risk. ### What is the Difference between Rate of Return and Yield? Rate of return and yield describe the performance of investments over a set period (typically one year), but they have subtle and sometimes important differences. The rate of return is a specific way of expressing the total return on an investment that shows the percentage increase over the initial investment cost. Yield shows how much income has been returned from an investment based on initial cost, but it does not include capital gains in its calculation. Rate of return can be applied to nearly any investment while yield is somewhat more limited because not all investments produce interest or dividends. Mutual funds, stocks, and bonds are three common types of securities that have both rates of return and yields. The formula for rate of return is: $\left[\left(\text{Current price}-\text{Original price}\right)/\text{Original price}\right]\times{100}$ In our earlier example, if a stock is bought for$50 and sold for $60, your return would be$10 for the investment. Adding the dividend of $1 during the time the stock was held, the total return is$11, including the capital gain and dividend. The rate of return is:

$\left(\60\left(\text{current price}\right)+\1\left(\text{dividend}\right)-\50\left(\text{original price}\right)\right)/\50=.22*100=\textbf{22\% rate of return}$

Consider a mutual fund, for example. Its rate of return can be calculated by taking the total interest and dividends paid and combining them with the current share price, then dividing that figure by the initial investment cost. The yield would refer to the interest and dividend income earned on the fund but not the increase - or decrease - in share price.

There are several different types of yield for each bond: coupon ratecurrent yield, and yield to maturity. Yield can also be less precise than the rate of return since it is often forward-looking, whereas the rate of return is backward-looking. Many types of annual yields are based on future assumptions that current income will continue to be earned at the same rate.


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# nLab Cite — fundamental infinity-groupoid in a locally infinity-connected (infinity,1)-topos

### Overview

We recommend the following .bib file entries for citing the current version of the page fundamental infinity-groupoid in a locally infinity-connected (infinity,1)-topos. The first is to be used if one does not have unicode support, which is likely the case if one is using bibtex. The second can be used if one does has unicode support. If there are no non-ascii characters in the page name, then the two entries are the same.

In either case, the hyperref package needs to have been imported in one's tex (or sty) file. There are no other dependencies.

The author field has been chosen so that the reference appears in the 'alpha' citation style. Feel free to adjust this.

### Bib entry — Ascii

@misc{nlab:fundamental_infinity-groupoid_in_a_locally_infinity-connected_(infinity,1)-topos,
author = {{nLab authors}},
title = {fundamental infinity-groupoid in a locally infinity-connected (infinity,1)-topos},
howpublished = {\url{http://ncatlab.org/nlab/show/fundamental%20infinity-groupoid%20in%20a%20locally%20infinity-connected%20%28infinity%2C1%29-topos}},
note = {\href{http://ncatlab.org/nlab/revision/fundamental%20infinity-groupoid%20in%20a%20locally%20infinity-connected%20%28infinity%2C1%29-topos/5}{Revision 5}},
month = jun,
year = 2020
}

### Bib entry — Unicode

@misc{nlab:fundamental_infinity-groupoid_in_a_locally_infinity-connected_(infinity,1)-topos,
author = {{nLab authors}},
title = {fundamental infinity-groupoid in a locally infinity-connected (infinity,1)-topos},
howpublished = {\url{http://ncatlab.org/nlab/show/fundamental%20infinity-groupoid%20in%20a%20locally%20infinity-connected%20%28infinity%2C1%29-topos}},
note = {\href{http://ncatlab.org/nlab/revision/fundamental%20infinity-groupoid%20in%20a%20locally%20infinity-connected%20%28infinity%2C1%29-topos/5}{Revision 5}},
month = jun,
year = 2020
}

### Problems?

Please report any problems with the .bib entries at the nForum.


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# Microstation v8i workspace configuration

microstation v8i workspace configuration # # MicroStation's UI allows the user to select a WorkSpace. cfg’s are the configuration files which let CAD managers customize MicroStation to specific disciplines, projects or tasks (we like control!). In ORD, OBM and OBD CONNECT Edition Products that overall usage is referred to as “The Configuration”. ProjectWise V8i Overview Part 2. The MicroStation V8i workspace levels are outlined below. This is especially useful with the Tasks Pane for getting a larger application workspace. See full list on envisioncad. EXE(In house version) Installs all the VDOT configuration and resource files including a desktop icon to run the VDOT configuration. The New ReadMe. Select a user from the list, then enter the appropriate information in the User Configuration File Name, Project Configuration File Name, and User Interface Namefields. In addition, we can use the _ENGINENAME to provide the 對applicable standard for the product that is uses. pltcfg files that are stored in. Root Menu for MicroStation V8i April 2014 1‐3 General Description The GDOT Root Menu is designed to: Lead users through MicroStation tasks with minimal training. 09). 1 introduced Workspace Profiles Allowed for the usage of MicroStation Workspaces in. In addition, there are three configuration variables that allow you to define the dictionary, language and location of core dictionaries. pcf. - Shows listing of last several files opened by MicroStation. WVDOH, in conjunction with Bentley, has developed a workspace for projects. Using these shortcuts to start MicroStation will start the FDOT Workspace environment properly with the FDOT. Designed for . MicroStation – Custom Tasks . com MicroStation Connect Workspace Overview. V8 2004, V8 XM, V8i Environment: Windows Area: Workspace S. MicroStation V8i The location where MicroStation looks for Project Configuration Files is coded into a configuration file within the application’s directory structure. c:\ ProgramData\Bentley\MicroStation V8i (SELECTseries)\WorkSpace\. plt files are replaced by . From the main MicroStation menu, choose Workspace|Configuration. Step 2: Modify the workspace configuration files: Option 1): . The configuration file for an unknown V8i platform will be created in the CADconform server location under the "Config" directory, for example: C:\ProgramData\Altiva Software\CADconform\Config\CADconform Custom. 31:33. WorkSpace. In the Category list box on the left of the window that pops up, select Task Navigation. Your user configuration (USERCFG) will be editable so that you may customize it. Work the way engineering works, where the job is. CGF, *. MicroStation V8i cannot be used to open DGN document in a managed work area. After the WorkSpace Configuration File has been processed, the WorkSet Configuration File is. pcf: Specifies the workspace project as "Electrical" A workspace, or MicroStation Configuration as it is renamed in MicroStation CONNECT Edition (CE), is designed to provide the flexibility to meet these varying requirements by defining a hierarchy of Configuration Levels at which Configuration Variables can be defined or augmented. Civil Features o. 09. 5. create ucf. pdf - Free download as PDF File (. AcadPan - MDL Application for MicroStation V8i (Apr 2014) Source code included (GNU General Public License) Download old versions for SE/J/2004. cfg" After that, in MicroStation go to Workspace > Configuration Look for MS_GEOCOORDINATE_USERLIBRARIES configuration variable, if it cannot be found you can create a new user library by clicking on the New button and put MS_GEOCOORDINATE_USERLIBRARIES as the Variable name and your system library file location as its New Value . Yes, the option of setting the desired color, style, weight, and level per user's preference (User 1 to User 5) is added for convenient. VDOT’s Work Space  msv8i_update_2015_CON. Some example lines sampled randomly from the file: • PS_APPS = $(MSDIR)Prg/ Each subsequent time MicroStation is started, the Welcome Page is substituted with the MicroStation Start Page, a replacement for MicroStation Manager. The MicroStation workspace will also function with PowerDraft but most of the VicRoads MDLs May 05, 2016 · Basic Microstation configuration files. 9 Mar 2017. In other words, you can have two icons, one to run MicroStation with the. At this point, it is worth noting that the configuration of MicroStation has been altered to offer greater flexibility and simplicity in the manner by which workspaces are managed. in ProjectWise Absorb Microstation configuration files (*. The new . co. work with ALL VERSIONS of MicroStation J, V8, V8i, V8i ss2 and V8i ss3). 916; Power Geopak: V8i Select Series 10 v. The workspace can be placed at any user desired location, however note that the adjusted paths should be configured as shown in section 1. One of the critical tasks is the installation and initial configuration of the MicroStation software. 615, Office 2010 and ProjectWise Interplot Organizer V8i version 08. pdf supplied with Workspace 2. " menu. Many of the MicroStation v8i dockable dialogs use the new ‘Pin & Roll’ functionality. cfg’ required –Stored in each application’s ‘\Configuration\WorkSpaces’folder The –wc argument tells MicroStation to look for a startu p configuration file in the location specified by the drive and path. These standard files were developed for use with MicroStation V8i (SELECTseries 2) version 8. Access to both the updated TDOT workspace and TDOT training materials are listed. MicroStation will ask you to give description for this user configuration. Right-click the shortcut and select Properties. Depending on your CADD system set-up, the configuration files can reside on a local machine or a server. 6 Mar 2019. • System - system level configuration files (Bentley managed) • Site - standards for your organisation Follow the setup procedure below to make the Icon functional. 31 Jan 2019. Configuration File Version 10. MicroStation Configuration Variables in V8. Along the left side, set the “Category” to “All (Alphabetical)”. In a TRIRIGA CAD Integrator/Publisher installation for MicroStation V8i (SELECTseries 2), the MS Version Found registry key contains the value 08. The WorkSpaces > Managed node in ProjectWise Administrator contains all the MicroStation workspace configuration settings blocks defined in the datasource, divided by level. In MicroStation V8i and previous versions, the overall usage of Configuration Files and Configuration Variables were referred to as Workspaces. 23 Jan 2014. 0 or via the above link supersedes it. Show the Value of a Configuration Variable. Jan 31, 2020 · PennDOT currently utilizes MicroStation V8i SS3. The ODOT workspace for MicroStation V8i can be downloaded from the ODOT. workspace. They include the Printer Driver Configuration File…and the Print Styles . Configuration Subarea: Workspaces How to configure MicroStation to. 608 . You can create a workspace profile using a MicroStation V8i or CONNECT Edition. - [Instructor] In this exercise,…we need to dig into some of the…MicroStation configuration settings…that are automating our printing environment. For MicroStation this would be the "\MicroStation\config\appl" folder. 02 Dated 7-24-20. There are two key predefined variables to use: _VERSION_X_XX and _ENGINENAME. Utilize existing V8i Workspace Configurations Ability to remap a MicroStation V8i Workspace to a MicroStation CONNECT Edition Configuration Helps transition existing V8i Workspaces to MicroStation CONNECT Edition Configurations (Workspaces and Worksets) MicroStation in place of the previously used pro_st3d. Select "Design Applications", choose "ACADPAN" and click "Add". Feb 17, 2021 · It contains a TDOT_Standards folder and a TDOT_ Standards. Please contact Engineering Division for information regarding the files for these software configurations and preference files. 26 Sep 2016. Click on Select Printer Driver Configuration file. MicroStation V8i Features/Concepts: o. O'Reilly members experience live online training, plus books, videos, and digital content from . There are some system and database configuration files in C:\Bentley\Program\MicroStation\config\, which are best left alone. MicroStationV8iQuickStartGuide. From user option list, select new… MicroStation will ask you to give description for this user configuration. Power Geopak V8i SS10. 1 May 2012. 85\MicroStation\config. C:\Program Files\Bentley\Workspace\Projects\CADDS_Metric. If you want to get information about all configuration variables in the current workspace, use MicroStation Debug. – System = 0. Join Jeanne Aarhus for an in-depth discussion in this video, Setting up workspace print configurations, part of MicroStation: Plotting in V8i. This session will discuss the differences between, and how to migrate, a V8i WorkSpace and CONNECT Configuration. however your Taskbar may not be setup by default for MS CONNECT. 3. cfg which is the main show • MSCONFIG. If you want to load this application at MicroStation startup, go to "Workspace -> Configuration. T. Scroll down the list of configuration variables until you find “MS_MAINMENUDOCKINGBESIDE”. A workspace is a custom MicroStation environment or configuration. 19 Sep 2019. MicroStation V8 CAD Standards Training Guide (6/14/2004) (PDF, 975 KB) Note: The PDF listed below remains available at this link but is now obsolete with the release of Workspace 2. A workspace is a custom environment that configures MicroStation to a specific user configuration, project configuration, or interface configuration. Organization. Note: Files are updated periodically. Others may download and use at their own risk. MicroStation 101 - The Not Quite One Page Guide to Workspace Configurations by Karen Fugle - 10 March 2004. The TDOT configuration folder should be extracted to the following location and REPLACE the default Bentley configuration folder: C:\\ProgramData\\Bentley\\OpenRoads Designer CE\\. GEOPAK Civil Engineering Suite V8i (SS3) 08. Click OK to apply changes. Type MicroStation tutorial then click OK. There can be multiple WorkSpaces, # each which is represented by a configuration file in the$(_USTN_WORKSPACESROOT) # directory. MicroStation® The Georgia DOT Engineering Support & Service Group is committed to providing the highest quality statewide support for all engineering software. 01. cfg). cfg, which identifies the MicroStation directory – Then includes msconfig. Each of the various areas of the dialog box will be covered generally. At the bottom of this window, there is a tab for each of the data types that InRoads works with. Ensure plan consistency internally and externally. uk MicroStation V8i Guide for Highway Designers September 2015 Page 8 of 90 Version 2. Drawing templates used in MicroStation are called “seed files” and are included in the configuration files. Our custom startup configuration file defines the environment variables specifying the location of the NCDOT J and V8 workspaces. INTRODUCTION TO 3D PRIMITIVES AND BOOLEAN OPERATIONS - Duration: 30:37. Get Bentley MicroStation V8i now with O'Reilly online learning. . 0 1. MicroStation V8i (SELECTseries 3) V8. Microstation is a CAD application for 2D and 3D work, so this is not a normal blog post for me. Below the Organization level there is a new configuration level named Workspace. I needed to adjust certain preferences of the software. View the associated README file before downloading a file package. Whether downloaded from Select Services or installed from a CD‐ROM, the installation process is the same. Setup. ProjectWise V8i Managed Workspace. The workspace is kept up to date by the logon script and a copy of your preferences will be retained in a C:\WORK\MSV8i_USERCFG_Backup folder. -Define a custom location to configure MicroStation. V8i: System. GEOPAK Suite depending on the registry configuration. Microstation. Power InRoads - V8i. Background. Levels o. The 08. The Advanced tab is where you specify the workspace, color op. Required to support the Dynamic View capabilities in MicroStation V8i. These seed files are located on C:\Workspace\Workspace-CDOT_V8i\Standards-Global\MicroStation\Seed. Modify file zCDOT_system. com. designers. variable, which can be done through the Workspace->Configuration Menu. 918 Feb 04, 2012 · MicroStation V8i Essentials Training Volume 1 - Duration: 31:33. The list of Plot Configuration folders. setup of the associated configuration file. Use the same Workspace for V8i versions SS2, SS3 and SS4. Bentley MicroStation V8i SS3 (v8. CONNECT: System. You may see the plot config files available to your active Workspace. The configuration # variable _USTN_WORKSPACELABEL defines the label that the user sees in the UI. -wcC:\CAD Build\MicroStation V8i Config. 06 Jun 2016 By dgnviewer. Ver. Window:. Initialize the Tubero P&ID Parameter Setting dialog box, assign the layer(s) you created to corresponding user (User 1 to User 5), select desired Working Level radio button, dismiss the dialog box once done and start or continue working as usual. The server drive will need to be accessible to all the workstations running MicroStation V8i Edition. O. 09 and 08. MicroStation: V8i Select Series 10 v. Regardless of where the project data will reside, two folders are installed on each workstation: Included with the MicroStation workspace is a desktop icon; COL V8i SS2. Application. xx) and PowerInRoads V8i SS2 (v8. MicroStation. MicroStation V8i SS3 Update Essentials 401 — What’s New in SS3 — Part 1 This course covers the Print Dialog Box and the options and techniques you can use to get the most out of printing views. Development of VicRoads CADD Configuration Notes. • Levels. This page contains files for Power Geopak V8i SS10. 6 Sep 2013. Import MicroStation Configuration Files to ProjectWise Configuration Setting Blocks. MicroStation v8i. • Configuration files are simple text files – Execution starts at mslocal. You can create these manually in ProjectWise, or you can import existing workspace data using the Workspace Import Wizard. 4. WARNING: Be sure to make a copy of your existing MicroStation V8i&n. Automate MicroStation tasks. The new workspace has been tested with the following software versions (recommended versions in bold): Windows 7: • ProjectWise Explorer 08. This page on the Bentley web site list new variables. that automatically opens. Instead create a new configuration file that can be copied to a MicroStation config directory and used as the program launches. A configuration settings block is essentially a MicroStation configuration file and its corresponding values. 722 . 09 (V8i SS3) • Power Inroads 08. In many cases it is required to set MicroStation to use a custom Workspace, which could be or not be shared on the network, rather than using the one delivered by Bentley. Here are some quick methods to point MicroStation or PowerDraft to such workspaces: Configuring Managed Workspaces for. Change the value of variable, _CDOT-WORKSPACE, to match the path of your CDOT workspace. This workspace is continually updated so it is recommended that you check for revised files here often. Site. 9 Dec 2020. Included with the MicroStation workspace is a desktop icon;. Choose Workspace > Preferences. 1 The Workspace PackageThe Workspace Packageee The fully packaged workspace can be downloaded from the INDOT CAD Website . These V8i resource files are available at (Vermont Agency of Transportation V8 CADD Project Configuration & Resource Files) All Drawing file submitted to the VAOT must be V8i compatible. You should see the. Microstation V8i and InRoads SS2 Information The WVDOH is in the process of phasing out the use of Microstation V8i and InRoads SS2 software. Two seed files are available for the preparation of bridge drawings. Jun 01, 2000 · Bentley changed the rules with MicroStation/J. 05 May 2016 By dgnviewer. CFG – Completely reorganized, in-line documentation explains what it does – Don’t change it! CONFIGURATION SET-UP FOR MICROSTATION V8 This document describes how to configure MicroStation to implement CADDS Microstation V8 Specifications in CAD user’s environment. Our MaineDOT MicroStation/InRoads V8i SELECT Series 2 workspace can be downloaded by our consultant community via the links below. dgn. Optional: Close the . 111. 459 – Update 2. txt) or read online for free. pdf), Text File (. MaineDOT’s MicroStation/InRoads V8i SS2 Configuration Overview Our users have the flexibility to create project data that either resides locally on their workstation, or remotely on a network file server. If you already open it, close your file. . 2020. We have defined a user configuration for . o Configuring OHDOT Workspace for CONNECT o What to. Ensure that Department CAD Standards are followed. This means that the same ProjectWise Application for MicroStation could be used to initiate the application with the Bentley delivered workspace, the Tri-Service TS_WS_001 Workspace, or any other custom workspace. #1036: How to display V8i style TopoDOT tools in MicroStation. What are cfg’s? Nothing to do with chlorofluorocarbons and a lot more user friendly, . 3. Changing the MicroStation Layout to the XM version. 2 Creating a User Interface & Configuration Files 1. Disclaimer:. EXE(consultant version) or msv8i_update_2015. 07 (V8i SS2) • Power Inroads 08. Information in this document is based on software versions: MicroStation V8i (SELECT Series 2) version 08. 0. Check this page often to make sure you have the latest version. If you load this workspace to your system, you can have the same work environment that PennDOT's CADD operators use. Unable to remap mouse buttons · Use the same Workspace for V8i. This will help you to decide the level at which you want to start control of the workspace. 1. A workspace consists of a project configuration file, a user interface and a. This workspace will provide customization for the latest of the Bentley MicroStation and Geopak products. ucf" Specifies the workspace user as "Global Conform" wp: wp<WORKSPACE PROJECT>-wpElectrical. SS4. How to configure MicroStation to use a different Workspace than the delivered one. Alternate NCDOT V8 Consultant Workspace Setup. cfg file which contain the workspace setup. Main Toolbox. 443, Geopak V8i (SELECT Series 2) version 08. Repeat this step to configure workspace settings for additional users. The following information covers the content of MicroStation’s configuration files, and the order in which they are processed. The newest Workspace environment is due to be released in August of 2011. The ODOT standards, in the V8i workspace Standards folder, will be read-only to maintain the standards. You will see MicroStation Manager. This is a compressed file and contains the resource files for the VTrans CADD environments. cfg that was located in the config folder. I work for a school that requires all users that start Microstation up for the first time to have the same. dgn and Bridge-2D-Seed_CDOT. I will focus on configuring the files on a local machine. This video focuses on changes to MicroStation Configurations between MicroStation V8i and the MicroStation CONNECT Edition. 07 values are the only values that the CiMsStart application supports. Offline workspace and just double-click on DGN files to launch MicroStation V8i. Project. They are named Bridge-3D-Seed_CDOT. To change where MicroStation looks for PCF files, change the location in the appropriate configuration file using either a simple text editor such as Notepad, or the configuration file editor. Page 33- Express Modeler ProjectWise administrator must verify that the configuration variables are being loaded into MicroStation properly through the use of ProjectWise Managed Workspace and Configuration Settings Blocks (CSB). This opens the Configuration dialog box. 1,2,3,4,etc. In MicroStation V8i, these . 08. Now let’s create a new project. From the Presentation option menu, choose Toolbox as shown in the figure below. cfg – generated at install time – includes msdir. Oct 19, 2009 · Let’s create a new workspace that you will use for this tutorial until the end. See full list on la-solutions. 11. 11. …Continue using the chapter four file print configurations,…and using View groups, select the…Workspace Configurations model. cfg V8i SS1, SS1R and SS2 Addendum 3 Page 18-The Workspace Bar The Workspace Bar, also sometimes referred to as the InRoads Explorer Window, is your portal into which files are currently open and loaded into the InRoads software. GEOPAK Civil Engineering Suite V8i (SS2) 08. C:\ Program Files (x86)\Bentley\08. Learning is Here 14,710 views. A WorkSpace consisted of 5 levels of configuration including System, Application, Site, Project and User, with User and Project being selectable by the operator of the software. xx), are the official WSDOT drafting and design applications and versions. Configuration Assistant •Allows you to move V8i Workspaces to CONNECT Edition •Improvement over the Configuration Migration Wizard –Allows for multiple Users and Projects –Select individual users or projects as needed Download the V8-CADD Project Configuration. Understanding print configuration files: MicroStation: Plotting in V8i. …Using Windows Explorer, we need to navigate…to the folder. In many cases it is required to set MicroStation to use a custom Workspace, which could. 09 (V8i SS4) Windows 10: Oct 19, 2009 · Open your MicroStation. We have defined a user configuration for this tutorial. The WVDOH is in the process of phasing out the use of Microstation V8i and InRoads SS2 software. See your system administrator for your site specific MicroStation installation setup. 28 Jul 2014. Jun 06, 2016 · MicroStation Installation. MicroStation V8i SS2 Level I – ETRN# U8031A - A four day course for the student who has knowledge of the Microsoft Windows operating system and needs to learn the basic concepts of MicroStation V8i. within the ProjectWise Managed Workspace configuration detailed in this document. The following procedure has been tested in MicroStation v8i SS3 (08. Open your MicroStation. MicroStation/InRoads v8i SELECT Series 2 Downloads. This zip file contains a new MicroStation Workspace configured with two . These configuration variables apply to both Print Organizer and the Print dialog. cfgin folder <Unzip to folder>\Workspace-CDOT_V8i\in a text editor. Workspace has helped CAD managers, and users, be more productive, by providing a controlled environment for maintaining corporate standards, project standards, and also assist in implementing CAD. cfg: Defines a configuration file to read on startup: wa: wa<MDL APPLICATION>-waCADconform: Defines an MDL application to run on startup: wu: wu<WORKSPACE USER> "-wuGlobal Conform. These files should not be touched or edited. If you prefer to only use parts of the workspace, look under the V8i Workspace > Projects > English folder for such things as: symbology, fonts, cells, and seed files. 8 Oct 2012. In addition with being compatible with Version 8i MicroStation and Geopak, this new environment will also implement a new direction for MDOT in workspace configuration. 2. If you want to show the value of a single configuration variable, use keyin … The Workspace Preferences dialog contains a section with options and toggles specific to the Spell Checker. On the MicroStationUser Settingstab, you can customize workspace parameters for specific users: From the User Groupslist, filter the list of users by selecting All Users, Administrator, or Restricted Administrator. Introducing the Managed Workspace ProjectWise 8. 443 and other software by T. Select your Division, Districts or PDF requirement. These two variables will allow our configuration\ഠto set up separate frameworks for MicroStation V8i and MicroStation CE. Jul 01, 2011 · Recently I had to work with Bentley Microstation V8i from a network admin aspect. This document describes how to configure MicroStation to implement CADDS. A Workspace is a collection of projects, standards, and other . See Figure 3 When the properties box opens, append the following the text to the Target field (note that it begins with a space): See Figure 4 "C:\Program Files\Bentley\MicroStation V8i (SELECTseries Combined WorkSpace for MicroStation and ORD •The following structure used as an example –‘A_Combined_Workspace’ is the WorkSpace name –‘Project 123’ is the WorkSet being used •‘A_Combined_Workspace. Level Changes in the CONNECT Configuration. Contents of configuration file "C:\Program Files (x86)\Bentley\MicroStation V8i (SELECTseries)\MicroStation\config\appl\TopoDOT. MicroStation CONNECT incorporates a new WorkSpace structure called a Configuration. How to configure MicroStation to use a different Workspace than the. VicRoads provides all of their available MicroStation and InRoads configuration files to external contractors 'free of charge'. MicroStation V8 CAD Workspace Installation Guide (3/30/2018) (PDF, 314 KB) More detailed information on the configuration levels and variables can be found in the appendix. Bentley Systems continue to add new configuration variables to Microstation. For a default installation, you will find the project configuration files in C:\Bentley\Workspace\projects\ and user configuration files in C:\Bentley\Workspace\projects\. Converting V8i Workspaces Configuration Migration Wizard Select File>Settings>Configuration>About Configuration and you can verify that the entire ProjectWise Managed Configuration is running from your C: drive. D. Pin & Roll functions . Sep 02, 2015 · MicroStation V8i (SS3) 08. In most cases this means changing C:/Worksapce/Workspace-CDOT_V8i/ to <Unzip to folder>/ Workspace-CDOT_V8i/. Right-click  . 420 on the Windows 7 operating system. This new configuration file allows for variables to be used and handles the Microstation variables such as workspaces and seed files better than the standard cfg did. About Workspace, and use the location shown there for User Configuration. Proper utilization of configuration files gives you the flexibility of creating. Locate the heading MicroStation V8i SS3 Printing Essentials Library. 07 (V8i SS1) • MicroStation 08. This course is designed to teach the essential basic concepts of the MicroStation program interface, 2D File creation, employing the use of basic. User. Extract these files in your site's CADD Workspace directory. Centrally managing the workspace configuration within ProjectWise V8i provides for a consistent quality work environment for all users on the project, reducing errors and allowing the user to work in a disconnected mode from the central server. Geolabel C# Addin for MicroStation V8i/Bentley Map V8i. 615* * Note that the version of MicroStation SS3 listed above is fully backward compatible with Civil Suite SS2 WorkSpaces and WorkSets Bentley has long provided WorkSpaces to help configure MicroStation to meet the needs of your organization. 07. We will be using MicroStation V8i to open and use all drawings submitted during the design process and post design process. About Workspace - Information about your current Workspace configuration. All deliverables to WSDOT shall be in the official version and produced using current CAE resources unless otherwise stated in a specific WSDOT-Consultant agreement. Bentley configuration folder: C:\\ProgramData\\Bentley\\OpenRoads Designer CE\\. ink. Configuration\Workspaces\Road\Worksets\HQ16-0001. COL V8i SS2. 11 (V8i SS4) • MicroStation 08. To check the spelling in the active model, use the Spell checker from the Text task. For a first time MicroStationV8i user the out of the box _ Manager Interface will appear, the CTDOT user must first create a User Interface and secondly a User Configuration File, see Figure 2. microstation v8i workspace configuration


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# matlab matrix declaration

I am struggling with declaring some more complex matrices in matlab, perhaps you could help me out, I have an array of $T$ values / lets call it $y = [y_0, \hdots, y_T]$ (its a digital signal representing a sound).

I am using formula:

$$y_t= a_0 + \sum_{i=1}^p (a_i y_{t-i} + \epsilon_t), t \geq p,$$

in order to create a synthetic signal based on the one give using only previous $p$ values of $y_t$, where $p$ is significantly smaller than y. What I have to do, is find those $a_0, \vdots, a_p$ parametres in order to use LSE method.

Now here is what I need you guys to help me with: How do I create a matrix that looks like this:

$$M = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & \hdots & 0 \\ 1 & y_0 & 0 & 0 & 0 & \hdots & 0 \\ 1 & y_1 & y_0 & 0 & 0 & \hdots & 0 \\ 1 & y_2 & y_1 & y_0 & 0 & \hdots & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ 1 & y_{T-1} & y_{T-2} & \hdots & \hdots & \hdots & y_{T-p} \\ \end{bmatrix} \in R^{T+1xp+1}$$

Thanks for any help

edit: how to format LaTeX here?

-
you may want to consider this ( meta.stackoverflow.com/questions/76902/… ) for handling formulas.. too difficult to read otherwise, sorry. –  Acorbe Oct 17 '12 at 10:33

You seem to need a matrix that represents a sort of convolution. In Matlab the toeplitz function is relevant here.

See the following example

>> y=[1 2 3 4 5 6 7];
>> toeplitz(y,[y(1) zeros(1,length(y)-1)])

ans =

1     0     0     0     0     0     0
2     1     0     0     0     0     0
3     2     1     0     0     0     0
4     3     2     1     0     0     0
5     4     3     2     1     0     0
6     5     4     3     2     1     0
7     6     5     4     3     2     1

So your code should look like the follwing

 M = [ones(length(y),1)  toeplitz(y,[y(1) zeros(1,length(y)-1)]) ];
M = M(:,1:p+1);

-
M = zeros(length(y) + 1);


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# Inverse spectral results on even dimensional tori

Gordon, C; Guerini, P; Kappeler, T; Webb, D (2008). Inverse spectral results on even dimensional tori. Annales de l'institut Fourier, 58(7):2445-2501.

## Abstract

Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum determines the even part of the potential. In dimension two, we also obtain information about the odd part of the potential. We obtain counterexamples showing that the genericity condition is needed even in the case of two-dimensional tori. Examples also show that the spectrum of the Laplacian defined by a connection on a line bundle over a flat torus determines neither the isometry class of the torus nor the Chern class of the line bundle.

In arbitrary dimensions, we show that the collection of all the spectra Spec(Q;L,∇), as ∇ ranges over the translation invariant connections, uniquely determines the potential. This collection of spectra is a natural generalization to line bundles of the classical Bloch spectrum of the torus.

## Abstract

Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum determines the even part of the potential. In dimension two, we also obtain information about the odd part of the potential. We obtain counterexamples showing that the genericity condition is needed even in the case of two-dimensional tori. Examples also show that the spectrum of the Laplacian defined by a connection on a line bundle over a flat torus determines neither the isometry class of the torus nor the Chern class of the line bundle.

In arbitrary dimensions, we show that the collection of all the spectra Spec(Q;L,∇), as ∇ ranges over the translation invariant connections, uniquely determines the potential. This collection of spectra is a natural generalization to line bundles of the classical Bloch spectrum of the torus.

## Statistics

### Citations

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