text:
# Isomorphism notion between sets of triples

Graph Isomorphism is natural problem which is most widely believed to have intermediate complexity between $P$ and $NP$-complete. GI can be thought as deciding the existence of an isomorphism between two sets of node pairs. I'm trying to develop a notion of isomorphism between sets of triples.

We are given two hyper-graphs $G1$ and $G2$ such that the set of hyperedges ($E_1$ and $E_2$) consists of triples of 3 nodes $\{t_1, t_2, t_3 \}$. We say that Hyper-graphs $G1$ and $G2$ are isomorphic if there is bijection $f$ from $V_1$ to $V_2$ such that pair $\{u,v\} \in E1$ if and only if $\{f(u),f(v) \} \in E2$. We say $\{u, v \} \in E$ if there is a triple (hyperedge) $\{ u, v, z\} \in E$ for some node $z$.

Is it $NP$-complete to decide the existence of such isomorphism between two hyper-graphs $G1$ and $G2$?

Your problem reduces to graph isomorphism, so is not $\mathsf{NP}$-complete unless the polynomial hierarchy collapses.

In fact, you've essentially already given the reduction in your question: given a 3-uniform (=every hyperedge has size 3) hypergraph $G$, construct from it the graph $f(G)$ which has the same vertex set, and such that $\{u,v\} \in E(f(G))$ iff there exists a $z \in V$ such that $\{u,v,z\} \in E(G)$. (When $G$ is a hypergraph, I use $E(G)$ to mean the set of hyperedges.) Then $G_1$ and $G_2$ are isomorphic-in-your-sense iff $f(G_1) \cong f(G_2)$ as graphs. It is not hard to check that this reduction only takes polynomial time (note that $|E(f(G))| \leq |V(G)| |E(G)|$).

It is also probably worth mentioning that there is already a well-established notion of hypergraph isomorphism that is different from your notion. If we consider a hypergraph $G$ as a vertex set $V$ together with a collection of hyperedges $E \subseteq P(V)$ (each hyperedge is a subset of $V$), then two such hypergraphs are isomorphic if there is a bijection $\pi\colon V_1 \to V_2$ such that $E_2 = \pi(E_1)$. (Here I am abusing notation twice: by "$\pi(E_1)$" I mean $\{\pi(e) : e \in E_1\}$ and by $\pi(e)$ for $e \subseteq V$ I mean $\{\pi(v) : v \in e\}$.) Hypergraph isomorphism in this sense is Karp-equivalent to graph isomorphism, but by a slightly less immediate reduction than from your problem. However, fast (in theory) algorithms for hypergraph isomorphism are often more difficult than those for graph isomorphism (see, e.g. Babai and Codenotti, FOCS 2008).

• So, in my notion triple $\{ 1,2,3\}$ is mapped to triple$\{1,2,6\}$ but in standard isomorphism triple $\{ 1,2,3\}$ is mapped to triple$\{1,2,3\}$. You are saying those lead to equivalent notions. Am I missing something? – Mohammad Al-Turkistany Jun 26 '13 at 21:53
• Pair $\{u,v\} \in E1$ if and only if $\{f(u),f(v) \} \in E2$ is equivalent to saying that triple with pair $\{u,v\} \in E1$ if and only if triple with pair $\{f(u),f(v) \} \in E2$. This is because pairs only occur inside triples (hyperedges). – Mohammad Al-Turkistany Jun 26 '13 at 22:20
• I didn't quite follow your first comment, but the standard notion of iso (as in the 3rd paragraph of my answer) is definitely not the same as your notion. Consider G1 on 6 vertices consisting of the hyperedges {1,2,4}, {2,3,5}, {1,3,6} and G2 on 6 vertices to consist of the hyperedges in G1 in addition to the hyperedge {1,2,3}. In your notion, these two are "isomorphic" but they are definitely not isomorphic in the usual sense, for they have a different number of hyperedges. – Joshua Grochow Jun 27 '13 at 2:49
• Here's a more complicated example where they have the same number of hyperedges, are isomorphic in your sense, but not in the usual sense. For brevity I omit commas in triples. Verts are labelled a,b,c,...,j. Let S = {abc, bde, cef, egh, fhi, hij} be a set of triples. Then H1 = S union {bec} and H2 = S union {efh}. – Joshua Grochow Jun 27 '13 at 3:00
• The point is that your notion is essentially considering the 1-skeleton of a 2-dimensional simplicial complex, but forgets which triangles are 2-simplices or are "unfilled" triangles. The usual notion of hypergraph iso coincides with the notion of iso for simplicial complexes. – Joshua Grochow Jun 27 '13 at 3:00


text:
# $\lim _{x\to 0}\left(\frac{\tan\left(x\right)-x}{x-\sin\left(x\right)}\right)$ without L'Hopital's Rule

Here are the functions:

a) $\displaystyle\lim _{x\to 0}\left(\frac{\tan\left(x\right)-x}{x-\sin\left(x\right)}\right)$

If I used L'Hopital's rule the limit is $2$

b) $\displaystyle\lim _{x\to 0}\:\frac{e^x\cdot \:\sin\left(x\right)-x\cdot \left(1+x\right)}{x^3}$

here $\dfrac{1}{3}$

c) $\displaystyle\lim _{x\to 0}\left(\frac{\ln\left(\sin\left(3 x\right)\right)}{\ln\left(\sin\left(7x\right)\right)}\right)$

and here $1$

but the problem is that I am not allowed to use L'Hopital's rule, can you give me ideas for another type of approaches?

UPDATE:

I apologize, I see there is some discussion and confusion among people, which obviously goes beyond my functions, but still I wanted to explain that I have been missing a lots of lectures recently due to illness and last week I got $0$ points for using L'hopital because we have not learnt it, so my guess was that we are not allowed this time either, but I just talked to my tutor and he told me that just in the last lecture, they introduced L'hopital rule to us so I am free to use it. I'm very sorry.

• Hint: Use the identity $\lim\limits_{x\to 0}\frac{\sin x}{x}=1$. This will work for the first one, and I'd bet the others as well. – The Count Jan 31 '17 at 18:15
• @TheCount Are you sure only that works for the first one? Because I get an indetermined form when using that... – DonAntonio Jan 31 '17 at 18:23
• @TheCount: How exactly are you using that in the first case? – Henning Makholm Jan 31 '17 at 18:23
• @DonAntonio Well, it sure looks like one that it would work on. I'll write it out to check. – The Count Jan 31 '17 at 18:25
• @HenningMakholm see above (and soon below) – The Count Jan 31 '17 at 18:25

a) use the fact that $\tan{x}=x+x^3/3+o(x^3)$ and $\sin{x}=x-x^3/6+o(x^3)$ to get

$${\tan{x}-x\over x-\sin{x}}={{x^3\over 3}+o(x^3)\over {x^3\over 6}+o(x^3)}=2+o(1)$$

So the limit is $2$

b) for this one we need $e^x=1+x+x^2/2+o(x^2)$ to write

$${e^x\cdot\sin{x}-x(1+x)\over x^3}={x+x^2+{x^3\over 3}-x-x^2+o(x^3)\over x^3}={1\over 3}+o(1)$$

So the limit is $1/3$

c) the last one is even simpler

$${\ln{\sin{7x}}\over \ln{\sin{3x}}}={\ln{7x}+\ln{\sin{7x}\over 7x}\over \ln{3x}+\ln{\sin{3x}\over 3x}}$$

Now keeping in mind $\sin{x}/x\to 1$ the limit is equal to

$$\lim_{x\to 0}{\ln{7}+\ln{x}\over \ln{3}+\ln{x}}=\lim_{x\to 0}{{\ln{7}\over \ln{x}}+1\over {\ln{3}\over \ln{x}}+1}=1$$

• Always a topic of discussion: If L'Hospital rule is not allowed (because it involves derivatives), are Taylor expansions then allowed? – imranfat Jan 31 '17 at 18:27
• Good point by imranfat. Of course this could be allowed, as a means to force students to use Taylor developments, yet without any explantion it'd be absurd, at least imo, to allow Taylor but forbidding l'Hospital. – DonAntonio Jan 31 '17 at 18:28
• Especially since what you actually do when finding and using the Taylor expansions is exactly the same as using L'Hospital repeatedly until you reach nonzero coefficients -- just with some identical factorials above and below, and with some boilerplate arguments about why the procedure works added in. – Henning Makholm Jan 31 '17 at 18:36
• I'll quote myself: Taylor expansions and L'Hospital rule are essentially equivalent, even if not necessarily in practice. I think no-L'Hospital (and no-Taylor) exercises are a good tool to develop creativity and reasoning skills of students. – Vincenzo Oliva Jan 31 '17 at 18:37
• I dont think there's a l'Hospital vs Taylor expansions discussion here. To each its own. It is the logic behind the use of Taylor expansions to evaluate limits when l'Hospital is forbidden that we're debating (or sort of...). I commented above one possible reason, but in this case that seems to be exaggerated. – DonAntonio Jan 31 '17 at 18:49

format: plain


text:
Localization is an essential task for augmented reality, robotics, and self-driving car applications. It’s crucial for a system to know the exact pose (location and orientation) of the agent to do visualization, navigation, prediction, and planning.

Baidu released its massive self-driving Apolloscape dataset in March and now has a couple of ongoing challenges for ECCV 2018 Workshop: Vision-based Navigation for Autonomous Driving conference:

• Task 1: Vision-based fine-grained lane markings segmentation
• Task 2: Self-localization on the fly
• Task 3: 3D car instance understanding

I pick the self-localization problem and create the whole pipeline to localize a car which is based only on camera images.

This article covers the very beginning of the journey and includes the reading and visualization of the Apolloscape dataset for localization task. Implement PoseNet [2] architecture for monocular image pose prediction and visualize results. I use Python and Pytorch for the task.

NOTE: If you want to jump straight to the code here is the GitHub repo. It’s is still an ongoing work where I intend to implement Vidloc [7], Pose Graph Optimization [3,8] and Structure from Motion [9] pipelines for Apolloscape Dataset in the context of the localization task.

NOTE 2 (update Mar 12, 2019): Today I’m releasing the second part of my journey with Structure from Motion (SfM) pipeline and OpenGL visualization for Apolloscape ZPark Sample implemented on C++.

## Apolloscape Dataset

Apolloscape dataset emerged from the Baidu effort in 2017 to collect enough data with the modern sensors that can be used for self-driving car research. Dataset provides camera images, poses, dense LIDAR point clouds, 3d semantic maps, 3d lane markings, 2d segmentation labels. Eventually, they plan to reach 200K images, captured on 20km roads covering 5 sites from 3 cities. Initial dataset was released in March 2018 and continuously updated for the ongoing ECCV challenges.

For the challenge purpose, Apolloscape provides separate archives for the self-localization task. You can download the small (4Gb) self-localization-examples ZPark from Self-Localization Dataset page.

I use ZPark sample dataset for almost everything in this article from visualization to PoseNet training.

## Apolloscape Pytorch Dataset

For Pytorch I need to have a Dataset object that prepares and feeds the data to the loader and then to the model. I want to have a robust dataset class that can:

• support stereo and mono images
• support train/validation splits that came along with data or generate a new one
• support pose normalization
• support different pose representations (needed mainly for visualization and experiments with loss functions)
• support filtering by record id
• support general Apolloscape folder structure layout

I am not putting here the full listing of the Apolloscape dataset and concentrate solely on how to use it and what data we can get from it. For the full source code, please refer to the Github file datasets/apolloscape.py.

Here how to create a dataset:

from datasets.apolloscape import Apolloscape
from torchvision import transforms

# Path to unpacked data folders
APOLLO_PATH = "./data/apolloscape"

# Resize transform that is applied on every image read
transform = transforms.Compose([transforms.Resize(250)])

transform=transform, train=True, pose_format='quat',
stereo=True)
print(apollo_dataset)

Output:

Dataset: Apolloscape
Record: None
Train: None
Normalize Poses: False
Stereo: True
Length: 1499 of 1499
Cameras: ['Camera_2', 'Camera_1']
Records: ['Record001', 'Record002', 'Record003', 'Record004', 'Record006', 'Record007', 'Record008', 'Record009', 'Record010', 'Record011', 'Record012', 'Record013', 'Record014']

APOLLO_PATH is a folder with unpacked Apolloscape datasets, e.g. $APOLLO_PATH/road02_seg or $APOLLO_PATH/zpark. Download data from Apolloscape page and unpack iot. Let’s assume that we’ve also created a symlink ./data/apolloscape that points to \$APOLLO_PATH folder.

We can view the list of available records with a number of data samples in each:

# Show records with numbers of data points
recs_num = apollo_dataset.get_records_counts()
recs_num = sorted(recs_num.items(), key=lambda kv: kv[1], reverse=True)
print("Records:")
print("\n".join(["\t{} - {}".format(r[0], r[1]) for r in recs_num ]))

Output:

Records:
Record008 - 122
Record007 - 121
Record006 - 121
Record012 - 121
Record001 - 121
Record009 - 121
Record010 - 121
Record003 - 121
Record013 - 120
Record004 - 120
Record002 - 120
Record011 - 120
Record014 - 50

We can draw a route for one record with a sampled camera image:

from utils.common import draw_record

# Draw path of a record with a sampled datapoint
record = 'Record008'
draw_record(apollo_dataset, record)
plt.show()

Output:

Record008 path and sampled stereo images pair (top). Blue - record path. Red - image pair location. Green - path projection on z-plane.

Alternatively, we can see all records at once in one chart:

# Draw all records for current dataset
draw_record(apollo_dataset)
plt.show()

Output:

All records from the dataset on one chart. Path projection connects the end of one record and the beginning of the next record.

Another option is to see it in a video:

from utils.common import make_video

# Generate and save video for the record
make_video(apollo_dataset, outfile=outfile)

Output (cut gif version of the generated video):

Generated video sample for Record008

For the PoseNet training we will use mono images with zero-mean normalized poses and camera images center-cropped to 250px:

# Resize and CenterCrop
transform = transforms.Compose([
transforms.Resize(260),
transforms.CenterCrop(250)
])

# Create train dataset with mono images, normalized poses, enabled cache_transform
transform=transform, train=True, pose_format='quat',
normalize_poses=True, cache_transform=True,
stereo=False)

# Draw path of a single record (mono with normalized poses)
record = 'Record008'
draw_record(apollo_dataset, record)
plt.show()

Output:

Normalised poses and mono images resized and cropped to 250px.

Implemented Apolloscape Pytorch dataset also supports cache_transform option which is when enabled saves all transformed pickled images to a disk and retrieves it later for the subsequent epochs without the need to redo convert and transform operations every image read event. Cache saves up to 50% of the time during training time though it’s not working with image augmentation transforms like torchvision.transforms.ColorJitter.

Also, we can get the mean and the standard deviation that we need later to recover true poses translations:

poses_mean = train_dataset.poses_mean
poses_std = train_dataset.poses_std
print('Translation poses_mean = {} in meters'.format(poses_mean))
print('Translation poses_std  = {} in meters'.format(poses_std))

Output:

Translation poses_mean = [  449.95782055 -2251.24771214    40.17147932] in meters
Translation poses_std  = [123.39589457 252.42350964   0.28021513] in meters

You can find all mentioned examples in Apolloscape_View_Records.ipynb notebook.

And now let’s turn to something useful and more interesting, for example, training PoseNet deep convolutional network to regress poses from camera images.

In general case, online localization task formulation goes like this: find the current robot pose $\mathbf{X}_t$ given its previous state $\mathbf{X}_{t-1}$ and current sensors observations $\mathbf{Z}_t$:

PoseNet deep convolutional neural network regresses robot pose from monocular image; thus we are not taking in account previous robot state $\mathbf{X}_{t-1}$ at all:

Our observation sensor is a camera that gives us a monocular image $\mathbf{I}_t$. After removing subscript indexes for simplicity, we can define our task as to find a pose $\mathbf{X}$ given a monocular image $\mathbf{I}$.

where $\mathbf{X}$ represents the full pose with translation $\mathbf{x}$ and rotation $\mathbf{q}$ components:

Rotation is represented in quaternions because they do not suffer from a wrap around $2\pi$ radians as Euler angles or axis-angle representations and more straightforward to deal than 3x3 rotation matrices.

For more information about the selection of different pose representation for deep learning refer to the excellent paper “Geometric loss functions for camera pose regression with deep learning” by Alex Kendall et al.

## PoseNet Architecture

I build a DNN-based regressor for camera pose on ResNet and modify it by adding a global average pooling layer after the last convolutional layer and introducing a fully-connected layer with 2048 neurons. Finally, it’s concluded with 6 DoF camera pose regressor for translation $(x, y, z)$, and rotation $(q_1, q_2, q_3, q_4)$ vectors.

A PoseNet architecture with feature extractor network and regressors for camera translation and rotation. Feature extractor can be a pretrained on ImageNet ResNet18, ResNet34 or ResNet50.

A Pytorch implementation of the PoseNet model using a mono image:

import torch
import torch.nn.functional as F

class PoseNet(torch.nn.Module):

def __init__(self, feature_extractor, num_features=128, dropout=0.5,
track_running_stats=False, pretrained=False):
super(PoseNet, self).__init__()
self.dropout = dropout
self.feature_extractor = feature_extractor
fc_in_features = self.feature_extractor.fc.in_features
self.feature_extractor.fc = torch.nn.Linear(fc_in_features, num_features)

# Translation
self.fc_xyz = torch.nn.Linear(num_features, 3)

# Rotation in quaternions
self.fc_quat = torch.nn.Linear(num_features, 4)

def extract_features(self, x):
x_features = self.feature_extractor(x)
x_features = F.relu(x_features)
if self.dropout > 0:
x_features = F.dropout(x_features, p=self.dropout, training=self.training)
return x_features

def forward(self, x):
x_features = self.extract_features(x)
x_translations = self.fc_xyz(x_features)
x_rotations = self.fc_quat(x_features)
x_poses = torch.cat((x_translations, x_rotations), dim=1)
return x_poses

For further experiments I’ve also implemented stereo version (currently it’s simply processes two images in parallel without any additional constraints), option to switch off stats tracking for BatchNorm layers and Kaiming He normal for weight initialization [4]. Full source code is here models/posenet.py

## PoseNet Loss Functions

As a loss function I use a weighted combination of losses for translation and orientation as described in the original PoseNet paper [2]:

Scaling factor $\beta$ was introduced to balance the losses of two variables expressed in different units and of different scales. Weighting param depends on the task itself and should be selected as a model hyper-parameter.

Example of parameter $\beta$ influence on convnet performance on Chess scene from 7Scenes.
Source: Alex Kendall [2]

The second option for a loss function is to use a learning approach to find an optimal weighting for translation and orientation:

$\hat{\sigma}_x^2, \hat{\sigma}_q^2$, homoscedastic uncertainties, represent free scalar values that we learn through backpropagation with respect to the loss function. Their effect is to decrease or increase the corresponding loss component automatically. And $\log \hat{\sigma}_x^2, \log \hat{\sigma}_q^2$ are the corresponding regularizers that prevent these values to become too big.

In practice, to prevent the potential division by zero, authors [1] suggest learning $\hat{s} := \log \hat{\sigma}^2$ which is more numerically stable. So the final loss expression looks like:

Initial values for $\hat{s}_{x}$ and $\hat{s}_q$ could be set via a best guess and I follow the suggestion from paper and set them to the values of $\hat{s}_{x} = 0, \hat{s}_q = -3.0$

For more details on where it came from and intro to Bayesian Deep Learning (BDL) you can refer to an excellent post by Alex Kendall where he explains different types of uncertainties and its implications to the multi-task models. And even more results you can find in papers “Multi-task learning using uncertainty to weigh losses for scene geometry and semantics.” [5] and “What uncertainties do we need in Bayesian deep learning for computer vision?.” [6].

Pytorch implementation for both versions of a loss function is the following:

class PoseNetCriterion(torch.nn.Module):
def __init__(self, beta = 512.0, learn_beta=False, sx=0.0, sq=-3.0):
super(PoseNetCriterion, self).__init__()
self.loss_fn = torch.nn.L1Loss()
self.learn_beta = learn_beta
if not learn_beta:
self.beta = beta
else:
self.beta = 1.0

def forward(self, x, y):
# Translation loss
loss = torch.exp(-self.sx) * self.loss_fn(x[:, :3], y[:, :3])
# Rotation loss
loss += torch.exp(-self.sq) * self.beta * self.loss_fn(x[:, 3:], y[:, 3:]) + self.sq
return loss

If learn_beta param is False it’s a simple weighted sum version of the loss and if learn_beta is True it’s using sx and sq params with enabled gradients that trains together with other network parameter with the same optimizer.

## PoseNet Training Implementation Details

Now let’s combine it all to the training loop. I use torch.optim.Adam optimizer with learning rate 1e-5, ResNet34 pretrained on ImageNet as a feature extractor and 2048 features on the last FC layer before pose regressors.

from torchvision import transforms, models
import torch.optim as optim
from datasets.apolloscape import Apolloscape
from utils.common import save_checkpoint
from models.posenet import PoseNet, PoseNetCriterion

APOLLO_PATH = "./data/apolloscape"

# ImageNet normalization params because we are using pre-trained
# feature extractor
normalize = transforms.Normalize(mean=[0.485, 0.456, 0.406],
std=[0.229, 0.224, 0.225])

# Resize data before using
transform = transforms.Compose([
transforms.Resize(260),
transforms.CenterCrop(250),
transforms.ToTensor(),
normalize
])

# Create datasets
transform=transform, normalize_poses=True, pose_format='quat', train=True, cache_transform=True, stereo=False)
transform=transform, normalize_poses=True, pose_format='quat', train=False, cache_transform=True, stereo=False)

# Select primary device
if torch.cuda.is_available():
device = torch.device('cuda')
else:
device = torch.device('cpu')

# Create pretrained feature extractor
feature_extractor = models.resnet34(pretrained=True)

# Num features for the last layer before pose regressor
num_features = 2048

# Create model
model = PoseNet(feature_extractor, num_features=num_features, pretrained=True)
model = model.to(device)

# Criterion
criterion = PoseNetCriterion(stereo=False, learn_beta=True)
criterion = criterion.to(device)

# Add all params for optimization
param_list = [{'params': model.parameters()}]
if criterion.learn_beta:
# Add sx and sq from loss function to optimizer params
param_list.append({'params': criterion.parameters()})

# Create optimizer

# Epochs to train
n_epochs = 2000

# Main training loop
val_freq = 200
for e in range(0, n_epochs):
train(train_dataloader, model, criterion, optimizer, e, n_epochs, log_freq=0,
poses_mean=train_dataset.poses_mean, poses_std=train_dataset.poses_std,
stereo=False)
if e % val_freq == 0:
stereo=False)

# Save checkpoint
save_checkpoint(model, optimizer, criterion, 'zpark_experiment', n_epochs)

A little bit simplified train function below with error calculation that is used solely for logging purposes:

def train(train_loader, model, criterion, optimizer, epoch, max_epoch,
log_freq=1, print_sum=True, poses_mean=None, poses_std=None,
stereo=True):

# switch model to training
model.train()

losses = AverageMeter()

epoch_time = time.time()

gt_poses = np.empty((0, 7))
pred_poses = np.empty((0, 7))

end = time.time()
for idx, (batch_images, batch_poses) in enumerate(train_loader):
data_time = (time.time() - end)

batch_images = batch_images.to(device)
batch_poses = batch_poses.to(device)

out = model(batch_images)
loss = criterion(out, batch_poses)

# Training step
loss.backward()
optimizer.step()

losses.update(loss.data[0], len(batch_images) * batch_images[0].size(0) if stereo
else batch_images.size(0))

# move data to cpu & numpy
bp = batch_poses.detach().cpu().numpy()
outp = out.detach().cpu().numpy()
gt_poses = np.vstack((gt_poses, bp))
pred_poses = np.vstack((pred_poses, outp))

# Get final times
batch_time = (time.time() - end)
end = time.time()

if log_freq != 0 and idx % log_freq == 0:
print('Epoch: [{}/{}]\tBatch: [{}/{}]\t'
'Time: {batch_time:.3f}\t'
'Data Time: {data_time:.3f}\t'
'Loss: {losses.val:.3f}\t'
'Avg Loss: {losses.avg:.3f}\t'.format(
epoch, max_epoch - 1, idx, len(train_loader) - 1,
batch_time=batch_time, data_time=data_time, losses=losses))

# un-normalize translation
unnorm = (poses_mean is not None) and (poses_std is not None)
if unnorm:
gt_poses[:, :3] = gt_poses[:, :3] * poses_std + poses_mean
pred_poses[:, :3] = pred_poses[:, :3] * poses_std + poses_mean

# Translation error
t_loss = np.asarray([np.linalg.norm(p - t) for p, t in zip(pred_poses[:, :3], gt_poses[:, :3])])

# Rotation error
q_loss = np.asarray([quaternion_angular_error(p, t) for p, t in zip(pred_poses[:, 3:], gt_poses[:, 3:])])

if print_sum:
print('Ep: [{}/{}]\tTrain Loss: {:.3f}\tTe: {:.3f}\tRe: {:.3f}\t Et: {:.2f}s\t{criterion_sx:.5f}:{criterion_sq:.5f}'.format(
epoch, max_epoch - 1, losses.avg, np.mean(t_loss), np.mean(q_loss),
(time.time() - epoch_time), criterion_sx=criterion.sx.data[0], criterion_sq=criterion.sq.data[0]))

validate function is similar to train except model.eval()/model.train() modes, logging and error calculations. Please refer to /utils/training.py on GitHub for full-versions of train and validate functions.

The training converges after about 1-2k epochs. On my machine, with GTX 1080 Ti it takes about 22 seconds per epoch on ZPark sample train dataset with 2242 images pre-processed and scaled to 250x250 pixels. Total training time – 6-12 hours

PoseNet training on ZPark sample road from Apolloscape dataset, 2k epochs and auto learn of scale factor for combined translation and rotation loss function. Te - translation error in meters. Re - rotation error in degrees.

## PoseNet Results on Apolloscape dataset. ZPark sample road.

After 2k epochs of training, the model was managed to get a prediction of pose translation with a mean 40.6 meters and rotation with a mean 1.69 degrees.

Qualitative PoseNet model results after 2k epochs on train dataset (Left) and validation dataset (Right).

After learning, PoseNet criterion uncertainties became equal of $\hat{s}_{x} = 1.5606, \hat{s}_q = -3.8471$. Interestingly, these values are equivalent to the value of $\beta = 223.12$ which is close to those that can be derived from the PoseNet’ original paper [2].

## Full PoseNet model, training and visualization code

You can replicate all results from this article using my GitHub repo of the project.

## Further development

Established results are far from one that can be used in autonomous navigation where a system needs to now its location within accuracy of 15cm. Such precision is vital for a car to act safely, correctly predict the behaviors of others and plan actions accordingly. In any case, it’s a good baseline and building blocks of the pipeline to work with Apolloscape dataset that I can develop and improve further.

There many things to try next:

• Use temporal nature of a video.
• Rely on geometrical features of stereo cameras.
• Pose graph optimization techniques.
• Loss based on 3D reprojection errors.
• Structure from motion methods to build 3D map representation.

And what’s more importantly, all above-mentioned methods need no additional information but that we already have in ZPark sample road from Apolloscape dataset.

## References

1. Kendall, Alex, and Roberto Cipolla. “Geometric loss functions for camera pose regression with deep learning.” (2017).
2. Kendall, Alex, Matthew Grimes, and Roberto Cipolla. “Posenet: A convolutional network for real-time 6-dof camera relocalization.” (2015).
3. Brahmbhatt, Samarth, et al. “Mapnet: Geometry-aware learning of maps for camera localization.” (2017).
4. He, Kaiming, et al. “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification.” (2015).
5. Kendall, Alex, Yarin Gal, and Roberto Cipolla. “Multi-task learning using uncertainty to weigh losses for scene geometry and semantics.” (2017).
6. Kendall, Alex, and Yarin Gal. “What uncertainties do we need in bayesian deep learning for computer vision?.” (2017).
7. Clark, Ronald, et al. “VidLoc: A deep spatio-temporal model for 6-dof video-clip relocalization.” (2017).
8. Calafiore, Giuseppe, Luca Carlone, and Frank Dellaert. “Pose graph optimization in the complex domain: Lagrangian duality, conditions for zero duality gap, and optimal solutions.” (2015).
9. Martinec, Daniel, and Tomas Pajdla. “Robust rotation and translation estimation in multiview reconstruction.” (2007).


text:
Sega Genesis

(Difference between revisions)

For those without comedic tastes, the so-called experts at Wikipedia have an article about Sega Genesis.
“Genesis does.”
~ Sega on Sega Genesis
“What Nintendon't.”
~ Nintendon't on SEGA Genesis
“What about us? You know what do we get? No cool adverts. What about Mega Drive does?”
~ Europeans on when the USA had the "Genesis Does" advert
“Well, at least we are part of a majority”
~ Europeans and Japanese on the name of this 16-bit console (the Mega drive, that is)

One of the game consoles introduced in the first Book of the Holy Bible, Genesis is a video game console created by Phil Collins and Peter Gabriel that improves on the 8-bit graphics of the Coleco Adam and the Apple I used by Eve in the Garden of Eden by offering 16-bit graphics. Jesus christ himself proclaims Sega Genesis as his favorite console.

The Sega Genesis, also known as the Sega Mega Drive, was based on Amiga technology. It was killed and struck down into eternal oblivion by the SNES from Nintendo and hurled into the Abyss of the Damned by the Big Blue Satan, as hath been written in the apocryphal scripture Microsoft 95, chapters 80-386 of the Gospel according to Bill. Then, with the release of Sonic 3, and Sonic and Knuckles the Sega Genesis came back and spited the SNES and tossed it into the depths of Atari 5200.

The mascot and Lazarus symbol of the book of Sega Genesis, Sonic the Hedgehog, hath earned enough extra lives to outlive the Genesis; Sonic often appears in other Video Game Consoles.

Zombie platform

The Sega Slogan was "Genesis does what Nintendon't" for the Sega Genesis, yet Video Game Players did not buy into that belief. Sega Genesis games are therefore often run via emulation, as the Mega drive has become a zombie platform and hardly anyone wants their brains eaten anymore. The Genesis was mostly obliterated by the Amish using their Super Metric System Distortion Blaster. They then retreated to their home planet, Chaste 9.

Sega Sonic Mega Drive/Genesis

When Sonic the Hedgehog began to spread the word of the hedgehog, he deicided to tell the story of his original coming into this world. He used the Holy Sega Mega drive to tell the word in a fun, interactive form, a better idea than Jesus ever had. People were instantly hypnotised into thinking hedgehogs were cool and blue. Pleased with the initial success, God sent down the other two parts of the Holy Trinity of the Hedgehog, Knuckles and Tails, to assist Sonic. together, they made a further 3 games and a movie. God had never been richer. all should have been well but there was only one flaw in the Holy Genesis: Yuji Naka, the mortal chosen to do stuff for Sonic. Tempeted by Satan/Robotnik/Eggman, he cocked up and translated the European version of the Holy consle to 'Megadrive'. Therefore, the hedgehogian message was not so strong in Europe. Sonic called Yuji an asswipe and gave him the asswuping of a life time. God was content.

The Mega Drive/Genesis Unit

One day, the events of the first three Mega Man games unfolded in the Genesis world. Immediately after this, Dr. Wily blackmailed God to create the Holy Trinity of Robots: Buster Rod.G, Mega Water.S, and Hyper Storm.H. This forced Mega Man to repeatedly go back to Dr. Light's lab for weapons and items he acquired during his previous adventures, though Dr. Light decided to be an asshole and did not let Mega Man leave until he gets at least one item, regardless of weather or not he got a weapon. Soon Mega Man came face to face with the Genesis Unit. Although Buster Rod.G went as far as to fight him twice, they were all singlehandedly defeated. Having disgraced Wily, and upon their subsequent disowning, the Genesis Unit hid themselves from the world for many years, only to re-emerge recently as the rap group known as Buster Rod.G and the Funky Fresh Gang.

“Ah, those were the days. Too bad their story is only free for Europe and Japan, while America had to subscribe to the Sega Channel, which is sadly now defunct.”
~ God on the Genesis Unit

Religious Beliefs

It is said to most that Sega is in fact the original name of God and that Sega Mega Drive is just a part of the holy book, The Master System. Later a smaller version of The Master System was released, this was known as the Game Gear.

Although Sega does not like to admit it, it was in fact Sonic who created the Holy Sega Genesis. He used as a tool to spread the hedgehogian message of peace and hog. It was also he who brought the two other parts of the Holy Trinity of the Hedgehog, Fox, and Echidna to Earth. However, Sega did create the known gaming world so fair do's.

Add-on books of the Sega Bible

Sega CD

Sega had a stupid idea and made a book called the Sega CD. It was unpopular, and did not get placed in the bible. You could insert CDs into this book and read the Bible with more fun and awesomeness, but the damn thing costed \$250. On the plus side, it did have a few awesome testaments amoungst the crappy full motion video ones.

Sega 32X

Pretty much the same thing happened here. It was said that you could read the Bible in awesome 32-bit graphics, as suggested by the name, but it sucked and was a waste of money.

Sega WMS

A system that failed to make it to production. The Sega WMS (Well Marketed System) was failed from the beginning, as it implied that SEGA knew how to make decisions that would ultimately lead to the conception of a system people were willing to pay for. Funding was cut, and Sega moved on to the Buford (all lies.)

Sega Buford

In 1997 Sega decided to purchase rights to the design of the ENIAC. They saw a market for video game systems that weighted in excess of 20 tons and used enough electricity to power your mom's face. After obliterating the GDP of China on the Buford, Sega was forced to spend the remainder of the budget on an office lunch featuring Wawa Hoagies and Tahitian Treat Soda. They closed there doors on Februember 20th, smoked a fat one, and now all live in the mountains, searching for an idol of a Blue Hedgehog that if a previous employe finds, will allow them to claim their 401 K benefits. Search on, pioneers.

Sega 64x

In 1999, with the impending U.S. release of the final chapter of the Bible, the Sega Dreamcast, Sega wanted to assure that all of it's religious followers would be able to read the final book in all it's glory. At that time the Genesis had long been dead, so this extension module, coming in at a bargain bin price of \$5,999.99 USD was planned to be released in mass market as a way to experience the next generation of virtual holiness for the broke shitheads who did not wish to pay a mere \$1,099 USD more to purchase the complete Book of Dreamcast. The project was scrapped when Nintendo (also known as Satan) struck down the book of Dreamcast in 2001 and the name of Sega was disgraced forever until the second coming of Jesus-Sonic.

Sega 69x

The obvious addition to the Sega Bible. Essentially, it was the manual for all sorts of sexual maneuvers, most of which include a yak and KFC Bowls. It allowed for the mega sega explosion, during which worship of the holy console overtook Christianity as the world's major religion. The Pope later added the x in a drunken stupor because he believed that it made the name more "badass."

Quotes From The Book of Sega Genesis (AKA The Book of Sega Mega Drive)

1$\mathfrak{I}$n the beginning Sega created the heaven and the earth. 2And the earth was without form, and void; and 16-Bit Graphics were upon the face of the deep. And the Spirit of Sega moved upon the face of the waters. 3And Sega said, Let there be light: and there was Wonderboy in Monsterland. 4And Sega saw the light, that it was good: and Sega divided the light from the darkness, thus creating Alex Kidd. 5And Sega called the light Day, and the darkness he called Sega Time. And the evening and the morning were the first day, when he chilled and played Super-Hang-On for a while. 6And Sega said, Let there be a firmament in the midst of the graphics, and let it the side scrolling beat-em-ups from the normal style beat-em-ups. 7And Sega made the firmament, and divided the games which were under the firmament from the Streets of Rage which were above the firmament: and it was so. 8And Sega called the firmament Sonic the Hedgehog. And the Control Pad and the Reset Button were the second day. 9And Sega said, Let the waters under the heaven be gathered together unto one place, and let the dolphin appear. And so the one known as Ecco The Dolphin appeared. 10And Sega called the dry land Earth; and the gathering together of the waters called he Seas: and Sega saw that it was good. For a laugh he also created crap games like Zero Wing. 11And Sega said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. The Shining Force and Phantasy Star were formed. 12And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after the hit that was Sonic the Hedgehog, Sega decided he would make himself a sequel. 13And the evening, the morning and Mortal Kombat were the third day. 14And Sega said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: Let there be Word Cup Italia '90!


text:
2 added clarification on group structure

This may be a fairly simple question. Suppose G is a (T0) topological group. Assume that G is path-connected, locally path-connected, and semilocally simply connected, so that covering space theory applies.

Question: Is it true that for any element of $\pi_1(G,e)$ (where e is the identity element of G), there exists a [ADDED: continuous] homomorphism from $S^1$ to $G$ having that element of $\pi_1(G,e)$ as its homotopy class?

Another way of formulating this is that there is a set map:

$$\operatorname{Hom}(S^1,G) \operatorname{Hom}_{cts}(S^1,G) \to \pi_1(G,e)$$

The subscript cts is to indicate continuous.

(when G is abelian, the left side has a group structure too [ADDED: under pointwise multiplication], and the Eckmann-Hilton principle tells us that we get a group homomorphism).

1. Is the set map surjective in all cases (regardless of whether G is abelian)?
2. Does the image of $\operatorname{Hom}(S^1,G)$ generate $\pi_1(G,e)$ as a group (this is equivalent to surjectivity when $G$ is abelian)?
3. Does surjectivity work for Lie groups? Compact Lie groups?
4. Does the weaker formulation (2) work for Lie groups?

I have a sketch of an argument/proof that may show (4) (basically, using properties of one-parameter subgroups), but I'm hoping somebody will have a clean proof that works in general for topological groups.

1

# Each element of fundamental group of a topological group represented by homomorphism?

This may be a fairly simple question. Suppose G is a (T0) topological group. Assume that G is path-connected, locally path-connected, and semilocally simply connected, so that covering space theory applies.

Question: Is it true that for any element of $\pi_1(G,e)$ (where e is the identity element of G), there exists a homomorphism from $S^1$ to $G$ having that element of $\pi_1(G,e)$ as its homotopy class?

Another way of formulating this is that there is a set map:

$$\operatorname{Hom}(S^1,G) \to \pi_1(G,e)$$

(when G is abelian, the left side has a group structure too, and the Eckmann-Hilton principle tells us that we get a group homomorphism).

1. Is the set map surjective in all cases (regardless of whether G is abelian)?
2. Does the image of $\operatorname{Hom}(S^1,G)$ generate $\pi_1(G,e)$ as a group (this is equivalent to surjectivity when $G$ is abelian)?
3. Does surjectivity work for Lie groups? Compact Lie groups?
4. Does the weaker formulation (2) work for Lie groups?

I have a sketch of an argument/proof that may show (4) (basically, using properties of one-parameter subgroups), but I'm hoping somebody will have a clean proof that works in general for topological groups.


text:
# How do I show that there are no other solution

1. Sep 20, 2011

### flyingpig

1. The problem statement, all variables and given/known data

[PLAIN]http://img90.imageshack.us/img90/834/unledml.png [Broken]

3. The attempt at a solution

OKay first of all I showed that x is indeed a solution. But I need to state the Axioms of Fields first.

[PLAIN]http://img194.imageshack.us/img194/2548/unledtao.png [Broken]

i.e.

$$a + (b - a) = (b - a) + a$$ by A2

$$= b + (-a + a)$$ by A1

$$= b + 0$$ by A4

Hence b = b

Showing that it is the only solution is tough for me because I don't know what that means. I am guessing at the end of the proof I would show that x = b - a?

Here goes

$$a + x = b$$
$$a + (-a) + x = b + (-a)$$
$$0 + x = b + (-a)$$ By A4
$$x = b + (-a)$$ By A3

$$x = b - a$$ and say it is the only solution?

Thanks

Last edited by a moderator: May 5, 2017
2. Sep 21, 2011

### PAllen

One way to do it is to let x=b-a+h, and show contradiction unless h=0.

3. Sep 21, 2011

### flyingpig

But we haven't learned proof by contradiction yet. So I can't use that.

4. Sep 22, 2011

### flyingpig

Any comments...? I'll take it even if i am wrong.

5. Sep 22, 2011

### Staff: Mentor

Unfortunately, contradiction is the standard way of proving statements about the uniqueness of something. This technique is not related to the axioms you have to use, so it should be fine to use.

6. Sep 22, 2011

### flyingpig

BUt what was wrong with what I did? I posted this because I wasn't confident

7. Sep 22, 2011

### flyingpig

Without wasting everyone's time...

Proof

Let x = b - a + h

a + x = a + (b - a + h)

= (a + (-a)) + (b + h) by A2

= 0 + b + h By A4

= b + h

Now we have a + x = b + h

Stuck...

8. Sep 22, 2011

### Staff: Mentor

Given a + x = b, you showed that there was a solution, x = b - a.

Now suppose that y $\neq$ x, is also a solution. Can you take it from there?

9. Sep 22, 2011

### flyingpig

Are you referring to Pallen's method? Where did y come from?

10. Sep 22, 2011

### HallsofIvy

What you did was show that b- a $is$ a solution. You did not show that it was the only solution, which was the point of the exercise.

11. Sep 22, 2011

### flyingpig

No I meant this part

$$a + x = b$$
$$a + (-a) + x = b + (-a)$$
$$0 + x = b + (-a)$$ By A4
$$x = b + (-a)$$ By A3

Doens't that prove that x can only be x = b + (-a)?

12. Sep 22, 2011

### Punkyc7

I dont think so, it shows x is a solution but not the only one. Now assume y is a solution

13. Sep 22, 2011

### flyingpig

Assume y is NOT a solution
a + y = b

a + (-a) + y = b + (-a)

0 + y = b + (-a)

y = b + (-a)

y = b - a

But this contradicts x $$\neq$$ y

Woah!

14. Sep 22, 2011

### Punkyc7

Assume y is a solution where y does not equal x
.
.
.
.

15. Sep 22, 2011

### flyingpig

Isn't that what I just showed? If I assume y is a solution I would just go back to my original post and redo that proof again?

16. Sep 22, 2011

### Punkyc7

you said assume y is not a solution, yes and no because y is not x so its different but it gets you the same thing so y=x contradiction

17. Sep 22, 2011

### flyingpig

Oh, I should have said y is solution, but my math follows is correct right?

18. Sep 22, 2011

### Punkyc7

if y is not a solution does it make any sense to say for example 0=2?

19. Sep 22, 2011

### flyingpig

No I meant like

20. Sep 22, 2011

### Punkyc7

yeah that works


text:
## Ugg Boots With Fur On The Outside that the lower brain stem may also play

The power of this persuasion method comes from the feeling of obligation to reciprocate the concession you initially gave. People will be more receptive to grant your true (and smaller) request after they declined the first (and bigger) one. They will feel embarrassed to turn down the second favor, especially if it’s much easier to comply than the Ugg Red Boots
first request.

But the Ugg Boots With Fur On The Outside
bulk of this disc deals with love. The title track brims https://www.uggbootssingapore.nu with poetic imagery describing the beauty of a man’s beloved. “You are golden/Precious as a prayer flying up through the air/While the rain is falling/Golden, timeless as a kiss/Baby, I don’t wanna miss another perfect moment/To tell you how I feel/The day you strolled in, my heart was stolen/’Cause you are https://www.uggbootssingapore.nu golden.” He also adds, “You are goodness, forgiveness/Of the purest kind.” In similar territory, “Better Man” finds a guy saying that his relationship with the lady he loves has made him exactly that.

Before treatment I had suffered for over thirty years with fibromyalgia. During treatment I had a period of nearly three weeks that I was completely pain free! I was once again able to walk daily up to two miles at a time. This had not happened for many, many years. Unfortunately the adjustments to the upper cervical region did not hold for me. I feel certain that Dr. Whitcomb was right when he advised me that this was do to the fact that I was forced to sleep in a recliner every night for additional spine issues in thoracic area. Dr. Whitcomb was the first, and only doctor who ever gave me any lasting relief. Let alone almost three weeks of total pain relief from fibromyalgia. Dr. Whitcomb definitely found a very important part of this puzzle called fibromyalgia. Is it the total answer to this insidious disease? I not sure, but this I do know. He has found at least a partial cause of fibromyalgia, and other issues caused from upper cervical misalingnment. I believe that the lower brain stem may also play some part in fibromyalgia, and since leaving clinic I have found Ugg Mens Leather Sandals
other doctors who believe this.

## Ugg Mens Treadlite of the combined search strategy electronic searching and manual searches

Considering what I pay for (\$150 per year) Short Uggs
including the extra statistical reporting, user backup restore https://en.wikipedia.org/wiki/UGG (thankfully I haven’t needed it since), 10 tera of disc space, unlimited email, and a few other amenities, I am rather satisfied with iPower. Yes, there have been glitches, but when I signed them on, they were almost as new as I was!

As might be expected in a community made up of volunteers, feelings run high over these apparently dry questions of philosophy. Just as there are free software and open source factions that work together for a common cause, but eternally snipe at each other over details, so the Wikipedia community harbors two groups that agree to disagree on what is the proper scope for the project: the deletionists and the inclusionists. Here’s what Wikipedia itself has to say on them:

Together, with the boys, I started looking at bunk beds on the net. We wanted https://www.uggbootssingapore.nu the frame to be rigid, well made and safe with a guard rail that would stop whoever slept on the top, from falling out. We had to make sure the beds would fit where we wanted them to, so we took the measurements from the adverts and double checked by measuring the bedroom.

We aimed to identify all randomised controlled trials of strategies to influence the response to a postal questionnaire. Eligible studies were not restricted to medical surveys and included https://www.uggbootssingapore.nu any questionnaire topic in any population. Studies in languages other than English were included. Strategies requiring telephone contact were included, but strategies requiring home visits by investigators were excluded for reasons of cost. We searched 14 electronic bibliographical databases (table 1). Two reviewers independently screened each record for eligibility by examining titles, abstracts, and keywords. Records identified by either reviewer were retrieved. We searched the reference lists of relevant trials and reviews, Mens Uggs Boots
and two journals in which the largest number of eligible trials had been published (Public Opinion Quarterly and American Journal of Epidemiology). Reports of potentially relevant trials were obtained, and two reviewers assessed each for eligibility. We estimated the sensitivity of the combined search strategy (electronic searching and manual searches of reference lists) by comparing the trials identified by using this strategy with the Ugg Mens Treadlite
trials identified by manually searching journals. We used ascertainment intersection methods to estimate the number of trials that may have been missed during screening.2

## Uggs For Women down 5 of my 6 websites that won t update to

God is not proved objectively. What is proved objectively the electron, neutron or proton? Nobody has yet seen electrons, neutrons, protons, but the scientists say they are. If nobody has seen them why do you say they are? Scientists say, though we cannot see them, we can see their effect. https://www.uggbootssingapore.nu The mystics say the same thing: is not observed objectively, but we can see the effect. you see the universe running so intelligently? Can you see tremendous intelligence permeating the whole?

Some agents only care about their reputation and not your needs so they will do what benefits them most and not you. This is not always the case as Uggs Slip On Shoes
I have worked for some excellent agencies who have treated me great, but I had to learn to be firm about what I wanted as sometimes it felt like they were begging me to do a job I didn’t want to Ugg Trigo
do by saying ‘sure your travelling you need the money’. I found this very annoying, insulting and it used to frustrate me so much! My advice is to learn to say “no thank you that would not suit me, I want a . type of job”.

Hanging on to such stocks for an extensive period of time provides security as well as, eventually, the opportunity to sell at a profit. Know that it is never too early nor too late to embark upon a retirement plan. Obviously, the younger you start, the better off you’ll be in the long run.

Okay, I’ve narrowed it down: 5 of my 6 websites that won’t update to 3.8 are on HostMonster’s (same as BlueHost) “pro” web hosting package. The 6th website successfully updated when i tried again just now. I’d mis remembered where some of these sites are so thought they were spread over a couple of different types of hosting plans. I didn’t customize any settings for pro hosting that aren’t on my other https://en.wikipedia.org/wiki/UGG websites https://www.uggbootssingapore.nu so it would appear to be something in the default set up. All the sites in question have been out for at least two years so many WP version updates have been made without incident until now. Thanks to everyone for the suggestions. I would be very curious to know if others who have had problems can trace it to “pro” web hosting, especially of the BlueHost / Hostmonster variety.

Like so many people with type 2 diabetes, Uggs For Women
Daniel Wimer didn’t watch his blood sugar though as an RN, he had seen firsthand the serious damage caused by toxic blood sugar levels. He started using insulin more than 20 years ago, but stopped taking it until a few years ago. After a few health scares of his own, Wimer, now age 68 and living in Tampa, has his blood sugar and weight under control thanks to a combination of Byetta and insulin. Wimer shares his health struggles on his blog and in motivational talks as a member of the National Speaker Association of Central Florida. Read More

## Uggs Outfits months but you should examine feasible prices should you

When I was assembling my Power house https://en.wikipedia.org/wiki/UGG mod I would periodically power it up to make sure various components were working properly. I failed to remember that the capacitors in an ATX power supply hold quite a bit of juice after the unit is powered off. I had my hands inside with a pair of snips taking care of some wire ties and got quite the spark and jolt through my forearm from (I assume) shorting out a cap or two. That was the last time I had my hands near that thing without draining the residual power first.

Here are the first pictures of Intel Desktop Board Extreme Series DX79SI. This is the first socket LGA2011 we’ve seen that has eight DDR3 DIMM slots (four on either side of the socket, two DIMMs per channel), https://www.uggbootssingapore.nu every other board has barely enough room for four. LGA2011 supports quad channel DDR3 memory, yielding 33% bandwidth gain over triple channel DDR3 and 100% gain over dual channel DDR3. Despite its large memory area, the DX79SI sticks to standard ATX board Uggs Outfits
dimensions. This is thanks to some smart engineering.

An environment conducive to napping is quiet, dark and free from interruptions. If you sleep on a floor at work, keep a mat (like a yoga mat that rolls up) at work, and possibly a pillow and blanket, if that makes you more comfortable. Other tools of the trade to consider eye shades, ipod or walkman with restful music, or specific MP3 files designed to help you wind down and fall asleep.Napping is great for your health and productivity.

Eventually, before you make an application for a loan you should check you pleased with how and when you have the capacity to repay it. The majority of Uggs With Shoe Strings
unprotected and secured loans may set a fixed monthly reimbursement to get a set number of months, but you should examine feasible prices should you need to re pay the loan early.

I bought the drink rescue detox ice today and would like some more information on the directions on how to use it correctly because i know if you don’t use it right. Does rescue detox ice work to help pass drug test?. Does the rescue detox brand drink work to pass a drug test and if so how long does it take to work?.

Blind people do dream. Whether visual images will appear in their dream depends on whether they where blind at birth or became blind later https://www.uggbootssingapore.nu in Uggs Meme
life. But vision is not the only sense that constitutes a dream. Sounds, tactility, and smell become hypersensitive for the blind and their dreams are based on these senses.8.

In most cases of neurofibromatosis 1, patients can live normal and productive lives. In about 25 40% of patients there is an associated learning disability with or without ADHD. In some cases of neurofibromatosis 2, the damage to nearby vital structures, such as the cranial nerves and the brainstem, can be life threatening. When tumors are causing pain or disfiguration, surgery is thus far the only proven beneficial treatment option.

## Ugg Cindy can t read and need American Sign Language I might

Working with a like minded local lawyer our success rate is currently 100%. There are more to come. This is a frustrating waste of time for me as it is so unnecessary. What is more frustrating is the total lack of transparency following such a successful appeal. The appeal is successful, the ESA is restored but there appears to be no https://www.uggbootssingapore.nu other outcome. No acknowledgement of accountability on the part of Atos or its employee. The misery and extra unwelcome stress put upon our patient seem not to matter. Apologies do not exist. The tremendous waste of public money expended in Ugg Cuff Boot
dealing with the dramatic increase in levels of appeals is a disgrace.

“A stranger observing one of the launches could probably be forgiven for thinking https://en.wikipedia.org/wiki/UGG they had stumbled into a religious revival meeting,” Bell wrote to TechNewsDaily in an email. Bell now studies the culture of modern biomedical research, but before she got interested in scientists, she studied messianic religious movements in South Korea.

But it’s not all bad. exchange in twenty different languages, including Apache, Navajo, and Irish. Which is great because I see so many Irish here who have a heck of a time assimilating, what with the fact that they only speak Irish and not the King’s English. (You can also receive notices in American Sign Language l’d make a joke here but I might offend the deaf. But I guess since they can’t read and need American Sign Language I might as well let one rip. But I’ll refrain nevertheless.)

Thirdly, because the proposed new system will have little resilience or cohesion, the next government will find it necessary to overhaul the NHS again. This is not good for anyone, least of all the Grey Uggs Outfit
front line staff. But ironically this may be Lansley’s one great achievement: reforms designed and implemented so badly that another major NHS reform programme is guaranteed within five years.

That too hard and long for beginners to get approval from google adsense and maybe fifty fifty to success. I have the best and quickly solution for thats problem with third party sites like indyarocks and docstoc from my experience. In this Ugg Cindy
how to trick adsense tutorial only explain how to get approval 100% from google adsense with indyarocks. Indyarocks is a social networking similarly as facebook.

This page size is 185 KB. The average web page takes up 320 KB on the world wide web. The page size should ideally be less than 100 KB. We recommend that you should minify your HTML. Minifying THML refers to eliminating unnecessary bytes, such as extra spaces, line breaks, and indentation. For minifying HTML, you can use PageSpeed Insights Chrome Extension to generate an optimized version of your https://www.uggbootssingapore.nu HTML code.

## Ugg Boots Tights are diligent with your workouts and are more conscious of

This file does not contain the whole video cutscenes. It is a replacement that shows pictures of the cutscenes instead of the moving image video. The original video file is over 200mb, and i could never find it anywhere, don’t bother cause you Ugg Boots Tights

Just to get a paycheck and earn one’s own keep, one accepts just about any job. The inner voice that says help me I hate my job, thus begins early in the career. Eradicating this voice along with increase of income status then becomes the guiding light of one’s career path.

He’s not at all like his most famous role, steely DS James Hathaway in the detective drama Lewis. Nor is he the thespy princeling you might expect from the Fox dynasty. (His dad is James; his uncles are Edward and theatre producer Robert; his cousins include Freddie and Emilia). “Edward is the only real thespian,” he says when I ask what their Christmases are like. “Oh, maybe Freddie https://www.uggbootssingapore.nu as well, he’s pretty full of it. And my little brother Jack. But if you met me in the pub, would you think I was a thespian?”

Elya’s story takes Ugg Leather Sandals
place in a small town deep in the vast expanse of the Egypt that is usually forgotten. This is Upper Egypt, so named because it is upriver from Cairo and the delta. By the time the river that is Egypt’s lifeblood reaches the capital and then the Mediterranean Sea, it has coursed north from the border with Sudan, past the cities https://en.wikipedia.org/wiki/UGG and towns where people toil far from the political tumult of Tahrir Square, their struggles virtually invisible there.

Well, to expand on ‘best of the old models’ one thing that often comes up is that you have a reputation mechanism in traditional publishing, a mechanism which sometimes breaks, but which mostly works. Citizen journalism has to find https://www.uggbootssingapore.nu ways to generate the same kind of reputation mechanisms. Blogs are finding that, to some extent.

Exercise, exercise, exercise: Let us help you with this piece of the puzzle! !MPACT Training will set you up for success and we take your abilities, age and fitness level into consideration. You can’t lose!! Consistency is the key to your success: Remember, if you are diligent with your workouts and are more conscious of consuming fewer calories and eating balanced meals, you WILL see Ugg Adirondack Short
results. Just stick to your plan as often as possible. Be GREAT on your diet plan 85% of the time!

Obstetric benefitsLord Chesterfield said of the act of procreation that “the pleasure is momentary, the position ridiculous, and the expense damnable.” His first proposition has been refuted,23 but a pioneering study has confirmed the second.24 A clown, dressed as a chef de cuisine, entertained would be mothers for 12 15 minutes after in vitro fertilisation and embryo transfer. His saucy jokes were a recipe for success the pregnancy rate was 36% in those whom he entertained compared with 20% in the controls (adjusted odds ratio 2.67; 95% confidence interval 1.36 to 5.24).25 Clowning may cost effectively vitiate Lord Chesterfield’s last proposition.

## Ugg Boots Men Black are taking on the second shift which is a reference to

Going to Las Vegas this Christmas holiday? When you are that close to the Grand Canyon, you don’t want to miss out https://www.uggbootssingapore.nu on taking a helicopter tour. Just don’t try to wait until the last minute to book your tour. Tours on Grand Canyon helicopters are very popular and the seats fill up fast.

In Japan, there’s a word for it. Karoshi refers to death by overwork, a legal term that allows surviving family to petition a judge for compensation for damages from the government and the company. Toxicology and inquest are pending, but in the West we have no such legal designation of protracted corporate suicide.

Screening studyAll five maternity units in West Gtaland took part (see above). Prospective screening of oxygen saturation was conducted preductally (palm of right hand) and postductally (either foot) with identical pulse oximeters (Radical SET, version 4 (average time set on 8 seconds) with multisite LNOP YI sensors, Masimo, Irvine, CA, USA) on all newborn infants before routine neonatal physical examination. The oximeters were locked with a key code to ensure unchanged settings throughout the study period.

A group of wikis may have designated one “preferred wiki” to upload files to, with sharing of those files enabled. Among Wikimedia wikis, Wikimedia Commons works for this. If images are uploaded to Wikimedia Commons, they can be used in all Wikimedia wikis. Wikipedia) can only be used in pages of that wiki. Thus this should be done only if there is a special reason for it, such as locally replacing an image from Commons with a local version without changing the Ugg Baby Slippers
links. produced by n^2 = \sum_{k=1}^n(2k 1).)

You must create a caloric deficit, meaning https://www.uggbootssingapore.nu you burn more calories than you consume, to drop pounds. Creating this deficit can be tricky, though, because you can’t always accurately determine how much you burn. In your 40s, your metabolism may have slowed down, so it takes even fewer calories and more activity than it once did to prompt weight loss.

Just think about it. Many women today are taking on the “second shift,” which is a reference to the fact that they work full time outside the home and then take on the Ugg Boots Men Black
brunt of the household chores and child rearing, explains Johnson. As a result, Ugg Furry Slides
they are just too burned out to have sex at the end of the day. Men, of course, are lending a helping hand more than before and have their own pressures at work. Put this all together and it’s a recipe for a sexless relationship. Of course, there are those with physical ailments that https://en.wikipedia.org/wiki/UGG prevent them from having sex, and they should consult a doctor.

## Ugg Leather Shoes of life research Some were researchers of international standing who were asked to reflect on

Manufacturer and E Uggs Bow Tie Boots
tailer sites are basically just companies that can sell their product directly to their customers via a website. [6] They are just online stores. Most websites like this have an online catalog of their products for the consumer to look at and choose their desired product. Then if the product is shipped to the home there is a shipping fee, or some products like music or https://www.uggbootssingapore.nu books can just be directly downloaded. [7]

Sampling and data generationWe identified a purposive sample of 34 researchers and completed interviews with 32 (table 1). One person declined for personal reasons, and another was unavailable during the period of the study. Initially the researchers were identified from our systematic literature review,11 which aimed to determine what methods are being used in cancer studies and how best to include the views of patients in the development of services. We included papers on research methods published in 1980 Classic Tall Uggs
2004 that sought the views of people affected by cancer about end of life issues. This enabled us to identify researchers from a range of disciplines who were using diverse approaches to conducting end of life research. Some were researchers of international standing, who were asked to reflect on their own research https://www.uggbootssingapore.nu experience and give an overview as managers of many projects; others were comparatively junior researchers with more current “hands on” experience. Many had also worked on non cancer research. To follow up themes emerging from Ugg Leather Shoes
early interviews and to include more non cancer work, we interviewed two transcribers and researchers with experience of working in specialties such as HIV/AIDS, dementia, and education, thus enabling us to learn from research methods in other sensitive subjects.

Interviews, lasting on average an hour, explored individuals’ expectations, experiences, and opinions of electronic health records. The interviewers were five university employees (KC, AT, https://en.wikipedia.org/wiki/UGG DP, SC, and AR), all experienced qualitative researchers with no prior relationships with the interviewees. Early interviews were guided by topic guides (see appendix 4) designed for specific interviewee groups. As each case study progressed, the lead researcher at that site adapted interview guides and other data collection to respond to previously collected data and emerging themes. Nearly all interviews were audio recorded (table 1). For a few interviews, participants requested not to be recorded, and in such instances the researcher took notes. Professional transcribers transcribed the interviews verbatim, with the interviewers then checking the transcripts for accuracy. Copies of the transcripts were available to interviewees, although only a minority requested to see them; there were no cases of interviewees disputing the transcript contents.

## Ugg Boots Chocolate train bureau leaders on using the technological tools

Whether one wants to lose or gain weight, The Daily Plate is not a specific diet like Atkins, South Beach , or Zone, but rather a place where one can keep a food diary and learn how the foods eaten affect health, energy levels, etc., and why. It helps one take control and be responsible for one Ugg Classic Ii
own health! The Daily Plate is meant to “teach not preach” and is concerned with behavioral and habitual changes rather than dictating what should or should not be eaten.

2. Make it easy for users to recommend your site. Viral marketing is very important and Ugg Boots Chocolate
easy to tap on the Web. But give your users the tools. Some even go as far as giving incentives to those who recommend the site to their friends. If only 10 people go to your site, but these 10 people invite 10 more https://www.uggbootssingapore.nu that additional traffic that you get for FREE!

It is safe to assume that any interested buyer will want to know about the financial status of your business: what it makes (if anything); depreciation, staff wages, owner s wages, and tax liabilities. Collect your business s financial information, including: profit and loss statements; balance sheets; depreciation schedule; staff wages and expenses (benefits, etc.); owners wages and expenses; and owners personal tax returns. Monthly tabs allow the buyer to see when what time of year is more active than others.

Interestingly, the typescript contains a much more conventional account of Agee’s Alabama travels than the story within “Let Us Now Praise Famous Men.”Summers’ discovery calls into question the long held assumption that Fortune rejected Agee’s Alabama travelogue because of the article’s unrelenting experimentation. What now seems more likely is that “Let Us Now Praise Famous Men” is a radically reimagined https://en.wikipedia.org/wiki/UGG version of Agee’s Alabama experiences, and not merely a book version of his magazine piece.


text:
## sARI: a soft agreement measure for class partitions incorporating assignment probabilities.(English)Zbl 1474.62224

Summary: Agreement indices are commonly used to summarize the performance of both classification and clustering methods. The easy interpretation/intuition and desirable properties that result from the Rand and adjusted Rand indices, has led to their popularity over other available indices. While more algorithmic clustering approaches like $$k$$-means and hierarchical clustering produce hard partition assignments (assigning observations to a single cluster), other techniques like model-based clustering include information about the certainty of allocation of objects through class membership probabilities (soft partitions). To assess performance using traditional indices, e.g., the adjusted Rand index (ARI), the soft partition is mapped to a hard set of assignments, which commonly overstates the certainty of correct assignments. This paper proposes an extension of the ARI, the soft adjusted Rand index (sARI), with similar intuition and interpretation but also incorporating information from one or two soft partitions. It can be used in conjunction with the ARI, comparing the similarities of hard to soft, or soft to soft partitions to the similarities of the mapped hard partitions. Simulation study results support the intuition that in general, mapping to hard partitions tends to increase the measure of similarity between partitions. In applications, the sARI more accurately reflects the cluster boundary overlap commonly seen in real data.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 91C20 Clustering in the social and behavioral sciences

### Software:

clusterGeneration; mclust; R
Full Text:

### References:

 [1] Amodio S, D’Ambrosio A, Iorio C, Siciliano R (2015) Adjusted concordance index, an extension of the adjusted rand index to fuzzy partitions. arXiv preprint arXiv:1509.00803 [2] Banfield JD, Raftery AE (1993) Model-based Gaussian and non-Gaussian clustering. Biometrics 49(3): 803-821 · Zbl 0794.62034 [3] Bezdek JC (1981) Objective function clustering. In: Pattern recognition with fuzzy objective function algorithms. Springer, Boston, MA, pp 43-93 [4] Campello, RJGB, A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment, Pattern Recognit Lett, 28, 833-841, (2007) [5] Dempster, AP; Laird, NM; Rubin, DB, Maximum likelihood from incomplete data via the EM algorithm, J R Stat Soc Ser B (Methodol), 39, 1-38, (1977) · Zbl 0364.62022 [6] Downton, M.; Brennan, T., Comparing classifications: an evaluation of several coefficients of partition agreement, Classif Soc Bull, 4, 53-54, (1980) [7] Dunn, JC, A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J Cybern, 3, 32-57, (1973) · Zbl 0291.68033 [8] Fowlkes, EB; Mallows, CL, A method for comparing two hierarchical clusterings, J Am Stat Assoc, 78, 553-569, (1983) · Zbl 0545.62042 [9] Fraley, C.; Raftery, AE, Model-based clustering, discriminant analysis, and density estimation, J Am Stat Assoc, 97, 611-631, (2002) · Zbl 1073.62545 [10] Fraley, C.; Raftery, AE, Model-based methods of classification: using the mclust software in chemometrics, J Stat Softw, 18, 1-13, (2007) [11] Hartigan JA (1975) Clustering algorithms. Wiley, New York · Zbl 0372.62040 [12] Hubert, L.; Arabie, P., Comparing partitions, J Classif, 2, 193-218, (1985) · Zbl 0587.62128 [13] Huellermeyer, E.; Rifqi, M.; Henzgen, S.; Senge, R., Comparing fuzzy partitions: a generalization of the Rand index and related measures, IEEE Trans Fuzzy Syst, 20, 546-556, (2012) [14] Jaccard, P., Étude comparative de la distribution florale dans une portion des alpes et du jura, Bull de la Société Vaudoise des Sciences Naturelles, 37, 547-579, (1901) [15] MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Oakland, CA, USA 1:281-297 · Zbl 0214.46201 [16] McLachlan G, Krishnan T (2007) The EM algorithm and extensions, vol 382. Wiley, New York · Zbl 0882.62012 [17] McLachlan G, Peel D (2004) Finite mixture models. Wiley, New York · Zbl 0963.62061 [18] McNicholas, PD, Model-based clustering, J Classif, 33, 331-373, (2016) · Zbl 1364.62155 [19] Miyamoto S, Ichihashi H, Honda K (2008) Algorithms for fuzzy clustering. Springer, Berlin · Zbl 1147.68073 [20] Morey, LC; Agresti, A., The measurement of classification agreement: an adjustment to the Rand statistic for chance agreement, Educ Psychol Meas, 44, 33-37, (1984) [21] Qiu, W.; Joe, H., Separation index and partial membership for clustering, Comput Stat Data Anal, 50, 585-603, (2006) · Zbl 1431.62270 [22] Qiu W, Joe H (2015) clusterGeneration: random cluster generation (with specified degree of separation). R package version 1.3.4. https://CRAN.R-project.org/package=clusterGeneration [23] R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria [24] Rand, WM, Objective criteria for the evaluation of clustering methods, J Am Stat Assoc, 66, 846-850, (1971) [25] Scrucca, L.; Fop, M.; Murphy, TB; Raftery, AE, mclust 5: Clustering, classification and density estimation using gaussian finite mixture models, R J, 8, 289, (2016) [26] Steinley, D., Properties of the Hubert-Arabie adjusted Rand index, Psychol Methods, 9, 386, (2004) [27] Ward, JH, Hierarchical grouping to optimize an objective function, J Am Stat Assoc, 58, 236-244, (1963) [28] Wolfe JH (1963) Object cluster analysis of social areas. Ph.D. thesis, University of California
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# Correlated assets in Monte Carlo simulation

I'm trying to simulate $N$ correlated assets in Excel in order to estimate a basket option price.

For 2 assets, I correlated the two random variables $X_1$ and $X_2$ and then simulate the BlackScholes price increments. At the end, the correlation computed with Excel Function for the two stock prices is completely different.

So how do you correlate two BlackScholes stock prices with a correlation $\rho$ ?

I'd like to complete this step correctly before extending to $N$ assets with Cholesky decomposition..

• I don't really see what your question is. As you said, for each step you generate to independent $\mathcal{N}(0, 1)$ normals, e.g. $X_1$ and $X_2$ and then obtain correlated normals $Y_1 = X_1$ and $Y_2 = \rho X_1 + \sqrt{1 - \rho^2} X_2$. Or is the last equation what you were missing? – LocalVolatility Sep 22 '17 at 9:07
• I'm currently generating $Y_1$ and $Y_2$ with the formula you indicate. But for example if I take $\rho = 0.2$, the two correlated $Y_1$ and $Y_2$ roughly have 0.2 correlation, however the correlation between my two stock prices $S_1$ and $S_2$ is completely random (0.2 , 0, 0.8 etc...) – AlexM Sep 22 '17 at 9:32
• I don't know if that is where your misunderstanding is but you are correlating log returns and not prices. When you follow the above approach and then compute a sufficiently large sample of log returns, then you should find that the sample correlation is roughly $\rho$. – LocalVolatility Sep 22 '17 at 9:36
• That's was the misunderstanding, thank you !! – AlexM Sep 22 '17 at 9:57
• Can we also check that you are simulating many paths? If you're just generating one path, the the correlation of that is also a random number, which should have a mean matching that of your input. – will Sep 25 '17 at 7:32


text:
Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Chippy's Journeys

Stage: 2 Challenge Level:

How about using squared paper to draw out Chippy's routes?
What will $1$ square on the paper stand for in metres?