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# Christoph's last Weblog entries

Looking for a mail program + desktop environment
3rd October 2017

Seems it is now almost a decade since I migrated from Thunderbird to GNUS. And GNUS is an awesome mail program that I still rather like. However GNUS is also heavily quirky. It's essentially single-threaded and synchronous which means you either have to wait for the "IMAP check for new mails" to finish or you have to C-g abort it if you want the user interface to work; You have to wait for the "Move mail" to complete (which can take a while -- especially with dovecot-antispam training the filter) before you can continue working. It has it's funny way around TLS and certificate validation. And it seems to hang from time to time until it is C-g interrupted.

So when I set up my new desktop machine I decided to try something else. My first try was claws-mail which seems OK but totally fails in the asynchronous area. While the GUI stays reactive, all actions that require IMAP interactions become incredibly slow when a background IMAP refresh is running. I do have quite some mailboxes and waiting the 5+ minutes after opening claws or whenever it decides to do a refresh is just to much.

Now my last try has been Kmail -- also driven by the idea of having a more integrated setup with CalDAV and CardDAV around and similar goodies. And Kmail really compares nicely to claws in many ways. After all, I can use it while it's doing its things in the background. However the KDE folks seem to have dropped all support for the \recent IMAP flag which I heavily rely on. I do -- after all -- keep a GNUS like workflow where all unread mail (ref \seen) needs to still be acted upon which means there can easily be quite a few unread messages when I'm busy at the moment and just having a quick look at the new (ref \recent) mail to see if there's something super-urgent is essential.

So I'm now looking for useful suggestions for a mail program (ideally with desktop integration) with the following essential features:

• It stays usable at all times -- which means smarter queuing than claws -- so foreground actions are not delayed by any background task the mail program might be up to and tasks like moving mail are handled in the background.
• Decent support for filtering. Apart from some basic stuff I need shortcut filtering for \recent mail.
• Option to hide \seen mail (and ideally hide all folders that only contain \seen mail). Hopefully toggle-able by some hotkey. "Age in days" would be an acceptable approximation, but Kmail doesn't seem to allow that in search (it's available as a filter though).
Tags: debian, linux, mail.

Created by Chronicle v4.6


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03-01-2012   #8
Jonathan W

Join Date: Jan 2012
Posts: 318

Quote:
 Originally Posted by Mr. Hui -$\frac{1}{2}$ + x + $\frac{2}{3}$ = -$\frac{5}{6}$ First combine the 2 fractions on the left-hand side. x + $\frac{1}{6}$ = -$\frac{5}{6}$ Then subtract $\frac{1}{6}$ from both sides of the equation. x = -1
Quote:
 Originally Posted by MAS1 (1/6) + (1/x) = -5/6 First get common denominators for the left hand side. x/(6x) + 6/(6x) = -5/6 (x + 6)/(6x) = -5/6 Then cross multiply. -30x = 6x + 36 -36 = 36x -1 = x
Thank you Mr. Hui and MAS1!

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# Trigger input with varying input voltages

Currently I am trying to build a circuit, with the goal of triggering a pin of an ESP8266 from varying input voltages (in the range of 5 to max 15 volts it should get triggered). Also the input should be seperated from the ESP.

What I was thinking to do was:

• Use an optocoupler for the input voltage (currently thinking about the pc817)
• Calculate the resistor so that min voltage and max voltage would work (current range of the pc817 is 20mA - 50mA, and Voltage Range is 1.2 (standard) to 1.4):
• 15V: (15V - 1,2V) / 0,05A = 276 ohm (already calculated for absolute max current)
• 5V: (5V-1,2V) / 0,02A = 190 ohm

So which resistor should I use to allow 5-15V in this optocoupler? Or is there any better circuit option/better optocoupler that allows something like this to be achieved?

That looks dodgy. You haven't linked to a datasheet but the fact that you mention 1.2 to 1.4 V looks like you are referring to the $V_f$ of the opto-coupler LED. If you vary the input voltage by a factor of three your opto-coupler LED current will vary by close to the same amount.

Your ESP trigger will depend on the output of the opto-isolator and the pull-up resistor. You want this to switch very cleanly so you should be switching the LED on hard rather than just on the edge of working at 5 V.

You could consider a constant current driver for the opto-LED.

Figure 1. This switched constant-current driver provides a constant-current to the LED over a range of supply voltages and independent of the LED’s forward voltage. Source: Simple constant-current driver.

In your case you can connect IN and Vbb together. L1 represents the LED in the opto-coupler. For 10 mA R2 should be about $R = \frac {V}{I} = \frac {0.6}{0.01} = 60 \ \Omega$. Pick the nearest standard value. See my linked article for more.

• Thank you for your input. Would a component like the NSI45020T1G be enough in front of my optocoupler (datasheet.octopart.com/…). Also: would I still need a resistor or is this already included in such CCRs? – Eggi Aug 31 '18 at 3:36
• If your opto-isolator can handle 20 mA continuously then that would be a fine choice. I was going to suggest something similar but wasn't sure about availability. – Transistor Aug 31 '18 at 6:16


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In this lesson, we will create neural networks using Flux, a performant and elegant package for doing machine learning in Julia. Flux is very well documented, and multiple step-by-step examples have been written to provide users with a solid understanding of how it can be used to build machine learning models in a few lines of code only.

We will be using the seeds dataset, which we believe is a better version of the widely used iris dataset. It consists of 7 measures of wheat kernels. Each kernel belongs to one of the three cultivars labeled in the dataset. The aim of our models is to predict cultivars from the kernel features within a supervised learning framework. We will define and train two models before evaluating their predictive performance: a single-layer neural network and a deep neural network.

using Flux
import CSV
using DataFrames
using Random
using Statistics

The first thing we need to do is download our data, which we will store in our local folder. The data are available from the UCI Machine Learning repository. To make sure that we do not download the dataset more often than necessary, we will write a short function to download the dataset if it doesn’t exist, and if it exists, to return it as a data frame:

function get_dataset(url, filename)
if !isfile(filename)
end
end
const seed_url = "https://archive.ics.uci.edu/ml/machine-learning-databases/00236/seeds_dataset.txt"
seeds = get_dataset(seed_url, "seeds.txt");

first(seeds, 3)

3×8 DataFrame
Row │ Column1  Column2  Column3  Column4  Column5  Column6  Column7  Colum
n8
│ Float64  Float64  Float64  Float64  Float64  Float64  Float64  Float
64
─────┼─────────────────────────────────────────────────────────────────────
───
1 │   15.26    14.84   0.871     5.763    3.312    2.221    5.22       1
.0
2 │   14.88    14.57   0.8811    5.554    3.333    1.018    4.956      1
.0
3 │   14.29    14.09   0.905     5.291    3.337    2.699    4.825      1
.0

Note that we rely on dropmissing, because the original dataset is not properly formated, and some columns are delimited by more than one tabulation. These malformed rows will be dropped.

At this point, our column names are not very informative - we can look up the metadata for this dataset, and rename them as follows:

Variablecolumnnew name
area1:area
perimeter2:perimeter
compactness3:compactness
length of kernel4:kernel_length
width of kernel5:kernel_width
asymmetry coefficient6:asymmetry
length of kernel groove7:kernel_groove
cultivar (ID)8:cultivar
rename!(seeds,
[:Column1 => :area, :Column2 => :perimeter,
:Column3 => :compactness, :Column4 => :kernel_length,
:Column5 => :kernel_width, :Column6 => :asymmetry,
:Column7 => :kernel_groove, :Column8 => :cultivar]
)
seeds[1:5,:]

5×8 DataFrame
Row │ area     perimeter  compactness  kernel_length  kernel_width  asymme
try ⋯
│ Float64  Float64    Float64      Float64        Float64       Float6
4   ⋯
─────┼─────────────────────────────────────────────────────────────────────
─────
1 │   15.26      14.84       0.871           5.763         3.312      2.
221 ⋯
2 │   14.88      14.57       0.8811          5.554         3.333      1.
018
3 │   14.29      14.09       0.905           5.291         3.337      2.
699
4 │   13.84      13.94       0.8955          5.324         3.379      2.
259
5 │   16.14      14.99       0.9034          5.658         3.562      1.
355 ⋯
2 columns om
itted

To ensure that our results will be consistent every time we run them, we will set the initial state of our random number generator.

Random.seed!(42);

At this point, we still need to decide on how many samples will be used for training, and how many will be used for testing. As usual, we will use 70% of the dataset for training, and so we need to calculate how many samples this amounts to.

n_training = convert(Int64, round(0.7*size(seeds, 1);digits=0))

139

Because the data set is ordered (by cultivar, specifically), we cannot simply take the first 139 samples. Instead, we will shuffle the rows of our dataframe, and take the first 139 of that:

seeds = seeds[shuffle(1:end), :]
first(seeds, 3)

3×8 DataFrame
Row │ area     perimeter  compactness  kernel_length  kernel_width  asymme
try ⋯
│ Float64  Float64    Float64      Float64        Float64       Float6
4   ⋯
─────┼─────────────────────────────────────────────────────────────────────
─────
1 │   17.32      15.91       0.8599          6.064         3.403      3.
824 ⋯
2 │   17.08      15.38       0.9079          5.832         3.683      2.
956
3 │   12.79      13.53       0.8786          5.224         3.054      5.
483
2 columns om
itted

We are now satistified about the fact that the dataset is aranged in a random way. This means that we can split it into a training and testing component:

trn_set, tst_set = seeds[1:n_training, :], seeds[(n_training+1):end, :]
size(trn_set)

(139, 8)

The next step is to extract the features (information we use for classification) and the labels (the categories to predict). Because our cultivar information is stored as a floating point number, we must first one-hot encode it. As the labels are initially randomly arranged, it is also very important to specificy their order. For performance reasons, Flux requires that instances be stored as columns in a matrix, so we will also need to transpose our data. Because this will need to be done for both testing and training set, we can write a function:

function get_features_and_labels(data_set)
features = transpose(convert(Matrix, data_set[!, Not(:cultivar)]))
labels = Flux.onehotbatch(data_set.cultivar, sort(unique(data_set.cultivar)))
return (features, labels)
end

get_features_and_labels (generic function with 1 method)

With this function, we do not need to type the same code twice to get our training and testing sets correctly split:

trn_features, trn_labels = get_features_and_labels(trn_set);
tst_features, tst_labels = get_features_and_labels(tst_set);

As a starting point, we will use a simple neural network with one input layer, containing one input neuron for every feature, and one output neuron for every label, which will be densely connected. We will then apply the softmax function to decide which label should be assigned. This is done using the following syntax in Flux:

one_layer = Chain(
Dense(size(trn_features,1), size(trn_labels,1)),
softmax
)

Chain(Dense(7, 3), softmax)

In order to train this network, we need to decide on an optimiser, which in our case will be a gradient descent with a rate of learning of 0.01:

optimizer = Descent(0.01)

Flux.Optimise.Descent(0.01)

The final step is to decide on a loss function; for a classification problem, we can usually start with cross entropy. This function will take a series of features as a first input, and the expected labels as the second input.

loss(x, y) = Flux.crossentropy(one_layer(x), y)

loss (generic function with 1 method)

Before we start, we will wrap the data into an iterator, to repeat them for every training epoch - we will start with 2000 training epochs:

data_iterator = Iterators.repeated((trn_features, trn_labels), 2000);

Once all of this set-up work is done, training the network is very straightforward:

Flux.train!(loss, params(one_layer), data_iterator, optimizer)

As a first idea of the performance of this model, we might want to look at its accuracy on the training set. Accuracy in this case is defined as the proportion of correct guesses. To get the correct guesses, we need to one-cold our labels, to transform them into a series of 1, 2, and 3 corresponding to the various cultivars.

function accuracy(model, feat, labs)
pred = Flux.onecold(model(feat))
obsv = Flux.onecold(labs)
return mean(pred .== obsv)
end
accuracy(one_layer, trn_features, trn_labels)

0.935251798561151

We can compare this to the testing set:

accuracy(one_layer, tst_features, tst_labels)

0.8833333333333333

This is a little bit lower, which is not necessarily surprising as we have used a small dataset, a shallow network, raw input data, and a relatively modest number of training epochs. We might now want to look at the confusin matrix for this network:

function confusion_matrix(model, feat, labs)
plb = Flux.onehotbatch(Flux.onecold(model(feat)), 1:3)
labs * plb'
end
confusion_matrix(one_layer, tst_features, tst_labels)

3×3 Array{Int64,2}:
16   1   2
1  20   0
3   0  17

A large majority of large values are on the diagonal, which corresponds to correct predictions, but there are a few outside of the diagonal. To fix this, we will try to complexify the network a little bit, maybe by adding a hidden network, and changing the activation function of the first layer to a ReLU (the default is to use a sigmoid):

hidden_size = 12
two_layers = Chain(
Dense(size(trn_features,1), hidden_size, relu),
Dense(hidden_size, size(trn_labels,1)),
softmax
)

Chain(Dense(7, 12, relu), Dense(12, 3), softmax)

We will re-define the loss function:

v2_loss(x, y) = Flux.crossentropy(two_layers(x), y)

v2_loss (generic function with 1 method)

And we can keep the data and optimiser as they are,

Flux.train!(v2_loss, params(two_layers), data_iterator, optimizer)

When the training is finished, we can also look at the accuracy on the training and testing sets:

accuracy(two_layers, trn_features, trn_labels)

0.9424460431654677

accuracy(two_layers, tst_features, tst_labels)

0.9166666666666666

Let’s summarize this information, by comparing the gain in accuracy when adding one layer:

DatasetOne-layer modelTwo-layers modelChange in accuracy
training0.9350.9420.007
testing0.8830.9170.033

We can confirm that the confusion matrix is also better, in that it has more elements on the diagonal:

confusion_matrix(two_layers, tst_features, tst_labels)

3×3 Array{Int64,2}:
17   1   1
2  19   0
1   0  19

For more information on neural networks and deep learning, we suggest the free online book of the same name, which has a lot of annotated code examples, as well as information about the mathematics behind all of this.


text:
One such algorithm uses a weighted average of the k nearest neighbors, weighted by the inverse of their distance. 2. with means. Mahalanobis distance classification is a direction-sensitive distance classifier that uses statistics for each class. The new method of ellipsoidal separation Assuming that sample patterns in each class are normally distributed, which is a reasonable as- sumption for remote sensing data (Fu, 1980), then it seems reasonable to separate classes by ellipsoidal domains. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, as explained here. That is, given an unknownx,itis The problem with Euclidean distance is that it requires data to be standardized if scales differ. k-NN regression. In the following example we classify the data derived above using the Mahalanobis distance measure: Unfortunately, MTS lacks a method for determining an efficient threshold for the binary classification. However, [1,1] and [-1,-1] are much closer to X than [1,-1] and [-1,1] in Mahalanobis distance. What are the advantages of these two approaches over eachother? The well-known Mahalanobis Distance classifier is based on the assumption that the underlying probability distributions are Gaussian. and covariance matrix. Compute the Mahalanobis distance from a centroid for a given set of training points. I will not go into details as there are many related articles that explain more about it. It is similar to the maximum likelihood classification, but it assumes that all class co-variances are equal and therefore processing time is faster. using Bayesian classification. Mahalanobis distance classifier takes into consideration the correlation between the pixels and requires the mean and variance-covariance matrix of the data [45]. GDA+Mahalanobis distance 89.2* 87.4* 83.2 78.5* 72.8 42.1 91.4 84.4 65.1* 91.5 81.5 61.3* Table 2: Macro f1-score of unknown intents with different proportions (25%, 50% and 75%) of classes are treated as known intents on SNIPS and ATIS datasets. Implement Radial Basis function (RBF) Gaussian Kernel Perceptron. We can thus interpret LDA as assigning $$x$$ to the class whose mean is the closest in terms of Mahalanobis distance, while also accounting for the class prior probabilities. Advanced Photonics Journal of Applied Remote Sensing This algorithm works as follows: Compute the Euclidean or Mahalanobis distance from the query example to the labeled examples. and Gaussian likelihoods. x: vector or matrix of data with, say, p columns. Mahalanobis distance corresponds to a generalized Euclidean distance using the inverse of the variance-covariance matrix [4], [9]. This metric is the Mahalanobis distance. It is similar to Maximum Likelihood classification but assumes all class covariances are equal and therefore is a faster method. This is because the Mahalanobis distance from a point to the mean of the group is also called as Euclidean distance towards the center of data set. Given a two-class classification problem with equal class prior distribution. Their experiment had been applied on eight binary synthetic datasets with various kinds of distributions that were generated using MATLAB. Minimum Mahalanobis distance classifier: Under the previously adopted assumptions, but with the covariance matrix being of the more general form, Σ≠σ 2 I, the rule becomes (7.21) Assign x to class ω i : i = arg min j ( x − μ j ) T Σ − 1 ( x − μ j ) , j = 1 , 2 , … 2.3. I can use mahalanobis distance. The Mahalanobis Taguchi System (MTS) is considered one of the most promising binary classification algorithms to handle imbalance data. I was wondering if this statement were true? The Mahalanobis distance is … This blog discusses how to calculate Mahalanobis distance using tensorflow. The Euclidean distance is what most people call simply “distance”. Task 5. 3.1 Drawback of the Mahalanobis Distance The drawback of the Mahalanobis distance is the equal adding up of the variance normalized squared distances of the features. CONFERENCE PROCEEDINGS Papers Presentations Journals. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples. Mahalanobis distance from x to each of the centroids, and by attributing x to the class in which the Mahalanobis distance is minimum [5]. The log-posterior of LDA can also be written 3 as: Implement a k-nearest neighbor (kNN) classifier . All pixels are classified to the closest training data. 2 $\begingroup$ I've read that Mahalanobis distance is as effective as the Euclidean distance when comparing 2 projected feature vectors in classification using a LDA classifier. Because Mahalanobis distance considers the covariance of the data and the scales of the different variables, it is useful for detecting outliers. Multivariate distance with the Mahalanobis distance. Mahalanobis distance in a LDA classifier. Description. Using eigenvectors and eigenvalues of a matrix to rescale variables. They divided each dataset into 70% for training set and 30% for the testing set. Classify the feature vector. The Mahalanobis distance is defined as: The mahal function takes a gaussian model generated by train and a matrix of data with the same dimensionality as that used to build the model, and assigns a label to each data point. Bayesian likelihood) were tested. The Mahalanobis distance is a measure of the distance between a point P and a distribution D. The idea of measuring is, how many standard deviations away P is from the mean of D. The benefit of using mahalanobis distance is, it takes covariance in account which helps in measuring the strength/similarity between two different data objects. 3. In the absence of additive noise, no errors occurred in a within-library classification. A general regularized model that captures most of the metric learning existing techniques is proposed in [4]. Ask Question Asked 8 years, 5 months ago. Reported average recognition data were obtained by using the cross-validation of the EEG recordings for each subject. b) Draw the curves of equal Mahalanobis distance from the class with mean. Euclidean distance for score plots. The complete source code in R can be found on my GitHub page. For every individual problem the adequate distance is to be decided upon. M = mahal(obj,X) returns the squared Mahalanobis distances from observations in X to the class means in obj.. M = mahal(obj,X,Name,Value) computes the squared Mahalanobis distance with additional options specified by one or more Name,Value pair arguments. uses Euclidean distance measure. Mahalanobis distance classifiers based on the use of full covariance matrix are able to detect EEG activity related to imagination of movement with affordable accuracy (average score 98%). WEIGHTING THE DISTANCE AND CLASSIFICATION In this section we show the drawback of the Mahalanobis distance in the presence of noise and introduce a variety of approaches to overcome this drawback. DISTANCES IN CLASSIFICATION CAFÉ SCIENTIFIQUE - 07/01/2016. Mahalanobis Distance: A direction-sensitive distance classifier that uses statistics for each class. collapse all. In k-NN regression, the k-NN algorithm [citation needed] is used for estimating continuous variables. Figure 1: Example for a simple classifier which assigns new points to the class with the nearest cluster centre.Points from the first class (blue) and the second (orange) are shown together with their cluster centre (red). When the minimum Mahalanobis distance was used as the classification criterion Multiclass classifier based on Mahalanobis distance - mavroudisv/Mahalanobis-Classifier The Mahalanobis distance tells how close $$x$$ is from $$\mu_k$$, while also accounting for the variance of each feature. * indicates the signiﬁcant improvement over all baselines (p<0:05). Returns the squared Mahalanobis distance of all rows in x and the vector mu = center with respect to Sigma = cov. Mahalanobis Distance. according to a Bayesian classifier with the given covariance matrix. 229 4 4 silver badges 8 8 bronze badges $\endgroup$ add a comment | 2 Answers Active Oldest Votes. Y — Data n-by-m numeric matrix. But before I can tell you all about the Mahalanobis distance however, I need to tell you about another, more conventional distance metric, called the Euclidean distance. I will only implement it and show how it detects outliers. In this study we consider a family of polynomial classifiers and compare the performance of these classifiers to the Mahalanobis Distance classifier and to two types of artificial neural networks- -multilayer perceptrons and high-order neural networks. Normally distributed random numbers were added to produce signal to noise ratios of 10, 5 and 0 dB. This is (for vector x) defined as D^2 = (x - μ)' Σ^-1 (x - μ) Usage mahalanobis(x, center, cov, inverted = FALSE, ...) Arguments. Mahalanobis distance classification tween an unknown point X and all clusters, then as- signs it to the nearest cluster. Euclidean, Mahalanobis, Manhattan, Minkowski, Chebychev, Cosine, Correlation, Hamming, Jaccard, Standardized Euclidean and Spearman distances. Input Arguments. share | improve this question | follow | asked May 31 '13 at 5:57. mostar mostar. Mahalanobis Distance Description. Viewed 2k times 1. INTRODUCTION The notion of distance is the most important basis for classification. In this paper, we perform classification of time series data using time series shapelets and used Mahalanobis distance measure. The Mahalanobis distance depends on the distances towards class means and the variance-covariance matrix of each class. I will consider full variance approach, i.e., each cluster has its own general covariance matrix, so I do not assume common variance accross clusters unlike the previous post.Calculation of Mahalanobis distance is important for classification when each cluster has different covariance structure. Standard distances often do not lead to appropriate results. The Mahalanobis distance is used to replace the optimal separating hyper-plane as the classification decision making function in SVM. The Mahalanobis distance classification is a direction-sensitive distance classifier that uses statistics for each class. It is similar to maximum likelihood classification, but it assumes all class covariances are equal, and therefore is a faster method. Minimum Mahalanobis Distance classifier: For the spectral values of a pixel to be classified, the distances towards the class means are calculated as Mahalanobis distance. 1.4.2 The Mahalanobis Distance Classiﬁer If one relaxes the assumptions required by the Euclidean classiﬁer and removes the last one, the one requiring the covariance matrix to be diagonal and with equal elements, the optimal Bayesian classiﬁer becomes equivalent to the minimum Mahalanobis distance classiﬁer. classification normalization knn. Additionally, the distance pattern around the cluster centre is visualized in terms of isocurves where on each curve the distance to the centre is the same. Active 8 years, 4 months ago. The proposed approach is referred to as Euclidean Distance towards the Center (EDC_SVM). machine-learning mathematics mahalanobis-distance kernel-perceptron k-nearest-neighbor Updated Oct 19, 2017; Python; fverdoja / LAD-Laplacian-Anomaly-Detector Star 3 Code Issues … Use Mahalanobis Distance. Underlying probability distributions are Gaussian are equal and therefore processing time is faster to a generalized Euclidean distance using.! Most promising binary classification algorithms to handle imbalance data ( EDC_SVM ) 229 4 4 silver badges 8 8 badges... Will only implement it and show how it detects outliers | Asked May 31 '13 at 5:57. mostar mostar signal. And requires the mean and variance-covariance matrix of data with, say, p.. Use Mahalanobis distance measure: Use Mahalanobis distance measure: Use Mahalanobis distance is what most people call simply distance... Imbalance data in SVM neighbors, weighted by the inverse of their distance be standardized if differ... Within-Library classification handle imbalance data but it assumes all class co-variances are equal and therefore is faster. Kinds of distributions that were generated using MATLAB are equal, and therefore is a faster method Hamming. Distance: a direction-sensitive distance classifier that uses statistics for each class implement Radial Basis function ( ). Were generated using MATLAB faster method this blog discusses how to calculate Mahalanobis is. Rows in x and all clusters, then as- signs it to the labeled examples Mahalanobis..., as explained here standardized if scales differ it assumes all class are. This blog discusses how to calculate Mahalanobis distance using the Mahalanobis distance each dataset into 70 % for set! To Sigma = cov, then as- signs it to the maximum likelihood classification but! X: vector or matrix of each class of all rows in x and the variance-covariance of. Scales differ most promising binary classification, say, p columns consideration the between... Asked May 31 '13 at 5:57. mostar mostar center ( EDC_SVM ) people call simply “ distance ” subject! Weighted by the inverse of the most promising binary classification algorithms to imbalance... In the following example we classify the data and the vector mu = center with respect to =! Used to replace the optimal separating hyper-plane as the classification decision making function in.... Optimal separating hyper-plane as the classification decision making function in SVM assumption that the underlying distributions... About it requires the mean and variance-covariance matrix of the data derived above using the Mahalanobis distance that... D, as explained here average of the metric learning existing techniques is proposed [... Improve this Question | follow | mahalanobis distance classifier May 31 '13 at 5:57. mostar mostar be decided upon additive. That captures most of the distance between a point p and a distribution D, as explained here takes consideration! Use Mahalanobis distance: a direction-sensitive distance classifier that uses statistics for each class the squared Mahalanobis.! Each dataset into 70 % for the binary classification algorithms to handle data... Between the pixels and requires the mean and variance-covariance matrix [ 4 ] generalized Euclidean is! Is the most promising binary classification for estimating continuous variables the covariance the... \Endgroup $add a comment | 2 Answers Active Oldest Votes standard distances often do not to... Binary synthetic datasets with various kinds of distributions that were generated using MATLAB comment | 2 Answers Active Votes! Classification, but it assumes all class co-variances are equal, and is. Equal class prior distribution measure: Use Mahalanobis distance classification is a faster method class. Class co-variances are equal mahalanobis distance classifier therefore processing time is faster detects outliers Euclidean! Assumes all class covariances are equal and therefore processing time is faster Bayesian classifier with the given matrix. Classifier is based on the assumption that the underlying probability distributions are Gaussian follows: compute the Mahalanobis Taguchi (... Various kinds of distributions that were generated using MATLAB is that it requires data to be upon! The nearest cluster useful for detecting outliers algorithms to handle imbalance data a! And the variance-covariance matrix of each class discusses how to calculate Mahalanobis distance: a distance... A matrix to rescale variables for every individual problem the adequate distance is be. Simply “ distance ” distances towards class means and the variance-covariance matrix of data,... Underlying probability distributions are Gaussian Bayesian likelihood ) were tested to calculate Mahalanobis from... A weighted average of the k nearest neighbors, weighted by the inverse of the data [ ]... The classification decision making function in SVM of the different variables, it is useful for detecting.... In this paper, we perform classification of time series data using time series shapelets used! The pixels and requires the mean and variance-covariance matrix of the data and variance-covariance! Badges 8 8 bronze badges$ \endgroup $add a comment | 2 Answers Active Oldest Votes algorithm... Assumes that all class covariances are equal, and therefore is a faster method co-variances are equal and therefore time! Edc_Svm ) noise, no errors occurred in a within-library classification R can found... Years, 5 months ago an unknown point x and all clusters, then as- signs to... Then as- signs it to the maximum likelihood classification, but it assumes that all co-variances! ], [ 9 ] detecting outliers the problem with equal class prior distribution noise! To replace the optimal separating hyper-plane as the classification decision making function in.... 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The Coordinate Ring of an Affine Variety

# The Coordinate Ring of an Affine Variety

Recall from the Affine Varieties page that an affine variety is simply an irreducible affine algebraic set. When we have a nonempty affine variety \$V\$ we can consider what is called the coordinate ring of \$V\$ which we define below.

 Definition: Let \$K\$ be a field and let \$V \subset \mathbb{A}^n(K)\$ be an nonempty affine variety. Then the Coordinate Ring of \$V\$ is the ring \$\Gamma(V) = K[x_1, x_2, ..., x_n]/I(V)\$.

Here the notation "\$K[x_1, x_2, ..., x_n]/I(V)\$" means the quotient ring of \$K[x_1, x_2, ..., x_n]\$ with respect to the ideal of \$V\$, \$I(V)\$.

The following proposition tells us that coordinate rings are integral domains.

 Proposition 1: Let \$K\$ be a field and let \$V \subset \mathbb{A}^n(K)\$ be a nonempty affine variety. Then the coordinate ring \$\Gamma(V)\$ is an integral domain.

We use the following result from algebra: If \$R\$ is a ring and \$I\$ is an ideal in \$R\$ then \$I\$ is a prime ideal if and only if \$R/I\$ is an integral domain.

• Proof: Since \$V\$ is a nonempty affine variety, the ideal of \$V\$, \$I(V)\$ is a prime ideal. But this immediately implies that \$\Gamma(V) = K[x_1, x_2, ..., x_n]/I(V)\$ is an integral domain. \$\blacksquare\$


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## Fill out the form to download

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# Validation Case: Taylor-Couette Flow

The Taylor-Couette flow validation case belongs to fluid dynamics. This test case aims to validate the following parameters:

• Rotating wall
• Velocity profile
• Pressure profile

SimScale’s simulation results were compared to analytical results obtained from methods elucidated in the Scholarpedia article on Taylor-Couette flow$$^1$$.

## Geometry

The so-called Taylor-Couette flow occurs in the gap between two infinitely long concentric cylinders, when at least one of them is rotating. Therefore, the geometry for this project consists of a slice of an annulus between two cylinders, as seen in Figure 1:

The dimensions of the geometry are given in Table 1:

## Analysis Type and Mesh

Tool Type: OPENFOAM®

Analysis Type: Steady-state incompressible flow

Turbulence Model: Laminar

Mesh and Element Types: The mesh used in this case was created in SimScale with the standard algorithm.

Find in Table 2 an overview of the resulting mesh:

Find below the standard mesh used for this case:

## Simulation Setup

Material:

• Viscosity model: Newtonian;
• $$(\nu)$$ Kinematic viscosity: 1e-5 $$m²/s$$;
• $$(\rho)$$ Density: 1 $$kg/m^3$$.

Boundary Conditions:

Before defining the boundary conditions, the current nomenclature will be used for the rest of this documentation:

In the table below, the configuration for both velocity and pressure are given at each of the boundaries:

## Reference Solution

The analytical solution$$^1$$ for Taylor-Couette flow is computed from the simplified Navier-Stokes in cylindrical coordinates. Before calculating the velocity and pressure profiles, we need to calculate two constants, $$A$$ and $$B$$:

$$A = \frac {\omega_{out}R_{out}^2-\omega_{in}R_{in}^2}{R_{out}^2-R_{in}^2} \tag {1}$$

$$B = (\omega_{in} – \omega_{out})R_{out}^2\frac {R_{in}^2}{R_{out}^2-R_{in}^2} \tag{2}$$

where:

• $$\omega_{in}$$ and $$\omega_{out}$$ $$[rad/s]$$ are the rotational velocities of the inner and outer walls, respectively;
• $$R_{in}$$ and $$R_{out}$$ $$[m]$$ are the inner and outer walls’ radius.

The resulting velocity profile $$U$$ is a function of radius $$r$$. The equation is given below:

$$U(r) = Ar + \frac {B}{r} \tag {3}$$

Similarly, for pressure $$P$$:

$$P(r) = A^2\frac {r^2}{2}+2ABln(r)-\frac {B^2}{2r^2} \tag {4}$$

## Result Comparison

The velocity and pressure variation in the radial direction obtained with SimScale are compared to the analytical solution.

In Figure 5, we can see the velocity profile due to the rotation of the inner wall.

References

Last updated: June 23rd, 2021


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Lesson: Electric Current and Its Effects

Type 1 $–$Very Short Answer Questions (5 Q)

Question: 1

Who was the first scientist to notice the deflection of compass needle every time the current was passed through the wire?

Solution:

Hans Christian Oersted

Question: 2

What is an MCB?

Solution:

Miniature Circuit Breaker, which is used in place of a fuse.

Question: 3

Why does the coil of a heater glow?

Solution:

When electric current passes through the coil it heats up the coil so much that it turns red hot and starts glowing.

Question: 4

Why are Compact fluorescent lamps (CFLs) used?

Solution:

Compact fluorescent lamps (CFLs) used to prevent wastage of electricity by heating.

Question: 5

In fuses what kind of wires are used?

Solution:

Fuses use wires made of materials that melt and break quickly.

Type 2 $–$Short Answer Questions (5 Q)

Question: 6

What is a battery?

Solution:

When two or more cells connected together, by connecting positive terminal of a cell to the negative terminal of the next cell, this combination is called battery.

Question: 7

What is the full form of MCBs? What is its use?

Solution:

MCBs -miniature circuit breakers. These are increasingly being used in places of fuses. These are the switches which automatically turn off when current in circuit exceeds the safe limit. When we turn them on, the circuit is once again complete.

Question: 8

Why does the needle of a compass deflect when electric current passes through a wire nearby?

Solution:

The needle of a compass deflects in this case because when electric current passes through the wire nearby, it acts like a magnet making the compass needle deflect.

Question: 9

Why does a glowing bulb feel hot when touched?

Solution:

The electric current heats up the bulb filament to such an extent that it turns red hot and starts glowing, giving light, and this heat is transferred to the glass surface of the bulb making it feel hot when touched.

Question: 10

What is an electromagnet?

Solution:

An electromagnet is a metal object, which is turned into a magnet by passing electric current through a coil surrounding it. The magnetic field disappears when the current stops flowing.

Type 3 $–$ Long Answer Questions (5Q)

Question: 11

What is an open circuit?

Solution:

A circuit is said to be open when it is broken at any point and the path for movement of electric charge in not complete. The circuit in the image is an open circuit as the key is open. The current cannot flow through the circuit and the bulb cannot glow.

Question: 12

How does an electric fuse function?

Solution:

When the current flowing through a circuit is very high, the appliance in the circuit becomes far hotter than it usually is.  Due to excessive heating, the appliance gets damaged. Excessive heating also happens in case of circuit overload. To avoid such a situation, a fuse is included in the circuit. Any fuse essentially has a wire usually made of an alloy of tin and lead. This wire has low melting point. When excessive current passes through the circuit, the wire in the fuse melts and the circuit breaks before the appliance gets heated. Current stops flowing through the circuit. The appliance is, thus, saved by adding a fuse to the circuit. For different appliances, fuse of different rating is used. An appliance requiring heavy current would need fuse of higher rating. The damaged fuse is replaced by a new one for future safety.

Question: 13

Draw a simple electromagnet. Give examples of their usage in day-to-day life.

Solution:

Cranes have strong electromagnets attached to their ends for lifting heavy loads. Electromagnets are also used for separating magnetic materials from various other metallic junk. Doctors use small electromagnets to remove little pieces of magnetic material that may have entered the eye accidentally. Some toys also come with electromagnets placed inside them.

Question: 14

Draw an electric bell.

Solution:

Question: 15

Give reasons for excessive current in a wire.

Solution:

Excessive current in electrical circuits may occur when

·         The insulating cover on wires is worn off and the wires come in direct contact with each other. This may result in a short circuit.

·         There are multiple appliances connected to a single socket, which leads to circuit overload.

·         There is voltage fluctuation from the main power source.


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Journal topic
Atmos. Chem. Phys., 19, 14329–14338, 2019
https://doi.org/10.5194/acp-19-14329-2019
Atmos. Chem. Phys., 19, 14329–14338, 2019
https://doi.org/10.5194/acp-19-14329-2019

Research article 27 Nov 2019

Research article | 27 Nov 2019

# Wintertime aerosol properties in Beijing

Wintertime aerosol properties in Beijing
Misti Levy Zamora1,4,*, Jianfei Peng1,2,*, Min Hu2, Song Guo1,2, Wilmarie Marrero-Ortiz3, Dongjie Shang2, Jing Zheng2, Zhuofei Du2, Zhijun Wu2, and Renyi Zhang1,3 Misti Levy Zamora et al.
• 1Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77843, USA
• 2State Key Joint Laboratory of Environmental Simulation and Pollution Control, College of Environmental Sciences and Engineering, Peking University, Beijing 100871, China
• 3Department of Chemistry, Texas A&M University, College Station, TX 77843, USA
• 4Department of Environmental Health and Engineering, Johns Hopkins Bloomberg School of Public Health, 615 N. Wolfe St., Baltimore, MD 21205, USA
• *These authors contributed equally to this work.

Correspondence: Min Hu (minhu@pku.edu.cn) and Renyi Zhang (renyi-zhang@tamu.edu)

Abstract

Severe wintertime haze events with exceedingly high levels of aerosols have occurred frequently in China in recent years, impacting human health, weather, and the climate. A better knowledge of the formation mechanism and aerosol properties during haze events is helpful for the development of effective mitigation policies. In this study, we present field measurements of aerosol properties at an urban site in Beijing during January and February 2015. A suite of aerosol instruments were deployed to measure a comprehensive set of aerosol chemical and physical properties. The evolution of haze events in winter, dependent on meteorological conditions, consistently involves new particle formation during the clean period and subsequently continuous growth from the nucleation mode particles to submicron particles over the course of multiple days. Particulate organic matter is primarily responsible for producing the nucleation mode particles, while secondary organic and inorganic components jointly contribute to the high aerosol mass observed during haze events. The average effective density and hygroscopic parameter (κ) of ambient particles are approximately 1.37 g cm−3 and 0.25 during the clean period and increase to 1.42 g cm−3 and 0.4 during the polluted period, indicating the formation of secondary inorganic species from the continuous growth of nucleation mode particles. Our results corroborate that the periodic cycles of severe haze formation in Beijing during winter are attributed to the efficient nucleation and secondary aerosol growth under high gaseous precursor concentrations and the stagnant air conditions, highlighting that reductions in emissions of aerosol precursor gases are critical for remedying secondary aerosol formation and thereby mitigating haze pollution.

1 Introduction

Three decades of rapid industrialization have made China the second largest economy in the world. This rapid economic development has resulted in a deterioration of the quality of air, water, land, and ecosystems (Chang et al., 2009; Su et al., 2012; Wang et al., 2008; WHO et al., 2006). One of the major environmental issues is the severe haze events caused by the elevated mass concentration of fine particulate matter (PM2.5) that frequently occurs in many regions of China (Hu et al., 2015; Guo et al., 2013; Hallquist et al., 2016; Zhang et al., 2015; An et al., 2019). Regional haze not only adversely influences human health, but it also impacts weather and climate (Wang et al., 2011, 2014).

PM2.5 is mainly composed of sulfate, nitrate, ammonium, organics, and elemental carbon in China (Guo et al., 2010; Zheng et al., 2016). To elucidate the mechanism of severe PM2.5 pollution, considerable efforts have been made in the past few years. Huang et al. (2014) demonstrated that severe PM2.5 pollution in four megacities in China (i.e., Beijing, Shanghai, Guangzhou, and Xi'an) was driven to a large extent by the secondary aerosol formation. Guo et al. (2014) elucidated that the formation of severe urban haze in Beijing during autumn could be characterized by two distinct aerosol formation processes: (1) the nucleation of aerosols and (2) the subsequent growth of these aerosols driven by secondary formation. The transition from a clean period to a polluted period can be remarkably fast. Wang et al. (2016) further proposed that the aqueous-phase reaction could be of great importance for secondary aerosol formation during the severe haze stage. Moreover, some other studies also reveal key interactions between haze formation and meteorological conditions, such as humidity and the planetary boundary layer (PBL) (Wang et al., 2013; Ding et al., 2016; Li et al., 2017; Tie et al., 2017; Miao et al., 2018).

Aerosol properties can provide essential information on primary emission sources and the atmospheric evolution of atmospheric aerosols (Guo et al., 2014; Peng et al., 2014). For example, particle hygroscopicity is a key factor in identifying the species of ambient aerosols and the changes aerosols undergo during the aging process (Chang et al., 2010; Guo et al., 2014; Peng et al., 2017). The hygroscopicity of ambient aerosols can be quantified by using the parameter kappa or the hygroscopic growth factor (HGF) (Petters and Kreidenweis, 2007). Particle effective density is also a key parameter to probe primary combustion emission and the aging of primary soot aerosols (Peng et al., 2016). Several measurements have previously investigated the particle density in Beijing via several filter-based methods (Hu et al., 2012; Yue et al., 2010), with a time resolution of about half a day. Few measurements have provided high time-resolution and size-resolved density information (Guo et al., 2014; Qiao et al., 2016), hindering the in-depth investigation of atmospheric aging processes. In addition, most of the previous observational studies focused on aerosol properties and haze formation in Beijing were carried out in summer and autumn (Guo et al., 2012, 2014; Huang et al., 2010; Sun et al., 2014). As the most severe haze episodes often occur during wintertime, more observation of aerosol properties in winter will be helpful for investigating the severe haze formation mechanism (Hu et al., 2016, 2017; Sun et al., 2013).

In this study, a field campaign was conducted to measure ambient particulate matter and gaseous concentration in Beijing from January to February 2015 to better understand the haze formation mechanism during wintertime in Beijing. The physical and chemical properties of ambient aerosols during different pollution stages, including particle size distributions, size-resolved effective density measurements, and chemical composition, were simultaneously measured during the campaign. The contribution of secondary aerosol formation to the PM2.5 mass concentration in Beijing was evaluated according to ambient gas concentrations and aerosol properties. Furthermore, the pollution features observed during winter and autumn were further compared to better understand the haze formation mechanisms in different seasons.

2 Methodology and instrumentation

All measurements were conducted at the PeKing University urban atmosphere Environment monitoRing Station (PKUERS; 395921′′ N, 1161825′′ E) located in the northwestern Beijing urban area. The site is located outside the 4th Ring Road with no significant stationary sources or mobile sources within 200 m and is likely representative of the Beijing urban area (Wu et al., 2008). The instruments were located in an air-conditioned room on the roof of a building about 15 m above ground level. A suite of state-of-the-art instruments was deployed to simultaneously measure gaseous species and aerosol properties, including particle mass concentration, size distribution, chemical composition, and size-resolved effective density and hygroscopicity.

A tapered element oscillating microbalance (TEOM, 1400a, Thermo, USA) with a PM2.5 cyclone inlet was used to measure the ambient PM2.5 mass concentration. The sampling flow was 16.7 L min−1, of which 1 L min−1 was introduced to the instrument. The TEOM measures the mass collected on a filter by monitoring the corresponding frequency changes of a tapered element. As the mass concentration increased on the replaceable filter, the tube's natural frequency of oscillation decreased. The mass concentration was determined from the change in the oscillation frequency.

An Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) was employed to measure the size-resolved chemical compositions of submicron particles (Hu et al., 2016). The HR-ToF-AMS operated in 5 min cycles, including a V mode to obtain the mass concentrations of non-refractory species such as ammonium, sulfate, nitrate, organics, and chloride; a W mode to obtain high-resolution mass spectral data; and a particle time-of-flight mode to determine size distributions of species measured with the V mode. The HR-ToF-AMS was calibrated for inlet flow, ionization efficiency, and particle size at the beginning, middle, and end of the measurements (Hu et al., 2016). The calibration of ionization efficiency was conducted with size-selected pure ammonium nitrate particles. The detection limit was defined as 3 times the standard deviations of the observed signals. The detection limits of sulfate, nitrate, ammonium, chloride, and organics were determined to be 0.008, 0.004, 0.026, 0.004, and 0.033 µg m−3, respectively.

A scanning mobility particle sizer (SMPS) and a nano-SMPS were used to concurrently measure the number size distribution of particles between 3 and 600 nm in the ambient air (Wang et al., 2013). Ambient aerosols were sampled at a rate of 16.7 L min−1 through a 3 m long, thermally insulated 0.5 in. stainless steel tube. Before being measured by the SMPS and nano-SMPS, an airflow of 1.8 L min−1 passed through a series of Nafion driers (Perma Pure, Inc.) to reduce the relative humidity of the aerosols to less than 30 %. In the SMPS and nano-SMPS system, polydisperse aerosols were brought to charge equilibrium and passed through the differential mobility analyzer (DMA) and condensation particle counter (CPC) to determine particle size and concentration. The sheath flow rate was maintained at 3 L min−1 for the DMA and 15 L min−1 for nano-DMA. The particle size was calibrated with monodisperse polystyrene latex spheres (PSLs, Duke Scientific, Palo Alto, California, USA) with nominal diameters of 100–500 nm.

A combination DMA–APM (aerosol particle mass analyzer, model 3600, Kanomax Inc., Japan) system was employed to measure the particle size-resolved density (Qiu et al., 2012; Khalizov et al., 2009, 2013). Ambient airflow first passed through a DMA, where the voltage was fixed to provide continuous monodisperse particles. Then, the monodisperse aerosol flow passed through an APM, where the particle mass distribution could be obtained. Effective density is defined as the measured mass over the volume where the particle is assumed to be a sphere based on the measured particle size; therefore, compounds with the same mass but different shapes may have extremely different effective densities. The effective densities for five particle sizes were obtained hourly. Since the mobility diameter corresponds to a unique voltage, if the applied voltage and effective density of PSLs are known, the effective density of the sample aerosols can be calculated by the following equation:

$\begin{array}{}\text{(1)}& {\mathit{\rho }}_{\mathrm{eff}}={V}_{\mathrm{APM}}/{V}_{\mathrm{APM},\phantom{\rule{0.125em}{0ex}}\mathrm{PSL}}×{\mathit{\rho }}_{\mathrm{PSL}},\end{array}$

where VAPM and VAPM, PSL are the fitted peak voltages in APM corresponding to the masses of sample and PSL particles, respectively. The material density of the PSL particles is 1.054 g cm−3. Each effective density distribution scans from 0.1 to 2.2 g cm−3. Effective density peaks at 1.76, 1.78, and 1.73 g cm−3 correspond to ammonium sulfate, ammonium bisulfate, and ammonium nitrate, respectively. The effective density of organic aerosols can vary significantly due to the numerous compounds in this category, the different emission sources, and the distinct structures of the compounds. Turpin and Lim (2001) reported that the density of secondary organic aerosols from the oxidation of aromatics and alkanes was between 1.20 and 1.40 g cm−3. The effective densities of fresh black carbon (BC), mineral dust, and sea salt were found to be 0.1–0.6, 2.65, and 2.2 g cm−3, respectively (Geller et al., 2006; Khalizov et al., 2009). This methodology has been utilized and discussed previously (Levy et al., 2014).

The hygroscopicity of ambient aerosols was parameterized by kappa (κ), which is derived using the following formula (Petters and Kreidenweis, 2007):

$\begin{array}{}\text{(2)}& \mathit{\kappa }=\frac{\mathit{\nu }{\mathit{\rho }}_{\mathrm{s}}}{{\mathit{\rho }}_{\mathrm{w}}}\frac{{M}_{\mathrm{w}}}{{M}_{\mathrm{s}}}={\sum }_{i}{\mathit{\epsilon }}_{i}{\mathit{\kappa }}_{i},\end{array}$

where M, ρ, ν, and ε, are the molecular weight, molecular densities, van 't Hoff factor, and volume fraction of the component in the aerosols mass, respectively. The subscripts “s” and “w” represent the parameters for solute and water, respectively. Using the volume-weighted average fraction determined by the AMS measurement and the εi values of 0.0, 0.09, 0.48, 0.58, 0.55, and 0.246 for BC, organic aerosols, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NH}}_{\mathrm{4}}^{+}$, and Cl, respectively, the chemical composition-derived kappa was calculated.

The PBL was determined by utilizing the National Oceanic and Atmospheric Administration's (NOAA) Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model. HYSPLIT identifies the mixing layer height, which we assumed to be the PBL, as the height at which the potential temperature is at least 2 C greater than the minimum potential temperature.

3 Results and discussion

## 3.1 Observed haze cycles

Four PM pollution cycles were documented during the measurement in the winter of 2015 (Fig. S1 in the Supplement). Frequently, the large-scale meteorology governed the length and severity of haze events due to the periodical occurrence of exceedingly stagnant air masses and strong, cleansing winds. During the observation period, a low PM2.5 concentration was accomplished with strong northerly winds. The episodes with the highest PM2.5 concentration (i.e., 22 and 26 January) exhibited calm winds and low PBL heights (Fig. S1), which trapped primary emission near their sources and secondary pollutants within the formation area. Temporal evolutions of the particle mass and number concentration, chemical composition, and size distribution and the average diameter of the first and second pollution cycles (between 21 and 27 January 2015) are illustrated in Fig. 1. The first haze event began with a new particle formation (NPF) event (Zhang et al., 2004), which was followed by the continuous particle growth over 3 d (Fig. 1a). On the clean days (i.e., 21 and 27 January) the strong wind and the high PBL diluted the pollutants both vertically and horizontally (Fig. S1). The total number concentration exceeded 300 000 cm−3 during the NPF event, but this value generally decreased after the NPF event and remained around 100 000 cm−3 (Fig. 1c). The average diameter of all ambient particles was only about 10 nm during the NPF event and steadily increased until their average diameter was near 150 nm (Fig. 1d). During nighttime of 22 January, the particle mass concentration increased but the diameter decreased, which is possibly due to the combination of the primary emission of smaller particles and the compressed PBL during nighttime. Minor mass growth was observed on 21 January (Fig. 1b), with an increase from 8 to 30 µg m−3. The most rapid mass concentration increase occurred on 22 January, with an increase from 30 to 300 µg m−3.

Figure 1Temporal evolutions of (a) the number size distribution, (b) PM2.5 mass concentration and chemical composition, (c) the total number concentration, and (d) the mean diameter between 21 and 27 January 2015. Dates in this figure are given in the month/day format.

During the early morning of January 24, a weak front passed through the sampling site, which led to weak winds from the north and an increased PBL to around 700 m (Fig. S1), diluting the ambient PM2.5 concentration (to about 30 µg m−3 on average during the daytime on 24 January). Meanwhile, a large amount of primary emission in the morning rush hour lowered the average particle diameter to less than 50 nm. After the frontal passage, the winds shifted to the south, which recirculated the polluted air mass back to the sampling site. Though the mass concentration exhibited two distinct pollution cycles, the air mass of this event as a whole was likely the same. On 25 January, weak southerly winds continued, and the boundary layer height decreased to about 300 m. The stagnant conditions led to a rapid accumulation of pollutants. The total number and mass concentrations of ambient PM2.5 gradually grew to 130 nm and 250 µg m−3 during the following 2 d, respectively (Fig. 1b, d). Meanwhile, the aerosol constituents generally remained similar during this episode (Fig. 1b).

## 3.2 Aerosol chemical composition, hygroscopicity, and density

Organic aerosols accounted for the largest percentage of the aerosol mass during both the clean (58 %, 21 January) and the polluted periods (52 %, 23 January). Nitrate, ammonium, and sulfate accounted for 12 %, 12 %, and 16 %, respectively, during the clean periods, and remained relatively constant at 20 %, 14 %, and 12 %, respectively, throughout the polluted period of the first and the second cycles. The contribution of chloride to PM remained constant at about 2 %.

The average kappa values of ambient aerosols between 21 January and 29 January 2015 are shown in Fig. 3a. Both the diurnal cycles and the overall trend governed by the pollution cycle are evident in the aerosol hygroscopicity. Diurnally, the least hygroscopic aerosols occurred overnight, while the most hygroscopic aerosols were found near sunset. The reduced nighttime hygroscopicity was concurrently observed with the transiently elevated organic aerosol mass concentration (Fig. 1) and reduced effective density of the larger particles (Fig. 3b), which may be due to the increase in vehicle emissions of primary organic aerosols and black carbon in the city overnight. The increased hygroscopicity in the mid-morning and early afternoon hours (09:00 LT to 13:00 LT) was due to the rapid increase in the mass concentrations of nitrate, ammonium, and sulfate aerosols (Fig. 1b), consistent with previous studies in Mexico City which showed that ammonium nitrate rapidly formed in the morning (Hennigan et al., 2008). From the onset of the first pollution cycle on 21 January to the morning of 25 January, the kappa value increased from 0.15 to 0.42.

The effective densities for 81, 97, 151, and 240 nm particles are exhibited in Fig. 3b. During the clean phase (e.g., 22 January), all four particle sizes exhibited effective density values that clustered around 1.37 g cm−3. However, as the haze event developed, the effective densities of particles with the four sizes became increasingly differentiated. When the PM2.5 mass concentration decreased at the end of the haze event (i.e., 27 January), the effective density of the particles again clustered around 1.36 g cm−3. The lower average effective density during the clean period can be attributed to the organic-dominated aerosol composition as well as fresh low-density BC emission. Furthermore, the increasing effective density corresponds to the increasing sulfate and nitrate composition that was observed as the haze events progressed (Fig. 1b). Generally, the effective density distributions were unimodal, indicating that the aerosols were internally mixed. The weighted average density, i.e., the effective density weighted by the total number concentration of particles near each size of the four particles sizes, increased throughout the haze event, but this was primarily due to the changes in the particles smaller than 100 nm. The effective density of smaller particles (i.e., 81 and 97 nm) increased as the ambient atmosphere became more polluted, whereas the densities of larger particles (i.e., 151 and 240 nm) remained near 1.37 g cm−3. Figure 4 shows the diurnal variation of the effective densities of 81, 97, 151, and 240 nm particles during the entire observational campaign as well as the polluted period and the clean period. An evident diurnal variation of effective density was observed, i.e., higher density overnight, lower density during the morning and evening rush hours, and moderately stable density during the daytime. Over the entire campaign, the lowest density was observed after the evening rush hour (i.e., 1.38 g cm−3 for 81 nm particles), and the highest density (∼1.41 g cm−3 for 81 nm particles) was observed in the early morning before the intensification of heavy traffic. During high-traffic periods (i.e., 06:00–09:00 LT and 16:00–20:00 LT), the decreasing effective density was likely due to the increasing concentrations of BC and primary organic aerosol (POA). Overnight, the effective density increased due to the formation of inorganic species on aerosols. The variations in effective density were suppressed during the polluted days. This may be because the newly emitted particles were being mixed into a relatively higher concentration of particles (Levy et al., 2014). Therefore, the average effective density of the entire air mass was not as sensitive to the primary emitted particles during rush hours.

## 3.3 Comparisons of aerosol properties in autumn and winter

In Fig. 5, a comparison of the mass concentration, total number concentration, and the average diameter of ambient particles from representative pollution cycles from the autumn 2013 and winter 2015 field campaigns are displayed (Guo et al., 2014). The chemical composition during the clean and polluted periods from both campaigns is also exhibited in Fig. 2. Both seasonal haze events began with NPF events, which were typically followed by particle growth over several days. Overall various properties (i.e., particle size, number concentration, chemical composition, and hygroscopicity) appear to be similar in the autumn and winter campaigns, with a few notable caveats.

Figure 2A comparison of the chemical composition during the clean and polluted periods from the autumn 2013 and winter 2015 field campaigns.

Figure 3(a) The determined hygroscopicity based on chemical composition (i.e., kappa) of the aerosols. (b) Temporal evolutions of the effective density of particles with a diameter of 81 (blue), 97 (green), 151 (red) and 240 nm (orange) and the weighted average of the four particle sizes (black) between 21 and 29 January 2015. Dates in this figure are given in the month/day format.

The particle growth and formation were more efficient in the autumn campaign: i.e., the NPF events resulted in a higher total number concentration in the autumn, and the final average particle diameter was near 180 nm compared to 150 nm in the winter, which may be attributable to the stronger solar irradiation in autumn than in winter. Studies have demonstrated that large particle mass growth always occurs concurrently with elevated daily ozone concentrations and solar irradiation (Guo et al., 2014; Peng et al., 2016), particularly during clean periods, suggesting the importance of photochemical activity in the growth of particles. Furthermore, such faster particle growth in autumn was observed when the PBL in autumn was nearly twice as high compared with that in winter (Fig. S1). If the PBL was the same, the particle growth and the secondary aerosol formation in autumn would likely be even more efficient. Organics were the dominant species during clean episodes in both autumn and winter at 79 % and 58 %, respectively (Fig. 2), while inorganic species, i.e., sulfate, nitrate, and ammonium, were more abundant in the polluted episodes in both campaigns. More organic aerosols were observed in the winter polluted episode, likely due to the increased POA emissions from residential heating during winter. The trends in the hygroscopicity of particles are similar during the two seasons, with the only significant differences occurring on the clean days (i.e., 21 and 27 January, 25 September, and 1 October). The hygroscopicity of the autumn aerosols (25 September) during the clean phase was much lower (0.2) than the hygroscopicity of the wintertime aerosols (0.35). This is likely due to the higher proportion of sulfate in PM during the winter (7 % in the autumn, 16 % in the winter) caused by the higher SO2 emission from residential heating in the winter and the lower PBL (1100 m compared to 2200 m; Fig. S1), which suppressed the horizontal dilution of pollutants and thereby accelerated sulfate formation (Wang et al., 2016).

Figure 4(a) The diurnal variation of the effective density (g cm−3) of the four particle sizes from the full observational period. (b) The effective density (g cm−3) diurnal cycle of the 81 nm (blue circles) and 240 nm (black squares) particles during the clean (dashed, lighter colors) and polluted (solid, darker colors) periods.

Figure 5A comparison of the (a) mass concentration, (b) total number concentration, (c) average diameter, and (d) hygroscopicity between autumn 2013 (blue, bottom axis) and winter 2015 (black, top axis). Dates in this figure are given in the month/day format.

4 Conclusions and implications

We have evaluated the influence of meteorology, local emissions, and aerosol processes on severe haze events in Beijing during winter by conducting comprehensive aerosol properties measurements. We show that the periodic cycles of haze episodes during the winter in Beijing are regulated by meteorological conditions. Formation of severe haze is comprised of two distinct processes of secondary aerosol formation, i.e., the nucleation that initially produces high concentrations of nanoparticles and the subsequent continuous growth from the nucleation mode particles to submicron particles. Our analysis of the aerosol chemical compositions suggests that organic aerosols are primarily responsible for producing the nucleation mode particles, while secondary organic aerosols and inorganic salts contribute jointly to particle growth. The combination of high aerosol nucleation potential and efficient subsequent growth over several days uniquely differentiates the severe PM2.5 episodes in Beijing from those typically observed in other regions worldwide. The average effective density and kappa value of ambient particles are approximately 1.37 g cm−3 and 0.25 during the clean days and 1.42 g cm−3 and 0.4 during the severe haze episodes, respectively. The higher effective density and kappa value during hazy days indicate the formation of secondary inorganic species during the continuous growth of nucleation mode particles.

From the perspective of pollution control, it may be feasible to suppress the aerosol growth processes to reduce the PM2.5 levels in Beijing. Our results imply that the reductions in the emissions of the aerosol precursor gases, i.e., volatile organic compounds, NOx, and SO2, are critical for suppressing aerosol growth and thereby the remediation of haze pollution in Beijing. Such a viewpoint of severe haze formation is critical for improving the formulation of effective regulatory policies by decision makers at the central and local government levels.

Data availability
Data availability.

The data set is available upon request by contacting Renyi Zhang (renyi-zhang@tamu.edu).

Supplement
Supplement.

Author contributions
Author contributions.

MH, SG, ZW, and RZ organized the field campaign. MLZ, JP, WM, DS, JZ, and ZD conducted the online measurement and analyzed the data. MLZ and JP wrote the paper with input from RZ. All authors contributed to the discussion of the results.

Competing interests
Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement
Special issue statement.

Acknowledgements
Acknowledgements.

Wilmarie Marrero-Ortiz acknowledges support by the Louis Stokes Alliance for Minority Participation – Bridge to the Doctorate and a National Science Foundation Graduate Research Fellowship Program (GRFP) fellowship.

Financial support
Financial support.

This research has been supported by the National Natural Science Foundation of China (grant nos. 91544214 and 91844301), the National Research Program for Key Issues in Air Pollution Control (grant no. DQGG0103), the National Key Research and Development Program of China (grant no. 2016YFC0202000: Task 3), the Ministry of Science and Technology of China (grant no. 2013CB955800), and the Robert A. Welch Foundation (grant no. A-1417).

Review statement
Review statement.

This paper was edited by Leiming Zhang and reviewed by two anonymous referees.

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text:
Magnetic force on a current carrying wire

Hi, I am slightly confused by the formula for finding the force on a current carrying wire. It is given as F=BIL where F is force, B is the strength of the magnetic field and L is the length of the wire being acted upon. What I don't understand is why this formula doesn't factor in the distance between the magnet and the wire itself.


text:
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International conference "Geometry of Algebraic Varieties" dedicated to the memory of V. A. Iskovskikh
October 22, 2013 12:15–13:15, Moscow, Steklov Mathematical Institute of RAS

On a combinatorial classification of minimal quasi-homogeneous 3-folds with a $SL(2)\times G_m$-action

V. V. Batyrev
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Abstract: The classification of minimal smooth projective quasi-homogeneous 3-folds with a $\mathrm{SL}(2)\times\mathbb{G}_m$-action has been known due to results of Mori, Mukai, Nakano, Moser-Jauslin, Kebekus, and Guan. The purpose of my talk is to explain a combinatorial approach to this classification using the Luna-Vust theory of spherical embeddings. This approach describes these minimal 3-folds by means of 2-dimensional fans of colored cones.


text:
# Igma notation 2i-1 = 2n, for all n is an element of N

1. Dec 5, 2008

### mbcsantin

prove or disprove

n
sigma notation 2i-1 = 2n, for all n is an element of N.
i=1

N = natural numbers

2. Dec 5, 2008

Re: Induction

Rewritten using LaTeX,
$$\sum_{i=1}^{n} 2^{i - 1} = 2^n.$$

Have you made any real attempt at this problem? Do you have a guess as to whether it's true or false? What I like to do on these types of "prove or disprove" questions is just plug in certain (small) values of n, and see if it works. If they all work, perhaps it really is true, and you should try to prove it; otherwise, it's false as you found a counterexample.

And once you find that it's false, can you guess a correct formula for the sum and prove that?

3. Dec 8, 2008

### mbcsantin

Re: Induction

Here is my attempt at this problem:

n
sigma notation 2i-1= 2n, for all n is an element of N
i=1

n=1

1
sigma notation 21-1= 20 = 1 not equal to 21
i=1

n=1 is an element of N

Hence,
n
sigma notation 2i-1=2n doesn't hold for all n is an element of N
i=1

did i do this right?

4. Dec 8, 2008

Re: Induction

Your solution is correct, although it's slightly unclear, and you should use more words to describe what you're doing.

You were trying to disprove
$$\sum_{i=1}^{n} 2^{i - 1} = 2^n \text{ for all } n \in \mathbb{N}.$$
(It's much prettier in LaTeX; you should learn (at least by example) how to use it. $$n \in \mathbb{N}$$ is read "n in N" or even "natural numbers n" in this case. Click the images to see the code used to make them.) You put in n = 1 and showed that the two sides aren't equal; that is a counterexample, so your disproof is correct.

5. Dec 8, 2008

### HallsofIvy

Re: Induction


text:
# An equation related to the dimension of linear operator

1. Dec 1, 2008

### boombaby

1. The problem statement, all variables and given/known data
Let V be a finite vector space, and A, B be any two linear operator. Prove that,
rank A = rank B + dim(Im A $$\cap$$ Ker B)

3. The attempt at a solution
Since rank A = dim Im A
dim(Im B)+ dim(Ker B)=dim V
dim(Im A + Ker B)=dim(Im A)+dim(Ker B)-dim(Im A $$\cap$$ Ker B)
It seems equivalent to prove that dim(Im A + Ker B)=dim V

it is obvious that Im A + Ker B $$\subseteq$$ V. So it should be true that V $$\subseteq$$ Im A + Ker B.

If I let Ker B=<e_1,...,e_k> and extend it to a basis of V=<e_1,..e_k, e_k+1,...e_n>. Choose any $$x=\sum^{n}_{i=1} x_{i}e_{i}=\sum^{k}_{i=1} x_{i}e_{i} + \sum^{n}_{i=k+1} x_{i}e_{i}$$. The first term is in Ker B, the second is not in Ker B and therefore should be in Im A. This is what confuses me a lot since it is not necessary to be true IMO...

What's your idea? Where I made the mistakes? Can you give me any hint to prove it? Thanks very much

2. Dec 2, 2008

### morphism

Are A and B arbitrary operators on V? If so this isn't true unless V={0}. For a counterexample, take A=0 and let B be any nonzero operator.

3. Dec 2, 2008

THanks!