PLANET SICK-BOY: http://www.sick-boy.com
One of the surest signs that your impending wedding may not be the wisest of life choices is when your grandpa keels over at your bachelor party. If that doesn't change your mind, try having Gramps telling you, on his deathbed, that he never loved your grandmother. Despite these colossal warning signs, Ben (as in Affleck, Armageddon) decides to proceed as planned with his nuptials to his bland but beautiful fiancée (Maura Tierney, NewsRadio).
As if that wouldn't make things stressful enough, the two New Yorkers decide to take separate flights to Savannah, Georgia - where the wedding will take place - because Ben wants to spend time with his ailing granddad. His best man (Steve Zahn, You've Got Mail) stays behind with Ben, but, as they're about to board their flight, bails out because he forgot his shoes and the all-important rings.
Again Ben ignores this as an omen and hops on the plane, even though he is deathly afraid of flying. He is seated next to a woman named Sarah (Sandra Bullock, Practical Magic), who looks like Ally Sheedy heading back home for her 10-year Breakfast Club High School reunion. As it takes off, a seagull flies into the plane's engine, causing it to crash into that lovely `Welcome to NY' sign that graces the end of the runway at LaGuardia. This forewarning also goes unnoticed by Ben. Starting to get the impression that he's no super genius, eh?
Long story short, Ben saves Sarah and hauls her body out of the wreckage. After she comes to, he finds out that she also needs to get to Savannah tout suite in order to sell a failing bagel shop. The two decide to travel together and the following eighty or so minutes unfolds just like Planes, Trains & Automobiles, with each mode of transportation being less successful than the previous. But their predicament only seems to invigorate the dopey Ben except, of course, for that fact that he (duh!) falls in love with Sarah. Unfortunately, there is no `Where's your hand?' `Between two pillows.' `Those aren't pillows!' scene.
Don't let the ads fool you – Forces is no chick-flick. It's surprisingly funny and has a terrific look, thanks to director Bronwen Hughes (Harriet the Spy) and cinematographer Elliot Davis (Out of Sight), and culminates in an amazing finale that merges a big outdoor wedding and a powerful hurricane. As far as acting, Affleck does his best to make you forget about that abominable `animal cracker' scene from Armageddon, while Bullock does okay with her less meaty role. In spite of the strange transformation that her character goes through (from thick black eye makeup and crazy hair to…well, to Sandra Bullock), she gives her least annoying performance in years.
1:49 – PG-13 for some adult language and adult situation
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|
Clingo C API
C API for clingo providing high level functions to control grounding and solving.
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An instance of this struct has to be registered with a solver to observe ground directives as they are passed to the solver.
Not all callbacks have to be implemented and can be set to NULL if not needed. If one of the callbacks in the struct fails, grounding is stopped. If a non-recoverable clingo API call fails, a callback must return false. Otherwise clingo_error_unknown should be set and false returned.
Public Attributes | |
| bool(* | init_program )(bool incremental, void *data) |
| Called once in the beginning. More... | |
| bool(* | begin_step )(void *data) |
| Marks the beginning of a block of directives passed to the solver. More... | |
| bool(* | end_step )(void *data) |
| Marks the end of a block of directives passed to the solver. More... | |
| bool(* | rule )(bool choice, clingo_atom_t const *head, size_t head_size, clingo_literal_t const *body, size_t body_size, void *data) |
| Observe rules passed to the solver. More... | |
| bool(* | weight_rule )(bool choice, clingo_atom_t const *head, size_t head_size, clingo_weight_t lower_bound, clingo_weighted_literal_t const *body, size_t body_size, void *data) |
| Observe weight rules passed to the solver. More... | |
| bool(* | minimize )(clingo_weight_t priority, clingo_weighted_literal_t const *literals, size_t size, void *data) |
| Observe minimize constraints (or weak constraints) passed to the solver. More... | |
| bool(* | project )(clingo_atom_t const *atoms, size_t size, void *data) |
| Observe projection directives passed to the solver. More... | |
| bool(* | output_atom )(clingo_symbol_t symbol, clingo_atom_t atom, void *data) |
| Observe shown atoms passed to the solver. More... | |
| bool(* | output_term )(clingo_symbol_t symbol, clingo_literal_t const *condition, size_t size, void *data) |
| Observe shown terms passed to the solver. More... | |
| bool(* | output_csp )(clingo_symbol_t symbol, int value, clingo_literal_t const *condition, size_t size, void *data) |
| Observe shown csp variables passed to the solver. More... | |
| bool(* | external )(clingo_atom_t atom, clingo_external_type_t type, void *data) |
| Observe external statements passed to the solver. More... | |
| bool(* | assume )(clingo_literal_t const *literals, size_t size, void *data) |
| Observe assumption directives passed to the solver. More... | |
| bool(* | heuristic )(clingo_atom_t atom, clingo_heuristic_type_t type, int bias, unsigned priority, clingo_literal_t const *condition, size_t size, void *data) |
| Observe heuristic directives passed to the solver. More... | |
| bool(* | acyc_edge )(int node_u, int node_v, clingo_literal_t const *condition, size_t size, void *data) |
| Observe edge directives passed to the solver. More... | |
| bool(* | theory_term_number )(clingo_id_t term_id, int number, void *data) |
| Observe numeric theory terms. More... | |
| bool(* | theory_term_string )(clingo_id_t term_id, char const *name, void *data) |
| Observe string theory terms. More... | |
| bool(* | theory_term_compound )(clingo_id_t term_id, int name_id_or_type, clingo_id_t const *arguments, size_t size, void *data) |
| Observe compound theory terms. More... | |
| bool(* | theory_element )(clingo_id_t element_id, clingo_id_t const *terms, size_t terms_size, clingo_literal_t const *condition, size_t condition_size, void *data) |
| Observe theory elements. More... | |
| bool(* | theory_atom )(clingo_id_t atom_id_or_zero, clingo_id_t term_id, clingo_id_t const *elements, size_t size, void *data) |
| Observe theory atoms without guard. More... | |
| bool(* | theory_atom_with_guard )(clingo_id_t atom_id_or_zero, clingo_id_t term_id, clingo_id_t const *elements, size_t size, clingo_id_t operator_id, clingo_id_t right_hand_side_id, void *data) |
| Observe theory atoms with guard. More... | |
| bool(* clingo_ground_program_observer::acyc_edge) (int node_u, int node_v, clingo_literal_t const *condition, size_t size, void *data) |
Observe edge directives passed to the solver.
| [in] | node_u | the start vertex of the edge |
| [in] | node_v | the end vertex of the edge |
| [in] | condition | the condition under which the edge is part of the graph |
| [in] | size | the number of atoms in the condition |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::assume) (clingo_literal_t const *literals, size_t size, void *data) |
Observe assumption directives passed to the solver.
| [in] | literals | the literals to assume (positive literals are true and negative literals false for the next solve call) |
| [in] | size | the number of atoms |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::begin_step) (void *data) |
Marks the beginning of a block of directives passed to the solver.
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::end_step) (void *data) |
Marks the end of a block of directives passed to the solver.
This function is called before solving starts.
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::external) (clingo_atom_t atom, clingo_external_type_t type, void *data) |
Observe external statements passed to the solver.
| [in] | atom | the external atom |
| [in] | type | the type of the external statement |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::heuristic) (clingo_atom_t atom, clingo_heuristic_type_t type, int bias, unsigned priority, clingo_literal_t const *condition, size_t size, void *data) |
Observe heuristic directives passed to the solver.
| [in] | atom | the target atom |
| [in] | type | the type of the heuristic modification |
| [in] | bias | the heuristic bias |
| [in] | priority | the heuristic priority |
| [in] | condition | the condition under which to apply the heuristic modification |
| [in] | size | the number of atoms in the condition |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::init_program) (bool incremental, void *data) |
Called once in the beginning.
If the incremental flag is true, there can be multiple calls to clingo_control_solve().
| [in] | incremental | whether the program is incremental |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::minimize) (clingo_weight_t priority, clingo_weighted_literal_t const *literals, size_t size, void *data) |
Observe minimize constraints (or weak constraints) passed to the solver.
| [in] | priority | the priority of the constraint |
| [in] | literals | the weighted literals whose sum to minimize |
| [in] | size | the number of weighted literals |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::output_atom) (clingo_symbol_t symbol, clingo_atom_t atom, void *data) |
Observe shown atoms passed to the solver.
| [in] | symbol | the symbolic representation of the atom |
| [in] | atom | the aspif atom (0 for facts) |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::output_csp) (clingo_symbol_t symbol, int value, clingo_literal_t const *condition, size_t size, void *data) |
Observe shown csp variables passed to the solver.
| [in] | symbol | the symbolic representation of the variable |
| [in] | value | the value of the variable |
| [in] | condition | the literals of the condition |
| [in] | size | the size of the condition |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::output_term) (clingo_symbol_t symbol, clingo_literal_t const *condition, size_t size, void *data) |
Observe shown terms passed to the solver.
| [in] | symbol | the symbolic representation of the term |
| [in] | condition | the literals of the condition |
| [in] | size | the size of the condition |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::project) (clingo_atom_t const *atoms, size_t size, void *data) |
Observe projection directives passed to the solver.
| [in] | atoms | the atoms to project on |
| [in] | size | the number of atoms |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::rule) (bool choice, clingo_atom_t const *head, size_t head_size, clingo_literal_t const *body, size_t body_size, void *data) |
Observe rules passed to the solver.
| [in] | choice | determines if the head is a choice or a disjunction |
| [in] | head | the head atoms |
| [in] | head_size | the number of atoms in the head |
| [in] | body | the body literals |
| [in] | body_size | the number of literals in the body |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::theory_atom) (clingo_id_t atom_id_or_zero, clingo_id_t term_id, clingo_id_t const *elements, size_t size, void *data) |
Observe theory atoms without guard.
| [in] | atom_id_or_zero | the id of the atom or zero for directives |
| [in] | term_id | the term associated with the atom |
| [in] | elements | the elements of the atom |
| [in] | size | the number of elements |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::theory_atom_with_guard) (clingo_id_t atom_id_or_zero, clingo_id_t term_id, clingo_id_t const *elements, size_t size, clingo_id_t operator_id, clingo_id_t right_hand_side_id, void *data) |
Observe theory atoms with guard.
| [in] | atom_id_or_zero | the id of the atom or zero for directives |
| [in] | term_id | the term associated with the atom |
| [in] | elements | the elements of the atom |
| [in] | size | the number of elements |
| [in] | operator_id | the id of the operator (a string term) |
| [in] | right_hand_side_id | the id of the term on the right hand side of the atom |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::theory_element) (clingo_id_t element_id, clingo_id_t const *terms, size_t terms_size, clingo_literal_t const *condition, size_t condition_size, void *data) |
Observe theory elements.
| element_id | the id of the element | |
| terms | the term tuple of the element | |
| terms_size | the number of terms in the tuple | |
| condition | the condition of the elemnt | |
| condition_size | the number of literals in the condition | |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::theory_term_compound) (clingo_id_t term_id, int name_id_or_type, clingo_id_t const *arguments, size_t size, void *data) |
Observe compound theory terms.
The name_id_or_type gives the type of the compound term:
| [in] | term_id | the id of the term |
| [in] | name_id_or_type | the name or type of the term |
| [in] | arguments | the arguments of the term |
| [in] | size | the number of arguments |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::theory_term_number) (clingo_id_t term_id, int number, void *data) |
Observe numeric theory terms.
| [in] | term_id | the id of the term |
| [in] | number | the value of the term |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::theory_term_string) (clingo_id_t term_id, char const *name, void *data) |
Observe string theory terms.
| [in] | term_id | the id of the term |
| [in] | name | the value of the term |
| [in] | data | user data for the callback |
| bool(* clingo_ground_program_observer::weight_rule) (bool choice, clingo_atom_t const *head, size_t head_size, clingo_weight_t lower_bound, clingo_weighted_literal_t const *body, size_t body_size, void *data) |
Observe weight rules passed to the solver.
| [in] | choice | determines if the head is a choice or a disjunction |
| [in] | head | the head atoms |
| [in] | head_size | the number of atoms in the head |
| [in] | lower_bound | the lower bound of the weight rule |
| [in] | body | the weighted body literals |
| [in] | body_size | the number of weighted literals in the body |
| [in] | data | user data for the callback |


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|
CS Dungeon
1.0a
A simple game made by amateurs
|
The MetaGameController is responsible for switching control between the high level contexts of the application, eg the Main Menu and Gameplay systems. More...
Public Member Functions | |
| void | ToggleMainMenu (bool show) |
| Turn the main menu on or off. More... | |
Public Attributes | |
| MainUIController | mainMenu |
| The main UI object which used for the menu. More... | |
| Canvas[] | gamePlayCanvasii |
| A list of canvas objects which are used during gameplay (when the main ui is turned off) More... | |
| GameController | gameController |
| The game controller. More... | |
The MetaGameController is responsible for switching control between the high level contexts of the application, eg the Main Menu and Gameplay systems.
| void Platformer.UI.MetaGameController.ToggleMainMenu | ( | bool | show | ) |
Turn the main menu on or off.
| show |
| GameController Platformer.UI.MetaGameController.gameController |
The game controller.
| Canvas [] Platformer.UI.MetaGameController.gamePlayCanvasii |
A list of canvas objects which are used during gameplay (when the main ui is turned off)
| MainUIController Platformer.UI.MetaGameController.mainMenu |
The main UI object which used for the menu.


Bang + Olufsen
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“Support Vector Machines should be in the tool bag of every civilized person.”
Patrick Henry Winston 71
Support Vector Machine (SVM) learning is a supervised learning technique that may be used as a binary classification system or to find a regression formula. Support vector machines are a “maximum margin classifier. SVM finds the separating hyperplane with the maximum margin to its closest data points.” 72
Although there are many mathematical approaches to solving SVM, many of which include kernels, let us first describe the Linear SVM used for binary classification. Consider a situation where we need to distinguish between two circumstances, or classes.
In an imaginary biochemistry laboratory, researchers discover a novel enzyme found in different tissues throughout the human body. Biochemists purify the enzyme from several cadavers and several different tissue types. Literature suggests that this newly found enzyme has two isozymes, 1) Alpha has a high reaction rate and 2) Beta has a lower reaction rate. It now seems like a simple task to learn which isozymes you possess. Carry out kinetic enzyme analysis on the purified samples then attempt to classify them.
Once you have carried out the kinetic analysis you then determine the Michaelis–Menten constant, \(K_M\). The \(K_M\) constant is plotted on a single axis and produces the graphic below.
In test #1, we can see the two isozymes can easily separated by activity alone. Figure 1 demonstrates that the data is linearly separable. The dataset is linearly separable if a single straight line can partition the data. In more general terms, “if the classes are linearly separable, it can be shown that the algorithm converges to a separating hyperplane.” 73 As Cortes and Vapnik indicate the hyperplane is the decision boundary of any high dimension feature space, considering a hyperplane has one less dimension than its n-dimensional space.
Incidentally, in Patrick Winston’s lecture on SVM, he calls SVM the “widest street approach.” 74 Why does Professor Winston use this term? There are many possible streets which can be traced but the goal is to find the widest street. Many streets may be drawn in our example, but requiring the widest street leads to one. In fact, “an optimal hyperplane is here defined as the linear decision function with maximal margin between the vectors of the two classes.” 75
Adding the prosaic phrase widest street smartly leads to the idea that a widest decision boundary also has the greatest ability to generalize.
However in real life, linearly separabale data is rarely the case. Most often the activities are mixed as shown in test #2.
If we were trying to find:
\[\begin{equation} \frac{1}{2} \widehat W (X_{\oplus} ~-~ X_{\ominus}) \end{equation}\]
Where \(\widehat W ~= \left ( \frac{x_1}{||x||}, ~ \frac{x_2}{||x||} \right )\) and \(X_{\oplus}\) and \(X_{\ominus}\) represent data points that are labeled either positive or negative.
Suppose that \(X_{\oplus}\) and \(X_{\ominus}\) are equidistant from the decision boundary:
Where \(a\) represents the region above the hyperplane;
\[\begin{equation} W^T X_{\oplus} + b = a \end{equation}\]
and where \(-a\) represents the region below the hyperplane or decision boundary.
\[\begin{equation} W^T X_{\ominus} + b = -a \end{equation}\]
Subtracting the two equations:
\[\begin{equation} W^T (X_{\oplus} ~-~ X_{\ominus}) = 2a \end{equation}\]
Divide by the norm of w:
\[\begin{equation} \widehat W^T (X_{\oplus} ~-~ X_{\ominus}) = \frac{2a}{||W||} \end{equation}\]
In the case above, the activities overlap hence determining which isozyme is Alpha or Gamma is more difficult. In 1995, C. Cortes and V. Vapnik introduced the mathematics and ideas for “Soft Margins” or non-separable training data.79
The same is true of an n-dimensional system.
The first mention of an SVM like system is by Vapnik and Lerner in 1963, where the two described an implementation of a non-linear generalization called a Generalized Portrait algorithm.80 As research has progressed, the types and complexity of SVM implementations have grown to encompass many circumstances. The ability of SVM to deal with different problems and handle different decision boundary shapes has made SVM a potent tool.
For example, this experiment has chosen to investigate three possible decision boundary shapes for the two-class protein data. The three mathematical constructs which will be tested are:
Three common SVM kernel formulae investigated are:
It is essential to note, at this time, there are no reliable rules for which kernel, i.e., boundary shape, to use with any given data set.
Plots of 4 common SVM boundary shapes:
The simplest form of SVM utilizes a hyperplane as a separating element between the positive and control protein observations. This type of implementation is denoted as SVM-Linear (svm-lin) in this report. Here the mathematics is more easily described and can even be shown with a simple 2-dimensional graphic.
Given a set of labeled pairs of data:
\[\begin{equation} \{(X_1, ~y),~ ...,~ (X_m, ~y)\},~~~ y \in \{1, ~-1\}, ~~~ where ~X^{m~x~n} \in \Re \end{equation}\]
For mathematical convenience, the labels are a set of values 1 or -1.
Therefore, we may write.
\[\begin{equation} f(x_i) = \left\{ \begin{array}{cc} x \geq 0; ~y = 1 \\ x < 0; ~y = -1 \end{array} \right. \end{equation}\]
This is no different than is currently done in beginner level algebra. As is shown in the example below, the same is true for higher-dimensional problems.
Will be described and calculated in more detail in this report. However, there are alternative implementations of SVM.
In this experiment, three implementations of SVM have been used. The three are denoted as SVM-Linear (svm-lin), SVM-Polynomial (svm-poly), and SVM-Radial Basis Function (svm-rbf).
The switches in the R/caret software are easy such that one can use a number of kernels by changing the name of method..
with differing amounts of hyperparameters to modify. The intuition for the svm-poly and svm-rbf is also fairly straightforward. Instead of using a linear hyperplane to bisect the hi-dimensional space, which describes the decision boundary, the mathematics for a polynomial curvilinear function or a radial basis function may be utilized.
Yet another measurable difference that was investigated in this experiment was the use of a kernel transformation. It is conceivable to envision a hyperplane with no transformations utilized. Alternatively, the kernel transformations of original data can be used to increase the ability of the function to differentiate between positively and negatively labeled samples. A mathematical treatment can be found by Christopher Burges.83
As the usage of SVM grew, different issues presented problems for defining and coding the decision boundary were found. In the simplest case, the data points that sit along the support vector are nicely and neatly on the positive or the negative side. This is known as a hard margin which delineates the decision boundary. In reality, the decision boundary may include positive or negative datapoints that sporadically cross the boundary. In the circumstance where the decision boundary has similar points on either side, a penalty may be enlisted to deter the mathematics from choosing a boundary that includes too many misfit datapoints. In 1995, Support Vector Machines were described by Vladimir Vapnik and Corinna Cortes while at Bell Labs dealt with the soft-margin that occurs in the above situation.84
SVM is a non-parametric approach to regression and classification models.
What is Non-parametric?
For that matter, what is parametric learning and models. Just as we have learned that machine learning models can be supervised, unsupervised, or even semi-supervised another characteristic between machine learning models is whether they are parametric or not.
In Webster’s dictionary 85 states a parameter is
Estimation of values which enter into the equation representing the chosen relation
“[An] independent variable through functions of which other functions may be expressed”, Frank Yates, a 20th-century statistician
Another excellent explanation of this idea includes;
Does the model have a fixed number of parameters, or does the number of parameters grow with the amount of training data? The former is called a parametric model, and the latter is called a non-parametric model. Parametric models have the advantage of often being faster to use, but the disadvantage of making stronger assumptions about the nature of the data distributions. Non-parametric models are more flexible, but often computationally intractable for large datasets.86
Since Support Vector Machines are best described as a system where increasing the amount of training data, the numbers of parameters may grow as well. Therefore SVM is a non-parametric technique. Considering this idea in more detail, the estimation of the decision boundary does not entirely rely on the estimation of independent values (i.e., the values of the parameters). SVM is fascinating because the decision boundary may only rely on a small number of data points, otherwise known as support vectors.
In short, one guiding idea of SVM is a geometric one. In a binary-class learning system, the metric for the concept of the “best” classification function can be realized geometrically87 by using a line or a plane (more precisely called a hyperplane when discussing multi-dimensional datasets) to separate the two labeled groups. The hyperplane that separates the labeled sets is also known as a decision boundary.
This decision boundary can be described as having a hard or soft margin. As one might suspect, there are instances where the delineation between the labels is pronounced when this occurs decision boundary produces a hard margin. Alternatively, when the demarcation between the labeled groups is not so well defined by a straight and rigid line, the decision boundary provided is a soft margin. In either case, researchers have built up mathematics to deal with hard and soft margins. As an aside, the use of penalization is one method for coping with data points that impinge on the boundary hyperplane.
By introducing a “soft margin” instead of a hard boundary, we can add a slack variable xi to account for the amount of a violation by the classifier, which later can be minimized.
In short, one guiding idea of SVM is a geometric one. In a binary-class learning system, the metric for the concept of the “best” classification function can be realized geometrically88 by using a line or a plane (more precisely called a hyperplane when discussing multi-dimensional datasets) to separate the two labeled groups. The hyperplane that separates the labeled sets is also known as a decision boundary.
| Algorithm | Training | Prediction |
|---|---|---|
| SVM (Kernel) | O\((n^2 p + n^3)\) | O\((n_s v_p)\) |
Where p is the number of features, n_s v_p is the number of support vectors
There are three properties that make SVMs attractive for data scientists:90
SVMs construct a maximum margin separator—a decision boundary with the largest possible distance to example points. This helps them generalize well.
SVMs create a linear separating hyperplane, but they have the ability to embed the data into a higher-dimensional space, using the so-called kernel trick. Often, data that are not linearly separable in the original input space are easily separable in the higher- dimensional space. The high-dimensional linear separator is actually nonlinear in the original space. This means the hypothesis space is greatly expanded over methods that use strictly linear representations.
SVMs are a nonparametric method—they retain training examples and potentially need to store them all. On the other hand, in practice they often end up retaining only a small fraction of the number of examples—sometimes as few as a small constant times the number of dimensions. Thus SVMs combine the advantages of nonparametric and parametric models: they have the flexibility to represent complex functions, but they are resistant to overfitting.
# Import data & data handling
c_m_TRANSFORMED <- read_csv("./00-data/02-aac_dpc_values/c_m_TRANSFORMED.csv",
col_types = cols(Class = col_factor(levels = c("0", "1")),
PID = col_skip(),
TotalAA = col_skip()))
Partition data into training and testing sets
set.seed(1000)
index <- createDataPartition(c_m_TRANSFORMED$Class, p = 0.8, list = FALSE)
training_set <- c_m_TRANSFORMED[ index,]
test_set <- c_m_TRANSFORMED[-index,]
Class_test <- as.factor(test_set$Class)
set.seed(1000)
start_time <- Sys.time() # Start timer
# tuneGrid = svmLinearGrid
svmLinearGrid <- expand.grid(C = c(2^(4.5), 2^5, 2^(5.5)))
# Create model, 10X fold CV repeated 5X
tcontrol <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
savePredictions = "final") # Saves predictions
lin_model_obj <- train(Class ~ .,
data = training_set,
method = "svmLinear",
trControl = tcontrol,
tuneGrid = svmLinearGrid)
end_time <- Sys.time() # End timer
end_time - start_time # Display time
## Time difference of 4.094683 mins
## Support Vector Machines with Linear Kernel
##
## 1873 samples
## 20 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 1685, 1686, 1686, 1686, 1686, 1685, ...
## Resampling results across tuning parameters:
##
## C Accuracy Kappa
## 22.62742 0.9482199 0.8961196
## 32.00000 0.9484338 0.8965504
## 45.25483 0.9485402 0.8967687
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was C = 45.25483.
## 0 1
## 250 217
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 234 16
## 1 9 208
##
## Accuracy : 0.9465
## 95% CI : (0.922, 0.9651)
## No Information Rate : 0.5203
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.8926
##
## Mcnemar's Test P-Value : 0.2301
##
## Sensitivity : 0.9286
## Specificity : 0.9630
## Pos Pred Value : 0.9585
## Neg Pred Value : 0.9360
## Prevalence : 0.4797
## Detection Rate : 0.4454
## Detection Prevalence : 0.4647
## Balanced Accuracy : 0.9458
##
## 'Positive' Class : 1
##
fp_fn_svm_linear <- lin_model_obj %>% pluck("pred") %>% dplyr::filter(obs != pred)
# Write out to Outliers folder
write.table(fp_fn_svm_linear,
file = "./00-data/03-ml_results/fp_fn_svm_linear.csv",
row.names = FALSE,
na = "",
col.names = TRUE,
sep = ",")
nrow(fp_fn_svm_linear)
## [1] 482
## C pred obs rowIndex Resample
## 1 45.25483 0 1 1223 Fold01.Rep1
## 2 45.25483 0 1 1873 Fold03.Rep1
## 3 45.25483 0 1 1101 Fold05.Rep1
## 4 45.25483 0 1 1618 Fold04.Rep1
## 5 45.25483 0 1 1866 Fold01.Rep1
## 6 45.25483 0 1 1831 Fold05.Rep1
Partition data into training and testing sets
set.seed(1000)
index <- createDataPartition(c_m_TRANSFORMED$Class, p = 0.8, list = FALSE)
training_set <- c_m_TRANSFORMED[ index,]
test_set <- c_m_TRANSFORMED[-index,]
Class_test <- as.factor(test_set$Class)
set.seed(1000)
start_time <- Sys.time() # Start timer
# Create model, 10X fold CV repeated 5X
tcontrol <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
savePredictions = "final") # Saves predictions
poly_model_obj <- train(Class ~ .,
data = training_set,
method = "svmPoly",
trControl= tcontrol)
end_time <- Sys.time() # End timer
end_time - start_time # Display time
## Time difference of 6.494653 mins
## Support Vector Machines with Polynomial Kernel
##
## 1873 samples
## 20 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 1685, 1686, 1686, 1686, 1686, 1685, ...
## Resampling results across tuning parameters:
##
## degree scale C Accuracy Kappa
## 1 0.001 0.25 0.8927921 0.7837449
## 1 0.001 0.50 0.8931101 0.7842397
## 1 0.001 1.00 0.8995164 0.7972922
## 1 0.010 0.25 0.9069985 0.8125193
## 1 0.010 0.50 0.9182148 0.8352852
## 1 0.010 1.00 0.9243031 0.8476521
## 1 0.100 0.25 0.9266532 0.8524643
## 1 0.100 0.50 0.9326311 0.8645594
## 1 0.100 1.00 0.9340187 0.8674061
## 2 0.001 0.25 0.8935368 0.7851036
## 2 0.001 0.50 0.8997298 0.7977161
## 2 0.001 1.00 0.9046473 0.8077461
## 2 0.010 0.25 0.9208824 0.8406987
## 2 0.010 0.50 0.9316686 0.8625657
## 2 0.010 1.00 0.9356167 0.8705585
## 2 0.100 0.25 0.9672198 0.9342616
## 2 0.100 0.50 0.9670042 0.9338334
## 2 0.100 1.00 0.9649755 0.9297728
## 3 0.001 0.25 0.8969559 0.7920424
## 3 0.001 0.50 0.9014433 0.8012428
## 3 0.001 1.00 0.9110610 0.8207620
## 3 0.010 0.25 0.9339083 0.8670639
## 3 0.010 0.50 0.9365781 0.8724848
## 3 0.010 1.00 0.9464057 0.8923335
## 3 0.100 0.25 0.9688252 0.9375066
## 3 0.100 0.50 0.9704278 0.9407533
## 3 0.100 1.00 0.9690403 0.9379858
##
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were degree = 3, scale = 0.1 and C = 0.5.
## 0 1
## 246 221
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 238 8
## 1 5 216
##
## Accuracy : 0.9722
## 95% CI : (0.9529, 0.9851)
## No Information Rate : 0.5203
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9442
##
## Mcnemar's Test P-Value : 0.5791
##
## Sensitivity : 0.9643
## Specificity : 0.9794
## Pos Pred Value : 0.9774
## Neg Pred Value : 0.9675
## Prevalence : 0.4797
## Detection Rate : 0.4625
## Detection Prevalence : 0.4732
## Balanced Accuracy : 0.9719
##
## 'Positive' Class : 1
##
fp_fn_svm_poly <- poly_model_obj %>% pluck("pred") %>% dplyr::filter(obs != pred)
# Write CSV in R
write.table(fp_fn_svm_poly,
file = "./00-data/03-ml_results/fp_fn_svm_poly.csv",
row.names = FALSE,
na = "",
col.names = TRUE,
sep=",")
nrow(fp_fn_svm_poly)
## [1] 277
## degree scale C pred obs rowIndex Resample
## 1 3 0.1 0.5 0 1 1576 Fold01.Rep2
## 2 3 0.1 0.5 1 0 182 Fold09.Rep4
## 3 3 0.1 0.5 1 0 445 Fold06.Rep5
## 4 3 0.1 0.5 1 0 531 Fold09.Rep4
## 5 3 0.1 0.5 1 0 115 Fold05.Rep2
## 6 3 0.1 0.5 0 1 1780 Fold02.Rep2
Import data & data handling
c_m_TRANSFORMED <- read_csv("./00-data/02-aac_dpc_values/c_m_TRANSFORMED.csv",
col_types = cols(Class = col_factor(levels = c("0","1")),
PID = col_skip(), TotalAA = col_skip()))
#View(c_m_TRANSFORMED)
Partition data into training and testing sets
set.seed(1000)
index <- createDataPartition(c_m_TRANSFORMED$Class, p = 0.8, list = FALSE)
training_set <- c_m_TRANSFORMED[ index,]
test_set <- c_m_TRANSFORMED[-index,]
Class_test <- as.factor(test_set$Class)
set.seed(1000)
start_time <- Sys.time() # Start timer
# Create tuneGrid: Cost
tune.Grid = data.frame(expand.grid(C = 2^(seq(-5, 15, 2))))
# Create: 10X fold CV repeated 5X
tcontrol <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
savePredictions = "final") # Save predictions
rbf_model_obj <- train(Class ~ .,
data = training_set,
method = "svmRadialCost",
tuneGrid = tune.Grid,
trControl= tcontrol)
end_time <- Sys.time() # End timer
end_time - start_time # Display time
## Time difference of 2.423723 mins
## Support Vector Machines with Radial Basis Function Kernel
##
## 1873 samples
## 20 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times)
## Summary of sample sizes: 1685, 1686, 1686, 1686, 1686, 1685, ...
## Resampling results across tuning parameters:
##
## C Accuracy Kappa
## 3.1250e-02 0.9144721 0.8278653
## 1.2500e-01 0.9511031 0.9018251
## 5.0000e-01 0.9704221 0.9406791
## 2.0000e+00 0.9699937 0.9398269
## 8.0000e+00 0.9740562 0.9480186
## 3.2000e+01 0.9720247 0.9439679
## 1.2800e+02 0.9711714 0.9422795
## 5.1200e+02 0.9715980 0.9431324
## 2.0480e+03 0.9714916 0.9429197
## 8.1920e+03 0.9715980 0.9431330
## 3.2768e+04 0.9714916 0.9429209
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was C = 8.
## 0 1
## 245 222
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 238 7
## 1 5 217
##
## Accuracy : 0.9743
## 95% CI : (0.9555, 0.9867)
## No Information Rate : 0.5203
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9485
##
## Mcnemar's Test P-Value : 0.7728
##
## Sensitivity : 0.9688
## Specificity : 0.9794
## Pos Pred Value : 0.9775
## Neg Pred Value : 0.9714
## Prevalence : 0.4797
## Detection Rate : 0.4647
## Detection Prevalence : 0.4754
## Balanced Accuracy : 0.9741
##
## 'Positive' Class : 1
##
fp_fn_svmRadialCost <- rbf_model_obj %>% pluck("pred") %>% dplyr::filter(obs != pred)
# Write CSV in R
write.table(fp_fn_svmRadialCost,
file = "./00-data/03-ml_results/fp_fn_svmRbf.csv",
row.names = FALSE,
na = "",
col.names = TRUE,
sep=",")
nrow(fp_fn_svmRadialCost)
## [1] 243
## C pred obs rowIndex Resample
## 1 8 1 0 522 Fold01.Rep1
## 2 8 0 1 1579 Fold07.Rep1
## 3 8 0 1 1585 Fold02.Rep1
## 4 8 0 1 1587 Fold07.Rep1
## 5 8 1 0 141 Fold07.Rep3
## 6 8 1 0 94 Fold03.Rep1
SVM has shown that it is very versatile. Using the same amino acid dataset and by changing the type of function used to build the decision boundary one can get results in the high 90%. Even the linear SVM with no kernel transformation is able to find a hyperplane that with no more tuning than choosing a large enough range for the cost function.
It was seen that using a range for the cost starting at \(2^5\) and progressing toward \(2^{-15}\), stepping by one log, a wide range can be tested. Once the cost function range is narrowed a finer tuning can be carried out using one-quarter or one-half log steps. This further narrowing of the cost function may not need to be done since the one log steps seems anecdotally sufficient. This is an easy and powerful tool.
Patrick Henry Winston, 6.034 Artificial Intelligence, Fall 2010, Massachusetts Institute of Technology: MIT OpenCourseWare, http://ocw.mit.edu/6-034F10↩
Nika Haghtalab & Thorsten Joachims, CS4780/5780 - Machine Learning for Intelligent Systems, Fall 2019, Cornell University, Department of Computer Science, https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote09.html↩
Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning; Data Mining, Inference, and Prediction, https://web.stanford.edu/~hastie/ElemStatLearn/, 2017↩
Patrick Winston, 6.034 Artificial Intelligence, Fall 2010, Massachusetts Institute of Technology: MIT OpenCourseWare, http://ocw.mit.edu/6-034F10↩
C. Cortes, V. Vapnik, Machine Learning, 20, 273-297, 1995↩
C. Cortes, V. Vapnik, Machine Learning, 20, 273-297, 1995↩
Allison Horst, University of California, Santa Barbara, https://github.com/allisonhorst/stats-illustrations↩
Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning; Data Mining, Inference, and Prediction, https://web.stanford.edu/~hastie/ElemStatLearn/, 2017↩
C.Cortes, V.Vapnik, Machine Learning, 20, 273-297, 1995↩
V. Vapnik and A. Lerner, 1963. Pattern recognition using generalized portrait method. Automation and Remote Control, 24, 774–780↩
Vladimir Vapnik & Corinna Cortes, Machine Learning, 20, 273-297, 1995↩
Christopher Burges, Tutorial on Support Vector Machines for Pattern Recognition, D.M. & Knowl. Dis., 2, 121-167, 1998↩
Vladimir Vapnik & Corinna Cortes, Machine Learning, 20, 273-297, 1995↩
Webster’s third new international dictionary, ISBN 0-87779-201-1, 1986↩
Kevin P. Murphy, Machine Learning, A Probabilistic Perspective, MIT Press, ISBN 978-0-262-01802-9, 2012↩
Xindong Wu, et al., Top 10 algorithms in data mining, Knowl Inf Syst, 14:1–37, DOI:10.1007/s10115-007-0114-2, 2008↩
Xindong Wu, et al., Top 10 algorithms in data mining, Knowl Inf Syst, 14:1–37, DOI:10.1007/s10115-007-0114-2, 2008↩
Alexandros Karatzoglou, David Meyer, Kurt Hornik, ‘Support Vector Machines in R’, Journal of Statistical Software, April 2006, Volume 15, Issue 9.↩
Stuart Russell and Peter Norvig, Artificial Intelligence, A Modern Approach, Third Edition, Pearson, ISBN-13: 978-0-13-604259-4, 2010↩


The Homepage of 41#Exploer
The homepage of 41#Exploer shows the visitors about our company, including our unique culture and background stories, besides, the visitors can meet the team and our partners, and connect with us through the homepage.
The homepage of our company is a great way for people to learn more about our company and our unique culture. The visitors are able to see the developing history of the company, things we have done and how we shaped our values. The website also contains the company’s future plans and missions which allows people to see the targets we are approaching.


So I am finishing up Week 5 of Dev Bootcamp and I have gotten several good pairing sessions under my belt as well as some feedback from said pairing sessions. I have talked about the technical side of pairing (what it is, why it works), but this time, I want to discuss how I felt about it. I also want to talk about how I felt about the feedback I was given.
When I first started to approach pairing (and still a little now), I would start to get really nervous. I felt it was a combination of shyness and fear of my inadequacy. I was afraid I would hold the other person down. What I got was far different. I found the people I paired with to be in about the same boat as me. Some may have been a little ahead or behind, but no real discernible difference. What was super rewarding for me were moments when I was able to help someone through a concept they were struggling with. I was able to watch their "ah-ha" moment. It helped solidify in me the idea that "ok, I can actually do this." I won't say that my shyness has completely dissipated. I still find myself getting nervous when I pair with someone new. What has changed for me is the realization that we are all in this together and people want to help more than they want to tear you down.
As far as I can tell, this is my first experience where I get constant written feedback from my peers. All of the feedback I read was very positive, even when there were criticisms. I found that to be very encouraging. One recurring criticism was that I sometimes blur the line between driving and navigating and take control of the pair. My first reaction was to get defensive. "How dare they think I was messing up!" But when I took a step back and really thought about it I realized they were completely right. I did tend to run the session. Especially when I was excited about the material. I realized that though this helped me, it wasn't beneficial for the people I was pairing with. I was robbing them of a key aspect of their learning. After I realized this, I was able to make some corrections to how I did things and saw an immediate return.
The other aspect to feedback is giving it. I would always make a point of giving feedback right after a session. I wanted to make sure that my feelings and experiences were fresh in my mind. The trouble I had was making sure I hit all aspects of ASK (Actionable, Specific, Kind) feedback. I found it difficult to always pin point, what I considered, specific or actionable things. The other tricky thing is trying to give feedback that is uplifting but still effective. It really made me think about how to phrase my feedback. This had an unintended consequence. While I was thinking this hard about how to give the feedback, I would also reflect on my actions and find ways to improve myself. By giving feedback to others, I was unintentionally improving myself.
I would say that so far, the pairing and feedback process has been my favorite thing about my time at DBC. It has really helped me grow not just as a programmer but also as an individual.


@* * Copyright 2021 HM Revenue & Customs * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. *@ @import iht.constants.Constants.under325000 @import iht.constants.FieldMappings @this( ihtMainTemplateRegistration: iht_main_template_registration, inputYesNoRadioGroup: ihtHelpers.standard.input_yes_no_radio_group, previousAnswers: filter.previous_answers, errorSummary: ihtHelpers.custom.error_summary, formWithCSRF: FormWithCSRF ) @(ihtForm: Form[Option[Boolean]])(implicit messages: Messages, request: Request[_]) @ihtMainTemplateRegistration( title = messages("page.iht.filter.deceased.before.2022.heading"), browserTitle = Some(messages("page.iht.filter.deceased.before.2022.title")), isFullWidth = false, hasSignOut=false, hasTimeOut=false ) { @errorSummary(ihtForm) @formWithCSRF(iht.controllers.filter.routes.DeceasedBefore2022Controller.onSubmit, 'autoComplete -> "off") { @inputYesNoRadioGroup( ihtForm("value"), '_divClass -> Some("form-group"), '_legend -> Messages("page.iht.filter.deceased.before.2022.title"), '_legendClass -> "visually-hidden", '_fieldsetInline -> false )
} @previousAnswers(messages("iht.countries.englandOrWales")) }


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| DOSE: |
115 mg |
oral |
DXM |
(liquid) |
Drank (1) 115 mL bottle Robo Honey Cough. Severe stomach pains ($5.00 for all that honey and corn syrup!!) for about 40 minutes. Wheat Thins helped enormously with the cramps. DXM started having effects after about an hour. I got into some of my old records (vinyl), and had a very positive experience. I'm not a musician, but I tried to follow the suggestion of 'making music' by playing DJ and recording a mix tape. This was the second time I've tried this dose; I had planned to do more, but I just can't stomach the stuff they put in the syrup.
I would classify this as a nice plateau 1 experience: I had a gentle, soothing buzz that 'rolled' somewhat like E, but didn't falter. If nothing else, I've discovered that I like 'Donovan'... Also, burned some jasmine and patchoulli incense which seemed to heighten the experience. Stretching is also rewarding for me at this level, as is curling up on our overstuffed couch with the headphones on. My motor actions were very deliberate. even at this low dose I would NOT consider driving or going among the 'normals'. No visuals at this dose, and I can't say this is _quite_ like anything I've tried. It has elements of pot, heroin, ecstasy, but so far nothing like LSD, shrooms, or salvia (didn't like the last: felt like nitrous). The whole thing lasted a good 2 hours, with some time for chill down ('Scorn' or 'FSOL' worked well). Good luck, and stay safe.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


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Many IDB Cursors.
crbug.com/696055
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GenoSets provides several ways to load annotations from EMBL files.
Annotation files can be selected from a list of completed EMBL projects. GenoSets queries the EMBL database to find all completed projects and the user may select multiple files from a last for loading. The files are automatically downloaded and stored in the GenoSets database.
Important
Only chromosome files are included in the list of completed EMBL projects.
Plasmid and contig files must use an alternate method to load into GenoSets.
Files may be downloaded from EMBL and loaded into GenoSets by providing an INSD accession number. The accession id may contain a range which is useful for downloading contig sets. Additionally, multiple accessions may be loaded simultaneously by entering the accession ids separated by line, tab, column, or semicolon. A single accession id may also include the version number (<accession>.<version>). The latest version will be loaded if no version number is specified. If a range is specified, the sequence version will be ignored and the latest version will be loaded.
Example: To download all the contig files for Brucella abortus NCTC 8038, specify the accession range of ACJJ01000001-ACJJ01000045.
Example: To download plasmid pYJ016 for Vibrio vulnificus YJ016, specify accession AP005352.
A annotation method is created for each accession id. The method name is the accession id and the method version is in the format <accession>.<version> of the file. You do not need to set these in the wizard.


| |
ActiveTcl User Guide
|
|
|
- NAME
- bitmap - Images that display two colors
- SYNOPSIS
- image create bitmap ?name? ?options?
- DESCRIPTION
- CREATING BITMAPS
- -background
color
- -data
string
- -file
name
- -foreground
color
- -maskdata
string
- -maskfile
name
- IMAGE COMMAND
- imageName
cget option
- imageName
configure ?option? ?value option value
...?
- KEYWORDS
bitmap - Images that display two colors
image create bitmap ?name? ?options?
A bitmap is an image whose pixels can display either of two
colors or be transparent. A bitmap image is defined by four things:
a background color, a foreground color, and two bitmaps, called the
source and the mask. Each of the bitmaps specifies
0/1 values for a rectangular array of pixels, and the two bitmaps
must have the same dimensions. For pixels where the mask is zero,
the image displays nothing, producing a transparent effect. For
other pixels, the image displays the foreground color if the source
data is one and the background color if the source data is
zero.
Like all images, bitmaps are created using the image create command. Bitmaps support
the following options:
- -background color
- Specifies a background color for the image in any of the
standard ways accepted by Tk. If this option is set to an empty
string then the background pixels will be transparent. This effect
is achieved by using the source bitmap as the mask bitmap, ignoring
any -maskdata or -maskfile options.
- -data string
- Specifies the contents of the source bitmap as a string. The
string must adhere to X11 bitmap format (e.g., as generated by the
bitmap program). If both the -data and -file
options are specified, the -data option takes
precedence.
- -file name
- name gives the name of a file whose contents define the
source bitmap. The file must adhere to X11 bitmap format (e.g., as
generated by the bitmap program).
- -foreground color
- Specifies a foreground color for the image in any of the
standard ways accepted by Tk.
- -maskdata string
- Specifies the contents of the mask as a string. The string must
adhere to X11 bitmap format (e.g., as generated by the
bitmap program). If both the -maskdata and
-maskfile options are specified, the -maskdata option
takes precedence.
- -maskfile name
- name gives the name of a file whose contents define the
mask. The file must adhere to X11 bitmap format (e.g., as generated
by the bitmap program).
When a bitmap image is created, Tk also creates a new command
whose name is the same as the image. This command may be used to
invoke various operations on the image. It has the following
general form:
imageName option ?arg arg ...?
Option and the args determine the exact behavior
of the command. The following commands are possible for bitmap
images:
- imageName cget
option
- Returns the current value of the configuration option given by
option. Option may have any of the values accepted by
the image create bitmap command.
- imageName configure ?option?
?value option value ...?
- Query or modify the configuration options for the image. If no
option is specified, returns a list describing all of the
available options for imageName (see Tk_ConfigureInfo for information
on the format of this list). If option is specified with no
value, then the command returns a list describing the one
named option (this list will be identical to the corresponding
sublist of the value returned if no option is specified). If
one or more option-value pairs are specified, then the
command modifies the given option(s) to have the given value(s); in
this case the command returns an empty string. Option may
have any of the values accepted by the image create bitmap
command.
bitmap, image
Copyright © 1994 The Regents of the University of California.
Copyright © 1994-1996 Sun Microsystems, Inc.
Copyright © 1995-1997 Roger E. Critchlow Jr.


2.4. Multiplication of Matrices#
Row and Column Vectors
Column Matrices (Vectors): Column matrices, also known as column vectors, are matrices of size \(n \times 1\). In other words, they have \(n\) rows and only one column. Similarly, row matrices of size \(1 \times n\) are also referred to as row vectors. Vectors are essential objects in linear algebra and have various applications in mathematics, physics, computer science, and engineering.
For a column matrix \(A\) of size \(n \times 1\):
Each entry \(a_i\) in the column matrix \(A\) represents the element in the \(i^{th}\) row of the matrix.
Row Matrices (Row Vectors): For a row matrix \(B\) of size \(1 \times n\):
Each entry \(b_i\) in the row matrix \(B\) represents the element in the \(i^{th}\) column of the matrix.
Example: For example, if \(A\) is a column matrix of size \(3 \times 1\), it would look like this:
Likewise, if \(B\) is a row matrix of size \(1 \times 4\), it would look like this:
Both column matrices (vectors) and row matrices (row vectors) play a crucial role in linear algebra, and they are used to represent quantities such as position, velocity, and forces in physics, as well as data in various applications like machine learning and statistics.
Before we explain multiplying matrices. Let’s explain the multiplication of a row vector by a column vector. For row vector \(X\) and a column vector \(Y\). we have,
For a row vector \(X\) and a column vector \(Y\), where both have the same size \(n \times 1\), we perform the multiplication as follows:
The multiplication of the row vector \(X\) and column vector \(Y\) is given by the sum of the products of their corresponding entries:
This can be represented using summation notation as:
Where:
\(x_j\) represents the \(j\)-th entry in the row vector \(X\).
\(y_j\) represents the \(j\)-th entry in the column vector \(Y\).
The summation symbol \(\sum\) denotes the sum of the products of the corresponding entries, ranging from \(j=1\) to \(j=n\).
In other words, we multiply each entry in the row vector \(X\) by the corresponding entry in the column vector \(Y\), and then sum up these products to get the final result.
Example: For example, if we have:
The multiplication of the row vector \(X\) and column vector \(Y\) is:
Example: Evaluate \(\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}\begin{bmatrix} -2 \\ 1 \\ 4 \end{bmatrix}\).
Solution:
We have the row vector:
And the column vector:
To multiply the row vector \(X\) by the column vector \(Y\), we follow these steps:
Take the first entry of the row vector (\(1\)) and the first entry of the column vector (\(-2\)), then multiply them together: \((1) \times (-2) = -2\).
Take the second entry of the row vector (\(2\)) and the second entry of the column vector (\(1\)), then multiply them together: \((2) \times (1) = 2\).
Take the third entry of the row vector (\(3\)) and the third entry of the column vector (\(4\)), then multiply them together: \((3) \times (4) = 12\).
Finally, add up the results of these individual multiplications:
So, the result of multiplying the row vector \(X\) and the column vector \(Y\) is \(12\).
In summary, the multiplication of a row vector by a column vector is obtained by taking the dot product of the vectors. It involves multiplying each corresponding pair of entries and then summing up these products. The dot product is a common operation in linear algebra and has various applications in vector calculations and geometry.
For matrices \(A\) and \(B\), to form the product \(AB\), the number of columns of \(A\) must be equal to the number of rows of \(B\).
Consider a product \(AB\) where \(A\) has size \(m\times n\) and \(B\) has size \(n\times p\). Then, the product in terms of size of matrices is given by
We explain this using an example:
Example: Let \(A=\begin{bmatrix}3 & -1 \\ 0 & 2\end{bmatrix}\) and \(B=\begin{bmatrix}2 & 4 \\ 1 & 7\end{bmatrix}\). Evaluate \(AB\).
Solution: \(A\) is a \(2\times 2\) matrix, and \(B\) is a \(2\times 2\) matrix. Therefore, \(AB\) is \(2\times 2\) matrix as well. Evaluating each entry of \(AB\):
\((1,~1)\)-entry of a matrix \(AB\): We multiply row \(1\) of matrix \(A\) and column \(1\) of matrix \(B\) (It is similar to multiplying a row vector by a column vector).
\[\begin{align*} \left[\begin{array}{cc}3 & -1\\ 0 & 2\end{array}\right] \left[\begin{array}{>{\columncolor{blue!10}}cc}2 & 4 \\ 1 & 7\end{array}\right]\end{align*}\]\[\begin{align*} \text{$(1,~1)$-entry of a matrix $AB$}=\begin{bmatrix}3 & -1\end{bmatrix}\begin{bmatrix}2 & 1\end{bmatrix}=(3)(2)+(-1)(1)=3+2=5.\end{align*}\]\((1,~2)\)-entry of a matrix \(AB\): We multiply row \(1\) of matrix \(A\) and column \(2\) of matrix \(B\).
\[\begin{align*} \left[\begin{array}{cc}3 & -1\\0 & 2\end{array}\right] \left[\begin{array}{c>{\columncolor{blue!10}}c}2 & 4 \\ 1 & 7\end{array}\right]\end{align*}\]\[\begin{align*} \text{$(1,~2)$-entry of a matrix $AB$}=\begin{bmatrix}3 & -1\end{bmatrix}\begin{bmatrix}4 & 7\end{bmatrix}=(3)(4)+(-1)(7)=12-7=5.\end{align*}\]\((2,~1)\)-entry of a matrix \(AB\): We multiply row \(2\) of matrix \(A\) and column \(1\) of matrix \(B\).
\[\begin{align*} \left[\begin{array}{cc}3 & -1\\ 0 & 2\end{array}\right] \left[\begin{array}{>{\columncolor{blue!10}}cc}2 & 4 \\ 1 & 7\end{array}\right]\end{align*}\]\[\begin{align*} \text{$(2,~1)$-entry of a matrix $AB$}=\begin{bmatrix}0 & 2\end{bmatrix}\begin{bmatrix}2 & 1\end{bmatrix}=(0)(2)+(2)(1)=0+2=2.\end{align*}\]\((2,~2)\)-entry of a matrix \(AB\): We multiply row \(2\) of matrix \(A\) and column \(2\) of matrix \(B\).
\[\begin{align*} \left[\begin{array}{cc}3 & -1\\ 0 & 2\end{array}\right] \left[\begin{array}{c>{\columncolor{blue!10}}c}2 & 4 \\ 1 & 7\end{array}\right]\end{align*}\]\[\begin{align*} \text{$(2,~1)$-entry of a matrix $AB$}=\begin{bmatrix}0 & 2\end{bmatrix}\begin{bmatrix}1 & 7\end{bmatrix}=(0)(1)+(2)(7)=0+14=14.\end{align*}\]
Therefore, \(AB=\begin{bmatrix}5 & 5\\ 2 & 14\end{bmatrix}\).
Example: Compute \(AB\) where \(A=\begin{bmatrix}1 & 2 \\ -3 & 0 \\ 1 & -4 \end{bmatrix}\) and \(B=\begin{bmatrix} 1 & -1 & 2 \\ 3 & -2 & 1 \end{bmatrix}\).
Solution:
\(A\) is a \(3\times 2\) matrix, and \(B\) is a \(2\times 3\) matrix. Therefore,
\(AB\) is \(3\times 3\) matrix.
Evaluating the first row of \(AB\):
Evaluating the second row of \(AB\):
Evaluating the third row of \(AB\):
Therefore, \(AB=\begin{bmatrix} 7 & -5 & 4\\ -3 & 3 & -6\\ -11 & 7 & -2 \end{bmatrix}\).
In general, matrix multiplication is not commutative! (i.e, \(AB\neq BA)\). However, there are some examples where \(AB=BA\).
Example: Let \(A=\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}\) and \(B=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\). Then
Note that usually \(AB\) is different from \(BA\).
Refrences
Kuttler, Kenneth. “A First Course in Linear Algebra (Lyryx).” (2018).
Nicholson, W. Keith. “Linear Algebra with Applications (Lyryx).” (2018).


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Login Register {% include "partials/auth/login-form.html" %} {% include "partials/auth/register-form.html" %}


Before Change
assert (running_var is None or running_var.ndim == x.ndim)
if not isinstance(epsilon, theano.Variable):
epsilon = as_tensor_variable(epsilon)
if not isinstance(running_average_factor, theano.Variable):
running_average_factor = as_tensor_variable(running_average_factor)
inputs = [x, scale, bias, epsilon, running_average_factor]
output_types = [x.type(), scale.type(), scale.type()]
if running_mean is not None and running_var is not None:
inputs.append(running_mean)
After Change
def make_node(self, x, scale, bias, epsilon=1e-4,
running_average_factor=0.1,
running_mean=None, running_var=None):
x = as_tensor_variable(x)
scale = as_tensor_variable(scale)
bias = as_tensor_variable(bias)
epsilon = as_tensor_variable(epsilon)
running_average_factor = as_tensor_variable(running_average_factor)


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Inspired by DogFight by Opus Software (1983). New Game


Section 1.1 Sept. 24: The \(LU\) Factorization
Subsection 1.1.1 Warmup
To start, let's set some variable names. We'll call our space of \(3\times 3\) matrices \(M\) and its identity matrix \(I\text{.}\) Just press Evaluate (Sage)
. (There should be no output.) We'll then be able to refer to them in SageMath cells further down the page. We'll have to do this on each new page we load.
Warmup 1.1.1.
Recall that the commandC=B.with_added_multiple_of_row(i,j,l)
adds \(l\) times row \(j+1\) of \(B\) to row \(i+1\) of \(B\) and calls the new matrix \(C\text{.}\) Use Sage to build a \(3\times 3\) elimination matrix \(E\) out of \(I\) that adds 5 times row 1 to row 3. Confirm that your matrix does what it should by computing \(EA\text{,}\) where`Subsection 1.1.2 More Practice with \(A = LU\)
Exploration 1.1.1.
Consider the following system of 3 linear equations in 3 unknowns.
Perform the forward pass of elimination to find an equivalent upper triangular system. Write down this upper triangular system. What three row operations do you need to perform to make this work?
Use the information you just found to write a matrix decomposition \(A = LU\) (without explicitly finding any inverse matrices!) for the coefficient matrix \(A\) for this system of equations. (Be sure to multiply the matrices \(L\) and \(U\) to check your work.)
Then solve the system \(Ly = b\text{,}\) and subsequently the system \(Ux = y\text{.}\) (These are done easily enough by hand, but you can confirm your findings using Sage's .rref()
command.)
Exploration 1.1.2.
Of course, Sage can do this for us. Use the coefficient matrix from Exploration 1.1.1 to test the command.LU()
. What do you notice? What do you wonder?


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MASK OF DIMITRIOS, THE (director: Jean Negulesco; screenwriter: Frank Gruber/from Eric Ambler's novel "A Coffin for Dimitrios"; cinematographer: Arthur Edeson; cast: Sydney Greenstreet (Mr. Peters), Peter Lorre (Cornelius Latimer Leyden), Zachary Scott (Dimitrios Makropoulos), Faye Emerson (Irana Preveza),Victor Francen (Wladislaw Grodek), Steven Geray ( Bulic), Kurt Katch (Col. Haki), Marjorie Hoshelle (Anna Bulic), George Tobias (Fedor Muishkin), Eduardo Ciannelli (Marukakis), Florence Bates (Madame Chavez), David Hoffman (Konrad), Monte Blue (Abdul), 1944)
Reviewed by Dennis Schwartz
Warner Bros. could crank-out smashing suspense films like this one on a regular basis during the 1940s. With the war on and many of the leading men in the service, there was a place for character actors such as the Fat Man (Sydney Greenstreet)-and-The Little Man (Peter Lorre), to play together in starring roles, without romantic women co-stars. The handsome Zachary Scott made his starring debut in this one. Faye Emerson had recently married President Roosevelt's son, and therefore received top-billing, even though she had only a minor part.
The film was faithfully adapted from the novel of British author, Eric Ambler, and had more of a European feel to it than the ordinary American noir, though because of the dark lighting and the shadowy photography of renown film cinematographer Arthur Edeson- he also did "The Maltese Falcon," the film was able to retain its noir credentials despite lacking the usual cynicism of noir.
The film opens as we are told of how evil a man Dimitrios Makropoulos (Zachary Scott) is and onscreen it is written 1938. The next shot is of a Turkish beach and the discovery of Dimitrios' bloated body, with stab wounds, found as it is washed ashore.
Visiting Istanbul, attending a party, is a meek mystery writer from Holland, Cornelius Latimer Leyden (Peter Lorre). The head of the secret police, Colonel Haki (Katch), a fan of the writer, greets him at the party and tells him about the body that just washed ashore and a little something of Dimitrios, who was known internationally as a murderer, pimp, womanizer, smuggler, blackmailer, double-crosser, political assassin, spy, and thief. He was a treacherous man, a man without a heart, a soul, or a conscience. This intrigues the author, who accompanies the colonel to the police station before the body is disposed of. Leyden is interested enough in Dimitrios, that he decides to use him as a subject for his next book. All he has to do, is track down his life, find out who he was and why he did what he did. The colonel provides the writer with the dossier the police have on him and all the places he travelled to and committed his serious crimes. He tells him that the police were after him for 20 years but were never able to arrest him or get a photograph of him.
Leyden decides to go to Smyrna first, which in 1922, was a place under martial-law. The film uses flashback to tell the story. He is first seen in desperate need of money to leave the country. But he finds a perfect pigeon to rob, Konrad (Hoffman), whom he tempts by offering to sell him some stolen goods. He brings a partner, Abdul (Blue), along to the victim's apartment to help him rob the fence, but instead of just robbing him as planned, he knifes the fence to death and steals all his money. Abdul did not bargain for murder and is caught by the police and hung, while Dimitrios escapes to Athens.
Lorre prepares himself to travel through Smyrna, Athens, Sofia, Belgrade, Geneva, and finally to Paris, in order to trace the sinister criminal's path.
On board a train to Sophia, a portly, large-framed man, with a unique chuckle, Mr. Peters (Sydney Greenstreet), will share a train compartment with him. Peters is reading a book entitled "Pearls of Everyday Wisdom," while Leyden goes to sleep. He will mention to Leyden, the next morning, "There is not enough kindness in the world," and recommend a hotel to him on his stop in Sophia, one in which he will enter when Leyden is out and whereby he will thoroughly search his room. When Leyden returns, he is confronted by Peters pointing a gun at him and questioning him about what he knows about Dimitrios. Peters is interested that Leyden saw the body and that he had found it with no money on him and that he was wearing shabby clothes with the name Dimitrios sewn inside the coat. He proposes that they form an alliance and he will help Leyden get more information on Dimitrios from someone who knew him quite well, Wladislaw Grodek (Victor Francen), who now resides in Geneva. He tells him you will only get into trouble by going to Belgrade, that Grodek was a former master spy and knows what you want to know better than anyone else. He also offers him half a million French francs, as his share of the loot, of a scheme Peters has cooked up to get money for the information the two of them posssess.
While Leyden was in Sophia, before he met Peters in the hotel, he met a writer friend of his (Ciannelli ), who introduces him to the attractive Irana Preveza (Faye) in the smoky cabaret she operates, and she reluctantly tells her hard-luck story of meeting Dimitrios in 1923 and falling in love with him, despite knowing how despicable he was. After being broke and about to be turned over to the police by his landlord, he sneaks into her apartment, which is in the same dumpy hotel that he lives in, and she offers him a meal and a little money. The next day he returns with a large amount of money and pays her back with considerable interest, having blackmailed her rich married lover. He will eventually have to leave the country when he attempts to assassinate the head of Bulgaria, borrowing a huge sum of money from Irena, after she lies to the police to provide him with an alibi. She will never see him again or be paid back.
In Geneva, armed with the letter of introduction Peters gave him, Leyden finds out from Grodek how Dimitrios cruelly worked an espionage racket in Belgrade, by talking an insignificant, mousy clerk (Geray) in the war office into stealing documents of a minefield operation. He did it by trickily getting the clerk into gambling debts and forcing him to betray his country. The clerk ended up shooting himself, not able to live with his cowardly deed of betrayal to his country, in a time of conflict with Italy. As for Grodek, who was partners with Dimitrios in this endeavor, the stalworth Dimitrios double-crossed him and robbed the minefield plans, selling it to a higher bidder.
Leyden tells the amiable Peters, who was involved with Dimitrios in an earlier smuggling operation, one in which Dimitrios turned in all his cronies to save his own skin, that he is not interested in the blackmail money, but will meet him in his Paris apartment in order to get the full story. At last, in Paris, Peters tells Leyden that Dimitrios faked his death, that it is a man called Konstantin Gollos who was found on the beach, a member of their smuggling ring, and that Dimitrios is alive in Paris. There, they meet the suave and curt Dimitrios, who cuts a ruthlessly dashing figure, as Peters tells him they want a million francs in return for their silence in the matter of his faked death.
When Peters gets the money, he is gleeful for the moment, as the money is photographed as looking huge onscreen, looking more like monopoly money than real. But, surprisingly, Dimitrios appears in the doorway of their room and shoots Peters. He then goes to shoot Leyden, but the little man manages to knock the gun out of his hand and Peters gets the gun and points it at the cowering Dimitrios, begging for his life. When Leyden goes to get the police, offscreen we hear the shots being fired by Peters, and soon the police come to arrest him.  Peters tells Leyden, as he is being led away by the police, to send him a copy of the novel he will write about Dimitrios, saying: "I'll have a lot of time to read it where I'm going." He adds as the film dissolves: "You see, there's not enough kindness in the world."
The film deftly mixes fact with fiction, as Ambler's unremorseful anti-hero is based upon one of the world's greatest schemers, Basil Zaharoff, billionaire munitions king, whose early career mirrors the one of scheming Dimitrios Makropoulos.The rich flavor in the film comes from the lead character actors, who are indescribably witty and tacky, displaying good chemistry in working with each other, whose characterizations are most striking. They, along with the strong performance by Scott, give this pleasant thriller the life it needs to sustain it. The story itself, is too superficial to be anything more than a B type of programmer. But the film had a certain style to it that more than made up for the awkward telling of the story's ending.
REVIEWED ON 1/25/2000 GRADE: B-
Dennis Schwartz: " Ozus' World Movie Reviews"
http://www.sover.net/~ozus
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Dreamy Charcoal... even better Steamy charcoal. I love woody charcoal smell, so much that I love having it in my food too.  I do and I am nuts about them. I tried out my first first few charcoal based products in Soulflower Charcoal You Smell Good and LUSH Dark Angels and I love them to bits.
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 Best ever soap from LUSH... It works great for my oily skin, removes shine and oil for a long time and rescues breakout size slightly. My skin feels squeaky clean and supple. This does not dry me out. Unlike LUSH Dark Angels this one lathers really well, and wait for the best part.... It does not melt in your washroom ..and removes makeup.. hurray to that !!!! But 100gm will outlast its shelf life of 3 months, even if you use it twice a day, so give half of it to your best friend. Would totally recommend this LUSH gem to all oily skin beauties without second thoughts. This one is my buddy for life. Do you also love Charcoal smell ? Have you tired LUSH Coal Face ?


Cisco-IOS-XR-man-http-lighttpd-yang-cfg API API Reference
API generated from<EMAIL_ADDRESS>API Endpoint
http://{Controller-IP}:{Controller-Port}/restconf/config/network-topology:network-topology/topology/topology-netconf/node/inetri/yang-ext:mount/
URL '/' code: %2F
Schemes: http
Version: 1.0.0
Leaf Color Code:
Key  Mandatory  OptionalPaths
WEB - Update
Update operation of resource: web
webbody object
Successful operation
Internal Error
Response Content-Types: application/json
WEB - Create
Create operation of resource: web
webbody object
Successful operation
Internal Error
Response Content-Types: application/json
WEB - Delete
Delete operation of resource: web
Successful operation
Internal Error
Response Content-Types: application/json
WEB - Retrieve
Retrieve operation of resource: web
Successful operation
Internal Error
SERVER - Update
Update operation of resource: server
serverbody object
Successful operation
Internal Error
Response Content-Types: application/json
SERVER - Create
Create operation of resource: server
serverbody object
Successful operation
Internal Error
Response Content-Types: application/json
SERVER - Delete
Delete operation of resource: server
Successful operation
Internal Error
Response Content-Types: application/json
SERVER - Retrieve
Retrieve operation of resource: server
SERVICE - Update
Update operation of resource: service
servicebody object
Successful operation
Internal Error
Response Content-Types: application/json
SERVICE - Create
Create operation of resource: service
servicebody object
Successful operation
Internal Error
Response Content-Types: application/json
SERVICE - Delete
Delete operation of resource: service
Successful operation
Internal Error
Response Content-Types: application/json
SERVICE - Retrieve
Retrieve operation of resource: service
Successful operation
Internal Error
RESTCONF - Update
Update operation of resource: restconf
restconfbody object
Request Content-Types: application/json
Request Example
{
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}
Successful operation
Internal Error
Response Content-Types: application/json
RESTCONF - Create
Create operation of resource: restconf
restconfbody object
Request Content-Types: application/json
Request Example
{
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}
Successful operation
Internal Error
Response Content-Types: application/json
RESTCONF - Delete
Delete operation of resource: restconf
Successful operation
Internal Error
Response Content-Types: application/json
RESTCONF - Retrieve
Retrieve operation of resource: restconf
Successful operation
Internal Error
Response Content-Types: application/json
Response Example (200 OK)
{
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}
Schema Definitions
web_schema:
Webserver configuration commands
- server: object
-
Webserver configuration commands
-
- service: object
-
Web Service that needs to be activated
-
- restconf: object
-
Restconf specific configurations
-
- http-port: integer
-
Port number http server is listening on
- enable: null
-
Enable RESTCONF Service
- http-enable: null
-
Enable http connection in addition to https
- https-port: integer
-
Port number https server is listening on
Example
{
"server": {
"service": {
"restconf": {
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}
}
}
}
server_schema:
Webserver configuration commands
- service: object
-
Web Service that needs to be activated
-
- restconf: object
-
Restconf specific configurations
-
- http-port: integer
-
Port number http server is listening on
- enable: null
-
Enable RESTCONF Service
- http-enable: null
-
Enable http connection in addition to https
- https-port: integer
-
Port number https server is listening on
Example
{
"service": {
"restconf": {
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}
}
}
service_schema:
Web Service that needs to be activated
- restconf: object
-
Restconf specific configurations
-
- http-port: integer
-
Port number http server is listening on
- enable: null
-
Enable RESTCONF Service
- http-enable: null
-
Enable http connection in addition to https
- https-port: integer
-
Port number https server is listening on
Example
{
"restconf": {
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}
}
restconf_schema:
Restconf specific configurations
- http-port: integer
-
Port number http server is listening on
- enable: null
-
Enable RESTCONF Service
- http-enable: null
-
Enable http connection in addition to https
- https-port: integer
-
Port number https server is listening on
Example
{
"http-port": "integer",
"enable": [ null ],
"http-enable": [ null ],
"https-port": "integer"
}