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## arXiv Analytics

### arXiv:hep-ph/9304209AbstractReferencesReviewsResources

#### Search for the intermediate Mass Higgs Signal at TeV $eγ$ colliders

Published 1993-04-03Version 1

The intermediate mass Higgs (IMH) can be abundantly produced through the process $e^-\gamma \rightarrow W^-H\nu$ at TeV $e^-\gamma$ colliders, which are realized by the laser back-scattering method. We search for the signature of $W^-H \rightarrow (jj)(b\bar b)$ plus missing transverse momentum, with and without considering the $b$-tagging. We also analyse all the potential backgrounds from $e^-\gamma \rightarrow W^-Z\nu,\,W^-W^+e^-,\,ZZe^-,\, \bar t b\nu$ and $t\bar t e^-$. With our selective acceptance cuts these backgrounds are reduced to a manageable level. We find that for the entire intermediate mass range 60 -- 150~GeV the Higgs discovery should be viable. We also present detail formulas for the helicity amplitudes of these processes.

Comments: Latex(Revtex), 30 pages, 8 figures in postscript format (uuencoded), NUHEP-TH-93-3
Journal: Phys.Rev. D48 (1993) 1035-1047
Categories: hep-ph
Related articles: Most relevant | Search more
arXiv:1211.1976 [hep-ph] (Published 2012-11-08, updated 2012-12-04)
Indirect Probes of the MSSM after the Higgs Discovery
arXiv:1003.5494 [hep-ph] (Published 2010-03-29, updated 2011-06-08)
Study of CP violation in $Λ_c^+$ decay
arXiv:1105.2484 [hep-ph] (Published 2011-05-12, updated 2011-08-15)
A simple relation between the gamma N -> N(1535) helicity amplitudes

format: plain


text:
## Precalculus (10th Edition)

$f(x)=x^3−3x^2+2x$
If $c$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “factor” of the function. We can see from the graph that $0$, $1$ and $2$ are zeros of the function. Hence, $f(x)=a(x-0)(x−1)(x−2)\\ f(x)=a(x^3−3x^2+2x)$ When $a=1$, the function becomes $f(x)=x^3−3x^2+2x$ Thus, one possible polynomial function that might have the given graph is $f(x)=x^3−3x^2+2x$


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Create MGD77 headers from A77 files

## Synopsis¶

gmt mgd77header GEODAS-id.a77 [ -Hheadervalues.txt ] [ -Mf[item]|r|t ] [ -V[level] ] [ --PAR=value ]

Note: No space is allowed between the option flag and the associated arguments.

## Description¶

mgd77header generates an MGD77 header by reading A77 data (i.e., the data record portion of MGD77 files), determines temporal and spatial extents, ten degree boxes crossed, and data columns present. Optionally, it can also read an input file consisting of header field values (-H) to be included in program output. Header field values determined from data and read from input are output in either MGD77 format or as a list.

## Required Arguments¶

NGDC-ids

Can be one or more of five kinds of specifiers:

1. 8-character GEODAS IDs, e.g., 01010083, JA010010etc., etc.
2. 2-character agency codes which will return all cruises from each agency.
3. 4-character <agency><vessel> codes, which will return all cruises from those vessels.
4. =list, where list is a table with GEODAS IDs, one per line.
5. If nothing is specified we return all cruises in the data base.

(See mgd77info -L for agency and vessel codes). If no file extension is given then we search for files with one of the four known extensions. The search order (and the extensions) tried is MGD77+ (“.nc”), MGD77T (“.m77t”), MGD77 (“.mgd77” ) and plain text file (“.dat”). Use -I to ignore one or more of these file types). Cruise files will be looked for first in the current directory and second in all directories listed in $MGD77_HOME/mgd77_paths.txt [If$MGD77_HOME is not set it will default to \$GMT_SHAREDIR/mgd77].

## Optional Arguments¶

Obtain header field values from the input text file. Each row of the input file should consist of a header field name and its desired value, separated by a space. See below for a sample header file and for the full list of header field names.
-Mf[item]|r|t
List the meta-data (header) for each cruise. Append f for a formatted display. This will list individual parameters and their values, one entry per output line, in a format that can be searched using standard UNIX text tools. Alternatively, append the name of a particular parameter (you only need to give enough characters - starting at the beginning - to uniquely identify the item). Give - to display the list of all parameter names. You may also specify the number of a parameter. For the raw, punchcard-formatted MGD77 original header block, append r instead. For the M77T format, append t instead.
-V[level] (more …)
Select verbosity level [c].
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
--PAR=value
Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.

Format_Acronym MGD77

Source_Institution SOEST - UNIV. OF HAWAII

Country USA

Platform_Name KILO MOANA

Platform_Type_Code 1

Platform_Type SHIP

## Names of All MGD77 Header Fields¶

Survey_Identifier

Format_Acronym

Data_Center_File_Number

Parameters_Surveyed_Code

File_Creation_Year

File_Creation_Month

File_Creation_Day

Source_Institution

Country

Platform_Name

Platform_Type_Code

Platform_Type

Chief_Scientist

Project_Cruise_Leg

Funding

Survey_Departure_Year

Survey_Departure_Month

Survey_Departure_Day

Port_of_Departure

Survey_Arrival_Year

Survey_Arrival_Month

Survey_Arrival_Day

Port_of_Arrival

Geodetic_Datum_Position_Determination_Method

Bathymetry_Instrumentation

Magnetics_Instrumentation

Gravity_Instrumentation

Seismic_Instrumentation

Seismic_Data_Formats

Format_Type

Format_Description

Topmost_Latitude

Bottommost_Latitude

Leftmost_Longitude

Rightmost_Longitude

Bathymetry_Digitizing_Rate

Bathymetry_Sampling_Rate

Bathymetry_Assumed_Sound_Velocity

Bathymetry_Datum_Code

Bathymetry_Interpolation_Scheme

Magnetics_Digitizing_Rate

Magnetics_Sampling_Rate

Magnetics_Sensor_Tow_Distance

Magnetics_Sensor_Depth

Magnetics_Sensor_Separation

Magnetics_Ref_Field_Code

Magnetics_Ref_Field

Magnetics_Method_Applying_Res_Field

Gravity_Digitizing_Rate

Gravity_Sampling_Rate

Gravity_Theoretical_Formula_Code

Gravity_Theoretical_Formula

Gravity_Reference_System_Code

Gravity_Reference_System

Gravity_Corrections_Applied

Gravity_Departure_Base_Station

Gravity_Departure_Base_Station_Name

Gravity_Arrival_Base_Station

Gravity_Arrival_Base_Station_Name

Number_of_Ten_Degree_Identifiers

Ten_Degree_Identifier

gmt mgd77header km0201 -Hkmheaderitems.txt -Mf > km0201.h77


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## 2.6 Benchmarking

Comparing the performance of different learners on multiple tasks and/or different resampling schemes is a recurrent task. This operation is usually referred to as “benchmarking” in the field of machine-learning. The mlr3 package offers the benchmark() function for convenience.

### 2.6.1 Design Creation

In mlr3 we require you to supply a “design” of your benchmark experiment. By “design” we essentially mean the matrix of settings you want to execute. A “design” consists of Task, Learner and Resampling.

Here, we call benchmark() to perform a single holdout split on a single task and two learners. We use the benchmark_grid() function to create an exhaustive design and instantiate the resampling properly, so that all learners are executed on the same train/test split for each task:

library(data.table)
design = benchmark_grid(
learners = list(lrn("classif.rpart"), lrn("classif.featureless")),
resamplings = rsmp("holdout")
)
print(design)
bmr = benchmark(design)

Instead of using benchmark_grid() you could also create the design manually as a data.table and use the full flexibility of the benchmark() function. The design does not have to be exhaustive, e.g. it can also contain a different learner for each task. However, you should note that benchmark_grid() makes sure to instantiate the resamplings for each task. If you create the design manually, even if the same task is used multiple times, the train/test splits will be different for each row of the design if you do not manually instantiate the resampling before creating the design.

Let’s construct a more complex design to show the full capabilities of the benchmark() function.

# get some example tasks

# get some learners and for all learners ...
# * predict probabilities
# * predict also on the training set
library(mlr3learners)
learners = c("classif.featureless", "classif.rpart", "classif.ranger", "classif.kknn")
learners = lapply(learners, lrn,
predict_type = "prob", predict_sets = c("train", "test"))

# compare via 3-fold cross validation
resamplings = rsmp("cv", folds = 3)

# create a BenchmarkDesign object
print(design)
## 8: <TaskClassif>        <LearnerClassifKKNN> <ResamplingCV>

### 2.6.2 Execution and Aggregation of Results

After the benchmark design is ready, we can directly call benchmark():

# execute the benchmark
bmr = benchmark(design)

Note that we did not instantiate the resampling instance manually. benchmark_grid() took care of it for us: Each resampling strategy is instantiated once for each task during the construction of the exhaustive grid.

After the benchmark, we can calculate and aggregate the performance with $aggregate(): # measures: # * area under the curve (auc) on training # * area under the curve (auc) on test measures = list( msr("classif.auc", id = "auc_train", predict_sets = "train"), msr("classif.auc", id = "auc_test") ) bmr$aggregate(measures)
##    nr  resample_result       task_id          learner_id resampling_id iters
## 1:  1 <ResampleResult> german_credit classif.featureless            cv     3
## 2:  2 <ResampleResult> german_credit       classif.rpart            cv     3
## 3:  3 <ResampleResult> german_credit      classif.ranger            cv     3
## 4:  4 <ResampleResult> german_credit        classif.kknn            cv     3
## 5:  5 <ResampleResult>         sonar classif.featureless            cv     3
## 6:  6 <ResampleResult>         sonar       classif.rpart            cv     3
## 7:  7 <ResampleResult>         sonar      classif.ranger            cv     3
## 8:  8 <ResampleResult>         sonar        classif.kknn            cv     3
##    auc_train auc_test
## 1:    0.5000   0.5000
## 2:    0.8023   0.6703
## 3:    0.9984   0.7940
## 4:    0.9872   0.7183
## 5:    0.5000   0.5000
## 6:    0.8958   0.7625
## 7:    1.0000   0.9181
## 8:    0.9977   0.9247

Subsequently, we can aggregate the results further. For example, we might be interested which learner performed best over all tasks simultaneously. Simply aggregating the performances with the mean is usually not statistically sound. Instead, we calculate the rank statistic for each learner grouped by task. Then the calculated ranks grouped by learner are aggregated. Since the AUC needs to be maximized, we multiply with $$-1$$ so that the best learner gets a rank of 1.

tab = bmr$aggregate(measures) ranks = tab[, .(learner_id, rank_train = rank(-auc_train), rank_test = rank(-auc_test)), by = task_id] print(ranks) ## task_id learner_id rank_train rank_test ## 1: german_credit classif.featureless 4 4 ## 2: german_credit classif.rpart 3 3 ## 3: german_credit classif.ranger 1 1 ## 4: german_credit classif.kknn 2 2 ## 5: sonar classif.featureless 4 4 ## 6: sonar classif.rpart 3 3 ## 7: sonar classif.ranger 1 2 ## 8: sonar classif.kknn 2 1 ranks[, .(mrank_train = mean(rank_train), mrank_test = mean(rank_test)), by = learner_id][order(mrank_test)] ## learner_id mrank_train mrank_test ## 1: classif.ranger 1 1.5 ## 2: classif.kknn 2 1.5 ## 3: classif.rpart 3 3.0 ## 4: classif.featureless 4 4.0 Unsurprisingly, the featureless learner is outperformed. ### 2.6.3 Plotting Benchmark Results Analogously to plotting tasks, predictions or resample results, mlr3viz also provides a autoplot() method for benchmark results. library(mlr3viz) library(ggplot2) autoplot(bmr) + theme(axis.text.x = element_text(angle = 45, hjust = 1)) We can also plot ROC curves. To do so, we first need to filter the BenchmarkResult to only contain a single Task: autoplot(bmr$clone()$filter(task_id = "german_credit"), type = "roc") All available types are listed on the manual page of autoplot.BenchmarkResult(). ### 2.6.4 Extracting ResampleResults A BenchmarkResult object is essentially a collection of multiple ResampleResult objects. As these are stored in a column of the aggregated data.table(), we can easily extract them: tab = bmr$aggregate(measures)
rr = tab[task_id == "sonar" & learner_id == "classif.ranger"]$resample_result[[1]] print(rr) ## <ResampleResult> of 3 iterations ## * Task: sonar ## * Learner: classif.ranger ## * Warnings: 0 in 0 iterations ## * Errors: 0 in 0 iterations We can now investigate this resampling and even single resampling iterations using one of the approaches shown in the previous section: measure = msr("classif.auc") rr$aggregate(measure)
## classif.auc
##      0.9181

# get the iteration with worst AUC
perf = rr$score(measure) i = which.min(perf$classif.auc)

# get the corresponding learner and train set
print(rr$learners[[i]]) ## <LearnerClassifRanger:classif.ranger> ## * Model: - ## * Parameters: list() ## * Packages: ranger ## * Predict Type: prob ## * Feature types: logical, integer, numeric, character, factor, ordered ## * Properties: importance, multiclass, oob_error, twoclass, weights head(rr$resampling$train_set(i)) ## [1] 4 9 12 13 15 18 ### 2.6.5 Converting and Merging ResampleResults It is also possible to cast a single ResampleResult to a BenchmarkResult using the converter as_benchmark_result(). task = tsk("iris") resampling = rsmp("holdout")$instantiate(task)

##   2    iris classif.featureless       holdout     1        0      0


text:
# diophantus

Hello, this is beta version of diophantus. If you want to report about a mistake, please, write to hello@diophantus.org

#### The density of critical percolation clusters touching the boundaries of strips and squares

06 Apr 2007 cond-mat.dis-nn, cond-mat.stat-mech arxiv.org/abs/0704.0901
Abstract. We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our theoretical results follow from conformal field theory, and are compared with high-precision numerical simulation. For example, we show that the density of clusters touching both boundaries of an infinite strip of unit width (i.e. crossing clusters) is proportional to $(\sin \pi y)^{-5/48}\{[\cos(\pi y/2)]^{1/3} +[\sin (\pi y/2)]^{1/3}-1\}$. We also determine numerically contours for the density of clusters crossing squares and long rectangles with open boundaries on the sides, and compare with theory for the density along an edge.

# Reviews

There are no reviews yet.


text: For what you want to do, you should run dnf remove totem and cancel the operation at the y/n question. That would show you what would be removed together with totem itself. Asking for dnf list --autoremove totem only shows the status of the package totem itself, and as it is user-installed, it would not be a candidate for being autoremoved, and thus not listed.


text:
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# Nonagon: How is it in Shape?

## Know in Detail about the Nine Sided Polygon

Last updated date: 25th Mar 2023
Total views: 71.7k
Views today: 0.56k

Does Geometry interest you? Then do you know how many sides a nonagon has? A nonagon is a kind of polygon that consists of nine sides and nine angles. The term ‘nonagon’ has been derived from the Latin word ‘nonus’, which means nine, and the Greek word ‘gon’, which means sides. It also has another name, ‘enneagon’, that is derived from the Greek word ‘enneagonon’, translating to nine corners. Despite ‘enneagon’ being a more appropriate term for this shape, ‘nonagon’ is more often used owing to the simplicity of the name and its convenience in use.

Regular Nonagon

## Different Types of Nonagon

Based on their sides, angles, and vertices, nonagons can be categorised as follows:

• ccc: A regular nonagon has nine sides of equal length and nine interior angles, each of which measures 1400, and has exterior angles measuring 400 each. It has nine lines of symmetry and rotational equilibrium of order nine. All regular nonagons are convex.

• Irregular Nonagon: An irregular nonagon does not have all sides or all interior angles equal. However, the sum of all the nine interior angles measures up to 12600. Irregular nonagons can be both convex and concave.

• Convex Nonagon: A convex nonagon has all nine vertices pointing outwards. All interior angles of this type of nonagon measure less than or equal to 1800 and all diagonals are bounded by the closed figure. Convex nonagons can be both regular and irregular.

• Concave Nonagon: A concave nonagon has at least one vertex pointing inwards, having an interior angle that is greater than 1800. It has at least one diagonal lying outside the closed figure. Therefore, all concave nonagons are irregular.

## Properties of a Regular Nonagon

• All 9 sides are of equal length. For instance, in a nonagon ABCDEFGHI, AB = BC = CD = DE = EF = FG = GH = HI = IA.

• It comprises 9 interior angles, each measuring 1400. Hence, ∠ABC = ∠BCD = ∠CDE = ∠DEF = ∠EFG =∠FGH = ∠GHI = ∠HIA = ∠IAB.

• All 9 interior angles add up to 1260°. Therefore, ∠ABC + ∠BCD + ∠CDE + ∠DEF + ∠EFG + ∠FGH + ∠GHI + ∠HIA + ∠IAB = 12600.

• It consists of 9 exterior angles, each measuring 400.

• It has 27 diagonals, that is, AC, BD, CE, DF, EG, FH, and GI.

Properties of a Regular Nonagon

Note: Even in an irregular nonagon, the sum of the interior angles will be 12600.

## Some Formulas Related to a Regular Nonagon

### Perimeter

The formula for the perimeter (P) of a regular nonagon ABCDEFGHI

P = 9a,

where a = length of each side of the nonagon, since all 9 sides are equal in a regular nonagon,  that is, a = AB = BC = CD = DE = EF = FG = GH = HI = IA.

Sample Problem: Determine the perimeter of a regular nonagon, each of whose sides measures 9 cm.

Solution: It is given that a = 9 cm.

Since Perimeter (P) = 9a,

Then, the required perimeter P = 9 x 9 cm

= 81 cm

### Area

The formula for determining the area of a regular nonagon ABCDEFGHI is as follows:

Area (A) = $\frac{9}{9}$ (a2cot $\frsc{π}{9}$ )

where a = side length = AB = BC = CD = DE = EF = FG = GH = HI = IA, and π = 1800.

### Angles

There are three major angle formulas concerned with regular nonagons - sum of interior angles, individual interior angles, and exterior angles. They can be elaborated as follows:

• Sum of Interior Angles - It is the sum of the measures of all the interior angles taken together in a nonagon. The formula for the sum of interior angles in a regular nonagon is given below:

Sum of the interior angles = (n-2) x 1800, where n = number of sides

In nonagon ABCDEFGHI, n = 9

Therefore,

Sum of the interior angles = (9 -2) x 1800

= 12600

• Individual Interior Angle - The measure of an individual interior angle in a regular nonagon can be obtained by dividing the sum of all the interior angles by the number of sides in the nonagon. The formula to obtain the value of an individual interior angle of a regular nonagon is given below:

One interior angle = (n-2) x 1800/n, where n = number of sides

In nonagon ABCDEFGHI, n = 9

Hence,

Sum of the interior angles = (9-2) x 1800/9

= 1400

• Exterior Angle - An exterior angle is an angle formed by any side of a nonagon and the extension of its adjacent side. The formula to find the value of an exterior angle is given below:

Exterior angle = 3600/n, where n = number of sides

In nonagon ABCDEFGHI, n = 9

Therefore,

Exterior angle = 3600/9

= 400

Nonagons may not be as commonly observed as other shapes, like circles, squares, and triangles, but their application in art and architecture is no less crucial. The following image is that of the US Steel Building, Pittsburgh, Pennsylvania. Although it may look like a triangular structure at a glance, taking a closer look will reveal its nonagonal aspects, that is, the 6 extra line segments ingrained in the magnificent architecture.

US Steel Building, Pittsburgh, Pennsylvania

## Conclusion

To summarise the concept of nonagon, it is a two-dimensional figure (polygon) with nine sides and nine angles. It has 4 major types - regular, irregular, convex, and concave. Most of the properties and formulas are only applicable to regular nonagons, which have equal sides, and their interior and exterior angles are also equal, each measuring 1400 and 400, respectively. However, all nonagons have a total interior angle sum of 12600.

## FAQs on Nonagon: How is it in Shape?

1. What are some real world examples of Nonagons?

The US Steel Building in Pittsburgh, Pennsylvania, is in the shape of an irregular nonagon. In daily life, we come across certain objects, like coins, drinking glasses, table-tops, etc., that are shaped like regular or irregular nonagons.

2. How many dimensions does a nonagon have?

A nonagon has two dimensions. Thus, it is a 2D figure or shape.


text:
## § Center of a tree

• The remoteness / eccentricity of a vertex $v$ is its distance from its furthest node. $r(v) \equiv \max_{w \in V} d(v, w)$.
• The center of a tree is the vertex with minimum remoteness.

#### § Claim: center is on any diameter.

• Let $D$ be the diameter of length $L$.
• Let $c$ be the center. We claim that $c$ lies on $D$. If so, we are done.
• If not, then there is a path from $c$ to some vertex $v$ in $D$. Let WLOG the endpoints of the diameter be $s$ and $e$, and such that $v$ is further from $s$ than $e$. That is: $d(s, v) \geq s(v, e)$. In a picture:
s----------v---e
|
n
|
n-c--n
|
n

• Key idea: the important distance is the distance from $v$ to $s$. So we can forget everything in a radius of $d(v, e)$, as the distance $d(v, e) < d(v, s)$, and $d(c, e) < d(c, s)$. But if we forget the structure around $v$ in a radius of $e$, all we are left with is:
s-------------------v
|
|
c

where clearly $v$ is closer to $s$ than to $c$, and thus $c$ cannot be the center. In some sense, we are making a large scale/coarse structure argument, where the large scale structure is dominated by $d(s, v)$, which is all that matters.
• For any node $n$ in the subtree hanging from $v$, we have $d(n, v) \leq d(v, e)$, since otherwise the path $s-v-n$ would become a path longer than the diameter, contradicting the maximality of the diameter.
• Hence, we have $d(n, v) \leq d(v, e) \leq d(v, s)$, where the second inequality comes from the assumption of $s$ and $e$. So $s$ is the node that is furthest from $v$ amongst all nodes in the graph.
• But now notice that $d(c, s) = d(c, v) + d(v, s)$, and this is the longest distance from $c$ to any other node. This implies that $d(c, s) > d(v, s)$ as $d(c, v) > 0$.
• This contradicts the minimality of the eccentricity of $c$: the longest distance from $c$ to

#### § Claim: center is median of any diameter

We've already seen that center is on the diameter. Now if a center node is not on the median, the distance to the furthest node (start/end) can be improved by moving the center node closer to the median. So the best choice is to have the center be at (one of the) medians.

#### § Claim: center does not change by removing all leaf vertices

We've shown that the center is the median of all diameters. Removing all leaves removes two elements at the beginning and end of all diameters, leaving the median (the center) invariant.


text: we can only give. Likewise 65.4 is measured as 65. So, the modes are 2 and 3. First-type data elements (separated by spaces or commas, etc. Frequency distributions are often displayed in a table format, but they can also be presented graphically using a histogram. Construct the cumulative frequency distribution . The answer is ... no we can't. Frequency Distribution. The quick way to do it is to multiply each midpoint by each frequency: And then our estimate of the mean time to complete the race is: Very close to the exact answer we got earlier. Viewed 2k times 2. class So, F = 22, = 12, = 20.5 and i = 10. I want to calculate the median of a frequency distribution for a large number of samples. Online frequency distribution statistics calculator which helps you to calculate the grouped mean, median and mode by entering the required values. So let's fill that in, median is equal to the mean. Now for each X value we have 18, 33, 10, 6, and 33 frequencies respectively. This changes the midpoints and class boundaries. Median from a Frequency Distribution with Ungrouped Data . Frequency Distribution Calculator. In fact, for a normal distribution, mean = median = mode. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter. Find the Mean of the Frequency Table. Find the median of the followng distribution : Wages (in Rs) No. 3, 4.5, 7, 8.5, 9, 10, 15 There are 7 data points and 7/2=3.5 so the median is the 4th number, 8.5. of each number. which is 175 - 179: When we say "Sarah (there can be more than one mode): 62 appears three times, more often than the other values, so Mode = 62. Alex then makes a Grouped Frequency Table: So 2 runners took between 51 and 55 seconds, 7 took between 56 and 60 seconds, etc, Suddenly all the original data gets lost (naughty pup!). Suzie has $$15$$ albums, so the median is the $$8th$$ result (Remember we can use $$(15 + 1) \div 2$$). Since $$\frac{100}{2}$$ belongs to the cumulative frequency (65) of the class interval 69.5 – 79.5, therefore 69.5 – 79.5 is the median class. Or there may be more than one mode. Measures of dispersion i.e. Median of a frequency distribution. If there is an even number of data, then median will be the mean of the two central numbers. C. Frequency polygon. We call it "61 - 65", but it really includes values from 60.5 up to (but not including) 65.5. Mathematics: A Complete Course with CXC Questions - Volume 1, Page 392. 2.1. 2. Median from a Frequency Distribution with Grouped Data Mathematics: A Complete Course with CXC Questions - Volume 2, Page 883 2 Main Techniques of determining the Median with Grouped Data of labourers. Step 4 :     Find the width h of the median class interval Step 5 :     Find the cumulative frequency C of the class preceding the median class. Each of the samples have a number of classes (3 in … You dig them up and measure their lengths (to the nearest mm) and group the results: The Median is the mean of the 25th and the 26th length, so is in the 170 - 174 group: The Modal group is the one with the highest frequency, The marks 2 and 3 have the highest frequency. Null values) then it will return the number of array elements from the data array. This starts with some raw data (not a grouped frequency yet) ...To find the Mean Alex adds up all the numbers, then divides by how many numbers:Mean = 59+65+61+62+53+55+60+70+64+56+58+58+62+62+68+65+56+59+68+61+6721 Mean = 61.38095... To find the Median Alex places the numbers in value order and finds the middle number.In this case the median is the 11th number:53, 55, 56, 56, 58, 58, 59, 59, 60, 61, 61, 62, 62, 62, 64, 65, 65, 67, 68, 68, 70Me… May be determined through the graphic presentation of data points with a frequency distribution for incredibly.: values and their frequency median of frequency distribution how often each value occurs ) set of data then. 300 – 400 … in a table format, but it really includes values from 60.5 to. For other ideas when you stumble on the number of data points with frequency! Of array elements from the data and compare them  17 '' excel returns an array of values! 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In ascending order information from a frequency distribution before it and 5 scores after it n't really.. Follows: Measures of central Tendency and location i.e from a frequency distribution and determine the median data that been. Fill that in, median, skewness, and by the class midpoint of. Have 18, 33, 10, 6, and 33 frequencies respectively: the! Two employees for being unable to put numbers to him in an ascending order data he to. 9 months ago 364 days old and still be called  17 '' has been arranged an! Calculating the less than type cumulative frequency distribution median, mode and median exactly. Arranged in an easy-to-digest fashion that of 50 – 60 be f2 includes. Asked 7 years, 9 months ago ( i.e by calculating the less than type cumulative frequency is median... Call it  61 - 65 '', but it really includes from! 1: Prepare a table format, but it really includes values from to... But they can also be presented graphically using a histogram of your data - mean median! 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Are simple algorithms to calculate the median of a Cauchy distribution with mean and. 3 have the highest frequency example: you grew fifty baby carrots using special soil distribution gives the monthly of! Also be presented graphically using a histogram of your data shows the frequency of the samples have number... Have the highest frequency and get some more practice along the way up to but... The graphic presentation of data points with a frequency distribution have analyzed, it seems that some are! You stumble on the number of books they read in the form of Ogives is used to the!, it seems that some numbers are necessary multiply the frequency distribution calculator in Rs ) no construct frequency! Class 30 – 40 be f1 and that of 50 – 60 be f2 in, median mode! The students of class X the first step in turning data into information is to create a distribution including... 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Some numbers are necessary median of frequency distribution let me go back to my scratchpad.! Data shows the frequency distribution for a set of array values which is used to group the values from up. Modal value, Alex places the numbers in ascending order, then type f: and further write of.


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# set epslatex in gnuplot is not giving labels correctly in the output when generated from latex file

I am using set terminal epslatex color to generate .tex file but when I used it to generate final .div file than xlabel,ylabel, xtics,ytics etc. are not coming in output. My code is

set term epslatex color
set out "gnu1.tex"
set title "pip-latency-comparison"
set xlabel "Number of Hops"
set ylabel "Latency (sec)"
set xrange [1:6]
set yrange [0:450]
set key at 5.5,350
set termoption dashed
unset log
set xtic auto
set ytic auto
set style line 1 lt 2 lw 3 lc 7 pt 1
set style line 2  lw 3 lc 8 pt 2
set style line 3  lw 3 lc 5 pt 3
set style line 4  lw 3 lc 6 pt 5
plot "gnu1.dat" u 1:2 t "PIP" ls 1 w linespoints,\
"gnu1.dat"   u 1:3 t "Flush" ls 2  w linespoints,\
"gnu1.dat"  u 1:4 t "PSFQ"  ls 3 w linespoints,\
"gnu1.dat" u 1:5 t "Fetch" ls 4 w linespoints
set output

and in my Latex file

\documentclass{article}
\usepackage{graphicx}
\usepackage{color}
\begin{document}
\input{gnu1.tex}
\end{document}

-
For me your example works fine (gnuplot 4.6.4). But you must look at the Postscript file, the DVI output cannot be displayed correctly (at least xdvi can't). BTW: If you compile the plot separately you can use the standalone terminal option. – Christoph Nov 14 '13 at 9:00
@Christoph, I didn't get it. My version is 4.4, so how can i produce proper output without changing the version ? – pcoder Nov 14 '13 at 9:27
@Chritoph, OK got it. The Postscript file is giving the correct output. So now first I am converting it to .ps using 'dvips -o file.ps file.dvi' and then finally to pdf using ps2pdf. – pcoder Nov 14 '13 at 9:33


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# Start a new discussion

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• CommentRowNumber1.
• CommentAuthorHarry Gindi
• CommentTimeMay 23rd 2010

So, I have some pending changes on operad that I made in the sandbox and am waiting for a go-ahead to post from the interested parties, but I was also wondering if someone would be willing to write up a follow-up to the very nice definition of an operad as a monoid in the blah blah monoidal category. That is, it seems like this should give us a very nice way to define an algebra, but I don't know how one would actually go about doing it.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeMay 23rd 2010

I’ve posted the sandbox write-up already. You did a nice job, Harry.

Regarding your question, there’s very closely related material over at club (actually a generalization), but I’ll try to get to this particular case a little later tonight.

• CommentRowNumber3.
• CommentAuthorHarry Gindi
• CommentTimeMay 23rd 2010
• (edited May 23rd 2010)

Thanks!


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Bi-layer Kinetic Inductance detectors for space observations between 80-120 GHz

Abstract : We have developed Lumped Element Kinetic Inductance Detectors (LEKID) sensitive in the frequency band from 80 to 120~GHz. In this work, we take advantage of the so-called proximity effect to reduce the superconducting gap of Aluminium, otherwise strongly suppressing the LEKID response for frequencies smaller than 100~GHz. We have designed, produced and optically tested various fully multiplexed arrays based on multi-layers combinations of Aluminium (Al) and Titanium (Ti). Their sensitivities have been measured using a dedicated closed-circle 100 mK dilution cryostat and a sky simulator allowing to reproduce realistic observation conditions. The spectral response has been characterised with a Martin-Puplett interferometer up to THz frequencies, and with a resolution of 3~GHz. We demonstrate that Ti-Al LEKID can reach an optical sensitivity of about $1.4$ $10^{-17}$~$W/Hz^{0.5}$ (best pixel), or $2.2$ $10^{-17}$~$W/Hz^{0.5}$ when averaged over the whole array. The optical background was set to roughly 0.4~pW per pixel, typical for future space observatories in this particular band. The performance is close to a sensitivity of twice the CMB photon noise limit at 100~GHz which drove the design of the Planck HFI instrument. This figure remains the baseline for the next generation of millimetre-wave space satellites.
Keywords :
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-01141710
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Submitted on : Wednesday, February 16, 2022 - 11:07:51 AM
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A. Catalano, J. Goupy, Hélène Le Sueur, A. Benoit, O. Bourrion, et al.. Bi-layer Kinetic Inductance detectors for space observations between 80-120 GHz. Astronomy and Astrophysics - A&A, EDP Sciences, 2015, 580, pp.A15. ⟨10.1051/0004-6361/201526206⟩. ⟨in2p3-01141710⟩

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Definitions

# Analytic signal

In mathematics and signal processing, the analytic representation of a real-valued function or signal facilitates many mathematical manipulations of the signal. The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. They can be discarded with no loss of actual information, if we are willing to deal with a complex-valued function instead. And that turns out to make certain attributes of the signal more accessible and facilitate the derivation of modulation and demodulation techniques, especially single-sideband. As long as the manipulated function has no negative frequency components (that is, it is still analytic), the conversion from complex back to real is just a matter of discarding the imaginary part. The analytic representation is a generalization of the phasor concept.

## Definition

If $x\left(t\right),$  is a real-valued signal with Fourier transform $X\left(f\right),,$  and $U\left(f\right),$  is a unit step function, then the function:

begin{align} X_mathrm{a}(f) & stackrel{mathrm{def}}{=} begin{cases} 2 X(f), & mbox{for } f > 0, X(f), & mbox{for } f = 0, 0, & mbox{for } f < 0, end{cases} &= X(f)cdot 2 U(f) end{align}

contains only the non-negative frequency components of $X\left(f\right).,$  And the operation is reversible, due to the Hermitian property of $X\left(f\right),$ :

$X\left(f\right) =$
begin{cases} {1 over 2} X_mathrm{a}(f), & mbox{for } f > 0, X^*(|f|), & mbox{for } f < 0. quad quad mbox{complex conjugate} end{cases}

The inverse Fourier transform of $X_mathrm\left\{a\right\}\left(f\right),$ is the analytic signal:

begin{align} x_mathrm{a}(t) &= mathcal{F}^{-1}{X(f)} * mathcal{F}^{-1}{2 U(f)} quad quad mbox{convolution} &= x(t) * left[delta(t) + jcdot {1 over pi t} right] &= x(t) + jcdot left[x(t) * {1 over pi t}right] &= x(t) + jcdot hat{x}(t), end{align}

where $hat\left\{x\right\}\left(t\right),$ is the Hilbert transform of $x\left(t\right),,$ and $j,$ is the imaginary unit.

Example 1:  $x\left(t\right) = cos\left(omega_0 t\right),$, for some parameter $omega_0 > 0,$

$hat\left\{x\right\}\left(t\right) = cos\left(omega_0 t -begin\left\{matrix\right\} frac\left\{pi \right\}\left\{2\right\} end\left\{matrix\right\}\right) = sin\left(omega_0 t\right),$
$x_mathrm\left\{a\right\}\left(t\right) = cos\left(omega_0 t\right) + jcdot sin\left(omega_0 t\right) = e^\left\{j omega_0 t\right\},$   (The 2nd equality is Euler's formula.)
This is a complex-valued signal with increasing phase (positive frequency).

It also follows from Euler's formula that $cos\left(omega_0 t\right) = begin\left\{matrix\right\} frac\left\{1\right\}\left\{2\right\} end\left\{matrix\right\}\left(e^\left\{j omega_0 t\right\}+e^\left\{-j omega_0 t\right\}\right).,$   So $x\left(t\right),$ comprises both positive and negative frequency components.  $x_mathrm\left\{a\right\}\left(t\right),$ is just the positive portion. When dealing with simple sinusoids or sums of sinusoids, we can deduce $x_mathrm\left\{a\right\}\left(t\right),$ directly, without determining $hat\left\{x\right\}\left(t\right)$ first.

Example 2:  $x\left(t\right) = cos\left(omega t+theta\right) = begin\left\{matrix\right\} frac\left\{1\right\}\left\{2\right\} end\left\{matrix\right\} \left(e^\left\{j \left(omega t+theta\right)\right\} + e^\left\{-j \left(omega t+theta\right)\right\}\right)$
$x_mathrm\left\{a\right\}\left(t\right) =$
begin{cases} e^{j |omega| t}cdot e^{jtheta} , & mbox{if} omega > 0, e^{j |omega| t}cdot e^{-jtheta} , & mbox{if} omega < 0. end{cases}

The removal of the negative frequency terms is also demonstrated in Example 3. We note that nothing prevents us from computing $x_mathrm\left\{a\right\}\left(t\right),$ for a complex-valued $x\left(t\right).,$  But it might not be a reversible representation, because the original spectrum is not symmetrical in general. So except for this example, the general discussion assumes real-valued $x\left(t\right).,$

Example 3:  $x\left(t\right) = e^\left\{-j omega_0 t\right\},$, for some parameter $omega_0 > 0,$

$hat\left\{x\right\}\left(t\right) = jcdot e^\left\{-j omega_0 t\right\},$
$x_mathrm\left\{a\right\}\left(t\right) = e^\left\{-j omega_0 t\right\} + j^2cdot e^\left\{-j omega_0 t\right\} = 0,$

Analytic signals are often shifted in frequency (down-converted) toward 0 Hz, which creates [non-symmetrical] negative frequency components. One motive is to allow lowpass filters with real coefficients to be used to limit the bandwidth of the signal. Another motive is to reduce the highest frequency, which reduces the minimum rate for alias-free sampling. A frequency shift does not undermine the mathematical tractability of the complex signal representation. So in that sense, the down-converted signal is still "analytic". However, restoring the real-valued representation is no longer a simple matter of just extracting the real component. Up-conversion is obviously required, and if the signal has been sampled (discrete-time), interpolation (upsampling) might also be necessary to avoid aliasing.

The complex conjugate of an analytic signal contains only negative frequency components. In that case also, there is no loss of information or reversibility by discarding the imaginary component. Obviously the real component of the complex conjugate is the same as the real component of the analytic signal. But in this case, its extraction restores the suppressed positive frequency components.

Another way to achieve a spectrum of negative frequencies is to frequency-shift the analytic signal sufficiently far in the negative direction. Extracting the real component again restores the positive frequencies. But in this case their order is reversed... the low-frequency component is now the high one. This can be used to demodulate a type of single sideband signal called lower sideband or inverted sideband.

## Applications

The analytic signal can also be expressed in terms of complex polar coordinates,  $x_mathrm\left\{a\right\}\left(t\right) = A\left(t\right)e^\left\{jphi\left(t\right)\right\},,$  where:

$A\left(t\right) = |x_mathrm\left\{a\right\}\left(t\right)| = sqrt \left\{ x^2\left(t\right) + hat\left\{x\right\}^2\left(t\right) \right\},$

$phi\left(t\right) = arg left\left\{ x_mathrm\left\{a\right\}\left(t\right) right\right\}.,$     (see arg function)

These functions are respectively called the amplitude envelope and instantaneous phase of the signal $x\left(t\right).,$  In the accompanying diagram, the blue curve depicts $x\left(t\right),,$ and the red curve depicts the corresponding $A\left(t\right).,$
The time derivative of the unwrapped instantaneous phase is called the instantaneous frequency:

$omega\left(t\right) stackrel\left\{mathrm\left\{def\right\}\right\}\left\{=\right\} phi \text{'}\left(t\right) = frac\left\{d\right\}\left\{dt\right\} phi\left(t\right).,$

The amplitude function, and the instantaneous phase and frequency are in some applications used to measure and detect local features of the signal. Another application of the analytic representation of a signal relates to demodulation of modulated signals. The polar coordinates conveniently separate the effects of amplitude modulation and phase (or frequency) modulation, and effectively demodulates certain kinds of signals.

The analytic signal can also be represented as:

 $x_mathrm\left\{a\right\}\left(t\right),$ $= left\left[A\left(t\right) e^\left\{jphi\left(t\right)\right\} e^\left\{-j omega_0 t\right\} right\right] e^\left\{j omega_0 t\right\}$ $= gamma \left(t\right)cdot e^\left\{j omega_0 t\right\},$

where

$gamma \left(t\right) = A\left(t\right)cdot e^\left\{j\left(phi\left(t\right) - omega_0 t\right)\right\} ,$

is the signal's complex envelope. The complex envelope is not unique; on the contrary, it is determined by an arbitrary $omega_0,$ assignment. This concept is often used when dealing with passband signals. If $x\left(t\right),$ is a modulated signal, $omega_0,$ is usually assigned to be a carrier frequency. In other cases it is selected to be somewhere in the middle of the frequency band. Sometimes $omega_0,$ is chosen to minimize

$int_\left\{0\right\}^\left\{+infty\right\}\left(omega-omega_0\right)^2|X_mathrm\left\{a\right\}\left(omega\right)|^2, domega.$

Alternatively , $omega_0,$ can be chosen to minimize the mean square error in linearly approximating the unwrapped instantaneous phase $phi\left(t\right),$:

$int_\left\{-infty\right\}^\left\{+infty\right\}\left(omega\left(t\right)-omega_0\right)^2 |x_mathrm\left\{a\right\}\left(t\right)|^2 , dt$

or another alternative (for some optimum $theta ,$):

$int_\left\{-infty\right\}^\left\{+infty\right\} left\left(phi\left(t\right)-\left(omega_0 t + theta\right) right\right)^2, dt.$.

## Extensions of the analytic signal to signals of multiple variables

The concept of analytic signal is well-defined for signals of a single variable which typically is time. For signals of two or more variables, an analytic signal can be defined in different ways, and two approaches are presented below.

### Multi-dimensional analytic signal based on an ad-hoc direction

A straightforward generalization of the analytic signal can be done for a multi-dimensional signal once it is established what is meant by negative frequencies for this case. This can be done by introducing a normalized vector $hat\left\{n\right\}$ in the Fourier domain and label any frequency vector $u$ as negative if $u cdot hat\left\{n\right\} < 0$. The analytic signal is then produced by removing all negative frequencies and multiply the result by $2$, in accordance to the procedure described for the case of one-variable signals. However, it should be noted that there is no particular direction for $hat\left\{n\right\}$ which must be chosen unless there are some additional constraints. Therefore, the choice of $hat\left\{n\right\}$ is ad-hoc, or application specific.

### The monogenic signal

The real and imaginary parts of the analytic signal correspond to the two elements of the vector-valued monogenic signal, as it is defined for one-variable signals. However, the monogenic signal can be extended to arbitrary number of variables in a straightforward manner, producing an $n + 1$ dimensional vector-valued function for the case of $n$ variable signals.

## Not to be confused with

In mathematics, particularly functions of a complex variable, an analytic function refers to a function which satisfies certain properties regarding differentiability. The concept of analytic signal should not be confused with analytic functions. See the analytic representation related to the Hilbert transform for a discussion about the relation between these two concepts.


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## Interpolation Basics

This article covers interpolation basics, and provides a numerical example of interpolation of a time signal.  Figure 1 illustrates what we mean by interpolation.  The top plot shows a continuous time signal, and the middle plot shows a sampled version with sample time Ts.  The goal of interpolation is to increase the sample rate such that the new (interpolated) sample values are close to the values of the continuous signal at the sample times [1].  For example, if...

## A Two Bin Solution

July 12, 2019
Introduction

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The Coding...

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Development of a Reduced-Delay 2nd-Order IIR Filter

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This blog describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.

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...

## A Lesson In Engineering Humility

Let's assume you were given the task to design and build the 12-channel telephone transmission system shown in Figure 1.

Figure 1

At a rate of 8000 samples/second, each telephone's audio signal is sampled and converted to a 7-bit binary sequence of pulses. The analog signals at Figure 1's nodes A, B, and C are presented in Figure 2.

Figure 2

I'm convinced that some of you subscribers to this dsprelated.com web site could accomplish such a design & build task....

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Some time ago I reviewed the manuscript of a book being considered by the IEEE Press publisher for possible publication. In that manuscript the author presented the following equation:

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Then, later it occurred to me that it might be useful for this blog's readers to be aware of algorithms for computing FFT twiddle factors. So,... what follows are two algorithms showing how to compute the individual twiddle factors of an N-point decimation-in-frequency...

## Free DSP Books on the Internet

While surfing the "net" I have occasionally encountered signal processing books whose chapters could be downloaded to my computer. I started keeping a list of those books and, over the years, that list has grown to over forty books. Perhaps the list will be of interest to you.

## Design IIR Butterworth Filters Using 12 Lines of Code

While there are plenty of canned functions to design Butterworth IIR filters [1], it’s instructive and not that complicated to design them from scratch.  You can do it in 12 lines of Matlab code.  In this article, we’ll create a Matlab function butter_synth.m to design lowpass Butterworth filters of any order.  Here is an example function call for a 5th order filter:

## The DFT Magnitude of a Real-valued Cosine Sequence

This blog may seem a bit trivial to some readers here but, then again, it might be of some value to DSP beginners. It presents a mathematical proof of what is the magnitude of an N-point discrete Fourier transform (DFT) when the DFT's input is a real-valued sinusoidal sequence.

To be specific, if we perform an N-point DFT on N real-valued time-domain samples of a discrete cosine wave, having exactly integer k cycles over N time samples, the peak magnitude of the cosine wave's...

## Four Ways to Compute an Inverse FFT Using the Forward FFT Algorithm

July 7, 20151 comment

If you need to compute inverse fast Fourier transforms (inverse FFTs) but you only have forward FFT software (or forward FFT FPGA cores) available to you, below are four ways to solve your problem.

Preliminaries To define what we're thinking about here, an N-point forward FFT and an N-point inverse FFT are described by:

$$Forward \ FFT \rightarrow X(m) = \sum_{n=0}^{N-1} x(n)e^{-j2\pi nm/N} \tag{1}$$  Inverse \ FFT \rightarrow x(n) = {1 \over N} \sum_{m=0}^{N-1}...

## Minimum Shift Keying (MSK) - A Tutorial

Minimum Shift Keying (MSK) is one of the most spectrally efficient modulation schemes available. Due to its constant envelope, it is resilient to non-linear distortion and was therefore chosen as the modulation technique for the GSM cell phone standard.

MSK is a special case of Continuous-Phase Frequency Shift Keying (CPFSK) which is a special case of a general class of modulation schemes known as Continuous-Phase Modulation (CPM). It is worth noting that CPM (and hence CPFSK) is a...

## Python scipy.signal IIR Filter Design

Introduction

The following is an introduction on how to design an infinite impulse response (IIR) filters using the Python scipy.signal package.  This post, mainly, covers how to use the scipy.signal package and is not a thorough introduction to IIR filter design.  For complete coverage of IIR filter design and structure see one of the references.

Filter Specification

Before providing some examples lets review the specifications for a filter design.  A filter...

## Delay estimation by FFT

Given x=sig(t) and y=ref(t), returns [c, ref(t+delta), delta)] = fitSignal(y, x);:Estimates and corrects delay and scaling factor between two signals Code snippet

This article relates to the Matlab / Octave code snippet: Delay estimation with subsample resolution It explains the algorithm and the design decisions behind it.

Introduction

There are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar,...

## Polyphase Filters and Filterbanks

ALONG CAME POLY

Polyphase filtering is a computationally efficient structure for applying resampling and filtering to a signal. Most digital filters can be applied in a polyphase format, and it is also possible to create efficient resampling filterbanks using the same theories.

This post will walk through a reference implementation of both the downsampling polyphase filter and a downsampling polyphase filterbank using scipy, numpy, matplotlib, and python. It should also highlight some of...

## Embedded World 2018 - More Videos!

March 27, 20181 comment

After the interview videos last week, this week I am very happy to release two more videos taken at Embedded World 2018 and that I am proud of.

For both videos, I made extensive use of my two new toys, a Zhiyun Crane Gimbal and a Sony a6300 camera.

The use of a gimbal like the Zhiyun makes a big difference in terms of making the footage look much more stable and cinematographic.

As for the Sony camera, it takes fantastic slow-motion footage and...

## Embedded World 2018 - The Interviews

March 21, 2018

Once again this year, I had the chance to go to Embedded World in Nuremberg Germany.  And once again this year, I brought my video equipment to try and capture some of the most interesting things at the show.

Something new this year, I asked Jacob Beningo if he would partner with me in doing interviews with a few vendors.  I would operate the camera while Jacob would ask the right questions to the vendors to make them talk about the key products/features that...

## Finally got a drone!

As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process.  When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce SEGGER's 25th anniversary video, the company bought a drone so we could get an aerial shot of the party (at about the 1:35 mark in this video).  Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...

## SEGGER's 25th Anniversary Video

Chances are you will find this video more interesting to watch if you take five minutes to first read the story of the week I spent at SEGGER's headquarters at the end of June.

The video is only a little more than 2 minutes long.  If you decide to watch it, make sure to go full screen and I would really love to read your thoughts about it in the comments down bellow.  Do you think a video like this succeeds in making the viewer want to learn more about the company?...

## Went 280km/h (174mph) in a Porsche Panamera in Germany!

Those of you who've been following my blog lately already know that I am going through some sort of mid-life crisis that involves going out there to meet people and make videos.  It all started with Embedded World early this year, then continued at ESC Boston a couple of months ago and the latest chapter just concluded as I returned from Germany after spending a week at SEGGER's headquarters to produce a video to highlight their 25th anniversary.

## Going back to Germany!

A couple of blog posts ago, I wrote that the decision to go to ESC Boston ended up being a great one for many different reasons.  I came back from the conference energized and really happy that I went.

These feelings were amplified a few days after my return when I received an email from Rolf Segger, the founder of SEGGER Microcontroller (check out their very new website), asking if I would be interested in visiting their headquarters...

## ESC Boston's Videos are Now Up

June 5, 2017

In my last blog, I told you about my experience at ESC Boston and the few videos that I was planning to produce and publish.  Here they are, please have a look and any feedback (positive or negative) is appreciated.

Short Highlight

This is a very short (one minute) montage of some of the footage that I shot at the show & conference.  In future shows, I absolutely need to insert clips here and there of engineers saying a few words about the conference (why they...

## Back from ESC Boston

NOT going to ESC Boston would have allowed me to stay home, in my comfort zone.

NOT going to ESC Boston would have saved me from driving in the absolutely horrible & stressful Boston traffic1.

NOT going to ESC Boston would have saved me from having to go through a full search & questioning session at the Canada Customs on my return2.

2017/06/06 update: Videos are now up!

So two days...

## Launch of Youtube Channel: My First Videos - Embedded World 2017

I went to Embedded World 2017 in Nuremberg with an ambitious plan; I would make video highlights of several exhibits (booths) to be presented to the *Related sites audience.  I would try to make the vendors focus their pitch on the essential in order to produce a one to three minutes video per booth.

So far my experience with making videos was limited to family videos, so I knew I had lots of reading to do and lots of Youtube videos and tutorials to watch.  Trade shows are...


text:
# How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$? [duplicate]

Possible Duplicate:
How can I calculate $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$?

How can we integrate $$\int_0^\frac{\pi}2\frac{\sin^nx}{\sin^nx+\cos^nx}dx , \,\,\,\,\,\,\,\,\, n\in N \quad?$$ Thanks for any hint.

-

## marked as duplicate by Amzoti, Brett Frankel, Micah, TMM, ThomasFeb 1 '13 at 21:50

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

I saw this question before. The first time I saw it it was a bit trickier. It said evaluate $\int_0^{\frac{\pi}{2}}\frac{1}{1+\tan^n(x)}dx$ –  Amr Feb 1 '13 at 20:25
sir Amr you saw it but i dont saw it before i posted my question i search in this site and cant find it because these question has different form (i m not trickier) –  Maisam Hedyelloo Feb 1 '13 at 20:33
@ Maisam Hedyelloo I didnt mean this! I saw it before in a book called "The art and craft of problem solving" (and not in this site). I was just saying a different form of the problem. –  Amr Feb 1 '13 at 20:37
Its OK. The copy I had, I borrowed it from my university's library. –  Amr Feb 1 '13 at 20:46
There is the same question here: math.stackexchange.com/questions/82489/… –  Tomás Feb 1 '13 at 20:51

## 1 Answer

Hint: Make the change of variable $u=\frac{\pi}{2} -x$, noting that $\sin\left(\frac{\pi}{2}-x\right)=\cos x$. Then replace the letter $u$ by $x$, and the answer will hit you.

Remark: The hint is given in the language of formal manipulations, but the idea is purely geometric.

-
That answer is surely mean. –  Pedro Tamaroff Feb 1 '13 at 20:22
Hmmmm.......... –  Anon Feb 1 '13 at 20:25
Andre-nicolas your answer is very nice thanks –  Maisam Hedyelloo Feb 1 '13 at 20:37


text:
# What is the electron configuration of Li+?

Feb 1, 2016

${\text{Li}}^{+} : 1 {s}^{2}$

#### Explanation:

Your starting point here will be the electron configuration of a neutral lithium atom, $\text{Li}$.

A quick look in the periodic table will reveal that lithium is located in period 2, group 1, and that it has an atomic number equal to $3$.

This means that a neutral lithium atom will have a total of $3$ electrons surrounding its nucleus.

Its electron configuration will be

$\text{Li: } 1 {s}^{2} \textcolor{red}{2} {s}^{1}$

Now, the lithium cation, ${\text{Li}}^{+}$, is formed when lithium loses the electron located on its outermost shell $\to$ its valence electron. This electron is located on the second energy level, in the 2s-orbital.

This means that the electron configuration of the ${\text{Li}}^{+}$ cation will be

${\text{Li}}^{+} : 1 {s}^{2}$

To write this using noble gas shorthand notation, use the electron configuration of the noble gas that comes before lithium in the periodic table.

Helium, $\text{He}$, has the electron configuration

$\text{He: } 1 {s}^{2}$

This means that you have

"Li"^(+): ["He"]

Here the notation $\left[\text{He}\right]$ is meant to represent the electron configuration of helium.


text:
Electronic Materials

# Dielectric breakdown

A dielectric in electromagnetic fields can lose its insulator properties if the field exceeds some critical value. The phenomena of the formation of a conductivity channel in a dielectric in the electric field is called dielectric breakdown. The minimal voltage value that leads a dielectric to a breakdown is called breakdown voltage Ubreak. Ohm’s law does not work in the dielectric state before the break, when current is raising gradually. This is called pre-breakdown state. Technically pre-breakdown state is characterised by an infinitely large current.

$\frac{dI}{dU}=\infty$

The breakdown voltage depends on the dielectric width, electric field and electrode configuration. It is characterised by the ability of the dielectric to resist the electric field. Electric durability of a dielectric is a minimal field when the breakdown starts:

${E}_{break}=\frac{{U}_{break}}{h}$

If breakdown occurs in a dielectric gas, and the electric was turned off after that, the gas can restore its insulation capabilities. Solid dielectrics can not restore insulation capabilities after the breakdown, as their insulation gets destroyed. Dielectric breakdown may happen as a result of electric, thermo or electrochemical processes in an insulator in the electric field. Breakdown of air and other gases is a result of strike and photoionisation.

### The mechanism of breakdown in gas

Some amount of electrons and ions in gas obtain additional speed and energy in an electric field. They move along, or opposite, the electric field, depending on the charge sign. Additional energy for a particle is:

$q{U}_{1}=qlE$

Additional energy also goes to the particles, colliding with them. And neutral atoms are ionising. The condition of ionisation is E > Ei, where Ei is an atom ionisation energy. Ionisation energy is characterised by ionisation potential:

${U}_{i}=\frac{{E}_{i}}{q}$

Ionisation potential is in the range 4-25V for different gases (or 4-25eV ionisation  energy).

When temperature and pressure are fixed, strike ionisation appears at some exact level of electric field, because q and l are fixed for gases. The larger the voltage applied to a gas, the faster breakdown occurs. If the impact on voltage is short, the breakdown voltage rises. Gas breakdown depends on the uniformity of the electric field. Uniform electric fields can be between electrodes with rounded edges, or between spheres, when the distance between them is smaller than their diameter.

For distance, one centimetre breakdown can occur at some exact level of temperature and pressure in 10-7 sec. First an electric spark appears between the electrodes that transforms into electric arc. Breakdown in non-uniform fields differs from breakdown in uniform field. Non-uniform field occurs between two electrodes with different shapes, like cutting-edge and plane, between wires, or spheres with a big distance between them. Gas breakdown features in non-uniform electric fields. First partial crown shock appears between electrodes in the electric field points with  maximum level of field, and it then transforms into a spark and then an electric arc when the field increases.

As an exercise, think and explain why breakdown is easier to make on the cutting-edge, than on the plane (in case of non-symmetrical electrodes cutting-edge-plane). What polarity should be on each electrode and why?

Liquid dielectrics are characterised by bigger electrical strength gases. Liquids usually contain impurities like water, gases and small particles of solids. It hinders the breakdown phenomena. High electrical strength of dielectric liquids is caused by a smaller travel path for the electrons in a liquid, than in the gas. Breakdown in clean liquids can happen because of overheating and liquid boiling in the places with the biggest concentration of impurities. Breakdown in a liquid at radio frequencies may occur during overheating caused by dielectric losses, and leads to dielectric liquid destruction. This is the reason why dielectric liquids are used at the frequencies lower than industrial ones.

Solid dielectrics may perform three kinds of breakdowns: electric, thermal and electrochemical. Each breakdown type occurs in the same semiconductor with different temperature and pressure, depending on the electric field, voltage, its intensity and duration, frequency and other parameters. Electrical breakdown of solid dielectrics is characterised with rapid growth. It grows for only 10-7 – 10-8 sec. Electric breakdown is an electric process.

Electric avalanche gradually and rapidly forms from the small amount of electrons in a solid. Growth of electronic avalanche is accompanied by photoionisation that accelerates the creation of conducting channel. Electrons are accelerated by an electric field, colliding with a crystal lattice, heating it till a melting state occurs. Pressure in the conduction channel leads to the cracks in a solid and its destruction. Electric breakdown is possible when conductivity and dielectric losses are absent in a solid.

For uniform solid dielectrics in a uniform electric field, electric breakdown can be a measure of electrical strength of a solid. Thin films may have bigger electric strength than bulk solids. This feature of thin dielectric films is widely used in microelectronics for insulation. Thermal breakdown occurs when thermal energy in a solid dielectric grows to the level bigger than can be dissipated by the dielectric, and the solid overheats. This process becomes avalanche manner.

Phenomena of a thermal breakdown may be resumed by heating the solid to its melting temperature. Breakdown voltage by heating of the dielectric, depends on the temperature, frequency and other parameters. The signs of thermal breakdown in a solid  is exponential with the decline of the breakdown voltage with temperature growth, and the decline of solid electric strength in the electric field.

Ionisation breakdown is a type of thermal breakdown. It’s typical for pored dielectrics, and breakdown occurs because of gas ionisation in pores. Pores surfaces are heated, which causes local temperature difference across the solid. This process may lead to the destruction of the solid. Electrochemical breakdown makes sense at high temperatures and humidity. This type of breakdown occurs in solids at AC and DC voltages at low frequencies, when the processes of declining isolation appears in a solid. Electrochemical breakdown takes some time, and is related to a solid conductivity. There can be a surface breakdown at solids with high electric strength. This is a breakdown of liquid or gas on the bulk solid surface, and the conducting channel occurs on the solid surface. Surface breakdown voltage is determined by the form of the solid and electrodes, their configuration and size.

Dielectrics can be used as insulators, capacitors and variable materials. Insulation dielectrics are used for separating electric conductors from each other, and separating parts of components, with different voltage potentials. Application of dielectrics for capacitors allows you to obtain the required capacitance values and type of capacitance temperature correlation. The capacitor dielectric can store and supply energy in an electric circuit. Or the dielectric capacitor can be used to divide AC and DC circuits. Some dielectrics can be used as capacitors and insulators at the same time. However, requirements for dielectrics for insulation and capacitor applications are different. An insulator should have high resistance, the capacitor should have high permittivity and small dielectric loss tangent. Capacitors with variable dielectrics can be used for increasing signal power, as a functional part of transformers, memory elements and other components.

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Posted by6 years ago
Archived

## Simple probability question?

the reason the title has a question mark, is I'm not sure if its a simple one or a difficult...just that I don't know how to work it out!

here is the question.

Monday - chance of rain 20%

Tuesday - chance of rain 25%

Wednesday - 35%

Thursday -10%

Friday - 15%

Saturday - 35%

Sunday - 50%

Assuming that the given % are entirely accurate what are the chances that it will rain on:

Just one day

Exactly 2 days

Exactly x days

48% Upvoted
Sort by
level 1
10 points · 6 years ago · edited 6 years ago

Other posters have explained this conceptually. I want to share a cool way to finish the calculation: generating functions.

Say you have a probability density: p(n) = probability of n days of rain. You can turn this into a polynomial, p(0)*x0 + p(1)*x1 + ..., called the generating function (g.f.).

If you only look at Monday, the g.f. is 0.80 + 0.20*x.

If you only look at Tuesday, the g.f. is 0.75 + 0.25*x.

What happens if you multiply these together? You get the sum of 4 terms:

0.80 * 0.75 = P[no rain Monday & no rain Tuesday] * x0

0.80 * 0.25 x = P[no rain Monday & rain Tuesday] * x1

0.20 x * 0.75 = P[ rain Monday & no rain Tuesday] * x1

0.20 x * 0.25 x = P[ rain Monday & rain Tuesday] * x2

In total, we get P[0 rainy days M-T]*x0 + P[1 rainy days M-T]*x1 + P[2 rainy days M-T]*x2. This is the g.f. for the probability of n days of rain on Monday and Tuesday.

To get the g.f. for the probability of n days of rain all week, we compute (.20*x+.80)*(.25*x+.75)*(.35*x+.65)*(.10*x+.90)*(.35*x+.65)*(.50*x+.50) = 4.59375*10-5 *x7 + 0.001211875*x6 + 0.0126315625*x5 + 0.06765*x4 + 0.2014890625*x3

• 0.334174375*x2 + 0.2858334375*x + .09696375, and now we can read off the answer from the coefficients.

level 2
2 points · 6 years ago

Upvote for you. Generating functions are amazing. (Look for the free ebook Generating Functionology.)

level 3
3 points · 6 years ago

I believe that's Generatingfunctionology!

level 1
7 points · 6 years ago · edited 6 years ago

The probability that it will never rain in that week is the product of the (1-x_i) where is the probability it will rain on day i. So 0.8 * 0.75 * 0.65 * 0.9 * 0.85 * 0.65 * 0.5= 0.09696375

Now for chance of rain on exactly one day, you have to sum the following probabilities : "it rains on monday, but not the other day" + "it rains on tuesday but not the other day" + ... you get the idea.

Hence if you want to write it nicely it would be

[; \sum_{i=1}^7 \left( \frac{x_i}{(1-x_i)} \times \prod_{j=1}^7 (1-x_j )  \right)  ;]

I don't think you could get a simpler formula because the probabilities are not the same for each day.

For exactly 2 days, it's more complicated because you have to sum over all possible couples of days ("it rains on monday and tuesday" + "monday and wednesday" + ...). So you get a sum of 7 Choose 2 = 21 terms. In each term you get the product of two "x_i" terms and of five (1-x_i) terms.

Now for "exactly n days", you get an even uglier formula that you could write like that :

[;  \sum_{1\leq i_1< \dots < i_x \leq 7} \left( \prod_{j=1}^n \frac{x_j}{(1-x_j)} \prod_{k=1}^{7} (1-x_k)  \right) ;]

This is not complicated at all for a computer. But if you want to do it by hand it would be difficult.

EDIT : formatting

level 1
3 points · 6 years ago · edited 6 years ago

A little tedious but easy one... Here you go:

P1 = Probability that it will rain only on Monday: 20% * (1 - 25%) * (1 - 35%) * (1 - 10%) * (1 - 15%) * (1 - 35%) * (1 - 50%)

P2 = Probability that it will rain only on Tuesday: (1 - 20%) * 25% * (1 - 35%) * (1 - 10%) * (1 - 15%) * (1 - 35%) * (1 - 50%)

P3 = Probability that it will rain only on Wednesday: (1 - 20%) * (1 - 25%) * 35% * (1 - 10%) * (1 - 15%) * (1 - 35%) * (1 - 50%)

P4 = Probability that it will rain only on Thursday: (1 - 20%) * (1 - 25%) * (1 - 35%) * 10% * (1 - 15%) * (1 - 35%) * (1 - 50%)

P5 = Probability that it will rain only on Friday: (1 - 20%) * (1 - 25%) * (1 - 35%) * (1 - 10%) * 15% * (1 - 35%) * (1 - 50%)

P6 = Probability that it will rain only on Saturday: (1 - 20%) * (1 - 25%) * (1 - 35%) * (1 - 10%) * (1 - 15%) * 35% * (1 - 50%)

P7 = Probability that it will rain only on Sunday: (1 - 20%) * (1 - 25%) * (1 - 35%) * (1 - 10%) * (1 - 15%) * (1 - 35%) * 50%

Probability that it will rain just one day: P1 + P2 + P3 + P4 + P5 + P6 +P7

Now define:

Pij = (product over all k != i,j of (1 - probability that it will rain on day k)) * (probability that it will rain on day i) * (probability that it will rain on day j)

Probability that it will rain exactly two days = sum over all i,j of all Pij, ordering does not matter (if you take P12 you don't have to take P21)

Extension to n days is trivial but tedious, you define P_ijk and then you sum...

Pijk = (product over all q != i,j,k of (1 - probability that it will rain on day q)) * (probability that it will rain on day i) * (probability that it will rain on day j) * (probability that it will rain on day k)

Probability that it will rain exactly three days = sum over all i,j,k of all Pijk, ordering does not matter (if you take P123 you don't have to take neither P213 nor P231 nor P321 nor P312)

level 2
2 points · 6 years ago

I'm assuming you meant to change the day of the week for P2 through P7? Otherwise it seems good!

level 3
1 point · 6 years ago · edited 6 years ago

Of course, I forgot to change the day! Thank you for spotting this one, edited!

level 1
3 points · 6 years ago
from fractions import Fraction # because accuracy

days = 7
p_rain = [Fraction(x, 100) for x in [20, 25, 35, 10, 15, 35, 50]]
totals = [Fraction(0)] * (days + 1)

for i in range(2 ** days):
days_w_rain = 0
case_prob = Fraction(1)

for b in range(days):
if i & (2 ** b):
# Rains on day b
days_w_rain += 1
x = p_rain[b]
else:
# Doesn't.
x = Fraction(1) - p_rain[b]

case_prob *= x

totals[days_w_rain] += case_prob

for i in xrange(days + 1):
print "Rains on", i, "days:", repr(totals[i]), float(totals[i])

Rains on 0 days: Fraction(77571, 800000) 0.09696375
Rains on 1 days: Fraction(914667, 3200000) 0.2858334375
Rains on 2 days: Fraction(534679, 1600000) 0.334174375
Rains on 3 days: Fraction(128953, 640000) 0.2014890625
Rains on 4 days: Fraction(1353, 20000) 0.06765
Rains on 5 days: Fraction(40421, 3200000) 0.0126315625
Rains on 6 days: Fraction(1939, 1600000) 0.001211875
Rains on 7 days: Fraction(147, 3200000) 4.59375e-05

level 1
[deleted]
4 points · 6 years ago

Assuming independence you can just construct all possible combinations of x days and then multiply all of the probabilities of the days in the combination with 1-probability for the days not in the combination. Then you sum over possible combinations. It's more a problem to write a program for than it is to do on paper.

ex P(rain on one day) = P(rain only monday) + P(rain only tuesday) + ...

= P(monday chance of rain)(1-P(tuesday chance of rain)(...) + (1-P(monday chance of rain))(P(tuesday chance of rain))(1-P(wednesday chance of rain))(...) + ...

level 1
2 points · 6 years ago

Chance to rain on exactly one day = (chance to rain only on Monday) + (times chance to rain only on Tuesday) + ... +(chance to rain only on Friday).

Chance to rain only on Monday = 20%*(100%-25%)*(100%-35%)*...*(100%-50%).

So the chance to rain only on monday equals chance to rain on monday times chance to NOT rain on every other day. Add all the odds of it raining on every other single day.

This seems really easy and straightforward, but I am having a hard time with more days.

level 1
1 point · 6 years ago

Ignoring weather patterns, chance to rain on any day (say Monday) is independent of chance to rain OR not rain on any other day. Lets start with two days of the week M:.20; T:.25; Chance that it rain on both days are P(A and B) = P(A) · P(B) } .20*.25 = 0.05. Now, chance that it will rain on exactly one day of the two is 1 - 0.80*0.75 = 0.4.

level 1
Original Poster1 point · 6 years ago

thanks for all the help guys, I've read through all your replies, which are very much appreciated...Im a lot closer to fully understanding it now.

level 1
Comment deleted6 years ago
level 2
1 point · 6 years ago

Obviously? There are plenty of parts of the world where the chance of rain from one day to the next can be completely uncorrelated for a period of more than a week. I happen to live in such a place. Even if the probablities weren't independent, a monte carlo simulation would require far more arithmetic than directly computing the answer.

level 3
Comment deleted6 years ago
level 4
1 point · 6 years ago

If you want to be pedantic, then that's true in a sense, but it's quite possible for the probabilities to be independent to within the margin of error of the forecast, which makes them independent for all practiical purposes.

level 5
Comment deleted6 years ago
level 6
1 point · 6 years ago

Says the guy who thinks monte carlo methods are the way to go for such a small problem size...

Frontal systems that take more than a day to pass through an area are far from the only possible cause of rain.

level 2
0 points · 6 years ago

It's not a dumb question at all.

level 3
1 point · 6 years ago

I also assume that the question comes from an assignment, and the instructor should specify that they are independent.

However, you're right that it isn't a dumb question if asked out of the blue.

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≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ 𝖕 𝖖 𝖗

Set Theory Symbols

∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟

Logic Symbols

¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ↔ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣

Calculus and Analysis Symbols

∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ

Greek Letters

𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔

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text:
bipolar junction current basic operation

I have seen this thread and I have a question about the picture describing the movement of electrons and holes.
Basic operation of a bipolar junction transistor

Consider this picture

Here is my step by step way of thinking. B-E is forward biased and B-C is reverse-biased. Because B-E is forward biased, electrons move to the right from the emitter region to the collector region (because p is so narrow). Holes try to "meet" with the electrons at the left pn junction, $i_{B1}$.

Isn't $i_{B2}$ exactly doing what $i_{B1}$ is doing: combining its holes with the electrons at the pn junction?

• I personally think it is confusing to draw holes and electrons on the same image. – jippie Feb 23 '16 at 17:35
• Base region is indeed very thin, also consider the fact the collector voltage. The electrons in the emitter an base region "see" a high collector voltage "in the distance", making them all happy and wanting to travel over there. Some of these electrons can gain enough energy from that distant voltage to be pulled through the base-collector depletion region. – jippie Feb 23 '16 at 17:43

1. Since B-E junction is forward biased, electrons move from emitter to base and holes move from base to emitter. (The majority carriers are injected to the other side). The current due to injection of holes is $i_{B1}$.
2. The electrons injected from emitter move to the collector region but a small recombination happens in the base while this travel. This base-recombination current is $i_{B2}$.
It is true that these excess holes will get recombined. But the holes in $i_{B1}$ recombines in emitter region where as the $i_{B2}$ holes recombination happens in the base. Hence they are shown as two different components of currents.