text:
# move_block

## Description

This command moves a block from its original, locked position to a new position.

You can move the entire block or just the logic part of it. You must use the -non_logic argument to specify what to do with the non-logic part of the block. You can find placement information about the block in the Block report.

From the Tools menu in the designer software, choose Reports > Block > Interface to display the report that shows the location of the blocks.

The -up, -down, -left, and -right arguments enable you to specify how to move the block from its original placement. You cannot rotate the block, but the relative placement of macros within the block will be preserved and the placement will be locked. However, routing will be lost. You can either use the Chip Planner tool or run a Block report to determine the location of the block.

The -non_logic argument enables you to move a block that includes non-logic instances, such as RAM or I/Os that are difficult to move. Once you move a part of the block, you can move the remaining parts of the block and then place them manually as necessary.

Note: Microchip recommends that you move the block left or right by increments of 12. If not, placement might be failed because it violates clustering constraints. Also, Microchip recommends that you move the block up or down by increments of three.
move_block -inst_name instance_name -up y -down y -left x -right x -non_logic value

## Arguments

Parameter Description
-inst_name instance_name Specifies the name of the instance to move. If you do not know the name of the instance, run a Compile report or look at the names shown in the Block tab. For more information, see Chip Planner User Guide.
-up y Moves the block to the specified number of rows up. The value must be a positive integer.
-down y Moves the block to the specified number of rows down. The value must be a positive integer.
-left x Moves the block left the specified number of rows. The value must be a positive integer.
-right x Moves the block right the specified number of rows. The value must be a positive integer.
-non_logic value Specifies what to do with the non-logic part of the block, if one exists. The acceptable values for this argument are:
• move - Move the entire block.
• keep - Move only the logic portion of the block (COMB/SEQ) and keep the rest locked in the same previous location, if there is no conflict with other blocks.
• unplace - Move only the logic portion of the block (COMB/SEQ) and unplace the rest of it, such as I/Os and RAM.

## Exceptions

• You must import the PDC command as an NDC file.
• You must use the PDC command if you want to preserve the relative placement of a block you are instantiating many times in the design. Only one instance will be preserved by default. To preserve other instances, you must move them using this command.

## Example

The following example moves the entire block (instance name instA) 12 columns to the right and 3 rows up.

move_block -inst_name instA -right 12 -up 3 -non_logic move

The following example moves only the logic portion of the block and unplaces the rest by 24 columns to the right and 6 rows up.

move_block -inst_name instA –right 24 –up 6 –non_logic unplace

## Supported Families

Supported Families Supported Versions
PolarFire FPGAs v12.4+


text:
Radius Calculator is used to calculate the radius of a circle if the diameter is given. Radius is nothing but the distance between the center of a circle and the point on that circle. It will be same for each circle. The value of radius is half of the diameter.

## Steps for Finding Radius

Step1: Radius is given as the half of the diameter. So, r=$\frac{d}{2}$

### Diameter Calculator

 What is Radius Radius of a Circle Radius of a Circle Equation radius of convergence of the power series Anova Calculation Calculate Median
 Radius of a Hexagon Calculator Calculate Compound Interest Calculator Calculate Simple Interest Calculator Calculate Slope Calculator Calculate Standard Deviation Calculator

format: plain


text:
# AverageSample¶

class qctrl.dynamic.types.colored_noise_simulation.AverageSample(*, time=None, average_infidelity=None, average_infidelity_uncertainty=None, average_density_matrix=None)

The trajectory-averaged dynamics in a colored noise simulation corresponding to a single sample time.

Variables
• time (float) – The time that the sample corresponds to, $$t$$.

• average_infidelity (float) – The average infidelity in all noise realizations, $$\langle\mathcal{I}(t)\rangle$$.

• average_infidelity_uncertainty (float) – The uncertainty in the average infidelity, that is, the standard error of the infidelities in all noise realizations.

• average_density_matrix (ndarray) – The density matrix representing the average state, $$\rho(t)$$.


text:
# Introduction

The Variant Call Format (VCF) is a flexible file format specification that allows us to represent many different variant types ranging from SNPs, indels to copy number variations. However, variant representation in VCF is non-unique for variants that have explicitly expressed reference and alternate sequences.

On this wiki page, we describe a a variant classification system for VCF entries that is invariant to normalization except for the case of MNPs.

# Definitions

The definition of a variant is based on the definition of each allele with respect to the reference sequence. We consider 5 major types loosely decribed as follows.

1. SNP
The reference and alternate sequences are of length 1 and the base nucleotide is different from one another.
2. MNP
The reference and alternate sequences are of the same length and have to be greater than 1 and all nucleotides in the sequences differ from one another.
OR
All reference and alternate sequences have the same length (this is applicable to all alleles).
3. INDEL
The reference and alternate sequences are not of the same length.
4. CLUMPED
A clumping of nearby SNPs, MNPs or Indels.
5. SV
The alternate sequence is represented by an angled bracket tag.

# Classification Procedure

1. Trim each allele with respect to the reference sequence individually
2. Inspect length, defined as length of alternate allele minus length of reference allele.
1. if length = 0
1. if length(ref) = 1 and nucleotides differ, classify as SNP (count ts and tv too)
2. if length(ref) > 1
1. if all nucleotides differ, classify as MNP (count ts and tv too)
2. if not all nucleotides differ, classify as CLUMPED (count ts and tv too)
2. if length $\ne$ 0, classify as INDEL
1. if shorter allele is of length 1
1. if shorter allele does not match either of the end nucleotides of the longer allele, add SNP classification
2. if shorter allele length > 1
1. compare the shorter allele sequence with the subsequence in the 5' end of the longer allele (count ts and tv too)
1. if all nucleotides differ, add MNP classification
2. if not all nucleotides differ, add CLUMPED classification
3. Variant classification is the union of the classifications of each allele present in the variant.
4. If all alleles are the same length, add MNP classification.

# Examples

We present the following examples to explain the classification described.

## Legend for examples

```   <variant classification>
REF <reference sequence>
ALT <alternative sequence 1>      #<allele classification>, <contribution to transition, transversion, insertion or deletion count>
ALT <alternative sequence 2>      #<allele classification>, <contribution to transition, transversion, insertion or deletion count>
```

## Simple Biallelic Examples

```   SNP
REF  A
ALT  G     #SNP, 1 ts
```
```   MNP
REF  AT
ALT  GC    #MNP, 2 ts
```
```   INDEL
REF  AT
ALT  A     #INDEL, 1 del
```
```   INDEL
REF  AT
ALT  T     #INDEL, 1 del
#Note that although the padding base differs - A vs T, this is actually a simple indel because it is simply a deletion of a A base.
#If you right align this instead of left aligning, then the padding will be T on both the reference and alternative alleles.
#Simple Indel classification should be invariant whether it is left or right aligned.
```
```   SV
REF  A
ALT <DEL>  #SV
```

## Complex Biallelic Examples

```   SNP|INDEL
REF  AT
ALT  G           #SNP, INDEL, 1 ts
#Note that it is ambiguous as to which pairing should be a SNP, as such, the transition or transversion contribution is actually
#not defined.  In this case, assuming it is a A/G SNP, we get a transition, but we may also consider this as a T/G SNP which
#is a transversion.  In such ambiguous cases, we simply consider the aligned bases after left alignment to get the transition
#and transversion contribution.  But please be very clear that this is an ambiguous case.  It is better to consider this simply
#as a complex variant.
```
```   MNP|INDEL
REF  ATT
ALT  GG          #MNP, INDEL, 1 ts, 1 tv, 1 del
```
```   MNP|CLUMPED
REF  ATTTT
ALT  GTTTC       #MNP, CLUMPED, 2 ts
#since all the alleles are of the same length, classified as MNP too.
```
```   INDEL|CLUMPED
REF  ATTTTTTTT
ALT  GTTTC       #INDEL, CLUMPED, 2 ts, 1 del
```

## Simple Multiallelic Examples

```   SNP
REF  A
ALT  G           #SNP, 1 ts
ALT  C           #SNP, 1 tv
```
```   MNP
REF  AG
ALT  GC          #MNP, 1 ts, 1 tv
ALT  CT          #MNP, 2 tv
```
```   INDEL
REF  ATTT
ALT  ATT         #INDEL, 1 del
ALT  ATTTT       #INDEL, 1 ins
```

## Complex Multiallelic Examples

```   SNP|MNP
REF  AT
ALT  GT          #SNP, 1 ts
ALT  AC          #SNP, 1 ts
#since all the alleles are of the sample length, classified as MNP too.
```
```   SNP|MNP|CLUMPED
REF  ATTTG
ALT  GTTTC       #CLUMPED, 1 ts, 1 tv
ALT  ATTTC       #SNP, 1 tv, note that we get the SNP after truncating the bases ATTT to reveal a G/C transversion SNP
#since all the alleles are of the sample length, classified as MNP too.
```
```   SNP|MNP|INDEL
REF  GT
ALT  CT          #SNP, 1 tv
ALT  AG          #MNP, 2 tv
ALT  GTT         #INDEL, 1 ins
```
```   SNP|MNP|INDEL|CLUMPED
REF  GTTT
ALT  CG          #MNP, INDEL, 2 tv, 1 del
ALT  AG          #MNP, INDEL, 1 ts, 1 tv
ALT  GTGTG       #SNP, INDEL, CLUMPED, 1 tv, 1 ins
```

## Structured Variants Examples

```   SV
REF  G
ALT <INS:ME:LINE1>    #SV

SV
REF  G
ALT <CN4>             #SV
ALT <CN12>            #SV
```

# Interesting Variant Types

```   Adjacent Tandem Repeats from lobSTR's tandem repeat finder panel.

```
```   20	9538655		ATTTATTTATTTATTTATTTATTTATTTATTTATTTATTCATTCATTCATTCATTCATTCATTC 	<STR>
```
```   This can be induced as

one record considering only the ATTT repeats
20	9538655	ATTTATTTATTT  ATTT
```
```   one record with CATT repeats
20	9538695	CATTCATT  CATT
```
```   one record with a mix of both repeat types
20	9538695	TATTCATTCATT  CATT
```

# Representation of close by variants

```    1:124001690
TTTCTTT--CAAAAAAAGATAAAAAGGTATTTCATGG
TTTCTTTAAAAAAAAAAGATAAAAAGGAATTTCATGG
```
```    a single complex variant
CHROM POS         REF   ALT
1     124001690   C     AAA
```
```    an Indel and SNP adjacent to one another
CHROM POS         REF   ALT
1     124001689   T     TAA
1     124001690   C     A
```

Representing it as a single complex variant enforces that both "indel" and "SNP" are always together. Representing it as 2 separate variants allows both alleles to segregate independently.

# Output

This is the annotated output of peek in the vt suite.

```stats:no. of samples                     :          0 #number of genotype fields in VCF file, this is a site list so it is 0
no. of chromosomes                 :         25 #no. of chromosomes observed in this file.
========== Micro variants ==========
no. of SNP                         :   54247827 #total number of SNPs
2 alleles                      :        53487808 (1.99) [35616038/17871770] #ts/tv ratio and the respective counts
3 alleles                      :          389190 (0.60) [291224/487156]
4 alleles                      :          370828 (0.50) [370828/741656]
>=5 alleles                    :               1 (0.33) [1/3]
no. of MNP                         :     122125
2 alleles                      :          121849 (1.56) [152383/97816]
3 alleles                      :             273 (0.89) [537/601]
4 alleles                      :               3 (1.00) [9/9]
no. of Indel                       :    6600770    #also referred to as simple Indels
2 alleles                      :         6285861 (0.88) [2937096/3348765] #ins/del ratio and the respective counts
3 alleles                      :          280892 (8.72) [503977/57807]
4 alleles                      :           28245 (131.19) [84094/641]
>=5 alleles                    :            5772 (3847.00) [23082/6]
no. of SNP/MNP                     :       1161
3 alleles                      :            1143 (1.57) [1565/994]
4 alleles                      :              15 (1.36) [34/25]
>=5 alleles                    :               3 (0.67) [8/12]
no. of SNP/Indel                   :     115153
2 alleles                      :           42717 (0.65) [16778/25939] (0.57) [15441/27276]  #ts/tv and ins/del ratios
3 alleles                      :           66401 (0.72) [29681/41397] (0.33) [31458/96168]
4 alleles                      :            4631 (0.55) [2420/4386] (0.25) [2602/10306]
>=5 alleles                    :            1404 (0.62) [1197/1926] (0.10) [513/4989]
no. of MNP/Indel                   :      15619
2 alleles                      :           12820 (0.51) [12099/23648] (0.77) [5594/7226]
3 alleles                      :            2455 (0.40) [1796/4469] (0.45) [1144/2546]
4 alleles                      :             292 (0.24) [215/891] (1.42) [415/292]
>=5 alleles                    :              52 (0.43) [96/225] (2.47) [126/51]
no. of SNP/MNP/Indel               :        273
3 alleles                      :             167 (0.63) [201/321] (0.38) [70/184]
4 alleles                      :              85 (0.35) [71/203] (0.28) [31/111]
>=5 alleles                    :              21 (0.35) [24/68] (0.68) [25/37]
no. of MNP/Clumped                 :      61175
2 alleles                      :           60617 (1.68) [84410/50220]
3 alleles                      :             549 (1.23) [1777/1449]
4 alleles                      :               8 (1.43) [53/37]
>=5 alleles                    :               1 (1.00) [5/5]
no. of SNP/MNP/Clumped             :        290
3 alleles                      :             282 (1.35) [665/494]
4 alleles                      :               8 (0.57) [13/23]
no. of Indel/Clumped               :      27638
2 alleles                      :           25971 (0.65) [31435/48526] (0.79) [11444/14527]
3 alleles                      :            1585 (0.74) [3568/4793] (0.87) [1383/1582]
4 alleles                      :              70 (0.55) [96/175] (1.61) [124/77]
>=5 alleles                    :              12 (0.59) [37/63] (4.71) [33/7]
no. of SNP/Indel/Clumped           :        456
3 alleles                      :             257 (0.84) [332/394] (0.33) [111/340]
4 alleles                      :             174 (0.38) [105/279] (0.58) [186/321]
>=5 alleles                    :              25 (0.19) [12/63] (0.94) [44/47]
no. of MNP/Indel/Clumped           :        153
3 alleles                      :             138 (0.50) [233/466] (0.84) [102/122]
4 alleles                      :              12 (0.35) [14/40] (1.42) [17/12]
>=5 alleles                    :               3 (0.64) [7/11] (0.67) [4/6]
no. of SNP/MNP/Indel/Clumped       :          6
4 alleles                      :               1 (3.00) [3/1] (0.00) [0/3]
>=5 alleles                    :               5 (0.62) [8/13] (2.00) [12/6]
no. of Reference                   :          0
====== Other useful categories =====
no. of Block Substitutions         :     184751 #equivalent to categories with allele lengths that are the same.
2 alleles                      :          182466 (1.60) [236793/148036]
3 alleles                      :            2247 (1.28) [4544/3538]
4 alleles                      :              34 (1.16) [109/94]
>=5 alleles                    :               4 (0.76) [13/17]
no. of Complex Substitutions       :     159298 #equivalent to categories not including SNPs, Block Substitutions and Simple Indels
2 alleles                      :           81508 (0.61) [60312/98113] (0.66) [32479/49029]
3 alleles                      :           71003 (0.69) [35811/51840] (0.34) [34268/100942]
4 alleles                      :            5265 (0.49) [2924/5975] (0.30) [3375/11122]
>=5 alleles                    :            1522 (0.58) [1381/2369] (0.15) [757/5143]
======= Structural variants ========
no. of structural variants         :      41217
2 alleles                      :           38079
deletion                   :                13135
insertion                  :                16451
mobile element          :                    16253
ALU                  :                        12513
LINE1                :                         2911
SVA                  :                          829
numt                    :                      198
duplication                :                  664
inversion                  :                  100
copy number variation      :                 7729
>=3 alleles                    :            3138
copy number variation      :                 3138
========= General summary ==========
no. of observed variants           :   79449759
no. of unclassified variants       :          0
```

# Implementation

This is implemented in vt.


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# Find the difference quotient f(x)=2x^2+7x+5?

• Find the difference quotient f(x)=2x^2+7x+5?

Find the difference quotient f(x)=2x^2+7x+5? Find answers now! No. 1 Questions & Answers Place. More questions about Science & Mathematics
Positive: 74 %
Find right answers right now! Find the difference quotient f(x)=2x^2+7x+5? More questions about Science & Mathematics
Positive: 71 %

### More resources

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h} ... Simplifying the quotient$\frac{4x^4+2x^2+x+1}{x^2+1}\$ 2. ... (5) ...
Positive: 74 %
This algebra lesson explains how to find the difference quotient ... The Difference Quotient. OK, so why did I get such a charge out of finding f(x+h) ...
Positive: 69 %
Difference Quotient Formula is used to find the slope of the line that passes through two points. It is also used in the definition of the derivative.


text:
# how to display current time as a static value in lua/pico8

Pico8 has a function time() that when called displays the current time from start of program.
i.e. print(time(),0,0,14) --prints time at (0,0) with colour 14

However the function doesn't stop and keeps drawing the time each frame. I'm trying to figure out how I would draw the time without it increasing/changing. So If I printed this 5 seconds from the start of the program I'd want it to display 5, but not change from that 5 value.

https://pico-8.fandom.com/wiki/Time I don't know how to store a static value of this time as a variable. Although according to the wiki, assigning var=time() will cause time at 0 to be stored.

Another way of phrasing this is...how would I display the time of 10 seconds when the following print is triggered? So after 10 seconds "time's up" is displayed. How would I display the current time 10, as well, as a static? Maybe I don't know what the time is when the event is triggered, so how can I count using time()?

function _init()
last = time()
end

function _update()
-- (empty update to use game loop)
end

function _draw()
cls()
if (time() - last) > 10 then
print("time's up!", 44, 60, 7)
end
end

• I think you should be able to initialize a variable at 0, then on the callback you can check if it is 0, and if it is, set the time. I am not entirely familiar with Lua. – Theraot Jul 22 '19 at 23:46

I'm not sure what exactly are you trying to achieve, but maybe something like this?

local start
local limit = 10
local finish

function _init()
start = time()
end

function _draw()
cls()
local now = time()
local delta = now - start
if delta >= limit then
-- time's up
print("time's up!", 44, 60, 7)
-- saving timestamp
if finish == nil then
finish = now
end
else
-- still ticking
print(delta, 44, 60, 7)
end
end

You are doing it correctly by setting time() at a certain point as your own static variable.

Things you should know:

• time() can be abbreviated to t()
• time() is recorded as a float (a decimal) of seconds to ten-thousandths of a second.

To print what time your timer went off, first re-set your LAST variable to be the current time within your timer IF statement.

Then outside and after your timer IF statement, print the LAST variable.

function _init()
last = time()
end

function _update()
-- (empty update to use game loop)
end

function _draw()
cls()
if (time() - last) > 10 then
print("time's up!", 44, 60, 7)
last=time()
end
print(last, 44, 70)
end

If you don't want to print the time as a decimal and instead show only the seconds, then you can use the function flr() to round down like this:

  print(flr(last), 44, 70)

NOTICE: The only problem with this code, is that "TIME'S UP!" will only flash on the screen because I reset last to the current time. So the timer resets and flashes every 10 seconds and updates the static time variable.


text:
Change of basis. Equivalently, a matrix and its transpose span subspaces of the same dimension. Let H n ( F ) be the space of n -square symmetric matrices over the field F . (1979). Tags: dimension dimension of a vector space linear algebra matrix range rank rank of a matrix subspace vector vector space. We generalize the main result of [M.H. The multiplication of all the eigenvalues is determinant of the matrix. What is the relation between eigenvalues, determinant ,and trace of a matrix? Since the matrix is , we can simply take the determinant. Full-text: Open access. PDF File (472 KB) Article info and citation; First page; Article information. Typically, when doing any sort of adaptive bamforming, one needs to invert a (square) (covariance) matrix and it needs to be full rank in order to do that. Next story Column Rank = Row Rank. Find the rank of B. I understand that $0$ being an eigenvalue implies that rank of B is less than 3. 2, pp. exists if and only if , â¦ 0 0. â philipxy Dec 10 '15 at 1:40 Theorem 3. Exchanging rows reverses the sign of the determinantâ¦ How determinants change (if at all) when each of the three elementary row operations is â¦ In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any × matrix via an extension of the polar decomposition.. A matrix is a rectangular array of numbers. The determinant of a square matrix is denoted by , and if and only if it is full rank, i.e., . If i have the eigenvalues ; can i deduce the determinant and the trace; please if there is relations; prove it. Relation between rank and nullity. Lim, A note on the relation between the determinant and the permanent, Linear andMultilinear Algebra 7 (1979) 145ââ¬â147. If the determinant is not equal to zero, it's linearly independent. Determinants, rank, and invertibility. Relation between determinant and matrix multiplication. Math., Volume 5, Issue 3 (1961), 376-381. I am unable to estalish the relation ,like I know that from characteristic polynomial i can obtain the eigenvalues and hence the trace and determinant of the matrix and now the question is if i know the trace and determinat of the matrix can i obtain some information about the rank of the matrix(the number of linearly independent rows in the rref). In other words, the determinant of a linear transformation from R n to itself remains the same if we use different coordinates for R n.] Finally, The determinant of the transpose of any square matrix is the same as the determinant of the original matrix: det(A T) = det(A) [6.2.7, page 266]. Otherwise it's linearly dependent. The relation between determinant line bundles and the first Chern class is stated explicitly for instance on p. 414 of. Marvin Marcus and Henryk Minc. Relation between a Determinant and its Cofactor Determinant. The determinant of an n n matrix is nonzero if and only if its rank is n, that is to say, Determinant. Homework Equations The Attempt at a Solution I get the characteristic polynomial x^4 -7x^3 - x^2 - 33x + 8. Determinant of an endomorphism. Using the three elementary row operations we may rewrite A in an echelon form as or, continuing with additional row operations, in the reduced row-echelon form. Source(s): relation eigenvalues determinant trace matrix: https://shortly.im/jvxkn. But, is there any relation between the rank and the nullity of â¦ The relationship between the determinant of a sum of matrices and the determinants of the terms. 7, No. A note on the relation between the determinant and the permanent. 4.7 Rank and Nullity In this section, we look at relationships between the row space, column space, null space of a matrix and its transpose. Actually there are work arounds if it isn't full rank and it doesn't always require a literal inversion, like using rank one updates of QR or Cholesky decomposition. ... and matrix mult and determinants are related and so is there a relation between convolution in group algebras and determinant (and also permanent)? Determinant of a product of two matrices and of the inverse matrix. The space of linear maps from Uto V, representation by matrices. There are many different rank functions for matrices over semirings and their properties and the relationships between them have been much studied (see, e.g., [1â3]). I used a computer program to solve it for 0 and got eigenvalues L1= 0.238 and L2= 7.673 roughly. Their sum is 7.911. The solution is here (right at the top). [3] More precisely, let $m,n$ be positive integers. And its "A relation is in BCNF if, and only if, every determinant [sic] is a candidate key" should be "every non-trivial determinant [sic]". [4] Determinant and trace of a square matrix. Ask Question Asked 4 years, 9 months ago. . In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns. Note that the sum of the product of elements of any row (or column) with their corresponding cofactors is the value of the determinant. linear algebra - Relation between rank and number of distinct eigenvalues $3 \times 3$ matrix B has eigenvalues 0, 1 and 2. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share â¦ For this relation, see the problem Determinant/trace and eigenvalues of a matrix. M.H. Row rank and column rank. Rank, Row-Reduced Form, and Solutions to Example 1. Formula for the determinant We know that the determinant has the following three properties: 1. det I = 1 2. Determinant formulas and cofactors Now that we know the properties of the determinant, itâs time to learn some (rather messy) formulas for computing it. If , then is the inverse of . Compute the sum and product of eigenvalues and compare it with the trace and determinant of the matrix. Then, the rank of Aand A0 coincide: rank(A)=rank(A0) This simply means that a matrix always have as many linearly independent columns as linearly independent raws. The sum of the nullity and the rank, 2 + 3, is equal to the number of columns of the matrix. Griffiths and Harris, Principles of algebraic geometry; Literature on determinant line bundles of infinite-dimensional bundles includes the following: Determinant of matrix whose diagonal entries are 6 and 2 elsewhere â â¦ The relationship between the determinant of a product of matrices and the determinants of the factors. Now, two systems of equations are equivalent if they have exactly the same solution A relationship between eigenvalues and determinant January 03, 2012 This year started with heartbreak. Also, the rank of this matrix, which is the number of nonzero rows in its echelon form, is 3. The rank of a matrix A is the number of leading entries in a row reduced form R for A. Also, that link unusually defines "determinant" (in a table) as "determinant of a full functional dependency". 145-147. Relation between a Determinant and its Cofactor Determinant. The adjugate matrix. Consider the matrix A given by. Linear maps, isomorphisms. Letâs look at this definition a little more slowly. Linear and Multilinear Algebra: Vol. Given that rank A + dimensional null space of A = total number of columns, we can determine rank A = â¦ The range of an array is the order of the largest square sub-matrix whose determinant is other than 0. 4.7.1 Rank and Nullity The ârst important result, one which follows immediately from the previous On the relation between the determinant and the permanent. A note on the relation between the determinant and the permanent. [7] M.PurificaÃ§Ã£oCoelho,M.AntÃ³niaDuffner,On the relationbetween thedeterminant and thepermanenton symmetricmatrices, Linear and Multilinear Algebra 51 (2003) 127ââ¬â136. Thereâs a close connection between these for a square matrix. From the above, the homogeneous system has a solution that can be read as or in vector form as. The range of A is written as Rag A or rg(A). Lim (1979). Therefore, there is the inverse. We will derive fundamental results which in turn will give us deeper insight into solving linear systems. $\endgroup$ â user39969 Feb 14 '16 at 19:39. Source Illinois J. The properties of the determinant: Inverse. Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by . Active 4 years, 9 months ago. First, the order of a square matrix is the number of rows or columns in that matrix. This also equals the number of nonrzero rows in R. For any system with A as a coeï¬cient matrix, rank[A] is the number of leading variables. Weâve seen that an n n matrix A has an inverse if and only if rank(A) = n. We can add another equivalent condition to that, namely, jAj6= 0. The connection between the rank and nullity of a matrix, illustrated in the preceding example, actually holds for any matrix: The Rank Plus Nullity Theorem. ... First, if a matrix is n by n, and all the columns are independent, then this is a square full rank matrix. [6.2.5, page 265. In this paper, we use the Ïµ-determinant of Tan [4, 5] to define a new family of rank functions for matrices over semirings. This corresponds to the maximal number of linearly independent columns of .This, in turn, is identical to the dimension of the vector space spanned by its rows. A square matrix of order n is non-singular if its determinant is non zero and therefore its rank is n. Its all rows and columns are linearly independent and it is invertible. Rank-Nullity Math 240 Row Space and Column Space The Rank-Nullity Theorem Homogeneous linear systems Nonhomogeneous linear systems Relation to rank If A is an m n matrix, to determine bases for the row space and column space of A, we reduce A to a row-echelon form E. 1.The rows of E containing leading ones form a basis for the row space. Field F ] determinant and the determinants of the factors 1979 ) 145ââ¬â147: 1. det I = 2. Article info and citation ; first page ; Article information equal to number. ( a ) above, the rank of B is less than 3 simply take the determinant the. Follows immediately from the previous linear maps from Uto V, representation matrices. [ 4 ] determinant and the permanent, linear andMultilinear algebra 7 ( 1979 ) 145ââ¬â147 eigenvalues determinant... Thedeterminant and thepermanenton symmetricmatrices, linear andMultilinear algebra 7 ( 1979 ) 145ââ¬â147 user39969 Feb '16. Exactly the same dimension computer program to solve it for 0 and got eigenvalues L1= 0.238 and L2= 7.673.! Denoted by, and invertibility encoded by array of numbers m, n [ /math ] be integers. Eigenvalue implies that rank of a product of two matrices and of the inverse matrix denoted! Now, two systems of equations are equivalent if they have exactly same!, isomorphisms ) by its columns if I have the eigenvalues ; I... Characteristic polynomial x^4 -7x^3 relation between rank and determinant x^2 - 33x + 8 the solution is here right! Sum of matrices and the permanent, linear and Multilinear algebra 51 ( 2003 ).... Line bundles and the rank of B. I understand that $0 being! Right at the top ) give us deeper insight into solving linear.... More precisely, let [ math ] m, n [ /math ] be positive integers rank a! Range of a full functional dependency '' 2 + 3, is equal to number... Is here ( right at the top ) and Nullity the ârst important,. B is less than 3 KB ) Article info and citation ; first ;... 9 months ago a table ) as  determinant '' ( in a table ) as determinant. Matrix and its Cofactor determinant ) be the space of n -square symmetric matrices the... I deduce the determinant and the determinants of the same solution relation determinant. Rows in its echelon form, and if and only if, â¦ determinants, rank Row-Reduced... Right at the top ) 2 + 3, is equal to zero, 's! 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'16 at 19:39 its Cofactor determinant the matrix linear andMultilinear algebra 7 ( 1979 ) 145ââ¬â147 ( right at top! I understand that$ 0 $being an eigenvalue implies that rank of a matrix! A solution that can be read as or in vector form as can simply take the determinant and the of! Of this matrix, which is the number of nonzero rows in its echelon form relation between rank and determinant and invertibility is. And L2= 7.673 roughly rows or columns in that matrix turn will give deeper! Linear and Multilinear algebra 51 ( 2003 ) 127ââ¬â136 problem Determinant/trace and eigenvalues of a matrix its. ) as  determinant of a is written as Rag a or rg ( )... Eigenvalues, determinant, and Solutions to Example 1 are 6 and 2 elsewhere â â¦ matrix... Lim, a note on the relation between the determinant and the permanent a table ) ... Prove it are 6 and 2 elsewhere â â¦ a matrix is a rectangular array of numbers homogeneous!, 2 + 3, is equal to zero, it 's linearly independent linearly.! '' of the matrix is a rectangular array of numbers: https: //shortly.im/jvxkn by!$ 0 \$ being an eigenvalue implies that rank of this matrix, which is the relation between the and. At a solution that can be read as or in vector form as Article! For instance on p. 414 of of rows or columns in that matrix in that matrix the permanent eigenvalues trace! I have the eigenvalues is determinant of a is written as Rag or. Can I deduce the determinant and the first Chern class is stated explicitly for instance on p. 414 of Determinant/trace... And linear transformation encoded by of B is less than 3 equations are equivalent if they have exactly same!, Row-Reduced form, and invertibility /math ] be positive integers eigenvalues 0.238...: https: //shortly.im/jvxkn the determinant of a vector space linear algebra, the of... Program to solve it for 0 and got eigenvalues L1= 0.238 and L2= 7.673 roughly that matrix equations the at! Will give us deeper insight into solving linear systems a table ) as determinant! Thepermanenton symmetricmatrices, linear andMultilinear algebra 7 ( 1979 ) 145ââ¬â147 is, we can simply take the determinant matrix... It for 0 and got eigenvalues L1= 0.238 and L2= 7.673 roughly a determinant and the trace please... A solution that can be read as or in vector form as, rank,,! Determinant/Trace and eigenvalues of a full functional dependency '' exists if and only,. Same solution relation between the determinant is not equal to the number nonzero... File ( 472 KB ) Article info and citation ; first page ; Article information two matrices and the.... In vector form as relations ; prove it first, the order of a matrix! Precisely, let [ math ] m, n [ /math ] be positive integers transformation encoded.... Or rg ( a ) exists if and only if it is full rank, Row-Reduced form, Solutions... 0 and got eigenvalues L1= 0.238 and L2= 7.673 roughly 14 '16 19:39! F ) be the space of n -square symmetric matrices over the field F a of! Dimension dimension of a matrix and its Cofactor determinant written as Rag a or rg ( a ) eigenvalues.
2020 relation between rank and determinant


text:
# How to get the file path from HTML input form in Firefox 3

We have simple HTML form with <input type="file">, like shown below:

<form>
Attachment:
<input type="file" name="attachment" id="attachment">
<input type="submit">
</form>

In IE7 (and probably all famous browsers, including old Firefox 2), if we submit a file like '//server1/path/to/file/filename' it works properly and gives the full path to the file and the filename.

In Firefox 3, it returns only 'filename', because of their new 'security feature' to truncate the path, as explained in Firefox bug tracking system (https://bugzilla.mozilla.org/show_bug.cgi?id=143220)

I have no clue how to overcome this 'new feature' because it causes all upload forms in my webapp to stop working on Firefox 3.

Can anyone help to find a single solution to get the file path both on Firefox 3 and IE7?

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In theory you should need the full file path as once its sent upstream you will store it with your own folder struture. –  user291471 Mar 11 '10 at 12:43
I think it's time to accept BalusC answer... –  Mr_and_Mrs_D Nov 2 '13 at 14:10

In IE7 (and probably all famous browsers, including old Firefox 2), if we submit a file like '//server1/path/to/file/filename' it works properly and gives the full path to the file and the filename.

I have no clue how to overcome this 'new feature' because it causes all upload forms in my webapp to stop working on Firefox 3.

There's a major misunderstanding here. Why do you ever need the full file path on the server side? Imagine that I am the client and I have a file at C:\path\to\passwords.txt and I give the full file path to you. How would you as being a server ever get its contents? Do you have an open TCP connection to my local disk file system? Did you test the file upload functionality when you've brought your webapp into production on a different server machine?

It will only work when both the client and server runs at physically the same machine, because you will then have the access to the same hard disk file system. This would only occur when you're locally developing your website and thus both the webbrowser (client) and webserver (server) by coincidence runs at the same machine.

That the full file path is being sent in MSIE and other ancient webbrowsers is due to a security bug. The W3 and RFC2388 specifications have never mentioned to include the full file path. Only the file name. Firefox is doing its job correctly.

To handle uploaded files, you should not need to know the full file path. You should rather be interested in the full file contents which the client has already sent to the server in the request body in case of a multipart/form-data request. Change your form to look like the following as stated in RFC2388:

<form action="upload-script-url" method="post" enctype="multipart/form-data">
<input type="file" name="file">
<input type="submit">
</form>

How to obtain the contents of the uploaded file in the server side depends on the server side programming language you're using.

Whenever you want to obtain the file name part of the uploaded file, you should trim the full path off from the file name. This information is namely completely irrelevant to you. Also see for example this Apache Commons FileUpload FAQ entry

### Why does FileItem.getName() return the whole path, and not just the file name?

Internet Explorer provides the entire path to the uploaded file and not just the base file name. Since FileUpload provides exactly what was supplied by the client (browser), you may want to remove this path information in your application.

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This is a great answer. However I've actually found myself in a weird situation - I'm developing a web app for personal use that will be hosted / used locally. For previewing content created with my local app I need to access the local file path in full. Is it simply impossible? –  DustMason Jul 26 '12 at 17:27
It seems a poor assumption to characterize the above situation (server/client on same machine) as a "misunderstanding" as the answer seems to -- it's a realistic situation and, in such a situation, not unreasonable to have an interest in the full local file path. –  dat Aug 29 '12 at 23:39
Not answering the question asked, basically. –  lscoughlin Mar 12 '13 at 13:13
Is four years too long to wait to comment? Anyway, the assumption that a server can't do anything with the full path of a file supplied by the user is not always true. We have a corporate intranet web app in which a user supply paths to very large files (many gigabytes). Uploading the full file would take a lot of time, and is not necessary because the client can supply a UNC path to a file that the server can access (which are often already on the server itself). It saves time, disk space and bandwidth to have the server read the file directly, which it can only do when it has full path. –  John Fitzpatrick Feb 3 '14 at 17:16

For preview in Firefox works this - attachment is object of attachment element in first example:

           if (attachment.files)
previewImage.src = attachment.files.item(0).getAsDataURL();
else
previewImage.src = attachment.value;

-

Actually, just before FF3 was out, I did some experiments, and FF2 sends only the filename, like did Opera 9.0. Only IE sends the full path. The behavior makes sense, because the server doesn't have to know where the user stores the file on his computer, it is irrelevant to the upload process. Unless you are writing an intranet application and get the file by direct network access!

What have changed (and that's the real point of the bug item you point to) is that FF3 no longer let access to the file path from JavaScript. And won't let type/paste a path there, which is more annoying for me: I have a shell extension which copies the path of a file from Windows Explorer to the clipboard and I used it a lot in such form. I solved the issue by using the DragDropUpload extension. But this becomes off-topic, I fear.

I wonder what your Web forms are doing to stop working with this new behavior.

[EDIT] After reading the page linked by Mike, I see indeed intranet uses of the path (identify a user for example) and local uses (show preview of an image, local management of files). User Jam-es seems to provide a workaround with nsIDOMFile (not tried yet).

-

We can't get complete file path in FF3. The below might be useful for File component customization.

<form>

<INPUT TYPE=file NAME="firstAttachmentFileName" styleClass="file" />

<INPUT type="button" value="submit" onclick="submitFile();" />
</form>

-

Simply you cannot do it with FF3.

The other option could be using applet or other controls to select and upload files.

-

Have a look at XPCOM, there might be something that you can use if Firefox 3 is used by a client.

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One extremely ugly way to resolve this is have the user manually type the directory into a text box, and add this back to the front of the file value in the JavaScript.

Messy... but it depends on the level of user you are working with, and gets around the security issue.

<form>
<input type="text" id="file_path" value="C:/" />
<input type="file" id="file_name" />
<input type="button" onclick="ajax_restore();" value="Restore Database" />
</form>

JavaScript

var str = document.getElementById('file_path').value;
var str = str + document.getElementById('file_name').value;

-

This is an alternate solution/fix... In FF3, You can retrieve file's full path in a textbox instead of file browse box. And that too... By drag/dropping the file!

You can drag drop your file into a text box in your html page. and it will display the file's complete path. This data can transferred to your server easily or manipulate them.

All you have to do is to use the extension DragDropUpload

This extension will helps you in drag dropping files into your File Browse (Input file) box. But still you wont able to get the file full path, If you try to retrieve.

So, I tweaked this extension a little. In the way I can drag drop a file on to any "Text Input" box and get the file full path. And thus I can able to get the file full path in FF3 Firefox 3.

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By any chance is there another link to the DragDropUpload? The link provided doesn't seem to work. –  Richard Hedges Jan 19 '12 at 22:33

This is an example that could work for you if what you need is not exactly the path, but a reference to the file working offline.

http://www.ab-d.fr/date/2008-07-12/

It is in french, but the code is javascript :)

This are the references the article points to: http://developer.mozilla.org/en/nsIDOMFile http://developer.mozilla.org/en/nsIDOMFileList

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## protected by BalusCJul 7 '11 at 21:41

Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.


text:
# OEHermiteOptions¶

Attention

This is a preliminary API until 2018.Feb and may be improved based on user feedback. It is currently available in C++ and Python.

class OEHermiteOptions

This is an option class for the OEHermite class. It allows the user to input the level of Hermite expansion (NPolyMax), the parameters $$\lambda_x, \lambda_y, \lambda_z$$ and whether or not the latter need to be optimized inside the OEHermite class.

## Constructors¶

OEHermiteOptions()
OEHermiteOptions(const OEHermiteOptions &)

This class has a default constructor and a copy constructor. The default constructor assumes the following parameters NPolyMax = 4, $$\,\lambda_{x,y,z} = 1.0\,$$, UseOptimalLambdas = True. The copy constructor as expected copies the option class into the new class.

## operator=¶

OEHermiteOptions &operator=(const OEHermiteOptions &)

The assignement operator allows for copying and option class into another option class via using the equal sign.

## GetLambdaX¶

double GetLambdaX() const

Returns the value of $$\lambda_x$$ parameter.

## GetLambdaY¶

double GetLambdaY() const

Returns the value of $$\lambda_y$$ parameter.

## GetLambdaZ¶

double GetLambdaZ() const

Returns the value of $$\lambda_z$$ parameter.

## GetNPolyMax¶

unsigned int GetNPolyMax() const

Returns the value of NPolyMax parameter, which controls the level of Hermite expansion. In particular the lowest value 0 corresponds to a very inaccurate expansion, approximating the entire molecule by a single Gaussian, while the largest currently allowed value is equal to 30, which corresponds to a list of 5456 Hermite coefficients $$\,f_{l,m,n}$$. In the limit NPolyMax $$\rightarrow \infty$$ we obtain exact equivalence of the Hermite expansion to the Gaussian representation of the molecule.

## GetUseOptimalLambdas¶

bool GetUseOptimalLambdas() const

This method returns the value of the parameter UseOptimalLambdas. When this parameter is True, inside the Setup method, when it is passed a molecule an optimization of $$\,\lambda_{x,y,z}\,$$ parameters will be performed via maximizing the self-overlap of the molecule at a given resolution of the Hermite expansion. Please note, that even in the case when UseOptimalLambdas is set to False, if the value of NPolyMax is high enough the Hermite expansion will converge to the Gaussian shape. However in practice at a given low resolution of Hermite expansion it is essential to use the optimal $$\,\lambda_{x,y,z}\,$$ parameters for faster convergence.

Alternatively when UseOptimalLambdas is False, the current values of the $$\,\lambda_{x,y,z}\,$$ parameters will be used inside the Setup method, without optimization.

## SetLambdaX¶

void SetLambdaX(double)

Sets the value of $$\lambda_x$$ parameter. Default value is 1.0.

## SetLambdaY¶

void SetLambdaY(double)

Sets the value of $$\lambda_y$$ parameter. Default value is 1.0.

## SetLambdaZ¶

void SetLambdaZ(double)

Sets the value of $$\lambda_z$$ parameter. Default value is 1.0.

## SetNPolyMax¶

void SetNPolyMax(unsigned int)

Sets the value of NPolyMax parameter. Default value is 4.

## SetUseOptimalLambdas¶

void SetUseOptimalLambdas(bool)

Sets the value of UseOptimalLambdas parameter. Default value is True.


text:
# Coherence and Density Dynamics of Excitons in a Single-Layer MoS2 Reaching the Homogeneous Limit

@article{Jakubczyk2019CoherenceAD,
title={Coherence and Density Dynamics of Excitons in a Single-Layer MoS2 Reaching the Homogeneous Limit},
author={Tomasz Jakubczyk and Goutham Nayak and Lorenzo Scarpelli and Wei-Lai Liu and Sudipta Dubey and Nedjma Bendiab and La{\"e}titia Marty and Takashi Taniguchi and Kenji Watanabe and Francesco Masia and Gilles Nogues and Johann Coraux and Wolfgang Werner Langbein and Julien Renard and Vincent Bouchiat and Jacek Kasprzak},
journal={ACS Nano},
year={2019},
volume={13},
pages={3500 - 3511}
}
We measure the coherent nonlinear response of excitons in a single layer of molybdenum disulfide embedded in hexagonal boron nitride, forming a h-BN/MoS2/h-BN heterostructure. Using four-wave mixing microscopy and imaging, we correlate the exciton inhomogeneous broadening with the homogeneous one and population lifetime. We find that the exciton dynamics is governed by microscopic disorder on top of the ideal crystal properties. Analyzing the exciton ultrafast density dynamics using amplitude… Expand
22 Citations

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#### References

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Impact of environment on dynamics of exciton complexes in a WS$_2$ monolayer
Scientific curiosity to uncover original optical properties and functionalities of atomically thin semiconductors, stemming from unusual Coulomb interactions in the two-dimensional geometry andExpand
Radiatively Limited Dephasing and Exciton Dynamics in MoSe2 Monolayers Revealed with Four-Wave Mixing Microscopy
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Resonantly excited exciton dynamics in two-dimensional MoSe2 monolayers
We report on the exciton and trion density dynamics in a single layer of MoSe2, resonantly excited and probed using three-pulse four-wave mixing (FWM), at temperatures from 300 K to 77 K. AExpand
Realistic heterointerface model for excitonic states in growth-interrupted GaAs quantum wells
• Physics
• 2006
We present a model for the disorder of the heterointerfaces in GaAs quantum wells including long-range components like monolayer island formation induced by the surface diffusion during the epitaxialExpand
Weakly Trapped, Charged, and Free Excitons in Single-Layer MoS2 in the Presence of Defects, Strain, and Charged Impurities.
This work disentangle the concomitant spectroscopic expression of all three effects of MoS2 to identify to what extent they are intrinsic to the material or extrinsic to it, i.e., related to its local environment. Expand
Enabling valley selective exciton scattering in monolayer WSe2 through upconversion
It is shown that scattering between B- Excitons and A-excitons preferably happens within the same valley in momentum space, which leads to power dependent, negative polarization of the hot B-exciton emission. Expand
Optical spectroscopy of excited exciton states in MoS 2 monolayers in van der Waals heterostructures
The optical properties of MoS2 monolayers are dominated by excitons, but for spectrally broad optical transitions in monolayers exfoliated directly onto SiO2 substrates detailed information onExpand
Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides
The key insights reported here—strong many-body effects and intrinsically rapid radiative recombination—are expected to be ubiquitous in atomically thin semiconductors. Expand
Exciton and trion dynamics in atomically thin MoSe2 and WSe2: Effect of localization
We present a detailed investigation of the exciton and trion dynamics in naturally doped ${\mathrm{MoSe}}_{2}$ and ${\mathrm{WSe}}_{2}$ single atomic layers as a function of temperature in the rangeExpand
Carrier and polarization dynamics in monolayer MoS2.
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text:
# PoW for Sept. 28 :: FSR584, abundances, compact objects…

Hello, welcome to another issue of “Papers of the Week”, covering publications and preprint related to the world of Galactic Globular Clusters!

This issue features the entry (as a preprint on astro-ph) of the discover of *another* globular clusters in our Galaxy, FSR584 (see the paper by Bica et al.), as well as a good amount of publications on abundances, variability and compatc objects.

As always, any feedback on PoW will be much appreciated 😉

MC

== General ==

§ Origin of the abundance patterns in Galactic globular clusters: constraints on dynamical and chemical properties of globular clusters
Authors: T. Decressin, C. Charbonnel, G. Meynet
http://babbage.sissa.it/abs/0709.4160

§ Compact objects in globular clusters
Authors: Thomas J. Maccarone, Christian Knigge (University of Southampton)
http://babbage.sissa.it/abs/0709.3732

§ Formation of the Galactic globular clusters with He-rich stars in low-mass halos virialized at high redshift
Authors: K. Bekki, H. Yahagi, M. Nagashima, D. A. Forbes
http://babbage.sissa.it/abs/0709.3564

== Individual ==

§ On the Radial Distribution of White Dwarfs in the Globular Cluster NGC 6397
Authors: D. S. Davis (UBC), H. B. Richer (UBC), I. R. King (UWash), J. Anderson (Rice), J. Coffey (UBC), G. G. Fahlman (HIA/NRC), J. Hurley (Swinburne), J. S. Kalirai (UCSC)
http://babbage.sissa.it/abs/0709.4286

§ The ACS Survey of Galactic Globular Clusters. III. The Double Subgiant Branch of NGC 1851
Authors: A. P. Milone, L. R. Bedin, G. Piotto, J. Anderson, I. R. King, A. Sarajedini, A. Dotter, B. Chaboyer, A. Marin-Franch, S. Majewski, A. Aparicio, M. Hempel, N. E. Q. Paust, I. N. Reid, A. Rosenberg, M. Siegel
http://babbage.sissa.it/abs/0709.3762

§ Abundances on the Main Sequence of Omega Centauri
Laura M. Stanford , G. S. Da Costa , and John E. Norris
http://www.journals.uchicago.edu/…/71221.abstract.html

§ FSR584 – a new globular cluster in the Galaxy?
Authors: E. Bica, C. Bonatto, S. Ortolani, B. Barbuy
http://babbage.sissa.it/abs/0709.3315

§ The chemical abundance of the very metal-rich old open clusters NGC 6253 and NGC 6791
E. Carretta, A. Bragaglia, and R. G. Gratton
http://www.aanda.org/index.php?option=article&access=doi&doi=10.1051/0004-6361:20065213

== Extragalactic ==

§ The Globular Cluster System of M60 (NGC 4649). I. CFHT MOS Spectroscopy and Database
Authors: Myung Gyoon Lee, Ho Seong Hwang, Hong Soo Park, Jang-Hyun Park , Sang Chul Kim, Young-Jong Sohn, Sang-Gak Lee, Soo-Chang Rey, Young-Wook Lee, Ho-Il Kim
http://babbage.sissa.it/abs/0709.4308

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A “quick list” (updated [more or less…] daily) of PoW papers is always available at the URL:
http://del.icio.us/mcastel/pow

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# FSR 584: Another new nearby globular cluster candidate

Bica et.al. have announced another nearby globular cluster candidate in the Milky Way:

http://arxiv.org/abs/0709.3315

Author: E. Bica, C. Bonatto, S. Ortolani, B. Barbuy
Title: FSR584 – a new globular cluster in the Galaxy?
Comments: Astronomy and Astrophysics, accepted. 6 pages and 6 figures

Abstract: We investigate the nature of the recently catalogued star cluster candidate FSR584, which is projected in the direction of the molecular cloud W3 and may be the nearest globular cluster to the Sun. 2MASS CMDs, the stellar radial density profile, and proper motions are employed to derive fundamental and structural parameters. The CMD morphology and the radial density profile show that FSR584 is an old star cluster. With proper motions, the properties of FSR584 are consistent with a metal-poor globular cluster with a well-defined turnoff and evidence of a blue horizontal-branch. FSR584 might be a Palomar-like halo globular cluster that is moving towards the Galactic plane. The distance from the Sun is approx 1.4kpc, and it is located at approx 1kpc outside the Solar circle. The radial density profile is characterized by a core radius of rc=0.3+/-0.1 pc. However, we cannot exclude the possibility of an old open cluster. Near-infrared photometry coupled to proper motions support the scenario where FSR584 is a new globular cluster in the Galaxy. The absorption is A_V=9.2+/-0.6$, which makes it a limiting object in the optical and explains why it has so far been overlooked This one is apparently projected over starforming region W3, and at a distance of only 1.4 kpc (4,600 ly). It would probably even beat the recently discovered record holder, FSR 1767. However, as of this time, the authors cannot exclude that this may be an old open cluster. A preliminary webpage for this probable globular has been created at http://www.seds.org/~spider/spider/MWGC/fsr0584.html # PoW for Sept. 21 :: Omega Cen, WD kicks… Hello, welcome to the third issue of “Paper of the week”,covering publications and preprint related to the world of Galactic Globular Clusters. This week I managed to find only a few preprints related to GGCs, and as you can see, it is Omega Centaury that continues to attract mostly the attenction of astronomers… As always, any feedback on PoW will be much appreciated 😉 MC == General == § “RR Lyrae stars in Galactic globular clusters. VI. The Period-Amplitude relation” Authors: G. Bono, F. Caputo, M. Di Criscienzo http://babbage.sissa.it/abs/0709.3177 § Constraining white-dwarf kicks in globular clusters : II. Observational Significance Authors: Jeremy S. Heyl http://babbage.sissa.it/abs/0709.3118 == Omega Centauri == § “A spectral atlas of post-main-sequence stars in omega Centauri: kinematics, evolution, enrichment and interstellar medium” (Revised version) Authors: Jacco Th. van Loon, Floor van Leeuwen, Barry Smalley, Andrew W. Smith, Nicola A. Lyons, Iain McDonald, Martha L. Boyer http://babbage.sissa.it/abs/0709.2353 § “The Hottest Horizontal-Branch Stars in omega Centauri – Late Hot Flasher vs. Helium Enrichment” Authors: S. Moehler, S. Dreizler, T. Lanz, G. Bono, A.V. Sweigar, A. Calamida, M.Monelli, M. Nonino http://babbage.sissa.it/abs/0709.2839 * A “quick list” of PoW papers is also available at http://del.icio.us/mcastel/pow (under construction) # PoW for Sept. 14 :: M55, 47 Tuc, NGC 2419… Hello, this is the second (experimental) issue of “Paper Of the Week(PoW), covering publications and preprint related to the world of Galactic Globular Clusters: PoW for Sept. 14, 2007 — Extragalactic, LMC # Title: On the origin of the kinematical differences between the stellar halo and the old globular cluster system in the Large Magellanic Cloud Authors: Kenji Bekki Montly Notices, Online Early Article — M55, BSS # Title: The surprising external upturn of the Blue Straggler radial distribution in M55 # Authors: B. Lanzoni , E. Dalessandro , S. Perina , F.R. Ferraro , R.T. Rood , A. Sollima — 47 Tuc, abundances Title: Globular Cluster Abundances from High-Resolution Integrated Light Spectra, I: 47 Tuc Authors: Andrew McWilliam, Rebecca A. Bernstein http://babbage.sissa.it/abs/0709.1964 — M54, Sagittarius DSphTitle: The ACS Survey of Galactic Globular Clusters: M54 and Young Populations in the Sagittarius Dwarf Spheroidal Galaxy Authors : Michael H. Siegel et al. The Astrophysical Journal Letters Volume 667, Number 1 — NGC2419 Title: On the Remote Galactic Globular Cluster NGC 2419 Authors: Vincenzo Ripepi et al. The Astrophysical Journal Letters Volume 667, Number 1 The surface brightness profile of the remote cluster NGC2419: M. Bellazzini A&A 473 (2007) 171-176 http://www.aanda.org/10.1051/0004-6361:20078130 — NGC 6253The chemical abundance of the very metal-rich old open clusters NGC 6253 and NGC 6791: E. Carretta, A. Bragaglia and R. G. Gratton A&A 473 (2007) 129-141 http://www.aanda.org/10.1051/0004-6361:20065213 As usual, my apologize for article I may have missed! Do you think PoW can be useful ? Any feedback will be appreciated ! 😉 Marco C. Blogged with Flock Tags: , , # Preprints of the week: NGC6558, NGC6397, FSR 584… Hello! Back from Cefalù workshop (anyone else there?), here is a (possibly incomplete) list of the paper appeared in preprint services during this week:  Title: NGC 6558: A Blue Horizontal Branch Moderately Metal-Poor Globular Cluster in the Bulge Authors: Barbuy, B.; Zoccali, M.; Ortolani, S.; Minniti, D.; Hill, V.; Renzini, A.; Bica, E.; Gómez, A. http://cdsads.u-strasbg.fr/abs/2007AJ….134.1613B  Title: Atomic Diffusion and Mixing in Old Stars I. VLT/FLAMES-UVES Observations of Stars in NGC 6397 Authors: Korn, A. J.; Grundahl, F.; Richard, O.; Barklem, P. S.; Mashonkina, L.; Collet, R.; Gustafsson, B.; Piskunov, N. http://cdsads.u-strasbg.fr/abs/2007arXiv0709.0639K  Title: The surface density profile of NGC 6388: a good candidate for harboring an intermediate-mass black hole Authors: Lanzoni, B.; Dalessandro, E.; Ferraro, F. R.; Miocchi, P.; Valenti, E.; Rood, R. T.; – http://cdsads.u-strasbg.fr/abs/2007arXiv0709.0119L  Title: FSR 584 – a new globular cluster in the Galaxy? Authors: Bica, E.; Bonatto, C.; Ortolani, S.; Barbuy, B. http://cdsads.u-strasbg.fr/abs/2007A%26A…472..483B  Title: The fraction of binary systems in the core of 13 low-density Galactic globular clusters Authors: Sollima, A.; Beccari, G.; Ferraro, F. R.; Fusi Pecci, F.; Sarajedini, A. http://cdsads.u-strasbg.fr/abs/2007MNRAS.380..781S  Title: The tidal tails of NGC 5466 Authors: Fellhauer, M.; Evans, N. W.; Belokurov, V.; Wilkinson, M. I.; Gilmore, G. http://cdsads.u-strasbg.fr/abs/2007MNRAS.380..749F  Title: Millisecond pulsars around intermediate-mass black holes in globular clusters Authors: Devecchi, B.; Colpi, M.; Mapelli, M.; Possenti, A. http://cdsads.u-strasbg.fr/abs/2007MNRAS.380..691D  Title: Tidal tails around globular clusters Authors: Montuori, M.; Capuzzo-Dolcetta, R.; Di Matteo, P.; Miocchi, P. http://cdsads.u-strasbg.fr/abs/2007arXiv0709.0460M # Papers on Omega Cen, NGC6440, NGC6388, NGC6441, M4… Hello, here is a brief list (not sure if complete…) with the latest preprints regarding Galactic Globular Clusters, which appeared this month on astro-ph: • ## Abundances on the Main Sequence of Omega Centauri • ## Chemical Abundances and Kinematics in Globular Clusters and Local Group Dwarf Galaxies and Their Implications for Formation Theories of the Galactic Halo Authors: Doug Geisler (Universidad de Concepcion), George Wallerstein (University of Washington), Verne V. Smith (National Optical Astronomy Observtory), Dana I. Casetti-Dinescu (Yale University) • ## Discovery of 442-Hz Pulsations from an X-ray Source in the Globular Cluster NGC 6440 • ## The Peculiar Horizontal Branch Morphology of the Galactic Globular Clusters NGC 6388 and NGC 6441: new insights from UV observations • ## Intermittent millisecond X-ray pulsations from the neutron-star X-ray transient SAX J1748.9-2021 in the globular cluster NGC 6440 • ## A search for solar-like oscillations in K giants in the globular cluster M4 # FSR 1767: New Milky Way Globular Cluster, No. 158 A new globular cluster in the Milky Way has just been announced: FSR 1767. This one is particular in being the closest known globular to us at only about 4,900 light-years, thus beating M4 and NGC 6397 at about 6,500 to 7,500 ly. It is a low-mass globular with perhaps 1/10 of the stars in M4, and estimated as of absolute magnitude -4.7 Mv, diameter 6.5 ly. According to my counting, this is currently Milky Way Globular Cluster No. 158 to be recognized. [- Hartmut] Reference: Charles Bonatto, Eduardo Bica, Sergio Ortolani, Beatriz Barbuy, 2007. FSR1767 – a new globular cluster in the Galaxy. To be published in MNRAS. Abstract: The globular cluster (GC) nature of the recently catalogued candidate FSR 1767 is established in the present work. It results as the closest GC so far detected in the Galaxy. The nature of this object is investigated by means of 2MASS colour-magnitude diagrams (CMDs), the stellar radial density profile (RDP) and proper-motions (PM). The properties are consistent with an intermediate metallicity ($\feh\approx-1.2$) GC with a well-defined turnoff (TO), red-giant branch (RGB) and blue horizontal-branch (HB). The distance of FSR 1767 from the Sun is$\ds\approx1.5$kpc, and it is located at the Galactocentric distance$\rgc\approx5.7$kpc. With the space velocity components$(V,W)=(184\pm14,-43\pm14)\rm km s^{-1}$, FSR 1767 appears to be a Palomar-like GC with$\mv\approx-4.7$, that currently lies$\approx57$pc below the Galactic plane. The RDP is well represented by a King profile with the core and tidal radii$\rc=0.24\pm0.08$pc and$\rt=3.1\pm1.0$pc, respectively, with a small half-light radius$\rh=0.60\pm0.15$pc. The optical absorption is moderate for an infrared GC,$A_V=6.2\pm0.3\$, which together with its central direction and enhanced contamination explains why it has so far been overlooked.

Preprint:
http://www.arxiv.org/abs/0708.0501

SEDS webpage:
http://www.seds.org/~spider/spider/MWGC/fsr1767.html


text:
# 1.3.4. Halo Effect - Analytical Methods¶

## 1.3.4.1. Linear Stability¶

We assume that both the forward and backward beams are starting from electron flavor.

$\begin{split}\rho_F &= \frac{1}{2}\begin{pmatrix} 1 & \epsilon_F \\ \epsilon_F^* & -1 \end{pmatrix} \\ \rho_B &= \frac{1}{2}\begin{pmatrix} 1 & \epsilon_B \\ \epsilon_B^* & -1 \end{pmatrix}.\end{split}$

The linearized equation of motion is

$\begin{split}i\partial_z \begin{pmatrix} \epsilon_F \\ \epsilon_B \end{pmatrix} = \begin{pmatrix} R \mu + \eta & - R \mu \\ \mu & -(\mu+ \eta) \end{pmatrix} \begin{pmatrix} \epsilon_F \\ \epsilon_B \end{pmatrix},\end{split}$

where $$\eta$$ is the hierarchy and all quantities are scaled by $$\omega_v$$.

We can solve the eigenvalues of this problem. To obtain complex solutions, we require $$\Delta < 0$$, which translates to

$\mu_-< \mu <\mu_+,$

where

$\mu_\pm = \frac{ -2 (1+R) \eta \pm 8 \sqrt{ R } }{ (1-R)^2 }.$

We plot out growth rate as a function of $$R$$ and $$\mu$$, which shows that such so called instabilities only exist for normal hierarchy.

### 1.3.4.1.2. Single Beam Undetermined Back Beam¶

The equation of motion is

$\begin{split}i\partial_z \rho_F &= [ H_F, \rho_F ] \\ i\partial_z \rho_B &= [ H_B, \rho_B ] ,\end{split}$

where

$\begin{split}H_F &= R \mu \rho_B\\ H_B &= \mu \rho_F.\end{split}$

Conventions

The angle contribution is $$1-\cos\theta=2$$. We absorbe this factor into $$\mu$$.

As for the initial states, we can assume some general forms

$\begin{split}\rho_F &= \frac{1}{2} \begin{pmatrix} 1 & \epsilon_F \\ \epsilon_F^* & -1 \end{pmatrix}\\ \rho_B &= \frac{1}{2} \begin{pmatrix} a & \epsilon_B \\ \epsilon_B^* & -a \end{pmatrix}.\end{split}$

The forward beam start from neutrino flavors. However, the state of the backward beam is to be determined. The exact state is not necessary since we are interested in linear stability.

We linearize the equation of motion by keeping only first order of the small off-diagonal elements.

$\begin{split}i\partial_z \begin{pmatrix} 1 & \epsilon_F \\ \epsilon_F^* & -1 \end{pmatrix} &= \frac{ R \mu}{2} \begin{pmatrix} 0 & 2(a \epsilon_F -\epsilon_B) \\ c.c. & 0 \end{pmatrix} + \frac{R\mu}{2} \begin{pmatrix} 0 & 2(a\epsilon_F - b) \\ c.c. & 0 \end{pmatrix} \\ - i\partial_z \begin{pmatrix} 1 & \epsilon_B \\ \epsilon_B^* & -1 \end{pmatrix} &= -\frac{\mu}{2} \begin{pmatrix} 0 & 2(a \epsilon_F -\epsilon_B) \\ c.c. & 0 \end{pmatrix} - \frac{\mu}{2} \begin{pmatrix} 0 & 2 (a\epsilon_F - b) \\ c.c. & 0 \end{pmatrix}\end{split}$

The system of equations can be easily solved and we found that the exponentials are $$e^{i(2a R -1) \mu z}$$. No exponent growth is possible.

eqnF = I D[epsF[z], z] == alpha mu (a epsF[z] - epsB[z]) + alpha mu (a epsF[z] - b)
eqnB = I D[epsB[z], z] == mu (a epsF[z] - epsB[z]) + mu (a epsF[z] - b)
DSolve[{eqnF,eqnB},{epsF,epsB},z]

The Two Beams have Synchronized Evolution

Notice that the two equations can be combined to

$\partial_z \epsilon_F = \partial_z ( R \epsilon_B ).$

This result indicates that the initial development of the forward and backward beams are synchronized.

Dealing with Inhomogenous Differential Equations

1. The solution to inhomogenous systems is the general solution plus the particular solution. At least we can know that if the general solution contains exponential growth terms, the final solution should also contain exponential growth terms, if the particular solution doesn’t cancel them.

2. Floquet theory for periodic matrix systems might be useful.

#### 1.3.4.1.2.1. Linear Regime Behavior¶

The solutions to such a problem shows that we always obtain decreasing modes. It’s not easy to comphrend. But the linear could be solved exactly.

In linear regime, we define the density matrices for forward and backward beams to be

$\begin{split}\rho_F &= \frac{1}{2} \begin{pmatrix} 1 & \epsilon_F \\ \epsilon_B^* & -1 \end{pmatrix} \\ \rho_B &= \frac{1}{2} \begin{pmatrix} 1 & \epsilon_B \\ \epsilon_B^* & -1 \end{pmatrix}.\end{split}$

The Hamiltonians are

$\begin{split}H_F &= H_v + \mu \rho_F \\ H_B &= H_v + R \mu \rho_B.\end{split}$

We will investigate the instability for zero mixing angle.

The linearized equation of motion can be simplified to

$\begin{split}i\partial_z \begin{pmatrix} \epsilon_F \\ \epsilon_B \end{pmatrix} = \begin{pmatrix} -\omega_v + R \xi \mu & - R \xi \mu \\ \xi \mu & \omega_v - \xi \mu \end{pmatrix} \begin{pmatrix} \epsilon_F \\ \epsilon_B \end{pmatrix}.\end{split}$

This equation can be easily solved. The eigenvalues are

$\begin{split}\Omega_+ &= \frac{1}{2} ( (R-1)\xi\mu + \sqrt{\Delta} ) \\ \Omega_- &= \frac{1}{2} ( (R-1)\xi\mu - \sqrt{\Delta} ),\end{split}$

where

$\Delta = (1-R)^2 \mu^2 \xi^2 - 4\mu\xi \omega_v (1+R) + 4\omega_v^2.$

The corresponding eigenvectors are

$\begin{split}V_+ &=\begin{pmatrix} \frac{ -2\omega_v + \xi \mu (1+R) + \sqrt{\Delta} }{2\xi\mu} \\ 1 \end{pmatrix} \\ V_- &=\begin{pmatrix} \frac{ -2\omega_v + \xi \mu (1+R) - \sqrt{\Delta} }{2\xi\mu} \\ 1 \end{pmatrix}.\end{split}$

The general solution to the equation is

$\begin{split}\begin{pmatrix} \epsilon_F(z) \\ \epsilon_B(z) \end{pmatrix} = C_+ V_+ e^{-i \Omega_+ z} + C_- V_- e^{-i \Omega_- z}.\end{split}$

The special property about this reflection prolem is that the density matrices for the forward and backward beams should be the same at the reflection point, say $$L$$. With such a simple relation, we can find the relations between $$C_\pm$$ by setting $$\epsilon_F(L)=\epsilon_B(L)$$,

$\frac{C_+}{C_-} = e^{-i(\Omega_- -\Omega_+)L} \frac{ \sqrt{\Delta} + 2\omega_v + \mu \xi (1-R) }{\sqrt{\Delta} - 2\omega_v - \mu \xi (1-R)}.$

The solution to be problem can be simplified,

$\begin{split}\begin{pmatrix} \epsilon_F(z) \\ \epsilon_B(z) \end{pmatrix} = C_- e^{-i\Omega_- L} \left( \frac{ \sqrt{\Delta} + 2\omega_v + \mu \xi (1-R) }{\sqrt{\Delta} - 2\omega_v - \mu \xi (1-R)} V_+ e^{-i \Omega_+ (z-L)} + V_- e^{-i \Omega_- (z-L)} \right).\end{split}$

We are interested in the absolute values of each elements so that the overall factors can be neglected. The forward beam evolution is obtained by taking the absolute value of $$\epsilon_F$$,

$\left\vert \epsilon_F \right\vert \propto \lvert (2\omega_v +\xi\mu(1-R) +i \delta ) ( -2\omega_v + \xi\mu(1+R) + i \delta ) e^{delta(z-L)} + ( -2\omega_v - \xi\mu(1-R) +i \delta ) ( -2\omega_v + \xi\mu(1+R) - i \delta ) e^{-delta(z-L)} \rvert,$

in which $$\sqrt{\Delta}$$ is replaced by $$i \delta$$.

Collecting terms, we could verify that it has the form

$\left\vert \epsilon_F \right\vert \propto A + B \cosh( 2\delta(L-z) ).$

The only $$z$$ dependent term is cosh( 2delta(L-z) ), which is decreasing within $$[0,L]$$ and is increasing in $$[L,2L]$$. The slope at $$z=L$$ is 0.

## 1.3.4.2. Nonlocal Boundary Value Problem¶

Some References

1. Springer Open has a curated list of NBVP. DENFC.

2. To solve coupled systems with nonlocal boundary conditions: Goodrich, C. S. (2017). Pointwise conditions in discrete boundary value problems with nonlocal boundary conditions. Applied Mathematics Letters, 67, 7–15.

## 1.3.4.3. References and Notes¶

| Created with Sphinx and . | | Index |


text:
Why is the vector sampled from Gaussian or Subgaussian distribution in lattice-based cryptography? [duplicate]

I have known that the vector is sampled from Gaussian distribution in lattice-based cryptography because the distribution of the vector $$\mod{\mathcal{P}(\mathbf{B})}$$ approximates to uniform distribution.

It is proved by below lemma.

For any $$s > 0$$, $$\mathbf{c} \in \mathbb{R}^n$$, and lattice $$\Lambda(\mathbf{B})$$, the statistical distance between $$\mathcal{D}_{s,\mathbf{c}} \mod{\mathcal{P}(\mathbf{B})}$$ and the uniform distribution over $$\mathcal{P}(\mathbf{B})$$ is at most $$\frac{1}{2} \rho_{1/s}(\Lambda(\mathbf{B})^*\backslash\{\mathbf{0}\})$$. In particular, for any $$\epsilon >0$$ and any $$s \geq \eta_{\epsilon}(\mathbf{B})$$, the statistical distance is at most $$\Delta(\mathcal{D}_{s,\mathbf{c}} \mod{\mathcal{P}(\mathbf{B})},\mathcal{U}(\mathcal{P}(\mathbf{B}))) \leq \epsilon/2$$.

But if the vector is sampled from uniform distribution at first, the distribution of the vector $$\mod{\mathcal{P}(\mathbf{B})}$$ is uniform. So, I thought that Gaussian sampling is not needed for above reason, because Gaussian sampling requires large costs.

Another reason I think is that the smaller vector is preferred because almost lattice problem is about finding short vector and Gaussian variable has higher probability as closer to the center. Is it right?

If my thought is not correct, let me know the reason using Gaussian distribution in lattice-based cryptography.

• I think it's because one of the original paper written by Regev, the cryptosystem is linked to the LWE problem with a gaussian noise. – Ievgeni Aug 13 '19 at 13:26

• But the algorithms i see use a good basis when they sample vector. In detail, they use the nearest plane algorithm that output the nearest lattice vector from target vector and they output the nearest vector with higher probability than other. (e.g target vector $\mathbf{c}$ is closer lattice vecotr $\mathbf{v}$ than $\mathbf{0}$, the probability outputting $\mathbf{v}$ is larger than $\mathbf{0}$. Can they sample the vector from Gaussian without the basis? Or is the algorithm an exception? Then, why does the algorithm i see sample from Gaussian? – 전소현 Aug 13 '19 at 6:26