text:
# A Generic Interface for Genomic Data

## Purpose

Genomic data are data satisfying the following the following conditions

1. Genomic: Linked to features of a reference genome.
2. Genomic: Organized into large sets of data.
3. Linked to a particular experimental condition.

We call data satisfying only the first two conditions annotations.

Genomic data usually arise from genomic technologies. Here are a few examples:

1. Genome analysis: SNP/CNV arrays, exome-seq, DNA-Seq
2. Biochemical analysis: ChIP-chip/ChIP-Seq, CLIP-Seq
3. Gene Expression Data: 3'-UTR array, exon array, smRNA-Seq, mRNA-Seq

This page will be a space to flesh out ideas about creating a generic interface between different genomic back ends and visualization front ends.

The immediate purpose is to make it easier to use a different back end with ExpressionPlot, but we also hope that this interface will be general enough to be useful for other front ends.

Regardless of its sources, genomic data analysis often compromises the following steps:

1. Processing of raw data: This step involves taking raw data off a machine and processing it to most basic form. This is typically highly platform-specific and done using manufacturer-provided software. For example, this would include imagine processing/base calling on an Illumina machine, or image processing/spot quantification on a microarray. It also includes basic quality filtering of sequence data, and background subtraction/normalization of microarray data.
2. Feature extraction: This step further processes the data from each sample to summarize specific genomic regions. For RNA-Seq or microarray this might be gene or splicing levels, and for ChIP-Seq this could be peak calls and associated read numbers. At this point the raw data of the previous step (read sequences or spot intensities) is abstracted out.
3. Statistical comparisons: This step involves statistical analyses to sort out significant events from noise. It typically involves the comparison of different samples or groups of samples.
4. Biological insight: This final step is the most nebulous and represents the true work of the computational biologist. Of all the possible events and comparisons that could be made, one must decide which ones are relevant and what new hypotheses can be gleamed from the data.

The goal of this document is to specify abstractly the requirements for an interface between the third and fourth steps. It should hide all of the complexities of the first three steps (which might be run as a standard pipeline regardless of the biological system), but still be general enough to encode all the information that might be of interest to browse, visual and compare data from a biological point of view.

In the case of ExpressionPlot, the first three steps are part of the back end and the front end is a tool to help with the fourth step. The purpose of this Interface, therefore, is to make it possible to exchange information from different back ends (including different genomes or genomic platforms) with different tools for biological insight.

## Definitions

### Data

In our set theory framework, data of all types are represented by functions onto some range $R$. $R$ can be any number of sets but is usually a cartesian product of some mixture of reals, integers and/or finite sets, allowing our data to have multiple dimensions. The dimensions can also be arbitrary-length tuples or subsets of these basic sets. We can formalize this with $R = \bigotimes_{i=1}^{n(R)} R_i$ and each $R_i = \mathbb R, \mathbb Z$ or some finite set. Arbritrary-length tuples are formalized with the star operator, $R_i = S^* := \bigcup_{d=0}^\infty S^d$, and subsets of arbitrary (finite) size as power sets, $R_i = \mathcal P(S)$ (power set of S).

### Genomes

In this framework, genome is any set of biological sequences. It can be a typical reference genome, such as mm9 or hg18, but it can also have extra sequences like transfected plasmid sequences. It could also be a proteome, where the sequences are the different proteins. In this framework, all of these types of sequences are still called chromosomes.

In the set theory formalization we denote a genome $\mathcal G$ as a set of $n(\mathcal G)$ chromosomes: $G=\{C_i\}_{i=1}^{n(\mathcal G)}$. Letting $n(C_i)$ denote the length of chromosome $i$, the chromosomes are linear sequences $C = x_1 \cdots x_{n(C)}$ taken from some finite alphabet $\mathcal A$.

### Features

Formally, a feature of a reference genome is a sequence of not necessarily contiguous genomic intervals. The intervals can be just position or both position and strand.

Typically the raw data will be processed with respect to a set, or multiple sets, of genomic features. These features can either be pre-defined, for example the set of UCSC knownGenes, recursively defined based on the data itself, or a mixture of the two.

As with experiments, genomic data can be linked to a single feature (such as the level of one exon), or to a tuple of features, (such as the relative levels of a set of isoforms of a gene, or the fraction of multiple different genotypes at particular locus).

In the set theory formalization, a feature $f$ is a sequence of $n(f)$ genomic intervals $i_1,\ldots,i_{n(f)}$. An interval is a 4-tuple of the chromosome, the start coordinate, the end coordinate and the strand: $i = (chr, start, end, strand)$ where

• $chr \in \mathcal G$
• $1 \le start \le end+1 \le n(chr)+1$
• and $strand \in \{+,-\}$.

The requirements for the start and end coordinates are that we use 1-based indexing and specify intervals inclusively (fully closed) so that the start and end coordinates are included in the interval. For example, the first 10 bases of the genome are specified with $start=1$ and $end=10$. A 1-base interval can be specified with $start=end$. In general we require $start \le end$ except for the special case of the empty interval where $start=end-1$. Although such an interval would be empty it is considered to lie between the two bases specified by $start$ and $end$. The meaning of this is not specified here, but one example would be an exon of length 0, also known as a resplicing site[1]. The empty intervals include the special cases $(start,end)=(n+1,n)$ and $(1,0)$, which indicate the position after the last base and before the first.

### Experiments

An experiment is a set of samples, each of which is characterized by a set of common variables (sometimes called phenoData). These can be of any dimension and type, and indicates things like genotypes (like wildtype or mutant), experimental conditions (like treated or untreated), and co-observed (but dependent) variables (like age, sex or blood pressure).

Genomic data can be linked to a single experiment (like a gene level), to n-tuples of experiments (like a fold-change in a pair of experiments, or statistics for groups of experiments), or, in general, to any sets of experiments.

In the set theoretical formulation an experiment $E$ has $n(E)$ samples. It is a function $E : [n(E)] \rightarrow R$ where $R$ is some appropriate data space.

### Annotation

An annotation is a set of features usually associated with other non-experimental variables. For example, it could be a set of genes and their names, or exons and their splice sites.

In the set theory formulation, an annotation is an ordered triple $\mathcal A = (\mathcal G, A,a)$ where $A=\{f_i\}_{i=1}^{n(\mathcal A)}$ is a set of features on the underlying genome $\mathcal G$ and $a:A \rightarrow R$ is the function giving the values of the associated variables in the appropriate data space. It is possible that among other numerical and string data some of the other variables are themselves features. For example, for coding transcripts the basic exon-intron structures could be the features in $A$ and the coordinates of the coding sequences, which are also features, could be a finite-set dimensions of $R$.

### Genomic Data

A genomic data set $\mathcal D=(\mathcal G, \mathcal A, E, D)$ is an underlying genome $\mathcal G=\mathcal G(\mathcal D)$, an annotation on that genome $\mathcal A=\mathcal A(D)$, an experiment $E=E(D)$, and a dependent variable function $D=D(\mathcal D)$. The domain of $D$ can formally be any family of (possibly ordered) groups of experiment samples or annotation features ($D : E^* \times A^* \to R$ where $S^*$ denotes the family of all finite tuples (of any length) taken from the set $S$ and $R$ denotes the range of the function). The function $D$ is not necessarily defined over the entire domain. For example, it might only be defined for tuples of a fixed length.

### Project

A genomic project is a family $\mathcal P=\{\mathcal D_i\}_{i=1}^{n(\mathcal P)}$ of genomic data sets with a common underlying genome and experiment: $\mathcal D_i=(\mathcal G, E, \mathcal A_i, D_i)$.

### Map

Different annotations can be linked together by a map, which can be thought of as a bipartite graph whose two parts are annotations. Maps can be between different genomes, for example between mouse and human genes, between different types of annotations, such as between genes and alternative splicing events of a single, or both. In general the maps are many-to-many so, for example, one human gene could be mapped onto two different mouse genes or vice versa. The nature of the map is not specified here. For example, maps could be used to represent overlapping features (like exons contained in genes), or just nearby features (like ChIP-Seq binding peaks located in promoter regions). Automaps (from one annotation onto itself) are also permitted, and these could be used, for example, to represent interactomes. In addition to the information about which features are linked, each such link can have auxiliary variables. For example, for gene maps between organisms these variables might give the number of bases from each genome that are aligned, or a perhaps string encoding the alignment itself. For an automap representing an interactome, the auxiliary variables might represent the strength and evidence for the interaction.

Should there be a type of genomic data that has links in a map as a dimension of its domain?

In the set theory formulation, a map is an ordered 4-tuple $\mathcal M=(\mathcal A_1, \mathcal A_2, L, m)$ where $\mathcal A_i$ are annotations, $L \subseteq A_1 \times A_2$ is the set of links between the feature sets of the annotations, and $m:L \rightarrow R$ is a function that gives the associated data for each link in the appropriate data space $R$.

Some maps are bijections (1-1 correspondences), so that they identify the features of $\mathcal A_1$ with those of $\mathcal A_2$. An example of this would be two different gene aggregations based on the UCSC knownIsoforms table. One might be the union of all the associated knownGene transcripts, and the other could be the intersection of those transcripts ("constitutive exons"). Although the annotations are different, there is a natural 1-1 correspondence between their gene models.

Maps, especially bijections, should be transitive, so that if $\mathcal M_1=(\mathcal A_1, \mathcal A_2, L_1, m_1)$ is a map from annotation $\mathcal A_1$ to $\mathcal A_2$ and $\mathcal M_2=(\mathcal A_2, \mathcal A_3, L_2, m_2)$ is a map from $\mathcal A_2$ to $\mathcal A_3$ then the compostition of the maps $\mathcal M_1 \circ \mathcal M_2$ is defined as $(\mathcal A_1, \mathcal A_3, L_3, m_1 \circ m_2)$ where $L_3 = \{(i,k) : \exists j \in A_2 : (i,j) \in L_1 \mbox { and } (j,k) \in L_2\}$.

Given a family of annotations $\mathcal A = \{\mathcal A_i\}$ and a family of maps $\mathcal M = \{\mathcal M_i\}$ defined on those annotations, we define the map graph whose nodes are the annotations and edges are the maps. An important algorithmic operation will be to find a map, if necessary by composing other maps, from one annotation to another. Weights of 0 could be placed on bijective edges and of 1 on non-bijective edges, and basic path-finding algorithms could be run efficiently, possibly with a maximum path-length restriction.

## Data Representation

With our set theoretic definition of a genomic project in hand we now propose a concrete interface to implement this definition. The basic building block of the interface will be a relational database. The engine is not specified here, only the table structures. We define different types of tables to represent the set theoretic objects described above. The actual names of the tables are specified in a separate configuration file. Ideally we will then create an API, for example using Perl's DBI scheme, that will allow the user to provide the project using any desired relational database engine. Although we think of interface as being composed of database tables, it is not strictly require that database software be running: it is possible a user of this system would simply generate flat files and then use the DBD::CSV interface to import them.

### Star tables

Before we define the tables that make up the Interface, we begin with a definition of star tables. These tables solve the problem of encoding $n$-tuples of varying length into a relational database.

Although $n$-tuples of fixed length are easy to encode (just use $n$ columns), when the length is varying this is not as straightforward. A typical example would be specifying the exons that make up a transcript. In short there are two solutions.

The flat format solution is to use strings to join together IDs representing the exons. Then a variable-length $n$-tuple can be represented in a single column. The star format solution is to create a table just to specify the tuples. Each row of this star table corresponds to a single index of a single tuple. It therefore would have an identifier column for the tuple, an index column, and one or more columns specifying the elements of tuple. The relative merits of the two methods are discussed elsewhere, but this interface will generally allow either specification.

### Genomes

Genomes will be specified in .2bit format. However, for many analyses the actual genomic sequence is not necessary.

### Features

Genomic features are specified in a table whose rows correspond to contiguous intervals. They are joined together into features by a combination of the feature_ID and index fields. This is a type of star table, with the features being the "tuples" and the intervals being their "elements".

interval table
column description
chr Chromosome of the interval. If there is an underlying .2bit file this should match. Otherwise any name can be used.
start Start position of the interval on that chromosome. start must always be less than or equal to end-1. We use 1-based indexing and fully closed intervals, so that

both the start and end positions are considered part of the interval. For example, to specify an interval of length 1 at position 2000 use start=2000 and end=2000. To specify the empty interval between 2000 and 2001 use start=2001 and end=2000.

end End position of the interval on that chromosome.
strand "+", "-" or the empty string "" for an unstranded interval
feature_ID This is an identifier for the feature of which this interval is a part.
idx This is the 1-based index of the interval within the feature. For example, for a transcript with 5 exons, the intervals (which would correspond to the exons) would have indices 1 through 5.

In MySQL you might define an interval table as follows ("interval" is a reserved word in MySQL). The table can have any name, such as "gene_interval" or "Stat1_peak" (you might have idx=1 throughout the table). However, the names of the columns are required.

 CREATE TABLE f_interval (
chrom VARCHAR(255) NOT NULL,
start INT(10) UNSIGNED NOT NULL,
end INT(10) UNSIGNED NOT NULL,
strand ENUM("+","-",""),
feature_id VARCHAR(255) NOT NULL,
idx INT(10) UNSIGNED NOT NULL,
INDEX cse (chrom, start, end),
INDEX feature_id (feature_id)
);

It is important to index the feature_ID field since that makes looking up the intervals in a given feature fast.

### Experiments

Experiments are specified in a table whose rows correspond to samples and columns correspond to different dimensions of the phenoData. The details of the data are specific to the scientific project but at least one column offering a unique ID must be included. This column should be called simply id.

With regards to indexing, the id column should definitely be indexed, as well as other columns on which one might want to search. The indexing might seem superfluous since many genomic projects involve only a few samples (sometimes only 2!). However there are many projects now that are becoming quite large and even some GWAS studies with several thousand patients. Therefore in the interest of scalability it is recommended to include the index as a matter of habit.

experiment table
column description
id A unique identifier for the sample.
... The rest of the columns are specifically defined for the experiment in question.

In MySQL you might define an experiment table as follows. This example shows a few made-up fields, but only the id field is absolutely essential.

 CREATE TABLE experiment (
id VARCHAR(255) PRIMARY KEY,
age FLOAT INDEX,
sex CHAR(1),
treatment VARCHAR(255),
INDEX age (age)
);

### Annotations

An annotation is a set of features along with the associated variables. Since the features are independently specified in an intervals table the annotation is specified in a table whose rows correspond to samples and columns correspond to different dimensions of the associated data. Similarly to the experiments, the details of the data are specific to the annotation but must include an id column with values corresponding to those of the feature_id column from the intervals table. Unlike the intervals table, in the annotation table the id column must be a unique key.

With regards to indexing, the id column should definitely be indexed, but that might be sufficient, since finding features by genomic location will already be efficient based on the indexing in the intervals table. The feature_id column of the intervals table corresponds to the id column of the annotation table. However, the relationship between the IDs is not necessarily a strict reference, since there could be features in the interval table that are not in the annotation table.

annotation table
column description
id A unique identifier for the underlying feature. These identifiers should correspond to identifiers from the intervals table.
... The rest of the columns are specifically defined for the experiment in question.

In MySQL you might define an annotation table as follows. This example shows a few made-up fields that might be associated with an annotation of genes. In general only the id field is absolutely essential.

 CREATE TABLE gene (
id VARCHAR(255) PRIMARY KEY,
geneSymbol VARCHAR(255),
len UNSIGNED INT,
percent_gc FLOAT
);

In terms of a data structure, an annotation would be fully specified by the pair of the intervals table and annotation table, and possibly also some sort of handle into the genome (like a path to the .2bit file).

### Genomic Data

A table represent a genomic data $\mathcal D=(\mathcal G, \mathcal A, E, D)$ has three groups of columns. The first group are columns that specify the annotation features and the second group specify the experimental features. All of these columns together form a unique key for the table. Finally, the third group specify the data.

As a data structure, a genomic data set consists of the annotation, the experiments, and a description of the first two groups of columns. This column description is given in a database table with the following fields:

annotation and experiment column description table
column description
name a string giving the name of the column
col_type (column type) whether it is an "annotation" column or an "experiment" column
dim (dimensionality) whether it is a "scalar" column, which specifies a single annotation or experiment, a "tuple" column, which specifies an arbitrary-length tuple of annotations or experiments, or a "set" column, which specifies an arbitrary sized set of annotations or experiments
format if it is a "tuple" or "set" column, whether it uses the "flat" or "star" encoding format (NULL if it is a scalar column)
sep if it uses the flat format, its separating character (NULL if it is not a flat format column)
star if it uses the star format, the name of its associated star table. In that table the "elements" would be identifiers into either experiment or annotation table. (NULL if it is not a star format column)

This would be a typical data definition for such a table:

 CREATE TABLE annot_exp_cols (name VARCHAR(255) PRIMARY KEY,
col_type ENUM("annotation","experiment") NOT NULL,
dim ENUM("scalar","tuple","set") NOT NULL,
format ENUM("flat", "star"),
sep CHAR(1),
star VARCHAR(255)
);

Note that the data columns are not described in this table. All the columns of the data table that are not annotation or experiment columns are assumed to be data columns.

#### Example: Gene levels

Here is an example data definition for a data table that can hold keep information about gene levels in an RNA-Seq data set.

 CREATE TABLE gene_levels (gene VARCHAR(255),
sample VARCHAR(255),
rpkm FLOAT
);

The associated column description table would be filled like this

 +--------+------------+--------+--------+------+------+
| name   | col_type   | dim    | format | sep  | star |
+--------+------------+--------+--------+------+------+
| gene   | annotation | scalar | NULL   | NULL | NULL |
| sample | experiment | scalar | NULL   | NULL | NULL |
+--------+------------+--------+--------+------+------+

The VARCHAR(255) type of gene and sample would be the same as the id columns from the annotation and experiments tables (but could in principle be something else).

#### Example: Gene Level Changes

To give a more complicated example, consider a table that represents the comparison of gene levels in two groups of samples. The groups will be stored in a star table, rather than as comma-separated values. The data definition could be like this:

 CREATE TABLE gene_level_changes (gene VARCHAR(255),
group1 INT UNSIGNED,
group2 INT UNSIGNED,
lfc float,
p float
);

Here group1 and group2 are integers, but any data type in principle could be used for the identifiers of the star table. lfc and p represent the log-fold-change and P-value of the changes. The star table would have the following data definition:

 CREATE TABLE experiment_groups (group_id INT UNSIGNED,
sample VARCHAR(255)
);

Since the groups are actually (unordered) sets there is no need for an idx column on this star table. Also note that the word group is reserved in MySQL, so the column name has to be something different. The values in the group_id column would then correspond to the values in the group1 and group2 columns of the gene_level_changes table. The values in the sample column would correspond to values in the experiment table.

The column description table for gene_level_changes would look like this:

 +--------+------------+--------+--------+------+-------------------+
| name   | col_type   | dim    | format | sep  | star              |
+--------+------------+--------+--------+------+-------------------+
| gene   | annotation | scalar | NULL   | NULL | NULL              |
| group1 | experiment | set    | star   | NULL | experiment_groups |
| group2 | experiment | set    | star   | NULL | experiment_groups |
+--------+------------+--------+--------+------+-------------------+

#### Data structure

The entire genomic data set data structure is specified by the following:

• the genome
• the gene annotation (which in turn specifies the names of the intervals and annotation table)
• the experiments table
• the column description table (which might be named something like gene_levels_annot_exp_cols), and
• the data table itself (called gene_levels and gene_level_changes in these two examples).

## Notes/Plans/Errata

• Add set variation to star table section (i.e. without index).
• Add primary keys to all the tables---e.g. feature_id + idx for intervals table
• It should be fairly straightforward to include star sets and power sets as part of ranges.
• Does a general system for representation of set theoretic structures in relational databases already exist?
• The genome should be folded into the annotation data structure.
• Power set is not correct since that would include infinite subsets. The notation $\mathcal F(S)$ has been used to indicate the family of finite subsets of a base set $S$, sometimes called the finite power set of $S$
• A Catchy name. How about "GINGER: a Generic INterface for GEnomic Relations"?


text:
# The Psycho Underworld King The teacher death

Author：Albert Category：urban Update time：2022-12-03 14:41:01

The time went by, and the conversation ended with a simple word,

The look on the parents face was embarrassment and shock, but the mother was the only one who felt guilty about what had happened before.

\ I told you it was a bad idea\ the mother said

\Mom it is necessary for us to do it, how long had that kid been going to embarrass us, that time with the honoured guest of ours.\

\ It was not his fault, liking him was not his problem, and what you want to say has succeeded.

So may you tell me what exactly was the problem?\

The yelling of the mom was so loud that even Albert heard him from his room.

But what was his deal with not listening to his mom complaining about the way that they dealt with his family member?

But what was being planned that night will be a shock to all the members of the family.

With the anger of the boss an order was given, a rush decision, one made by anger and hatred.

\ I want that **er to be dead\

That was the order, a rush and anger who had been there for nearly 15 years.

I went to sleep, no one could know what kind of news might be brought to their ears.

The sunrise, the morning is peaceful, the birds singing, and the maids are busy making breakfast.

\ Ring, ring, ring\

\Hello.\

\ Good morning General\

\Good morning, who is with me\

\I m detective Luis Margaret\

\what made you call me in this morning detective \

\I just want to tell you that retired sergeant Mikhail Renword has died.\

\....He was fine yesterday when he visited. \

\ Im sorry to tell you, but we found him dead in the bar that exists near the sea,

The reason was a heart attack\

\ Mikhail was healthy, every month he checked his health at the military doctor, if he was sick I could know \

\ We suspect that he might be murder but we did our investigation and the doctor told us that it wasn his first, get 3 years ago but thankfully he was saved\

\ was alcohol the reason\

alcohol and drugs\

\ How much and he is consuming them. \

\ from his closest friend, its probably more than seven years.\

\did you tell his family\

\ he has no family, thats why I called you\

\Yeah, I forget that, because of the job he couldn have any relationship.

He is a military one so the funeral will be held in the military tombs. \

\ Im sorry for what happened General. \

\ thank you, detective. \

The sadness was obviously on the fathers face, sudden death of a close friend, a loyal one.

The family members who were sitting at the food table saw the fathers expression, they knew that there was something off, the mother just wanted to ask but an annoying voice interrupted her.

\ clap, clap, clap…. \

With a Slipper voice and the way the one is wearing them moved heavenly and doing it on purpose.

Yep, Alberts slippers, the question that we could ask is why? What does he want to gain by doing that childish behaviour?

\ good morning everyone\

In a good mood, words come out of his mouth.

\Whats the deal with him?\ the sister said.

The sad look turned into anger just by seeing the face of the youngest.

\ What have you said to your teacher \

\ why the sudden question \

L9hwa\..... So bad \ with coldly way those words have been said.

\ What, how, when. \ the good son of the house said.

\ was that call now just... \ the mom said.

\ Yeah, a detective called me and told me the news.

It was drugs. \

\ What do you mean drugs, the teacher wouldn be someone to do that kind of thing\

\ he was found dead in a bar and the test shows that he consumed a lot of alcohol and 3 kinds of drugs.\

drug, they went too far for just a kill What was Albert thinking on his mind?

\ Hurry eat we should go to the funeral.

You are not coming right.\

\ I feel sorry for what happened yesterday, so may I make a visit with you all? \

\ sure my son. \

\ Why?.

You hated him \

\ Will, even though he was bad with me, he still taught me many things. \

\ At least you do have some consciousness in you. \

Many people gathered, the fact that he died from overconsuming drugs and alcohol, was hidden from the soldier, so his reputation won be damaged. Will Albert has another idea, but in the last, he backs it up.

\This is enough, let him die as an honourable soldier, but drugs that were new to me, I need to ask what they did exactly.\ his thoughts

The fireworks, the soldiers salute, and previous students cry after that passed one rumour was circling around the mouth of the people in the army.

The generals youngest son was the cause. Before he died he visited their house and the accident happened.

The gossip was full on the place over there, and the face of the family from shame and embarrassment of the news that was true.

Albert didn mind that he might be the cause, because he is someone who takes responsibility for what he has done, and he should take responsibility for this one too.

He was the cause and he has the reason, even though it came out of anger, but no one can say why.

Just as he wanted to speak, he was interrupted by the angry look of his father, and brother.

The look was saying everything,

Don cause any more trouble, we had enough of you .

The way it was would make anyone doesn t feel good, or he might just burn him down and he will cause much trouble.

But Albert took control of himself and put a smile on his face.

It was clear he had something in his mind.

Whether it is good or bad, only time will tell us.

The funeral ended there, everyone went there.

At the same time in the car.

\ What did you tell him yesterday \

\ Why does it matter?

Are you telling me that I might be the cause of his death? \

\ I just want to know what have you told him \

\ nothing, I just refused\

\really\

\Drugs are the reason, even a child will know this.

Whats got me to that? \

\ Its enough, that person has died, husband, you let someone like him be our friend, God knows what exactly he has done in the previous years. \

With the words of the mother, everyone shut their mouth and went home peacefully.

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text:
algebra Q (reposting with corrected notations)

by kayhm
Tags: algebra, corrected, notations, reposting
 P: 9 Is there a way to solve for A and B which are probabilities when: AN + BL = 1 (1 - A)^(M-1) x = k (1 - B)^(M-1) y = k It s ok to solve it for the limit case as N, L, and M go to infinity.
 Mentor P: 15,957 I'm not sure what you're looking for, but $$A=1-\sqrt[M-1]{\frac{x}{k}}$$ and $$A=1-\sqrt[M-1]{\frac{y}{k}}$$...

 Related Discussions Biology, Chemistry & Other Homework 0 Brain Teasers 6 Beyond the Standard Model 0 Current Events 1


text:
# How to Solve Number Word Problems Part 2

This is the second part of the the Solving Number  Word Problems Series. In this part, we will discuss how to solve various number problems.  Note that some of these problems are not really number problems per se, but the strategy in solving them is technically the same. You could say that they are really “number problems in disguise.”

We already had three problems in the first part of this series, so let’s solve the fourth problem.

Problem 4

If $8$ is subtracted from three times a number, then the result is $34$. What is the number?

Scratch work

In the How to Solve Number Word Problems Part 1, I mentioned that sometimes, if it is hard to convert the words in the problem to equations, it is helpful to think of a particular number. For example, in this problem, the phrase is “three subtracted from three times a number.” So, if we choose a number, say for example, $5$, we want to subtract $8$ from three times $5$. In numerical expression, that is $3(5) - 8$. So, if a number is $x$, the expression is $3x - 8$. Now, this $3x - 8$ results to $42$ as stated above. Intuitively, it is saying that $3x - 8$ is equal to $42$. That’s our equation!

Solution

Let $x$ be the number.

$3x - 8$ is 8 less than 3 times the number.

Now, $3x - 8 = 34$.

$3x - 8 + 8 = 34 + 8$

$3x = 42$

$x = 14$

Check: The problem says that if $8$ is subtracted three times the number, the result is $34$. Now, three times $14$ is $42$. Now, if we subtract $8$ from $42$ the result is $34$ and we are correct.

Problem 5

Separate $60$ into two parts such that the one exceeds the other by $24$. What are the numbers?

Scratch Work

If we separate $60$ into two parts, and one part is, for example, $10$, then the other part is $60 - 10$ which is $50$. This means that if one part of $60$ is $x$, then the other part is $60 - x$.

Now it says that the larger number exceeds the smaller number by $24$. This means that

larger number – smaller number = 24.

The only part left now is to choose which is larger, $x$ or $60 - x$. It won’t really matter.

Solution

Let $60 - x$ be the larger and $x$ be the smaller number.

Then,

$(60 - x) - x = 24$

$60 - 2x = 24$.

Subtracting $60$ from both sides results to

$-2x = -36$.

Dividing both sides by $-2$, we get

$x = 18$.

So, the smaller number is $18$ and the larger number is $60 - 18 = 42$.

Check: Is the sum of the two numbers is $60$? Does $42$ exceed $18$ by $24$? If both answers are yes, then we are correct.

Problem 6

The sum of the ages of Abby, Bernice, and Cherry is $76$. Bernice is twice as old as Abby, while Cherry is 4 years older than Abby. What are the ages of the three ladies?

Scratch Work

As I have mentioned above, some problems are really number problems in disguise. This problem is one of them.

From the problem, it is easy to see that the youngest in the group is Abby. Let us say, Abby is $20$. So, Bernice is twice as old or $2(20) = 40$ years old. Then, Cherry is four years older than Abby or $20 + 4 = 24$.

So, from this analysis, if Abby is $x$ years old, then, Bernice is $2x$. Since Cherry is four years older than Abby, then here age is $x + 4$.

In the first sentence, it says that the sum of the ages of the three ladies is $76$. Therefore, we must add their ages ($x$, $2x$ and $x + 4$) and equate it to $76$. That is our equation.

Solution

Let $x$ be Abby’s age, $2x$ be Bernice’s age and $x + 4$ be Cherry’s age.

$x + 2x + (x + 4) = 76$

$4x + 4 = 76$

$4x + 4 - 4 = 76 - 4$

$4x = 72$

Dividing both sides by $4$, we have $x = 18$.

So, Abby is $18$, Bernice is $2(18)$ and Cherry is $18 + 4 = 22$ years old.

Check: Is the sum of their ages $76$?

In the next post in this series, we are going to discuss how to solve problems involving consecutive integers.

### 2 Responses

1. March 19, 2014

[…] introduction to this series, we have learned How to Solve Number Problems Mentally. In Part 1 and Part 2, we have discussed the basic number word problems, and in Part 3, we have learned how to solve word […]

2. August 20, 2015

[…] (3) How to Solve Number Problems Part 2 […]


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# Magnetic field strength from a steel rod

Suppose I have a steel bar sitting on a desk, inside the Earth's magnetic field. Suppose the bar is solid and it a cylinder, 1 meter tall and 25cm in radius. The Earth's field points uniformly through the long axis of the cylinder.

Is there some way to determine the magnetic contribution coming from the steel bar? Is there even a magnetic signature since the time derivative of the magnetic field is 0? My thinking is yes, because steel is made of iron which is ferromagnetic. Therefore there should be some induced magnetization from the main earth field, which causes the steel to produce it's own field.

In short my question is: is there some way to estimate the field strength $$B = B(z)$$ along the longitudinal axis for some location $$z$$?

• What do you mean by "the magnetic contribution"? Jan 13, 2020 at 19:06
• As in, suppose the earth field without anything else is $B = B_0 \hat{z}$. Is it possible to calculate what the magnetic field might be at z = 2m; 1m above the steel bar? Does the steel bar produce an induced magnetic field of its own since it is within the Earth's? Jan 13, 2020 at 19:07
• Depends on what kind of steel this is, and its magnetic history.
– user137289
Jan 13, 2020 at 22:32

A long thin cylinder with a large permeability would acquire an approximately constant magnetization given by $$4\pi{\bf M}=\mu{\bf B}_{earth}$$ (in Gaussian units). The B field along the axis would be the same as that of a solenoid with B=$$\mu B_{earth}$$ at its center. For your, relatively fat cylinder, it is harder to calculate.


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# How do you factor y^4-14y^3+49y^2?

Sep 18, 2016

${y}^{2} \left(y - 7\right)$

#### Explanation:

Take out a common factor of ${y}^{2}$ first.

${y}^{2} \left({y}^{2} - 14 y \textcolor{red}{+ 49}\right) \text{ } \rightarrow \textcolor{red}{+ 49}$ a clue!

You should recognize $49$ as being a perfect square!

In ${\left(x + y\right)}^{2} = {x}^{2} + 2 x y + {y}^{2} = a {x}^{2} + b x + c$ there is always a special relationship between the coefficient of the second term (b) and the third term (c)

$\left(b \div 2\right) \text{ and then squared gives } c$.

If this relationship exists in the trinomial you will know you have a square of a binomial.

Let's look closer..... (14div2)^2 = 7^2=49!!

$\therefore {y}^{2} \textcolor{red}{\left({y}^{2} - 14 y + 49\right)} = {y}^{2} \textcolor{red}{{\left(y - 7\right)}^{2}}$

If you missed that, you can try to find factors of 49 which add to 14. This will give you factors of 7 and 7 anyway:

${y}^{2} \left(y - 7\right) \left(y - 7\right)$

=${y}^{2} {\left(y - 7\right)}^{2}$


text:
Article | Open | Published:

Novel biomineralization strategy in calcareous foraminifera

Abstract

This work shows that calcareous benthic foraminifera are capable of agglutinating sedimentary particles also. In particular, we focus on Melonis barleeanus. Traditionally considered a calcareous species, our data revealed the presence of minute (~3 μm) sedimentary particles (silicate grains) inside the chamber walls of the examined shells. These particles were arranged in a definitive and systematic pattern, and the similar grain chemical characterization and size suggested a relatively high degree of selectivity in both modern and fossil specimens. Based on these results, we propose that M. barleeanus is capable of agglutinating sedimentary particles during the formation of a new chamber. The analysis of other calcareous foraminiferal species (e.g., Cassidulina neoteretis, Lobatula lobatula, Nonionella stella) did not reveal the presence of silicate grains in the shell of the specimens analyzed confirming this to be a characteristic of M. barleeanus. Considering that the isotopic and chemical composition of this species is widely used in paleoclimatic and paleoceanographic reconstructions, we used a mixing model to better constrain the influence of sedimentary particles on M. barleeanus δ18O data. Our model showed that the calcite δ18O would increase by ~0.9–2‰ if 10 wt% of feldspars (i.e., anorthite, albite, orthoclase) and quartz, respectively, were included in the analyzed shell. Based on these results, we emphasize that it is of paramount importance to consider M. barleeanus unusual biomineralization strategy during the interpretation of geological records and to investigate the presence of similar processes in other calcareous foraminiferal species.

Introduction

All foraminifera are characterized by the presence of a shell (defined as “test” in foraminifera) that encloses the organism and separates it from the surrounding environment1. Such shell can be organic, agglutinated, or made of minerals precipitated by the foraminifer itself1. Among foraminifera, species that precipitate a shell of calcium carbonate (i.e., calcite or aragonite; CaCO3) are of particular importance because of their roles in the global carbon cycle and in paleoceanographic and paleoclimatic reconstructions2,3,4,5,6,7. Even so, the mechanisms behind the foraminiferal shell precipitation process (biomineralization) are not fully understood, yet8,9. In fact, there are many biological controls (overall defined as “vital effects”)10 that contribute to the shell precipitation in foraminifera, like the development of a delimited space where formation of a new chamber occurs11,12, production of organic sheets12,13, seawater endocytosis14,15, the presence of ion transporters9,16, and mitochondrial activity17. Considering that calcifying foraminifera are characterized by a variety of ecological and physiological differences, including the precipitation of a shell that can be calcitic or aragonitic, it is very likely that different species utilize diverse biomineralization processes to build their shell15, as suggested by the range of Mg concentrations measured among foraminiferal species18.

Calcareous foraminifera are a significant component of the global carbon cycle. For example, planktonic foraminiferal shells contribute to ~32–80% (0.36–0.88 Gt CaCO3 yr−1) of the calcite budget in deep oceanic settings2, whereas benthic foraminifera represent ~5% (0.03 Gt CaCO3 yr−1) of the accumulated CaCO3 in global reef sediments19. Even if biomineralization represents a sink for carbon, it is also a potential source of CO2 to the ocean-atmosphere system20, according to the simplified reaction:

$${{\rm{Ca}}}^{2+}+2{{\rm{HCO}}}_{3}^{-}={{\rm{CaCO}}}_{3}+{{\rm{CO}}}_{2}+{{\rm{H}}}_{2}{\rm{O}}$$

In calcareous foraminifera, the growth rate is influenced by the pH of the surrounding waters16. Therefore, the current increase in atmospheric CO2 concentration, and the consequent ocean acidification, is expected to impact foraminiferal biomineralization in a way that it is difficult to predict21. In addition, in seawater CaCO3 precipitation and dissolution are influenced by the saturation state of CaCO3 (Ω), which is function of [Ca2+], [CO32−], and the CaCO3 stoichiometric solubility product at in situ temperature, pressure, and salinity. Thus, also changes in Ω can impact foraminiferal shell precipitation22. Finally, several studies demonstrated the influence of additional environmental parameters, like temperature, salinity, food, pollution among others, on foraminiferal biomineralization processes and shell morphology23,24,25.

Considering the contribution of calcareous foraminifera to the global carbon cycle and their importance as geological archives8, it is fundamental to explore the possibly species-specific biomineralization processes in these organisms. Vital effects, ecological preferences (e.g., habitat), and environmental parameters (e.g., temperature, pH) can all influence the chemical and isotopic composition of foraminiferal shells, causing some deviations from the expected isotopic and chemical equilibrium fractionations as defined by laboratory experiments involving the inorganic precipitation of CaCO38,9,18,26. Interestingly, previous studies reported the presence of sedimentary grains within the calcareous shell of some benthic and planktonic foraminifera27,28,29. This aspect has to be considered and further investigated, at least in those species used to reconstruct changes in ocean circulation and climate through geological time. In fact, data collected using calcareous foraminiferal shells containing exogenous grains might be biased by the isotopic and chemical composition of such grains if their presence is unrecognized or unknown. This risk was already demonstrated for planktonic foraminifera, where the presence of silicate grains contaminated the Li isotope measurement conducted using an ion probe29.

In this study, we focus on Melonis barleeanus, a paleoceanographically-relevant calcareous benthic foraminiferal species7. In particular, we present a unique and vast microscopy and spectroscopy dataset collected analysing modern and fossil samples from the Arctic Ocean and Mediterranean Sea. Our data show that M. barleeanus, a calcareous species, is also capable of agglutinating sedimentary particles within its calcareous shell.

Results

Scanning electron microscopy (SEM) analysis of benthic foraminiferal species

We analysed 51 specimens from nine samples collected at different locations and time intervals (Tables 1 and 2; see Methods). Of the specimens examined, 61% showed the presence of minute sedimentary particles inside the chamber wall of the shell (Table 2; Figs 1 and 2). All the specimens with this feature (31 out of 51) belong to Melonis barleeanus (Williamson, 1858)30 (Figs 1a,b and 2a,b). None of the other species analysed (e.g., Cassidulina neoteretis, Lobatula lobatula, Nonionella stella) revealed a similar shell structure (Table 2).

Regardless of the sample origin (Arctic Ocean vs. Mediterranean Sea – Sicily) or age (modern vs. fossil), our data revealed that M. barleeanus was characterized by the presence of sedimentary particles within its calcite shell, although this was not a universal feature of this species. In fact, 24% of the M. barleeanus considered in this study did not have any grain embedded in their shell (Fig. 2b). When present, the spatial distribution of the sedimentary particles appeared to be well-organized and not random. More specifically, we found the grains to be arranged linearly, very often within the wall between two chambers (Figs 1b,c and 2a; Supplementary Table S1), in all the specimens analysed. These stretches of particles were between a few μm and several tens of μm long (Supplementary Table S2). The calcite layer on both sides of the grain stretches was found to be of variable thickness (Supplementary Table S2), even if this could be a consequence of the sample cross-section preparation. Some of the shell examined (19%) was characterized also by the presence of several particles organized as a group of a few tens of μm across. This group of grains was usually located at the base of one or more chambers (Fig. 2c; Supplementary Tables S1 and S2). In general, the silicate grains were disposed very close to each other regardless of their spatial organization (linear stretch vs. group; Figs 1b,c and 2a,c). Less frequently, grains were separated by a gap of ~1 to 10 μm (Supplementary Table S2). We noted that in a few cases some grains were arranged close to pores, which were generally visible only on the exterior of the shell and rarely within the chamber wall (Supplementary Table S2), although this might be the result of the type of section prepared (cross-section). Laminated calcite (secondary calcite)8 was identified on the edge of the shell of a few specimens (Supplementary Table S2).

In order to test for the possibility that the silicate grains observed in many of the M. barleeanus specimens examined could derive from the protocol used to prepare the foraminiferal samples prior analysis (i.e., polishing with Al2O3 powder and colloidal silica), several M. barleeanus specimens were analysed after the shell was mechanically fractured, but not embedded in epoxy and polished. Also in this case, the presence of silicate grains was recognized, confirming that the results of this study were not biased by the sample preparation protocol used.

Energy-dispersive X-ray spectroscopy (EDS) and electron backscattered diffraction (EBSD) analyses of silicate grains

Three hundred grains were analysed for size (see Methods). A high degree of variability was noted in the size of the grain incorporated in the shells, which ranged from 0.8 μm to 10.2 μm (average = 2.8 μm, SD = 1.4 μm) (Supplementary Table S3). Based on the visible portion of the grains, the layer containing sedimentary particles was at least 1–5 μm thick (Figs 1c and 2d). In general, particles were organized as a linear stretch and/or group regardless of size (Supplementary Tables S1–S3). No significant relationship was found between the grain size and the foraminiferal size neither in modern nor in fossil samples, independently from their geographic origin. Of the grains analysed for size, we examined 273 of them through energy-dispersive X-ray spectroscopy (EDS) (see Methods; Supplementary Table S3). Based on the semi-quantitative EDS chemical characterization (see Methods), we classified the particles analysed as quartz-like (grains composed of O and Si; Figs. 1d–g), which represented 49% of the particles examined (Supplementary Table S3), and feldspar-like (grains composed of O, Si, and Al and/or Ca and/or Na; Figs. 1d–g), which represented 29% of the particles analysed (Supplementary Table S3). This classification was confirmed by electron backscattered diffraction (EBSD) of selected grains (see Methods; Fig. 1h; Supplementary Fig. S1). Finally, 22% of the examined particles was not classified at all because the low spatial resolution of the EDS maps prevented unambiguous characterization of the grain chemical makeup.

Foraminifera from the Mediterranean Sea were mostly characterized by quartz-like particles compared to feldspar-like ones (55% vs. 13%, respectively; number of grains analysed = 53, of which 32% could not be unequivocally classified) (Supplementary Table S3). This finding applied to the samples from the Arctic Ocean, as well even if the difference in the grain distribution was smaller (47% quartz-like particles vs. 33% feldspar-like ones; number of grains analysed = 220, of which 20% could not be unequivocally classified) (Supplementary Table S3). It is possible that this diversity in grain distribution is a consequence of the different number of M. barleeanus specimens from the Mediterranean Sea vs. Arctic Ocean available for analysis (Table 2).

Discussion

Melonis barleeanus is an infaunal species widely used in paleoceanographic studies7,31,32. Traditionally considered a calcareous species33, our data indicate that M. barleeanus is also characterized by the presence of silicate grains within its shell. Even if, to our knowledge, one extant foraminiferal order is capable of secreting opaline silica (i.e., Silicoloculinida)34, we do not think that the silicate grains found within many of the M. barleeanus examined were precipitated by the foraminifer itself. In fact, the particles observed vary in their chemical makeup, size, and shape, thus making it highly unlikely that a single foraminiferal species could have been able to precipitate such a variety of grains. Instead, we think that it is more likely that the grains originated from the specimens’ surroundings and were agglutinated by the organism. Analysis of the sediment fraction <63 μm of a sample collected close to the foraminiferal sampling sites in the Arctic Ocean revealed the presence of quartz, feldspars, clay minerals, and mica, supporting this hypothesis. This hypothesis was also supported by the finding of a diatom frustule within the shell of one of the specimens investigated (Fig. 2e).

The systematic spatial arrangement of the grains within the shell of both modern and fossil foraminifera (Figs 1b,c and 2a,c) indicates that the presence of sedimentary particles in M. barleeanus is not a simple case of contamination or diagenesis. The presence of sedimentary particles within the shell of rotaliid species was already reported in a few benthic foraminiferal genera (i.e., Cibicides and Stomatorbina)27,28. In these foraminifera, grains were arranged as an almost continuous layer within the septal wall (Cibicides)27 or were contained within the aragonite material of the inner primary wall (Stomatorbina)28, a spatial distribution similar to the one we observed in M. barleeanus. Sedimentary particles were also reported for planktonic foraminifera (e.g., Globigerinoides)29. Even if a clear explanation for the presence of agglutinated grains in benthic foraminifera was not provided, it was proposed that the particles were not secreted by the foraminifer and were not contaminants35, a suggestion that agrees with our findings. In planktonic foraminifera, the presence of alumino-silicate grains within the shells analysed was explained as the consequence of calcite precipitation from seawater vacuoles containing small silicate grains29.

In foraminifera, seawater vacuolization8,15,29 is one of the processes involved in the formation of a new chamber. Even if this process was invoked to explain the presence of minute particles within the shell of planktonic species29, we do not think that seawater vacuolization is a satisfactory explanation of our results. In fact, our data showed that not all the M. barleeanus analysed were characterized by the presence of sedimentary particles. In addition, the investigation of additional specimens belonging to both epifaunal (e.g., Lobatula lobatula) and shallow infaunal (e.g., Cassidulina neoteretis) species did not reveal the presence of silicate grains within the shells examined (Table 2). If seawater vacuoles containing small sedimentary particles were responsible for our observations, then we would have expected silicate grains in all the specimens analysed, or at least in all the infaunal ones. Experiments involving Ammonia tepida demonstrated that vacuolized seawater was used as a source of Ca2+ and inorganic carbon involved in the calcification process of this species, but that seawater was not directly released at the extracellular calcification site15. Although it is uncertain if and to what extent the mineralization processes observed in one foraminiferal species can be applied to another one15, we think that seawater vacuoles might not be directly released at the calcification site in M. barleeanus, as well. In this context, seawater endocytosis cannot explain the presence (or absence) of sedimentary particle within the shell of this species. Additional studies, possibly involving culture experiments, are necessary to better constrain the role of seawater vacuoles during the chamber formation in M. barleeanus.

The presence of silicate grains within the shell of M. barleeanus might be explained by the accidental incorporation of foreign particles (e.g., detritus, sediment, algal cells, sponge spicules) forming a secondary shell (i.e., feeding cyst) surrounding the foraminifer’s original shell36,37. Laboratory observations showed that M. barleeanus was mostly free of a secondary shell when in the sediment37. However, one of the specimens analysed revealed the presence of a diatom among the particles incorporated (Fig. 2e), supporting the hypothesis that this species might incorporate some grains/detritus forming the secondary shell during the formation of a new chamber. Unfortunately, the data available do not allow us to draw a firm conclusion about this hypothesis. As an alternative, incorporation of sedimentary particles might occur also during the formation of a “delimited space” prior chamber formation8. In this case, it is possible that silicate grains surrounding the calcifying foraminifer might interact with the organic layer that defines the shape of the new chamber and that promotes crystal nucleation. According to this scenario, sedimentary particle simply adhere to the organic template and are incorporated during precipitation of the chamber wall. Even if this is a reasonable explanation of our data, we think that it is still an unsatisfactory one. In fact, the formation of a space that isolates the foraminifer from the surrounding environment is a common step during biomineralization process in perforate foraminifera8. Even so, we do not observe the presence of silicate grains in all the M. barleeanus specimens analysed and in the other perforate foraminiferal species included in this study (Table 2).

Our data showed that M. barleeanus preferred particles with a size comprised between 0.8 and 10.2 μm and with a quartz-like mineralogy (Supplementary Table S3). It is possible that the mineralogy of the sedimentary particles incorporated by this foraminiferal species reflect the diverse sediment composition at the Mediterranean Sea vs. Arctic Ocean sampling sites. However, considering that in the Arctic Ocean sediment analysed as part of this study the quartz content varied between 30 and 40% (vs. 47% as measured in the M. barleeanus specimens from the Arctic Ocean), we think that this species has a distinct preference for quartz-like sedimentary particles compared to feldspar-like ones (Supplementary Table S3). At this stage, we cannot draw a firm conclusion about the reason(s) of this preference, but we note that selectivity towards a particular mineralogy was demonstrated already for several species of agglutinated foraminifera38,39 and it was proposed for the miliolid species Rudoloculina hooperi40, as well. Based on our results and noting that the silicate grains are mostly associated with M. barleeanus primary calcite8, we propose that this species agglutinates sedimentary particles prior the formation of a new chamber.

If agglutination prior calcite precipitation is a strategy to promote calcite precipitation and/or to increase the test strength is unclear at this stage. Crystal nucleation on a pre-existing surface (heterogeneous nucleation) is energetically more advantageous compared to homogeneous crystal nucleation41; however, in foraminifera, the organic matrix (or primary organic sheet) represents the nucleation site for the first CaCO3 crystals8. Based on the compatibility of the calcite and quartz crystal lattices, it is unclear if precipitation of calcite on a quartz surface is possible42 or not43, but laboratory experiments showed that the presence of quartz seeds induced calcium carbonate nucleation in the bulk solution in unstable supersaturated solutions (domain of spontaneous precipitation)42. Considering the location of the sedimentary particles within M. barleeanus (mostly within the chamber wall), we think that it is more likely that silicate grains were incorporated to enhance the shell mechanical strength. Increased mechanical strength through agglutination was already hypothesized for some agglutinated foraminifera44.

Many conditions can affect shell precipitation in foraminifera, like pH, temperature, salinity, food, pollution, and environmental energy among others21,22,23,24,25. We note that nearby Arctic sites CAGE 15-2 880B and CAGE 15-2 893B (~900 m and 1200 m water depth, respectively), hereafter referred to as Core 880B MC and Core 893B MC, the temperature was 0.69 °C and 0.77 °C, salinity was 34.89‰ and 34.86‰, and pH ranged from 8.021 to 8.257. According to these data, we do not think that environmental conditions at the sampling sites represented an impediment to foraminiferal biomineralization.

The genes involved in the foraminiferal biomineralization processes are still unknown. Therefore, we can only speculate that the (facultative) agglutinated strategy adopted by some M. barleeanus specimens might be genetically controlled. The analysis of the complete small subunit ribosomal RNA gene (SSU rDNA) demonstrated that rotaliids and textulariids (Trochammina sp. and Eggerelloides scabrum) were closely related45. Therefore, it might be possible that some of the genes involved in the shell formation of agglutinated (textulariid) species might still be present in the genome of rotaliid species and that the expression of these genes might be triggered by conditions that remain uncertain at the moment. Interestingly, it was proposed that environmental conditions could have influenced the biomineralization pathway of the genus Miliammina46. A genetically controlled agglutinating biomineralization strategy can definitely explain why M. barleeanus, but also Cibicides floridanus27 and Stomatorbina28, are characterized by the presence of agglutinated particles within their shell.

Foraminifera are an important component of the global carbon cycle because of their role in the oceanic food webs47 and calcium carbonate precipitation2,19. Therefore, the effect that ocean acidification will have on this group of organisms is of a great interest. Published studies involving culture experiments and the investigation of natural samples21 showed that different foraminiferal species respond differently (from decalcification to higher calcification rates)21 to decreasing ocean pH values. In this context, the biomineralization strategy adopted by M. barleeanus provides a new insight regarding the strategies adopted by these unicellular organisms to build their shells. Published studies identified the presence of sedimentary particles within the shell of other calcareous foraminiferal species27,28,29, suggesting that agglutination prior (or during) calcification might not be a characteristic of M. barleeanus specimens only, even if it is possible that the presence of sedimentary particles within the shell of different calcareous foraminifera is a consequence of species-specific calcification pathways (see also29).

M. barleeanus is an important benthic species that is often used in paleoclimatic and paleoceanographic reconstructions7,31,32. In the light of the results of this study, we think that it is of fundamental importance to consider the M. barleeanus biomineralization strategy during the interpretation of geological records. Contamination of isotopic (or chemical) measurements due to the presence of silicate grains is a likely possibility, in particular when the presence of exogenous grains is not identified prior in-situ analysis (e.g., electron probe, ion probe, laser ablation). This risk was already demonstrated for Li isotope measurements conducted on planktonic foraminifera with an ion probe29. In this study, we used a mixing model to investigate the influence of sedimentary particles on δ18O data collected using M. barleeanus “contaminated” by the presence of silicate grains (Supplementary Fig. S2). Our calculations showed that the δ18O of a hypothetical pure calcite end-member would increase by ~0.9–2‰ if 10 wt% of feldspars (i.e., anorthite, albite, orthoclase) and quartz, respectively, were included in the analyzed calcite (Supplementary Fig. S2). The analytical (vs. theoretical) quantification of the influence of sedimentary particles on the isotopic data collected using “contaminated” M. barleeanus is going to be the focus of a follow-up study.

Future microscopy and spectroscopy studies using other benthic and planktonic foraminiferal species will be critical to gain a better insight about how frequently sedimentary particles can be found within the shell of paleoceanographically relevant foraminiferal species. In addition, culture-based experiments and molecular studies will help to better understand if the presence of silicate grains within the shell of benthic and planktonic foraminifera is a genetically-driven mechanism and what are the conditions that can trigger such unusual biomineralization strategy.

Methods

Foraminiferal sample preparation and data collection

Samples locations are listed in Table 1. Modern samples (Table 2) were preserved in a solution of deionized water and rose Bengal and stored at 4 °C. Samples were not sieved and the picking was performed directly on the wet sediment. Fossil samples (Table 2) were oven-dried first and then wet sieved at 63 μm. The residual fraction was oven-dried again prior foraminiferal picking. None of the foraminiferal specimens analysed for this study showed signs of dissolution.

Modern (recently dead and rose Bengal stained) and fossil foraminifera (Table 2) were treated following the same published protocol48. First, foraminifera were ultrasonically cleaned for a few seconds, so to remove any residual clays prior analysis. Organic matter was then removed as follows: (1) 2 rinses with ultrapure H2O; (2) 3 oxidative steps with hot buffered hydrogen peroxide (1:1 0.1 N extra pure NaOH, Acros Organics, and 30% low trace metals H2O2, Veritas) held at 70 °C for 30 minutes each step; (3) 5 rinses with ultrapure H2O. Finally, samples were leached 2 times with 0.001 N trace metal grade HNO3 (Fisher Scientific) followed by 2 final rinses in ultrapure H2O48. At the end of the procedure, several foraminifera showed few rose Bengal stained spots. Because of this, an additional oxidative step was performed, followed by 5 rinses with ultrapure H2O.

Samples were mounted in epoxy (EpoxyCure®, Buehler), and let dry overnight at room temperature. The epoxy mount was polished using 800 and 1200 grit silicon carbide papers (Buehler) and 1 μm Al2O3 powder (Mark V Laboratories) to expose the internal structure of each foraminiferal shell. In addition, several M. barleeanus specimens were mechanically broken on the longitudinal plane. Without any prior treatment, shell fragments were first inspected with a scanning electron microscope (SEM) Hitachi Tabletop Microscope TM-3000 (The Arctic University of Norway in Tromsø, Tromsø, Norway). Then, the fragments were carbon-coated and analysed with a SEM Zeiss Merlin VP Compact (The Arctic University of Norway in Tromsø, Tromsø, Norway).

For preparation of sample PC06 5 34–35 cm see49.

Scanning electron microscopy and energy-dispersive X-ray spectroscopy (EDS) were performed at The Arctic University of Norway in Tromsø (Tromsø, Norway) using an SEM Hitachi Tabletop Microscope TM-3000 equipped with a Bruker Quantax 70 EDS Detector. Measurements of several parameters (e.g., grain size, grain stretch length, thickness of calcite layer on both sides of the particle stretch; Supplementary Tables S2 and S3) were conducted analysing SEM pictures with the software ImageJ50. Prior measurement of the selected parameter(s), a scale was set using the scale bar associated with every picture analysed and the possibility to distinguish grain boundary was carefully evaluated. Reported grain size refers to the particle maximum diameter (Supplementary Table S3).

EDS chemical maps were generated for every M. barleeanus specimen characterized by the presence of sedimentary particles. These maps were visually inspected for qualitative analyses of element distribution within the studied material and phase identification. To distinguish the foraminiferal calcite from the sedimentary particles, we focused on the presence of aluminium (Al), calcium (Ca), oxygen (O), silicon (Si), and sodium (Na) in the material analysed. Data are reported in Supplementary Table S3 and were used in the calculations regarding grain distribution. Quartz-like grains were distinguished based on the presence of O and Si in the particles. Feldspar-like grains were identified based on the presence of O, Si, and Al and/or Ca and/or Na. Selected M. barleeanus specimens from Core 880B MC and Core 893B MC were also analysed with a SEM Zeiss Merlin VP Compact equipped with an EDS x-max 80 system by Oxford instruments, combined with the analytical software AZtec (The Arctic University of Norway in Tromsø, Tromsø, Norway). These samples were gold-coated prior analysis. These EDS data for chemical characterization are presented as point analyses and as a compositional map in Fig. 1. A list of the EDS conditions used in this study is given in Supplementary Table S4.

Phase identification via point analysis was conducted by electron backscattered diffraction (EBSD) using the SEM Zeiss Merlin VP Compact (The Arctic University of Norway in Tromsø, Tromsø, Norway) equipped with a NordlysNano EBSD detector from Oxford instruments. The AZtec software was used for data acquisition and processing into an EBSD point map. The electron image used for the EBSD point map is a layered image from backscatter and forescatter imaging. For EBSD analysis, the manually polished epoxy mount was chemically polished with a colloidal silica solution (OP-U, Struers) as the detector takes its signal from the uppermost 50 nm of the sample surface. The sample was tilted to an angle of 70°. A list including the EBSD conditions used in this study and the detected phases is given in the Supplementary Table S4.

Sediment sample analysis

A sediment sample from the Arctic Ocean was analysed to characterize the average mineralogical composition of the sediment in the area where Cores 880B MC and 893B MC were collected. In order to do so, the sediment fraction <63 μm was dried, mounted on carbon tape, and carbon-coated. EDS analysis of the sample were conducted using a SEM Zeiss Merlin VP Compact equipped with an EDS x-max 80 system by Oxford instruments, combined with the analytical software AZtec (The Arctic University of Norway in Tromsø, Tromsø, Norway).

Environmental conditions at Core 880B MC and Core 893B MC

To further investigate the possibility of a relationship between the presence of sedimentary particles within the shell of M. barleeanus and the environment in which the foraminifera calcified their shell, we collected several environmental parameters in proximity of Core 880B MC and Core 893B MC. These two sites were chosen because of the availability of environmental data and “living” (rose Bengal stained) M. barleeanus specimens for analysis (Table 2).

In proximity of Core 880B MC and Core 893B MC, temperature and salinity were measured with a CTD (Conductivity Temperature Depth) SBE 9 plus sensor, whereas pH was measured with a SBE25plus 1049. Close to the seafloor, temperature was 0.69 °C and 0.77 °C and salinity was 34.89‰ and 34.86‰ for locations near sites Core 880B MC and Core 893B MC, respectively. pH data were available from nearby stations and ranged from 8.021 to 8.257.

All data generated or analysed during this study are included in this published article (and its Supplementary Information files).

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Acknowledgements

The authors would like to acknowledge the captains and crewmembers onboard the R/V Helmer Hanssen for coring assistance and Dr. Daniel J. Fornari (WHOI – Woods Hole Oceanographic Institution) for operating the MISO TowCam deep-sea imaging system. The authors also thank Dr. Antonio Caruso (University of Palermo) for providing Melonis barleeanus samples from the Mediterranean Sea, Katarzyna Melaniuk and Andrea Schneider (CAGE – Centre of Arctic Gas Hydrate, Environment and Climate) for their help with the foraminiferal picking, and Dr. Rachael James (NOC - National Oceanography Centre Southampton) for providing core PC06. C.B. is indebted to Dr. Dustin Trail (University of Rochester) for allowing the use of his laboratory during sample preparation. The authors thank Dr. Dustin Trail and Dr. Barun Sen Gupta for providing useful comments on an early version of the manuscript. The authors are grateful to Dr. Sam Bowser (Wadsworth Center), Dr. Jim de Yoreo (PNNL - Pacific Northwest National Laboratory), Dr. Jonathan Erez (Hebrew University of Jerusalem), Dr. Frans Jorissen (University of Angers), Dr. Hiroshi Kitazato (Tokyo University of Marine Science and Technology), Dr. Aivo Lepland (NGU - Norwegian Geological Survey), and Dr. Claire Rollion-Bard (IPGP - Institute de Physique du Globe de Paris) for very useful discussions. The authors thank Dr. Lennart de Nooijer (NIOZ – Royal Netherlands Institute for Sea Research) and one anonymous reviewer for their constructive comments, which greatly improved the paper. This research was supported by the Research Council of Norway through its Centre of Excellence funding scheme for CAGE (project number 223259) and by the NORCRUST project (grant number 255150) (G.P.).

Author information

Affiliations

1. Department of Earth and Environmental Sciences, University of Rochester, Rochester, NY, 14627, USA

• C. Borrelli

• G. Panieri
3. Department of Geosciences, UiT The Arctic University of Norway in Tromsø, N-9037, Tromsø, Norway

• T. M. Dahl
•  & K. Neufeld

Contributions

C.B. and G.P. conceived the project. G.P. supported the overall analyses, C.B. prepared the samples prior analysis, and T.M.D. and K.N. helped in the collection of SEM, EDS, and EBSD data. C.B. wrote the manuscript and interpreted the results in collaboration with G.P. All authors reviewed the manuscript.

Competing Interests

The authors declare no competing interests.

Corresponding author

Correspondence to C. Borrelli.


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## NAME

```etex, einitex, evirtex - extended TeX

```

## SYNOPSIS

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## DESCRIPTION

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e-TeX is the first concrete result of an international research & development project, the NTS Project, which was established under the aegis of DANTE e.V. during 1992. The aims of the project are to perpetuate and develop the spirit and philosophy of TeX, whilst respecting Knuth's wish that TeX should remain frozen.

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The einitex and evirtex commands are e-TeX's analogues to the initex and virtex commands. In this installation, they are symlinks to the etex executable.

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## ENVIRONMENT

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## BUGS

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text:
# Leverage and Tracking difference

I am a little confused. I have calculated the tracking difference of an Index and a n ETF using the return getting 0,4% tracking difference per year. I have then leveraged both, the Index and the ETF to a lever of 2 getting 0.63% tracking difference per year. I have then done some testing with hypothecical value and got 10% unleveraged and 20% levaraged with an lever of 2. So, $$leveraged\ tracking\ difference = lever*(unleveraged\ tracking\ difference)$$ in the hypothetical case. In the real case, I am not getting an equality.

However the real case used a 5-year period and I calculated the annual return using the geometric mean. In the hypothetical case, I only simulated one year of return.

My question is. Should the tracking difference always be equal to my formula when leverage? if that is the case, I might have done some mistake in the real case. Else, it differs when a 5-period is used along with the geomtric mean.


text:
# Packing Plane Perfect Matchings into a Point Set

Abstract : Given a set $P$ of $n$ points in the plane, where $n$ is even, we consider the following question: How many plane perfect matchings can be packed into $P$? For points in general position we prove the lower bound of ⌊log2$n$⌋$-1$. For some special configurations of point sets, we give the exact answer. We also consider some restricted variants of this problem.
Keywords :
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.119-142

Littérature citée [40 références]

https://hal.inria.fr/hal-01349047
Contributeur : Coordination Episciences Iam <>
Soumis le : mardi 26 juillet 2016 - 17:40:28
Dernière modification le : jeudi 7 septembre 2017 - 01:03:44

### Fichier

2758-9775-2-PB.pdf
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### Identifiants

• HAL Id : hal-01349047, version 1

### Citation

Ahmad Biniaz, Prosenjit Bose, Anil Maheshwari, Michiel Smid. Packing Plane Perfect Matchings into a Point Set. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.119-142. 〈hal-01349047〉

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