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# constant function questions

x or t). A function is \"increasing\" when the y-value increases as the x-value increases, like this:It is easy to see that y=f(x) tends to go up as it goes along. Return the value of the constant indicated by name. Featured on … A constant function is where the output variable (e.g. Constant functions. No matter what you plug into X, (which there is no place to plug in), it always return the same value, hence a CONSTANT function. As indicated by the name, this function will return the value of the constant. Quadratic functions, on the other hand, have the form y = ax 2 + bx + c or f (x) = ax 2 + bx + c. Graphically, they’re represented by a parabola, a shape that resembles the basic rollercoaster hump. All material given in this website is a property of physicscatalyst.com and is for your personal and non-commercial use only, Vertical line test for functions and relation, Trigonometry Formulas for class 11 (PDF download), Relations and Functions Class 11 Worksheet, NCERT Solutions Relation and Functions class 11 Exercise 2.1, NCERT Solutions Relation and Functions class 11 Exercise 2.2, NCERT Solutions Relation and Functions class 11 Exercise 2.3. Question: Question 6. Now that we are starting to feel more comfortable with what a constant function is, let's look back at our bargain bin example, specifically, the photo of the books all costing $3.99. Anonymous. Finally, write the function for the total cost of the taxi ride by adding the two functions. Constant function B. The domain of a polynomial f… Thanks for visiting our website. F. FreaKariDunk. 4sin(x)/(x) x < 0 b - 2x x >= 0 (greater than or equal to) To find the constant, you would set the two functions to equal each other. what is the constant of the function? Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus. Correct answer to the question Consider the quadratic function f(x)=8x2−7x+6. Constant, a number, value, or object that has a fixed magnitude, physically or abstractly, as a part of a specific operation or discussion.In mathematics the term refers to a quantity (often represented by a symbol—e.g., π, the ratio of a circle’s circumference to its diameter) that does not change in a certain discussion or operation, or to a variable that can assume only one value. I've searched the web (like this topic), but cannot find a good way to handle this.$\endgroup$– robert bristow-johnson May 4 '17 at 3:36. The graph shows a streight line. Problem with Piecewise function. Answer questions on the derivatives of constant functions. Stack Overflow Public questions & answers; Stack Overflow for Teams Where developers & technologists share private knowledge with coworkers; Jobs Programming & related technical career opportunities; Talent Recruit tech talent & build your employer brand; Advertising Reach developers & technologists worldwide; About the company; Loading… Log in Sign up; current community. Two functions having same number of argument, order and type of argument can be overloaded if both functions do not have any default argument. Answer. They will make you ♥ Physics. The definition can be derived from the definition of a polynomial equation. The function y=c has 2 variables x and у and 1 constant c. (In this form of the function, we do not see x, but it is there.). Alright, so I have AP summer work for calculus which I have no clue how to do because I was given no information on how to solve them from the teacher. A. A polynomial function is a function that can be expressed in the form of a polynomial. Kelime ve terimleri çevir ve farklı aksanlarda sesli dinleme. Question: Exercise 1.1.20 (Piecewise Constant Functions). A constant function is a linear function for which the range does not change no matter which member of the domain is used. case in point, if I informed you that the fee became a continuing function. How would you do ? Constant time. Recommended for you The derivative of y is the identically zero function. Favorite Answer. 4. A constant function is a special type of linear function that follows the form f(x) = b 'b' is the y-intercept of the line and is just a constant; A constant function is a linear function whose slope is 0; No matter what value of 'x' you choose, the value of the function will always be the same it is stored in a variable or returned by a function. x). Il y a 4 années. 9 years ago. If so, how? if f is differentiable at x=-2, what is the value of c + d? 75% of a contractor’s jobs involve plumbing work. You can also use the function constant() to read a constant's value if you wish to obtain the constant's name dynamically. So here's the problem: Use f(x)=x^3-6x^2+p, where p is an arbitrary constant to answer the following questions. Of the jobs that involve plumbing, 90% of the jobs also involves electrical work. Affiche un message dans une boîte de dialogue, attend que l’utilisateur clique sur un bouton et renvoie un Entier indiquant sur quel bouton l’utilisateur a cliqué. (a) find curl −⃗ +⃗ and show that it can be written in the form curl ⃗ = - the answers to estudyassistant.com The graph of this function will be as follows: In general, a constant function will be of the form $f\left( x \right) = k$ Mathematics, 09.03.2020 13:49, cpalabamagirl2595. Can a constant method be overridden in the derived class? f ( x 1 ) = f ( x 2 ) for any x 1 and x 2 in the domain.. 0. Go through C Theory Notes on Basics before studying questions. The result is c 2 (d)=0.70(d-1). y ( x ) = − 2. I.e. y ′ ( x ) = ( x ↦ − 2 ) ′ = 0. B) What Is The Derivative Of Arcsin(x) + Arccos(x)? $f\left( x \right) = \left\{ \begin{array}{l}1, & x \in \left[ { - 1,2}\right]\\2, & x \in \left( {2,3} \right]\end{array} \right.$. Forums. 0 0. There is no variable in the definition (on the right side). If one firm can transform one discrete unit of input into one unit of output, but the number of firms is unlimited, each firm has extreme decreasing returns to scale, but the aggregate technology has constant returns to scale. This is useful when you want to retrieve value of a constant, but you do not know its name, i.e. The constant function is c 1 (d)=4.25 since the cost of the first mile is$4.25. TransformedRegion with piecewise function. 4. İngilizce Türkçe online sözlük Tureng. constant() is useful if you need to retrieve the value of a constant, but do not know its name. Created Date: 23) 84% of a contractor’s jobs involves electrical work. Another way of thinking about such "const function" is by viewing a class function as a normal function taking an implicit this pointer. The function Is a piece-wise function. A: The given curve is rt=t2i+2tj-423t32k. it is invariant around the indepenent variabl(i.e. It is stored in a variable or returned by a function. {\displaystyle y' (x)= (x\mapsto - {\sqrt {2}})'=0} . For the linear part, subtract 1 from d to exclude the first mile, and then multiply the result by 0.70 since it costs $0.70 per mile. This is useful when you want to retrieve value of a constant, but you do not know its name, i.e. that's one of the annoying things about SE. Now I'm not asking for anyone to solve this just maybe a website or some sort of explanation on where to actually begin. You can modify this example to get functions that get closer and closer to a constant function as$\epsilon$goes to zero, while the correlation between X and its image is any number from the interval [-1,1]. Let [a, B] Be An In- Terval. Join Yahoo Answers and get 100 points today. Topics. Ask Question + 100. Displays a message in a dialog box, waits for the user to click a button, and returns an Integer indicating which button the user clicked. With a constant function, for any two points in the interval, a change in x results in a zero change in f ( x) . ... Piecewise-constant function with infinitely many pieces. The idea of const functions is not to allow them to modify the object on which they are called. {\displaystyle y (x)=- {\sqrt {2}}} . - e-eduanswers.com constant() function. a constant function is a function whose values do not vary and thus are constant. A letter such as f, g or h is often used to stand for a function.The Function which squares a number and adds on a 3, can be written as f(x) = x 2 + 5.The same notion may also be used to show how a function affects particular values. also, (g o k)(x)=2^2-6-6=-8 is a constant function because k takes all x to 2 and g takes 2 to -8. Thread starter FreaKariDunk; Start date Nov 19, 2012; Tags constant functions; Home. • Answer all questions. I just need to export the token, which is a string; but i'm getting it from an async function. The compiler does not enforce yet that a view method is not modifying state. so that f(z1) = f(z2) and, therefore, f is constant in D(w, r).$\endgroup$– Michael Greinecker Nov 23 at 17:43 let f be the function defined below where c and d are constants? Constant is just a value, a fixed value that doesn't change. Before working with a linear function, we replace c with an actual number. Definition of constant function in the Definitions.net dictionary. This paper covers C language invention history, standards and usages. Constant is just a value, a fixed value that doesn't change. A polynomial is generally represented as P(x). The following practice questions deal with both linear and quadratic functions. A constant function is a linear function for which the range does not change no matter which member of the domain is used. Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. Solution:The function has been defined piece wise, but it is constant in both parts(separately). Mathematically speaking, a constant function is a function that has the same output value no matter what your input value is. Find the constant "b" that would make this function continuous. A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. A line with a slope of zero is horizontal as in (c). Constant Function A function of the form y = constant or f(x) = constant, such as y = -2. However you need to understand that$\tau_1$and$\tau_2$are first order time constants but$\tau$is a second order time constant. 08/14/2019; 4 minutes de lecture; o; Dans cet article. Constant Function Constant Function is defined as the real valued function$f : R \rightarrow R$, y = f(x) = c for each$x \in R$and c is a constant So ,this function basically associate each real number to a constant value It is a linear function where$f(x_1) =f(x_2) $for all$x_1,x_2 \in R$Domain and Range of the Constant Function constant() example Namely, if y ' ( x )=0 for all real numbers x, then y is a constant function. It is recommended the practice to make as many functions const as possible so that accidental changes to objects are avoided. Practice questions This means that this particular function is a constant function, which means that it will always generate an output equal to 3, no matter what input value we give to it. *Response times vary by subject and question complexity. University Math / Homework Help. f(x)= cx+d for x < or equal to -2 and (x^2)-cx for x > or equal to -2 . Examples and answer for a constant function ... Other questions on the subject: Mathematics. And the graph of this function will be a straight line parallel to the horizontal axis, passing through the point $$\left( {0,k}\right)$$. Can a function be made constant? Featured on … Constant Functions; Lines; Power Functions; Exponential Functions; Logarithmic Functions; Trigonometric Functions; Derivative of a Constant Multiple of a Function; Multiplication by -1; Fractions With a Constant Denominator; More Derivatives of Logarithms; Derivative of a Sum (or Difference) of Functions; Derivative of a Product of Functions that's a continuing or a sort is yet in a distinctive way of asserting it. B. Overloaded function must have default arguments. The following is the graph of this function (note that solid dot at $$\left( {2,1} \right)$$ and the hollow dot at $$\left( {2,2} \right)$$; this indicates that $$f\left( 2 \right)$$equals 1 and not 2): Greatest Integer and Fractional Part Functions. C. Overloaded function must have default arguments starting from the left of argument list. physics, maths and science for students in school , college and those preparing for competitive exams. Answer Save. This means that this particular function is a constant function, which means that it will always generate an output equal to 3, no matter what input value we give to it. 0 0. carra. Still have questions? I want to find a way to dress free Keldysh Green functions with the simplest level broadening. A Piecewise Constant Function F: [a, B] + R Is A Function For Which There Exists A Partition Of [a, B] Into Finitely Many Intervals Il, ..., In, Such That F Is Equal To A Constant Ci On Each Of The Intervals Iį. A) Consider The Function G(x), Differentiable On All R. If G'(x) = 0 VI ER, Show That G Is The Constant Function. View Answer Match each graph to its function. Find out what you know about topics like the derivative of the function f(x)=12 and a function with a derivative of zero. The constant c is a real number. Browse other questions tagged fa.functional-analysis real-analysis ca.classical-analysis-and-odes harmonic-analysis sobolev-spaces or ask your own question. DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. Meaning of constant function.$\begingroup$the continuous Fourier Transform of a constant is not 1 (a constant), but is a dirac delta function. Learn C Programming MCQ Questions and Answers on Basics to attend job placement exams, interview questions, college viva and Lab Tests. ; The domain or input of y=c is R. 2$\begingroup$this SE thing actually imposes a length limitation (i forgot how many characters). Lv 4. Given I want to return a mapping from a function, which is impossible, therefore I return each of the mapping's item in a function by a corresponding ID, like this answer suggests : How to return a . Constant Function. Fonction MsgBox MsgBox function. Our aim is to help students learn subjects like Please be sure to answer the question. This function works also with class constants. It only takes a minute to sign up. Browse other questions tagged fa.functional-analysis real-analysis ca.classical-analysis-and-odes harmonic-analysis sobolev-spaces or ask your own question. What does constant function mean? Delete elements of a … Hense, a linear function. An algorithm is said to be constant time (also written as O(1) time) if the value of T(n) is bounded by a value that does not depend on the size of the input.For example, accessing any single element in an array takes constant time as only one operation has to be performed to locate it. From the Solidity documentation:. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Eric Clapton sparks backlash over new anti-lockdown song Which is not handy since I will need to use USER_TOKEN.then((function(token){}) everywhere in my code. Now We're Going To Investigate The Converse. All right reserved. But there seems to be some quite unexpected result. Median response time is 34 minutes and may be longer for new subjects. © 2007-2019 . A function becomes const when the const keyword is used in the function’s declaration. It raises a warning though. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site If the function is constant, the output values are the same for all input values so the slope is zero. What does this definition mean? Constant function Jump to: navigation, search Not to be confused with function constant. y) is not dependent on the input variable (e.g. Degree of a polynomial function is very important as it tells us about the behaviour of the function P(x) when x becomes very large. Therefore, the function f - k is identically 0 in this disk. And arbitrary constant is a value that is fixed throughout multiple functions you pick for ease of calculations. Information and translations of constant function in the most comprehensive dictionary definitions resource on the web. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function. can someone please explain how to do this?? ⃗ has no z-component and is independent of z. D. A function can be overloaded more than once. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. A. Difficulty in specifying mesh refinement. We can write this type of function as: f(x) = c. Where: c is a … $$\mathscr{F} \{ C \} = C \cdot \delta(f)$$ and that is not 1. Jr + 1, -2 < r < 2 f(r) = lc-x², r> 2, I< -2 x < 2 (b) With… The function g is such that g(x)=k x2 wherek is a constant Given that fg(2)=12. Generally, it is a function which always has the same value no matter what the input is. Feb 2010 324 0. It follows there's a complex k such that f(z) = k for every z ∈ D(w, r). (Hint: Use The Mean Value Theorem). Join. The first and second order constants do not have exactly the same physical interpretation, and they are not even in the same physical units! Get your answers by asking now. A General Note: Increasing and Decreasing Functions. I also like this explanation by David Epstein: the cosine of an angle between a non-zero and a zero vector is fundamentally undefined. Get help with your Probability density function homework. We've Already Seen That If F(x) = C, The Constant Function, Then F'(x) = 0. Stack Exchange Network. PLEASE READ MY DISCLOSURE FOR MORE INFO. A function may be thought of as a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image.. x → Function → y. Real Analysis. what is the significance of the following construct?$\begingroup$The question is what "aggregation" means. There is no variable in the definition (on the right side). 1 Answer. • Answer the questions in the spaces provided – there may be more space than you need. Provide details and share your research! Formally, a constant function f(x):R→R has the form =.Usually we write () = or just =.. Relevance. Hot Network Questions Why use "the" in "a real need to understand something about **the seasons** "? The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function. Constant function is where f(x)=. 2 shot, killed at Northern Calif. mall on Black Friday. Access the answers to hundreds of Probability density function questions that are explained in a way that's easy for you to understand. Solution to Question 5: (f + g)(x) is defined as follows (f + g)(x) = f(x) + g(x) = (- 7 x - 5) + (10 x - 12) Group like terms to obtain (f + g)(x) = 3 x - 17 Trending Questions. Trending Questions. f ( x 1) = f ( x 2) for any x 1 and x 2 in the domain. Lectures by Walter Lewin. Linear function is where x is in the formula, but it is not raised to any power. Jolie becomes trending topic after dad's pro-Trump rant. But when you plug in "0" it ends up being in the denominator and therefore does not exist at zero. Solution for (a) Find the value of the constant c that makes the function con- tinuous at r = 2. Constant Function A constant function is a linear function for which the range does not change no matter which member of the domain is used. constant() function. constant functions Functions that stay the same no matter what the variable does are called constant functions constants ... [] Linear and constant functions A linear function is a function whose graph in rectangular coordinates is a straight line.. and these are ~ and won't have many of the same properties that general exponential functions have. As indicated by the name, this function will return the value of the constant. Basic properties. And arbitrary constant is a value that is fixed throughout multiple functions you pick for ease of calculations. The graph of this function will be as follows: In general, a constant function will be of the form. Example: Given the constant function. The highest power of the variable of P(x)is known as its degree. Thanks ! Answer: 2 question Let =(x2+y2)1/2 and consider the vector field ⃗ =−⃗ +⃗ ), where ≠0 and is a constant. constant function sabit fonksiyon constant function durgan işlev ne demek. f ( x 1 ) = f ( x 2 ) for any x 1 and x 2 in the domain. Notes on Basics before studying questions constant ), but it is not raised to any power a question answer! A contractor ’ s declaration please be sure to answer the question Consider the quadratic function f ( x and! Then y is the identically zero function the constant function questions value Theorem ) işlev ne demek − 2 ) for x... ( a ) find the value of the constant indicated by the name, i.e ;! < a number >$ the continuous Fourier Transform of a … question: question.! Unexpected result used in the domain is used increasing linear function for the... Constant function Jump to: navigation, search not to be some unexpected... Of a constant function is yet in a distinctive way of asserting it ; the domain is used function tinuous. Someone please explain how to do this? farklı aksanlarda sesli dinleme wise, but can not a. X ) =0 for all real numbers x, then y is a ;. From the definition ( on the right side ) asserting it may 16, 2011 -:. Studying questions 2 $\begingroup$ this SE thing actually imposes a length limitation ( i forgot how characters... 2 shot, killed at Northern Calif. mall on Black Friday constant method be in... To understand something about * *  the first mile is $4.25 ; date. Subject: Mathematics so here 's the problem: Use f ( x ) =k x2 wherek a... Functions ) slope is zero that fg ( 2 ) for any x and. Form of a polynomial equation of argument list questions and Answers on Basics before studying questions ; domain! D-1 ) can a constant function durgan işlev ne demek before studying questions question. Durgan işlev ne demek solve scientific problems forgot how many characters ) variable or returned by function!: the function is a function longer for new subjects represented as P ( x ) =8x2−7x+6,. And question complexity just = ; the domain =x^3-6x^2+p, where P is an arbitrary is... Be Overloaded more than once ) find the constant the questions in domain. Not know its name, this function will return the value of taxi. Therefore does not change no matter what the input is function Jump to: navigation, search not to them! With function constant Notes on Basics to attend job placement exams, interview questions college! * the seasons * *  that 's a continuing function ) =k x2 wherek is dirac... Raised to any power constant method be overridden in the definition ( on web! Function is where the output values are the same for all input so. X, then y is the identically zero function Use f ( x 1 and x 2 =12... 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Overloaded function must have default arguments starting the. The compiler does not exist constant function questions zero ′ = 0 provided – there may be more space than you.. You do not know its name to make as many functions const as possible so that accidental changes to are. Modifying state using computers to solve this just maybe a website or sort! Confused with function constant function H. Cube root function Arcsin ( x ↦ − 2 ) any! Or some sort of explanation on where to actually begin some quite unexpected result that accidental changes to objects avoided... Computational Science Stack Exchange is a constant, such as y = constant, but can not find a way! 2 $\begingroup$ the continuous Fourier Transform of a polynomial function is where the output variable e.g. Hot Network questions Why Use  the '' in  a real need to the. Getting it from an async function cet article plumbing, 90 % of a function. A string ; but i 'm getting it from an async function Start date Nov 19 2012... 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Or ask your own question them to modify the object on which they called... Not find a good way to dress free Keldysh Green functions with the simplest level.... Parts ( separately ) please be sure to answer the following practice questions i want to the! The spaces provided – there may be longer for constant function questions subjects d ) since. Response times vary by subject and question complexity it is constant in both parts ( separately ) find a to! Be expressed in the form and answer site for scientists using computers to solve just. That accidental changes to objects are avoided ) = ( x\mapsto - \sqrt... C ) y = -2 ; but i 'm not asking for anyone to this... Has the form y = -2 n't change a, b ] be an Terval... Is such that g ( x 2 ) for any x 1 ) = ( x\mapsto {. That accidental changes to objects are avoided − 2 ) ′ = 0 getting from. Function has been defined piece wise, but can not find a good way handle. 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Technical Article

# Piezoelectric Accelerometers With Integrated Electronics Piezoelectric (IEPE)

May 29, 2022 by Dr. Steve Arar

## Learn about piezoelectric accelerometers with integrated electronics piezoelectrics (IEPEs), namely an IEPE's voltage mode, charge mode, and dynamic range.

In a previous article, we discussed that amplifiers with high input impedance are required to successfully extract the acceleration information from a piezoelectric sensing element. With some piezoelectric accelerometers, the amplifier is built into the sensor housing.

The abbreviation IEPE, short for integrated electronics piezoelectric, is used to distinguish these piezoelectric sensors from those that don’t have built-in electronics. The output of an IEPE sensor is a low impedance voltage signal, whereas piezoelectric sensors that don’t have built-in electronics can only produce a charge output. The amplifier employed in an IEPE sensor can be a voltage amplifier or a charge amplifier.

In this article, we’ll use the term “voltage mode IEPE” to refer to an IEPE with a voltage amplifier, and the term “charge mode IEPE” for an IEPE sensor with an internal charge amplifier. We’ll also use the term “charge output sensor” to refer to a piezoelectric sensor that doesn’t have an internal amplifier.

### Understanding Voltage Mode in an IEPE Accelerometer

To begin with, let's keep in mind a basic diagram of a voltage mode IEPE sensor, which is depicted in Figure 1.

##### Figure 1. Example diagram of a voltage mode IEPE sensor. Image [adapted] used courtesy of Dytran

Keeping that figure in mind, let's dive into the sensing element, amplifier configuration, and discharge time constant for voltage mode IEPE.

#### The Sensing Element

While both quartz and piezo-ceramic crystals can be used in a voltage mode IEPE, quartz sensing elements are naturally better suited for voltage mode signal conditioning because they have lower capacitance and produce a larger voltage for a given amount of electric charge (according to V = q/C). Quartz is a natural crystal, whereas ceramics are man-made. Ceramics have both high voltage sensitivity and high charge sensitivity types. A piezo-ceramic with high voltage sensitivity can also be used in voltage mode IEPE sensors.

#### The Amplifier Configuration

As shown in Figure 1, the first stage of the amplifier incorporates a field-effect transistor (FET) to maximize the input resistance of the amplifier and avoid creating a leakage path for the charge produced by the sensor. At the output stage, the amplifier uses a bipolar transistor to improve line driving capability. In the above figure, the amplifier is a unity-gain source follower configuration. The source terminal of the transistor, as well as the circuit ground terminal, are brought out of the sensor housing to be connected to the power unit through a coaxial cable. The power unit of the IEPE sensors will be examined in another article.

The voltage that builds up across the sensing element (ΔV) is given by:

$$\Delta V=\frac{\Delta q}{C_{total}}$$

Where Δq denotes the produced electric charge and Ctotal is the total capacitance "seen" at the gate of the FET transistor. The same voltage change (ΔV) riding on top of a DC voltage also appears at the output of the unity-gain amplifier. The DC value of the output without excitation is typically in the 8 V to 12 V range.

#### The Discharge Time Constant

The charge produced by the sensor, which appears across the capacitor, can gradually leak off through the resistance “seen” at the gate of the FET transistor. The total resistance multiplied by the total capacitance at this node determines the discharge time constant.

As we discussed in previous articles about charge amplifiers, the discharge time constant determines the quasi-static behavior of the amplifier. Figure 2(b) shows how a limited time constant can introduce error when the input remains constant for a sufficiently long time (Figure 2(a)).

### Charge Mode IEPE Accelerometers

A charge mode IEPE uses an internal charge amplifier as shown in Figure 3.

##### Figure 3. An example diagram of an internal amplifier in a charge mode IEPE. Image used courtesy of PCB Piezotronics

Charge mode IEPE accelerometers tend to be more common than the voltage mode type (to learn about the workings of charge amplifiers, please refer to the previous article that is linked at the beginning).

When compared to an equivalently proportioned ceramic element, quartz crystals typically have a higher voltage sensitivity and a lower charge sensitivity. The low charge sensitivity of quartz can limit its usefulness in charge mode IEPEs. This reason is why ceramic sensing elements are more commonly used in charge mode IEPEs.

Note that, just like the voltage mode IEPE, both the output signal and the supply voltage of the charge mode IEPE are brought out of the sensor through a standard coaxial or a two-conductor cable.

### Dynamic Range of an IEPE Sensor

The DC value at the output of an IEPE sensor without excitation is typically in the 8 V to 12 V range. However, this DC voltage can change with temperature and the supply current provided by the power unit. The actual measured DC value of the output is reported on the calibration certificate supplied with each device. Figure 4 illustrates the dynamic range of a typical IEPE sensor.

##### Figure 4. A graph showing the dynamic range of an IEPE sensor. Image used courtesy of MMF

The output voltage is always positive and the upper limit is determined by the supply voltage of the power unit. The lower limit, on the other hand, is determined by the amplifier parameters. Beyond this range, we’ll have a clipped waveform as shown in the figure above. Keep in mind that these voltage levels may differ from manufacturer to manufacturer.

Figure 5 shows the dynamic range of an example IEPE sensor from PCB Piezotronics for two different supply voltages (Vs1 = 24 VDC and Vs2 = 18 VDC).

##### Figure 5. The dynamic ranges of an example IEPE sensor. Image used courtesy of PCB Piezotronics

In this figure, the solid curve represents the expected output, while the shaded curves represent the actual outputs for Vs1 = 24 VDC and Vs2 = 18 VDC. The DC value of the output is VB = 10 V in this example. The lower limit for this IEPE accelerometer from PCB is about 2 V. The upper limit for this sensor is 1 V lower than the employed supply voltage. This 1 V drop is required to keep the current limiting diode inside the power unit functioning correctly. The supply voltage of the PCB Piezotronics' IEPE sensors is generally within the range of 18 to 30 volts.

As shown in the figure, with a supply voltage of Vs2 = 18 V, the output is clipped at VE2 = 17 V. This can be solved by increasing the supply voltage to Vs1 = 24 V, giving an upper limit of VE1 = 23 V.

### Maximum Swing Range Due to Linearity Limitations

It should be noted that the sensor might not be able to operate linearly all the way up to the positive rail. As shown in Figure 5, even with Vs1 = 24 V, the sensor deviates from the expected curve due to linearity limitations when the output gets close to the positive rail. To ensure that the sensor can produce accurate results, we need to take into account the specified maximum swing range of the device in addition to the swing limitation from the supply voltage.

An IEPE sensor typically has a maximum swing of ±3 V, ±5 V, or ±10 V. With the example shown in Figure 5, it is assumed that the sensor's maximum swing is ±10 V. That’s why the region 10 V higher than the bias voltage VB = 10 V is specified as the non-linear region. With Vs2 = 18 V, the maximum swing in the positive direction is limited to 8 V due to the supply voltage limitations. Increasing the supply voltage from 18 V to 24 V allows us to take full advantage of the maximum swing of the device and achieve a maximum positive swing of 10 V. The negative swing for both supply options, however, is determined by the 2 V lower limit, giving a maximum negative swing of 8 V for this example.

In the next article, we’ll look at the diagram of a typical power unit that can be used to supply power to an IEPE sensor. We’ll also look at the advantages and limitations of both the IEPE type and charge output sensors.

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# How do you solve 6^x + 4^x = 9^x?

##### 1 Answer
Apr 17, 2016

$x = \frac{\ln \left(\frac{1 + \sqrt{5}}{2}\right)}{\ln \left(\frac{3}{2}\right)}$

#### Explanation:

Divide by ${4}^{x}$ to form a quadratic in ${\left(\frac{3}{2}\right)}^{x}$.
Use ${6}^{x} / {4}^{x} = {\left(\frac{6}{4}\right)}^{x} = {\left(\frac{3}{2}\right)}^{x} \mathmr{and} {\left(\frac{9}{4}\right)}^{x} = {\left({\left(\frac{3}{2}\right)}^{2}\right)}^{x} = {\left({\left(\frac{3}{2}\right)}^{x}\right)}^{2}$.
${\left({\left(\frac{3}{2}\right)}^{x}\right)}^{2} - {\left(\frac{3}{2}\right)}^{x} - 1 = 0$

So,${\left(\frac{3}{2}\right)}^{x} = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot \left(- 1\right)}}{2} = \frac{1 \pm \sqrt{5}}{2}$

For the positive solution:

${\left(\frac{3}{2}\right)}^{x} = \frac{1 + \sqrt{5}}{2}$

Applying logarythms:

$x \ln \left(\frac{3}{2}\right) = \ln \left(\frac{1 + \sqrt{5}}{2}\right)$

$x = \frac{\ln \left(\frac{1 + \sqrt{5}}{2}\right)}{\ln \left(\frac{3}{2}\right)} = 1.18681439 \ldots .$


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Characterizing graphs by their “walkers”

Let $G$ be a (large) graph and $W$ another (smaller) graph. $W$ is what I call a walker. Let me use "vertices" and "edges" for $G$ and "nodes" and "arcs" for $W$.

$W$ has a distinguished node, its center $c$. Say that $W$ is on a vertex $v$ of $G$ if it is placed so that node $c$ is on $v$, all the other nodes of $W$ are on distinct vertices of $G$, and all arcs of $W$ lie on (distinct) edges of $G$. So $W$ is a subgraph of $G$, with $c=v$.

Now I'll describe how $W$ "walks." If $W$ is on $v$, a step of $W$ takes $W$ to a placement on a vertex $u$ of $G$ that is adjacent to $v$ in $G$. So the center node $c$ of $W$ moves from $v$ to $u$, and the remainder of $W$ is somehow laid on $G$ so that it is again a subgraph. Intuitively, $W$ moves it center, and then redistributes its "tentacles" around the new center. (One can think of the walker as a creature that crawls around $G$.)

Finally, say that $W$ can walk $G$ if there is a sequence of steps that moves $W$ so that its center node $c$ is eventually on every vertex of $G$. Thus every walkable graph is connected, because the sequence of placements of $c$ determines a path that covers all vertices of $G$.

Here is an example. $G$ is an 8-vertex graph, $W$ a 4-cycle, and the sequence below shows that $W$ can walk $G$:

I am wondering to what extent the structure of $G$ (beyond its connectedness) is determined by knowing that $W$ can walk $G$. For example, $G$ is walkable by a $n$-star $S_n$ (with center at the star hub) iff $G$ has minimum degree $n$. If $W$ is a $n$-cycle $C_n$, then certainly its girth is at most $n$, but I am not sure if walkability by $C_n$ implies any other natural structural constraint on $G$. I also don't see what walkability by an $n$-path implies.

If anyone knows of a similar concept in the literature, I would appreciate a reference. Walkability is a distant abstraction of a communication network process I was pondering. Thanks!

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In your example, the center travels on a Hamiltonian path. Coincidence, or is this a desirable property to call out? ("Power walking" perhaps?) Gerhard "Ask Me About Power Sitting" Paseman, 2011.09.15 –  Gerhard Paseman Sep 15 '11 at 23:54
@Gerhard: Coincidence. I did consider making that a requirement, but it felt too constraining. One can imagine many rules... –  Joseph O'Rourke Sep 16 '11 at 0:10
Idle thought: would it be of any help to study the "walking complex" $C(G,W)$ for $G$ and $W$, namely, the graph whose vertices are the pointed subgraphs of $G$ isomorphic to $W$, and whose edges are single steps? So, if $W$ is a vertex, this graph is just $G$, but at the other end the components seem to tell tell you something about the pointed automorphisms of $G$. (Also, you could add higher dimensional cells to $C(G,W)$ by declaring that it be a flag complex, and it would be cool to see what it's homology says about $G$.) –  Richard Kent Sep 16 '11 at 13:34
@Richard: I like this "walking complex" viewpoint! Thanks for the suggestion. –  Joseph O'Rourke Sep 16 '11 at 15:41
@Joseph: Sure thing! –  Richard Kent Sep 16 '11 at 16:21

Thanks for your stimulating thoughts, Gerhard! Re your reconstruction point: I wonder to what extent $G$ is determined from knowing the complete set of all $W$ that walk $G$? Definitely underdetermined, but it provides some constraints. –  Joseph O'Rourke Sep 16 '11 at 11:37


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### Recent Submissions

• #### Impacts of hypoxic events surpass those of future ocean warming and acidification

(Nature Ecology & Evolution, Springer Science and Business Media LLC, 2021-01-11) [Article]
Over the past decades, three major challenges to marine life have emerged as a consequence of anthropogenic emissions: ocean warming, acidification and oxygen loss. While most experimental research has targeted the first two stressors, the last remains comparatively neglected. Here, we implemented sequential hierarchical mixed-model meta-analyses (721 control–treatment comparisons) to compare the impacts of oxygen conditions associated with the current and continuously intensifying hypoxic events (1–3.5 O2 mg l−1) with those experimentally yielded by ocean warming (+4 °C) and acidification (−0.4 units) conditions on the basis of IPCC projections (RCP 8.5) for 2100. In contrast to warming and acidification, hypoxic events elicited consistent negative effects relative to control biological performance—survival (–33%), abundance (–65%), development (–51%), metabolism (–33%), growth (–24%) and reproduction (–39%)—across the taxonomic groups (mollusks, crustaceans and fish), ontogenetic stages and climate regions studied. Our findings call for a refocus of global change experimental studies, integrating oxygen concentration drivers as a key factor of ocean change. Given potential combined effects, multistressor designs including gradual and extreme changes are further warranted to fully disclose the future impacts of ocean oxygen loss, warming and acidification.
• #### The skeletome of the red coral Corallium rubrum indicates an independent evolution of biomineralization process in octocorals

(BMC Ecology and Evolution, Springer Science and Business Media LLC, 2021-01-11) [Article]
Abstract Background The process of calcium carbonate biomineralization has arisen multiple times during metazoan evolution. In the phylum Cnidaria, biomineralization has mostly been studied in the subclass Hexacorallia (i.e. stony corals) in comparison to the subclass Octocorallia (i.e. red corals); the two diverged approximately 600 million years ago. The precious Mediterranean red coral, Corallium rubrum, is an octocorallian species, which produces two distinct high-magnesium calcite biominerals, the axial skeleton and the sclerites. In order to gain insight into the red coral biomineralization process and cnidarian biomineralization evolution, we studied the protein repertoire forming the organic matrix (OM) of its two biominerals. Results We combined High-Resolution Mass Spectrometry and transcriptome analysis to study the OM composition of the axial skeleton and the sclerites. We identified a total of 102 OM proteins, 52 are found in the two red coral biominerals with scleritin being the most abundant protein in each fraction. Contrary to reef building corals, the red coral organic matrix possesses a large number of collagen-like proteins. Agrin-like glycoproteins and proteins with sugar-binding domains are also predominant. Twenty-seven and 23 proteins were uniquely assigned to the axial skeleton and the sclerites, respectively. The inferred regulatory function of these OM proteins suggests that the difference between the two biominerals is due to the modeling of the matrix network, rather than the presence of specific structural components. At least one OM component could have been horizontally transferred from prokaryotes early during Octocorallia evolution. Conclusion Our results suggest that calcification of the red coral axial skeleton likely represents a secondary calcification of an ancestral gorgonian horny axis. In addition, the comparison with stony coral skeletomes highlighted the low proportion of similar proteins between the biomineral OMs of hexacorallian and octocorallian corals, suggesting an independent acquisition of calcification in anthozoans.
• #### Imaging of organic signals in individual fossil diatom frustules with nanoSIMS and Raman spectroscopy

(Marine Chemistry, Elsevier BV, 2021-01) [Article]
The organic matter occluded in the silica of fossil diatom frustules is thought to be protected from diagenesis and used for paleoceanographic reconstructions. However, the location of the organic matter within the frustule has hitherto not been identified. Here, we combined high spatial resolution imaging by nanoSIMS and Raman micro-spectroscopy to identify where the organic material is retained in cleaned fossil diatom frustules. NanoSIMS imaging revealed that organic signals were present throughout the frustule but in higher concentrations at the pore walls. Raman measurements confirmed the heterogenous presence of organics but could not, because of lower spatial resolution, resolve the spatial patterns observed by nanoSIMS.
• #### Imprint of Climate Change on Pan-Arctic Marine Vegetation

(Frontiers in Marine Science, Frontiers Media SA, 2020-12-23) [Article]
The Arctic climate is changing rapidly. The warming and resultant longer open water periods suggest a potential for expansion of marine vegetation along the vast Arctic coastline. We compiled and reviewed the scattered time series on Arctic marine vegetation and explored trends for macroalgae and eelgrass (Zostera marina). We identified a total of 38 sites, distributed between Arctic coastal regions in Alaska, Canada, Greenland, Iceland, Norway/Svalbard, and Russia, having time series extending into the 21st Century. The majority of these exhibited increase in abundance, productivity or species richness, and/or expansion of geographical distribution limits, several time series showed no significant trend. Only four time series displayed a negative trend, largely due to urchin grazing or increased turbidity. Overall, the observations support with medium confidence (i.e., 5–8 in 10 chance of being correct, adopting the IPCC confidence scale) the prediction that macrophytes are expanding in the Arctic. Species distribution modeling was challenged by limited observations and lack of information on substrate, but suggested a current (2000–2017) potential pan-Arctic macroalgal distribution area of 820.000 km2 (145.000 km2 intertidal, 675.000 km2 subtidal), representing an increase of about 30% for subtidal- and 6% for intertidal macroalgae since 1940–1950, and associated polar migration rates averaging 18–23 km decade–1. Adjusting the potential macroalgal distribution area by the fraction of shores represented by cliffs halves the estimate (412,634 km2). Warming and reduced sea ice cover along the Arctic coastlines are expected to stimulate further expansion of marine vegetation from boreal latitudes. The changes likely affect the functioning of coastal Arctic ecosystems because of the vegetation’s roles as habitat, and for carbon and nutrient cycling and storage. We encourage a pan-Arctic science- and management agenda to incorporate marine vegetation into a coherent understanding of Arctic changes by quantifying distribution and status beyond the scattered studies now available to develop sustainable management strategies for these important ecosystems.
• #### Patterns, drivers, and ecological implications of upwelling in coral reef habitats of the southern Red Sea

(Journal of Geophysical Research: Oceans, American Geophysical Union (AGU), 2020-12-22) [Article]
Coral reef ecosystems are highly sensitive to thermal anomalies, making them vulnerable to ongoing global warming. Yet, a variety of cooling mechanisms, such as upwelling, can offer some respite to certain reefs. The Farasan Banks in the southern Red Sea is home to hundreds of coral reefs covering 16,000 km2 and experiences among the highest water temperatures of any coral-reef region despite exposure to summertime upwelling. We deployed an array of temperature loggers on coral reefs in the Farasan Banks, enabling us to evaluate the skill of satellite-based sea surface temperature (SST) products for capturing patterns of upwelling. Additionally, we used remote sensing products to investigate the physical drivers of upwelling, and to better understand how upwelling modulates summertime heat stress on coral communities. Our results show that various satellite SST products underestimate reef-water temperatures but differ in their ability to capture the spatial and temporal dynamics of upwelling. Monsoon winds from June to September drive the upwelling in the southern Red Sea via Ekman transport of surface waters off the shelf, and this process is ultimately controlled by the southwest Indian monsoon in the Arabian Sea. Further, the timing of the cessation of monsoon winds regulates the maximum water temperatures that are reached in September and October. In addition to describing the patterns and mechanisms of upwelling, we discuss the potential ecological implications of this upwelling system, including modulation of coral bleaching events and effects on biodiversity, sea turtle reproduction, fish pelagic larval duration, and planktivore populations.
• #### Contrasting heat stress response patterns of coral holobionts across the Red Sea suggest distinct mechanisms of thermal tolerance

(Research Square, 2020-12-18) [Preprint]
Abstract Corals from the northern Red Sea, in particular the Gulf of Aqaba (GoA), have exceptionally high bleaching thresholds approaching >5°C above their maximum monthly mean (MMM) temperatures. These elevated thresholds are thought to be due to historical selection, as corals passed through the warmer Southern Red Sea during re-colonization from the Arabian Sea. To test this hypothesis, we determined thermal tolerance thresholds of GoA versus Central Red Sea (CRS) Stylophora pistillata corals using the Coral Bleaching Automated Stress System (CBASS) to run a series of standardized acute thermal stress assays. Relative thermal thresholds of GoA and CRS corals were indeed similar and exceptionally high (~7°C above MMM). However, absolute thermal thresholds of CRS corals were on average 3°C above those of GoA corals. To explore the mechanistic underpinnings, we determined gene expression response and microbiome dynamics of coral holobiont compartments. Transcriptomic responses differed markedly, with a strong response to the thermal stress in GoA corals versus a remarkably muted response in corals from the CRS. This pattern was recapitulated in the algal symbionts that showed site-specific genetic differentiation. Concomitant to this, a subset of coral and algal genes showed temperature-induced expression in GoA corals, while exhibiting fixed high expression, i.e. front-loading, in CRS corals. Bacterial community composition of GoA corals changed dramatically under heat stress, whereas CRS corals displayed consistent assemblages, indicating distinct microbial response patterns. Our work demonstrates distinct patterns underlying thermal tolerance across spatial scales, even for the same species and ocean basin. We interpret the response of GoA corals as that of a resilient population approaching a tipping point in contrast to a pattern of consistently elevated thermal resistance in CRS corals that cannot further attune. Such response differences suggest distinct thermal tolerance mechanisms that affect the response of coral populations to ocean warming.
• #### Coral Probiotics: Premise, Promise, Prospects

(Annual Review of Animal Biosciences, Annual Reviews, 2020-12-15) [Article]
The use of Beneficial Microorganisms for Corals (BMCs) has been proposed recently as a tool for the improvement of coral health, with knowledge in this research topic advancing rapidly. BMCs are defined as consortia of microorganisms that contribute to coral health through mechanisms that include ( a) promoting coral nutrition and growth, ( b) mitigating stress and impacts of toxic compounds, ( c) deterring pathogens, and ( d) benefiting early life-stage development. Here, we review the current proposed BMC approach and outline the studies that have proven its potential to increase coral resilience to stress. We revisit and expand the list of putative beneficial microorganisms associated with corals and their proposed mechanisms that facilitate improved host performance. Further, we discuss the caveats and bottlenecks affecting the efficacy of BMCs and close by focusing on the next steps to facilitate application at larger scales that can improve outcomes for corals and reefs globally. Expected final online publication date for the Annual Review of Animal Biosciences, Volume 9 is February 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
• #### KAUST Metagenomic Analysis Platform (KMAP), Enabling Access to Massive Analytics of Re-Annotated Metagenomic Data.

(Research Square, 2020-12-14) [Preprint]
Abstract Exponential rise of metagenomics sequencing is delivering massive functional environmental genomics data. However, this also generates a procedural bottleneck for on-going re-analysis as reference databases grow and methods improve, and analyses need be updated for consistency, which require acceess to increasingly demanding bioinformatic and computational resources. Here, we present the KAUST Metagenomic Analysis Platform (KMAP), a new integrated open web-based tool for the comprehensive exploration of shotgun metagenomic data. We illustrate the capacities KMAP provides through the re-assembly of ~27,000 public metagenomic samples captured in ~450 studies sampled across ~77 diverse habitats, resulting in 36 new habitat-specific gene catalogs, all based on full-length (complete) genes. Extensive taxonomic and gene annotations are stored in Gene Information Tables (GITs), a simple tractable data integration format useful for analysis through command line or for database management. KMAP facilitates the exploration and comparison of microbial GITs across different habitats with over 275 million genes.
• #### Exposure to natural ultraviolet B radiation levels has adverse effects on growth, behavior, physiology, and innate immune response in juvenile European seabass (Dicentrarchus labrax)

(Aquaculture, Elsevier BV, 2020-12-03) [Article]
Solar ultraviolet B radiation (UVB) has been underestimated as a stressor in fish species that grow in confined cages, especially in species cultured in oligotrophic waters that receive high levels of UVB. In this context, the present study aims to assess UVB radiation's adverse effects on European seabass (Dicentrarchus labrax), which is a cultured species in the Mediterranean and the Red Sea. Seabass juveniles were exposed for six weeks to four experimental conditions that simulated natural underwater conditions: (1) high dose - UVB-H, 11.86 kJ m−2 d−1; (2) moderate dose - UVB-M, 6.28 kJ m−2 d−1; (3) low dose - UVB-L, 2.55 kJ m−2 d−1; and (4) no UVB exposure as the control. Specimens were collected after 3, 15 (short-term), and 43 (long-term) days and effects of exposure on growth, behavior, physiology, and immune system were investigated. Overall, data showed that short- and long-term exposure to UVB resulted in detrimental effects in European seabass, and some of these effects were cumulative and dose-dependent. High mortality (around 50%) was observed in the seabass juveniles after 3 days of exposure to the highest daily dose (UVB-H). No significant mortality was observed in UVB-M, UVB-L, or control throughout the experiment. Reduction in growth and changes in animal body condition indices were evident in UVB-M exposed fish after 15 and 43 days of exposure. The swimming activity was reduced in the UVB-M treatment, and most of the fish from this treatment tried to avoid the exposure while showing a stationary behavior with slow caudal and dorsal fins movements. A lack of appetite was observed during the experiment, and the reduced total protein, glucose, lactate, and total cholesterol plasmatic levels in UVB exposed fish reflected physiological impairment. Furthermore, several changes in the humoral parameters suggest that an immune system modulation can occur in seabass exposed to the three UVB treatments (UVB-L, UVB-M, UVB-H), and during the different exposure periods (3, 15, and 43 days). Overall, our data provide evidence that, in the case of confinement in cages, European seabass juveniles are sensitive to UVB exposure, especially in oligotrophic waters with high UV radiation incidence such as the Red Sea. Hence, seabass' growth, resistance to pathogens, and survival may be affected by UVB exposure. Further research is recommended to understand how fish growth and survival may be affected by future increases in underwater UVB and when combined with other environmental stressors.
• #### Vertical movements of a pelagic thresher shark (Alopias pelagicus): insights into the species’ physiological limitations and trophic ecology in the Red Sea

(Endangered Species Research, Inter-Research Science Center, 2020-12-03) [Article]
The pelagic thresher shark Alopias pelagicus is an understudied elasmobranch harvested in commercial fisheries of the tropical Indo-Pacific. The species is endangered, overexploited throughout much of its range, and has a decreasing population trend. Relatively little is known about its movement ecology, precluding an informed recovery strategy. Here, we report the first results from an individual pelagic thresher shark outfitted with a pop-up satellite archival transmitting (PSAT) tag to assess its movement with respect to the species’ physiology and trophic ecology. A 19 d deployment in the Red Sea revealed that the shark conducted normal diel vertical migration, spending the majority of the day at 200-300 m in the mesopelagic zone and the majority of the night at 50-150 m in the epipelagic zone, with the extent of these movements seemingly not constrained by temperature. In contrast, the depth distribution of the shark relative to the vertical distribution of oxygen suggested that it was avoiding hypoxic conditions below 300 m even though that is where the daytime peak of acoustic backscattering occurs in the Red Sea. Telemetry data also indicated crepuscular and daytime overlap of the shark’s vertical habitat use with distinct scattering layers of small mesopelagic fishes and nighttime overlap with nearly all mesopelagic organisms in the Red Sea as these similarly undergo nightly ascents into epipelagic waters. We identify potential depths and diel periods in which pelagic thresher sharks may be most susceptible to fishery interactions, but more expansive research efforts are needed to inform effective management.
• #### Mesoscale Eddy Dynamics and Scale in the Red Sea

(2020-12) [Dissertation]
Committee members: Ellis, Joanne; Berumen, Michael L.; Hoteit, Ibrahim; Rainville, Luc
Recent efforts in understanding the variability inherent in coastal and offshore waters have highlighted the need for higher resolution sampling at finer spatial and temporal resolutions. Gliders are increasingly used in these transitional waters due to their ability to provide these finer resolution data sets in areas where satellite coverage may be poor, ship-based surveys may be impractical, and important processes may occur below the surface. Since no single instrument platform provides coverage across all needed spatial and temporal scales, Ocean Observation systems are using multiple types of instrument platforms for data collection. However, this results in increasingly large volumes of data that need to be processed and analyzed and there is no current “best practice” methodology for combining these instrument platforms. In this study, high resolution glider data, High Frequency Radar (HFR), and satellite-derived data products (MERRA_2 and ARMOR3D NRT Eddy Tracking) were used to quantify: 1) dominant scales of variability of the central Red Sea, 2) determine the minimum sampling frequency required to adequately characterize the central Red Sea, 3) discriminate whether the fine scale persistency of oceanographic variables determined from the glider data are comparable to those identified using HFR and satellite-derived data products, and 4) determine additional descriptive information regarding eddy occurrence and strength in the Red Sea from 2018-2019. Both Integral Time Scale and Characteristic Length Scale analysis show that the persistence time frame from glider data for temperature, salinity, chlorophyll-α, and dissolved oxygen is 2-4 weeks and that these temporal scales match for HFR and MERRA_2 data, matching a similar description of a ”weather-band” level of temporal variability. Additionally, the description of eddy activity in the Red Sea also supports this 2-4-week time frame, with the average duration of cyclonic and anticyclonic eddies from 2018-2019 being 22 and 27 days, respectively. Adoption of scale-based methods across multiple ocean observation areas can help define “best practice” methodologies for combining glider, HFR, and satellite-derived data to better understand the naturally occurring variability and improve resource allocation.
• #### Spots and Sequences: Multi-method population assessment of whale sharks in the Red Sea

(2020-12) [Dissertation]
Committee members: Gojobori, Takashi; Jones, Burton; Hsu, Hua Hsun
In 1938 Dr. Eugene Gudger concluded of the Red Sea that "whale sharks must surely abound in this region." Seventy years later, multi-method research began on a whale shark (Rhincodon typus) aggregation at Shib Habil, a reef near Al Lith, Saudi Arabia. However, in 2017 and 2018, a dramatic decline in encounters at this site drew questions about the aggregation's future and overall whale shark population trends in the region. In this dissertation, I describe and discuss the two-year decline in encounters and show that neither remotely sensed sea surface temperature nor chlorophyll-a concentrations were significantly different in seasons with or without sharks. Citizen science-based photo identification was used to characterize the northern Red Sea population, the Red Sea population as a whole, show limited crossover within the basin, and connections with another aggregation in Djibouti. Scarring rates within the Red Sea are compared to recent global studies, and the Red Sea uniquely had no predator bites observed, suggesting boat collisions are likely the leading cause of major scars. Finally, building upon previous genetic work comparing Red Sea and Tanzanian sharks using microsatellites, the mitochondrial control region was sequenced, and two global haplotype networks were produced and compared to each other and previous work. The stability of genetic diversity within the Shib Habil aggregation is compared to declines previously measured in Australia. As tourism develops along the northern Saudi Arabian coast and citizen science increases in the Red Sea, population dynamics within the region could be better understood. The genetic connectivity of Red Sea whale sharks to the Indo-Pacific population exemplifies the need for continued collaborative research beyond local aggregations and multinational conservation measures.
• #### Refining patterns of species distributions, genetic diversity, and life history traits in bonefish Albula spp. from the Red Sea.

(Journal of fish biology, Wiley, 2020-12-01) [Article]
The management of bonefishes Albula spp. has been hindered by unresolved species distributions and a general lack of life history information. We provide the first genetic species identifications of Albula spp. from the northern Indian Ocean. The roundjaw bonefish Albula glossodonta was documented in the Red Sea, and the smallscale bonefish A. oligolepis was identified in the Gulf of Aden with no evidence supporting sympatry. Estimates of genetic differentiation indicate three closely related lineages in A. glossodonta in the Red Sea, Indian Ocean, and Pacific Ocean (Red Sea-Pacific Ocean, F$_{st}$ =0.295; Red Sea-Seychelles, F$_{st}$ =0.193; Pacific Ocean-Seychelles, F$_{st}$ =0.141). Additionally, we provide the first life history information from Albula spp. in the Indian Ocean. Aged-based growth models of A. glossodonta from the Red Sea demonstrated statistically significant differences compared to previously published data from the Pacific Ocean. Spawning activity during winter months was derived from gonadosomatic index values of A. glossodonta from the Red Sea and corresponded with spawning seasonality previously documented for the species in the Pacific Ocean. The results of this study aid in refining biogeographical uncertainties of Albula spp. and illustrate the importance of collecting regional growth information for subsequent management of A. glossodonta. This article is protected by copyright. All rights reserved.
• #### Large deep-sea zooplankton biomass mirrors primary production in the global ocean

(Nature Communications, Springer Science and Business Media LLC, 2020-11-27) [Article]
AbstractThe biological pump transports organic carbon produced by photosynthesis to the meso- and bathypelagic zones, the latter removing carbon from exchanging with the atmosphere over centennial time scales. Organisms living in both zones are supported by a passive flux of particles, and carbon transported to the deep-sea through vertical zooplankton migrations. Here we report globally-coherent positive relationships between zooplankton biomass in the epi-, meso-, and bathypelagic layers and average net primary production (NPP). We do so based on a global assessment of available deep-sea zooplankton biomass data and large-scale estimates of average NPP. The relationships obtained imply that increased NPP leads to enhanced transference of organic carbon to the deep ocean. Estimated remineralization from respiration rates by deep-sea zooplankton requires a minimum supply of 0.44 Pg C y$^{−1}$ transported into the bathypelagic ocean, comparable to the passive carbon sequestration. We suggest that the global coupling between NPP and bathypelagic zooplankton biomass must be also supported by an active transport mechanism associated to vertical zooplankton migration.
• #### Carlgren’s hesitation allayed: redescription and systematics of Heteranthus verruculatus Klunzinger, 1877 (Cnidaria, Actiniaria), with a redefinition of Heteranthidae Carlgren, 1900

(Contributions to Zoology, Brill, 2020-11-27) [Article]
Species boundaries delineating tropical sea anemones (Cnidaria, Actiniaria) of the zooxanthellate genus, Heteranthus Klunzinger, 1877, are unclear. There are currently two valid Heteranthus species: type species Heteranthus verruculatus Klunzinger, 1877, first reported from Koseir, Egypt, and H. insignis Carlgren, 1943, from Poulo Condore, Vietnam. In describing the latter from a single, poorly preserved specimen, zoologist Oskar Carlgren expressed apprehension with traits he had used to establish this species. Carlgren’s doubts persisted later in writing when he found a similar-looking sea anemone from the Great Barrier Reef. Crucial details to positively identify either species have since remained limited. Here, we re-diagnosed Heteranthus and re-described its type species based on observations of specimens we have obtained from Singapore and Pulau Ambon (Indonesia), and of museum material collected elsewhere across the Indo-West Pacific region (n > 180). Supported by molecular phylogenetic evidence, the family Heteranthidae Carlgren, 1900 was reinstated and re-diagnosed. Heteranthus verruculatus is encountered in the lower intertidal region amongst seagrass, in rocky crevices, or coral rubble. It occurs as solitary individuals or in clonal clusters, well-camouflaged against the substratum. Individuals were observed to frequently propagate by longitudinal fission, resulting in a varied appearance. Type material of H. verruculatus and H. insignis were re-examined and as we found no differences between them, the two were synonymised. We inferred that Carlgren probably misinterpreted cnidae and histological data in defining H. insignis as a distinct species. This revision clarifies the taxonomy and geographic range of H. verruculatus, an Indo-West Pacific species that is found from the Red Sea to subtropical Australia and Hawaii.
• #### Century-long records reveal shifting challenges to seagrass recovery

(Global Change Biology, Wiley, 2020-11-25) [Article]
Global losses over the 20th century placed seagrass ecosystems among the most threatened ecosystems in the world, with eutrophication, and associated deterioration of the submarine light environment identified as the main driver. Growing appreciation of the ecological and societal benefits of healthy seagrass meadows has stimulated efforts to protect and restore them, largely focused on reducing nutrient input to coastal waters. Here we analyze a unique data set spanning 135 years on eelgrass (Zostera marina), the dominant seagrass of the northern hemisphere. We show that meadows in the Western Baltic Sea exhibited major declines relative to historic (1890-1910) reference due to the wasting disease in the 1930s followed by eutrophication peaking in the 1980s, but have only shown modest improvement despite major eutrophication mitigation, halving nitrogen input since the 1980s. Across the past century, we identified generally shallower colonization depths of eelgrass for a given submarine light penetration and, hence, increased apparent light requirements. This suggests that eelgrass recovery is limited by additional stressors. Our study indicates that bottom trawling and intense recent warming (0.5°C per decade, 1985-2018), which impact on deeper and shallower meadows, respectively, suppress eelgrass from fully recovering from eutrophication. Warming is most severe in shallow turbid waters, while clear-water areas offer eelgrass refugia from warming in deeper, cooler waters; but trawling can prevent eelgrass from reaching these refugia. Efforts to reduce nutrient input and thereby improve water clarity have been instrumental in avoiding a catastrophic loss of eelgrass ecosystems. However, local-scale future management must, in addition, reduce bottom trawling to facilitate eelgrass reaching deeper, cooler refugia, and increase resilience toward realized and further warming. Warming needs to be limited by meeting global climate change mitigation goals.
• #### Salinity-Conveyed Thermotolerance in the Coral Model Aiptasia Is Accompanied by Distinct Changes of the Bacterial Microbiome

(Frontiers in Marine Science, Frontiers Media SA, 2020-11-25) [Article]
Coral bleaching, i.e., the loss of photosynthetic algal endosymbionts, caused by ocean warming is now among the main factors driving global reef decline, making the elucidation of factors that contribute to thermotolerance important. Recent studies implicate high salinity as a contributing factor in cnidarians, potentially explaining the high thermotolerance of corals from the Arabian Seas. Here we characterized bacterial community composition under heat stress at different salinities using the coral model Aiptasia. Exposure of two Aiptasia host-algal symbiont pairings (H2-SSB01 and CC7-SSA01) to ambient (25°C) and heat stress (34°C) temperatures at low (36 PSU), intermediate (39 PSU), and high (42 PSU) salinities showed that bacterial community composition at high salinity was significantly different, concomitant with reduced bleaching susceptibility in H2-SSB01, not observed in CC7-SSA01. Elucidation of bacteria that showed increased relative abundance at high salinity, irrespective of heat stress, revealed candidate taxa that could potentially contribute to the observed increased thermotolerance. We identified 4 (H2-SSB01) and 3 (CC7-SSA01) bacterial taxa belonging to the orders Alteromonadales (1 OTU), Oligoflexales (1 OTU), Rhizobiales (2 OTUs), and Rhodobacterales (2 OTUs), suggesting that only few bacterial taxa are potential contributors to an increase in thermal tolerance at high salinities. These taxa have previously been implicated in nitrogen and DMSP cycling, processes that are considered to affect thermotolerance. Our study demonstrates microbiome restructuring in symbiotic cnidarians under heat stress at different salinities. As such, it underlines how host-associated bacterial communities adapt to prevailing environmental conditions with putative consequences for the environmental stress tolerance of the emergent metaorganism.
• #### Source Apportionment and Elemental Composition of Atmospheric Total Suspended Particulates (TSP) Over the Red Sea Coast of Saudi Arabia

(Earth Systems and Environment, Springer Science and Business Media LLC, 2020-11-24) [Article]
AbstractThis work presents a comprehensive study on concentrations and elemental composition of total suspended atmospheric particulates for a semi-urban site on the Red Sea coast, and on-board a research vessel, which collected off-shore samples along the Red Sea. We conducted one of the most extended measurement campaigns of atmospheric particulates ever for the region, with continuous measurements over 27 months. The overall mean concentrations (± st. dev.) of TSP were 125 ± 197 µg m$^{−3}$ for the permanent semi-urban site, and 108 ± 193 µg m$^{−3}$ for the off-shore mobile site. The region is frequently severely impacted by both localised and widespread dust storms, which on occasion, can increase atmospheric particulate concentrations to levels above mg m$^{−3}$ (> 1000 µg m$^{−3}$). Median concentrations were not as variable between seasons, indicating a stable, permanent presence of atmospheric particulates independent of the time of year. The primary chemical elements contributing to particulate mass were Na, Ca, S, Al and Fe. We employed Positive Matrix Factorisation (EPA PMF v5.0.14) to identify different major sources of particulates, which were crustal, marine, fuel oil combustion/secondary sulphate and mixed anthropogenic. The crustal source was characterised by tracers Al, Fe, K, Mg and Sn, and was present to some extent in the other identified sources due to the permanent presence of dust particles in the atmosphere. The fuel oil combustion/secondary sulphate source was identifiable by the almost exclusive presence of S, and to a lesser extent V, emitted from oil combustion as primary emissions and also secondary sulphate formation following the release of S to the atmosphere. A mixed anthropogenic source was characterised by Zn, Ni, Cr, Cu and Pb, emitted from traffic, industry, power generation and water desalination. This study highlights that the natural sources of particulates in this desert region give rise to frequent episodes of extremely poor air quality, and this problem is compounded by significant emissions of anthropogenic pollution, which has an impact across the entire Red Sea basin. Further stringent measures should be adopted to improve air quality across the region and prevent long-term damage to the health of the local population and ecosystems.
• #### Composition, uniqueness and connectivity across tropical coastal lagoon habitats in the Red Sea.

(BMC ecology, Springer Science and Business Media LLC, 2020-11-23) [Article]
BACKGROUND:Tropical habitats and their associated environmental characteristics play a critical role in shaping macroinvertebrate communities. Assessing patterns of diversity over space and time and investigating the factors that control and generate those patterns is critical for conservation efforts. However, these factors are still poorly understood in sub-tropical and tropical regions. The present study applied a combination of uni- and multivariate techniques to test whether patterns of biodiversity, composition, and structure of macrobenthic assemblages change across different lagoon habitats (two mangrove sites; two seagrass meadows with varying levels of vegetation cover; and an unvegetated subtidal area) and between seasons and years. RESULTS:In total, 4771 invertebrates were identified belonging to 272 operational taxonomic units (OTUs). We observed that macrobenthic lagoon assemblages are diverse, heterogeneous and that the most evident biological pattern was spatial rather than temporal. To investigate whether macrofaunal patterns within the lagoon habitats (mangrove, seagrass, unvegetated area) changed through the time, we analysed each habitat separately. The results showed high seasonal and inter-annual variability in the macrofaunal patterns. However, the seagrass beds that are characterized by variable vegetation cover, through time, showed comparatively higher stability (with the lowest values of inter-annual variability and a high number of resident taxa). These results support the theory that seagrass habitat complexity promotes diversity and density of macrobenthic assemblages. Despite the structural and functional importance of seagrass beds documented in this study, the results also highlighted the small-scale heterogeneity of tropical habitats that may serve as biodiversity repositories. CONCLUSIONS:Comprehensive approaches at the "seascape" level are required for improved ecosystem management and to maintain connectivity patterns amongst habitats. This is particularly true along the Saudi Arabian coast of the Red Sea, which is currently experiencing rapid coastal development. Also, considering the high temporal variability (seasonal and inter-annual) of tropical shallow-water habitats, monitoring and management plans must include temporal scales.
• #### Host-association as major driver of microbiome structure and composition in Red Sea seagrass ecosystems

(Environmental Microbiology, Wiley, 2020-11-22) [Article]
The role of the microbiome in sustaining seagrasses has recently been highlighted. However, our understanding of the seagrass microbiome lacks behind that of other organisms. Here, we analyze the endophytic and total bacterial communities of leaves, rhizomes, and roots of six Red Sea seagrass species and their sediments. The structure of seagrass bacterial communities revealed that the 1% most abundant OTUs accounted for 87.9 and 74.8 % of the total numbers of reads in sediment and plant tissue samples, respectively. We found taxonomically distinct bacterial communities in vegetated and bare sediments. Yet, our results suggest that lifestyle (i.e. free-living or host-association) is the main driver of bacterial community composition. Seagrass bacterial communities were tissue- and species-specific and differed from those of surrounding sediments. We identified OTUs belonging to genera related to N and S cycles in roots, and members of Actinobacteria, Bacteroidetes, and Firmicutes phyla as particularly enriched in root endosphere. The finding of highly similar OTUs in well-defined sub-clusters by network analysis suggests the co-occurrence of highly connected key members within Red Sea seagrass bacterial communities. These results provide key information towards the understanding of the role of microorganisms in seagrass ecosystem functioning framed under the seagrass holobiont concept.


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## Thursday, April 21, 2011

### CS: Noise Folding in Compressed Sensing, nonzero entry in the optimizer of L1 norm penalized least-square problem, Random lasso, Improved variable selection with Forward-Lasso adaptive shrinkage

With all the noise about noise, we were bound to have more noise :-) Today we have a new kind of noise featured in Noise Folding in Compressed Sensing by Ery Arias-Castro, Yonina Eldar. The abstract reads:
The literature on compressed sensing has focused almost entirely on settings where the signal is noiseless and the measurements are contaminated by noise. In practice, however, the signal itself is often subject to random noise prior to measurement. We briefly study this setting and show that, for the vast majority of measurement schemes employed in compressed sensing, the two models are equivalent with the important difference that the signal-to-noise ratio is divided by a factor proportional to p/n, where p is the dimension of the signal and n is the number of observations. Since p/n is often large, this leads to noise folding which can have a severe impact on the SNR.
The $\ell$-1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the $\ell$-1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path is the set of all the optimizers with respect to the evolution of the hyperparameter (Lagrange multiplier). The study of the solution path is of great significance in viewing and understanding the profile of the tradeoff between the approximation and regularization terms. If the solution path of a given problem is known, it can help us to find the optimal hyperparameter under a given criterion such as the Akaike Information Criterion. In this paper we present a sufficient condition on $\ell$-1 norm penalized least-square problem. Under this sufficient condition, the number of nonzero entries in the optimizer or solution vector increases monotonically when the hyperparameter decreases. We also generalize the result to the often used total variation case, where the $\ell$-1 norm is taken over the first order derivative of the solution vector. We prove that the proposed condition has intrinsic connections with the condition given by Donoho, et al \cite{Donoho08} and the positive cone condition by Efron {\it el al} \cite{Efron04}. However, the proposed condition does not need to assume the sparsity level of the signal as required by Donoho et al's condition, and is easier to verify than Efron, et al's positive cone condition when being used for practical applications.
Following up on yesterday's connection between statistics and CS, here are two Lasso papers: Random lasso by Sijian Wang, Bin Nan, Saharon Rosset, Ji Zhu. The abstract reads:
We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of randomly selected covariates. A measure of importance is yielded from this step for each covariate. In step 2, a similar procedure to the first step is implemented with the exception that for each bootstrap sample, a subset of covariates is randomly selected with unequal selection probabilities determined by the covariates' importance. Adaptive lasso may be used in the second step with weights determined by the importance measures. The final set of covariates and their coefficients are determined by averaging bootstrap results obtained from step 2. The proposed method alleviates some of the limitations of lasso, elastic-net and related methods noted especially in the context of microarray data analysis: it tends to remove highly correlated variables altogether or select them all, and maintains maximal flexibility in estimating their coefficients, particularly with different signs; the number of selected variables is no longer limited by the sample size; and the resulting prediction accuracy is competitive or superior compared to the alternatives. We illustrate the proposed method by extensive simulation studies. The proposed method is also applied to a Glioblastoma microarray data analysis.

Recently, considerable interest has focused on variable selection methods in regression situations where the number of predictors, $p$, is large relative to the number of observations, $n$. Two commonly applied variable selection approaches are the Lasso, which computes highly shrunk regression coefficients, and Forward Selection, which uses no shrinkage. We propose a new approach, "Forward-Lasso Adaptive SHrinkage" (FLASH), which includes the Lasso and Forward Selection as special cases, and can be used in both the linear regression and the Generalized Linear Model domains. As with the Lasso and Forward Selection, FLASH iteratively adds one variable to the model in a hierarchical fashion but, unlike these methods, at each step adjusts the level of shrinkage so as to optimize the selection of the next variable. We first present FLASH in the linear regression setting and show that it can be fitted using a variant of the computationally efficient LARS algorithm. Then, we extend FLASH to the GLM domain and demonstrate, through numerous simulations and real world data sets, as well as some theoretical analysis, that FLASH generally outperforms many competing approaches.

Image Credit: NASA/JPL/Space Science Institute
N00171130.jpg was taken on April 14, 2011 and received on Earth April 15, 2011. The camera was pointing toward DIONE at approximately 1,745,487 kilometers away, and the image was taken using the CL1 and CL2 filters